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  • 1.
    Adler, Mark
    et al.
    Brandeis Univ, Dept Math, Waltham, MA 02453 USA..
    Johansson, Kurt
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    van Moerbeke, Pierre
    Univ Louvain, Dept Math, B-1348 Louvain, Belgium.;Brandeis Univ, Waltham, MA 02453 USA..
    Tilings of Non-convex Polygons, Skew-Young Tableaux and Determinantal Processes2018Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 364, nr 1, s. 287-342Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper studies random lozenge tilings of general non-convex polygonal regions. We show that the pairwise interaction of the non-convexities leads asymptotically to new kernels and thus to new statistics for the tiling fluctuations. The precise geometrical figure here consists of a hexagon with cuts along opposite edges. For this model, we take limits when the size of the hexagon and the cuts tend to infinity, while keeping certain geometric data fixed in order to guarantee sufficient interaction between the cuts in the limit. We show in this paper that the kernel for the finite tiling model can be expressed as a multiple integral, where the number of integrations is related to the fixed geometric data above. The limiting kernel is believed to be a universal master kernel.

  • 2. Alberts, Tom
    et al.
    Binder, Ilia
    Viklund, Fredrik
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    A Dimension Spectrum for SLE Boundary Collisions2016Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 343, nr 1, s. 273-298Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider chordal SLE curves for , where the intersection of the curve with the boundary is a random fractal of almost sure Hausdorff dimension . We study the random sets of points at which the curve collides with the real line at a specified "angle" and compute an almost sure dimension spectrum describing the metric size of these sets. We work with the forward SLE flow and a key tool in the analysis is Girsanov's theorem, which is used to study events on which moments concentrate. The two-point correlation estimates are proved using the direct method.

  • 3. Andersson, John
    et al.
    Shahgholian, Henrik
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Weiss, Georg S.
    Uniform Regularity Close to Cross Singularities in an Unstable Free Boundary Problem2010Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 296, nr 1, s. 251-270Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We introduce a new method for the analysis of singularities in the unstable problem Delta u = chi{u> 0}, which arises in solid combustion as well as in the composite membrane problem. Our study is confined to points of "supercharacteristic" growth of the solution, i.e. points at which the solution grows faster than the characteristic/invariant scaling of the equation would suggest. At such points the classical theory is doomed to fail, due to incompatibility of the invariant scaling of the equation and the scaling of the solution. In the case of two dimensions our result shows that in a neighborhood of the set at which the second derivatives of u are unbounded, the level set {u = 0} consists of two C-1-curves meeting at right angles. It is important that our result is not confined to the minimal solution of the equation but holds for all solutions.

  • 4.
    Arnlind, Joakim
    et al.
    Inst Hautes Etud Sci.
    Bordemann, Martin
    Univ Haute Alsace, Lab MIA.
    Hofer, Laurent
    Univ Luxembourg.
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Shimada, Hidehiko
    Max Planck Inst Gravitat Phys.
    Noncommutative Riemann Surfaces by Embeddings in R-32009Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 288, nr 2, s. 403-429Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We introduce C-Algebras of compact Riemann surfaces ∑ as non-commutative analogues of the Poisson algebra of smooth functions on ∑. Representations of these algebrasgive rise to sequences of matrix-algebras for which matrix-commutators converge to Poisson-brackets as N → ∞. For a particular class of surfaces, interpolating between spheres and tori, we completely characterize (even for the intermediate singular surface) all finite dimensional representations of the corresponding C-algebras.

  • 5.
    Aspenberg, Magnus
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Yampolsky, Michael
    Mating Non-Renormalizable Quadratic Polynomials2009Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 287, nr 1, s. 1-40Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we prove the existence and uniqueness of matings of the basilica with any quadratic polynomial which lies outside of the 1/2-limb of M, is non-renormalizable, and does not have any non-repelling periodic orbits.

  • 6. Bao, Z.
    et al.
    Erdős, L.
    Schnelli, Kevin
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
    Local Law of Addition of Random Matrices on Optimal Scale2017Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 349, nr 3, s. 947-990Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The eigenvalue distribution of the sum of two large Hermitian matrices, when one of them is conjugated by a Haar distributed unitary matrix, is asymptotically given by the free convolution of their spectral distributions. We prove that this convergence also holds locally in the bulk of the spectrum, down to the optimal scales larger than the eigenvalue spacing. The corresponding eigenvectors are fully delocalized. Similar results hold for the sum of two real symmetric matrices, when one is conjugated by Haar orthogonal matrix.

  • 7. Bjerklöv, Kristian
    Dynamics of the quasi-periodic Schrodinger cocycle at the lowest energy in the spectrum2007Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 272, nr 2, s. 397-442Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we consider the quasi-periodic Schrodinger cocycle over T-d (d >= 1) and, in particular, its projectivization. In the regime of large coupling constants and Diophantine frequencies, we give an affirmative answer to a question posed by M. Herman [21, p.482] concerning the geometric structure of certain Strange Nonchaotic Attractors which appear in the projective dynamical system. We also show that for some phase, the lowest energy in the spectrum of the associated Schrodinger operator is an eigenvalue with an exponentially decaying eigenfunction. This generalizes [39] to the multi-frequency case (d > 1).

  • 8.
    Bjerklöv, Kristian
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    SNA's in the Quasi-Periodic Quadratic Family2009Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 286, nr 1, s. 137-161Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We rigorously show that there can exist Strange Nonchaotic Attractors (SNA) in the quasi-periodically forced quadratic ( or logistic) map (theta, x) -> (theta + omega, c(theta)x(1 - x)) for certain choices of c : T bar right arrow [3/2, 4] and Diophantine omega.

  • 9. Breuer, Jonathan
    et al.
    Duits, Maurice
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Universality of Mesoscopic Fluctuations for Orthogonal Polynomial Ensembles2016Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 342, nr 2, s. 491-531Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We prove that the fluctuations of mesoscopic linear statistics for orthogonal polynomial ensembles are universal in the sense that two measures with asymptotic recurrence coefficients have the same asymptotic mesoscopic fluctuations (under an additional assumption on the local regularity of one of the measures). The convergence rate of the recurrence coefficients determines the range of scales on which the limiting fluctuations are identical. Our main tool is an analysis of the Green's function for the associated Jacobi matrices. As a particular consequence we obtain a central limit theorem for the modified Jacobi Unitary Ensembles on all mesoscopic scales.

  • 10.
    Charlier, Christophe
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Claeys, Tom
    Institut de Recherche en Mathématique et Physique, Université Catholique de Louvain, Chemin du Cyclotron 2, Louvain-la-Neuve, 1348, Belgium.
    Large Gap Asymptotics for Airy Kernel Determinants with Discontinuities2019Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We obtain large gap asymptotics for Airy kernel Fredholm determinants with any number m of discontinuities. These m-point determinants are generating functions for the Airy point process and encode probabilistic information about eigenvalues near soft edges in random matrix ensembles. Our main result is that the m-point determinants can be expressed asymptotically as the product of m 1-point determinants, multiplied by an explicit constant pre-factor which can be interpreted in terms of the covariance of the counting function of the process.

  • 11.
    Dahl, Mattias
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Gicquaud, Romain
    Sakovich, Anna
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Asymptotically Hyperbolic Manifolds with Small Mass2014Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 325, nr 2, s. 757-801Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    For asymptotically hyperbolic manifolds of dimension n with scalar curvature at least equal to -n(n - 1) the conjectured positive mass theorem states that the mass is non-negative, and vanishes only if the manifold is isometric to hyperbolic space. In this paper we study asymptotically hyperbolic manifolds which are also conformally hyperbolic outside a ball of fixed radius, and for which the positive mass theorem holds. For such manifolds we show that the conformal factor tends to one as the mass tends to zero.

  • 12.
    de Woul, Jonas
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
    Exact Solution of a 2D Interacting Fermion Model2012Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 314, nr 1, s. 1-56Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study an exactly solvable quantum field theory (QFT) model describing interacting fermions in 2+1 dimensions. This model is motivated by physical arguments suggesting that it provides an effective description of spinless fermions on a square lattice with local hopping and density-density interactions if, close to half filling, the system develops a partial energy gap. The necessary regularization of the QFT model is based on this proposed relation to lattice fermions. We use bosonization methods to diagonalize the Hamiltonian and to compute all correlation functions. We also discuss how, after appropriate multiplicative renormalizations, all short- and long distance cutoffs can be removed. In particular, we prove that the renormalized two-point functions have algebraic decay with non-trivial exponents depending on the interaction strengths, which is a hallmark of Luttinger-liquid behavior.

  • 13.
    Ekholm, Tomas
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Frank, Rupert
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    On Lieb-Thirring inequalities for Schrödinger operators with virtual level2006Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 264, nr 3, s. 725-740Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider the operator H = - Delta- V in L-2(R-d), d >= 3. For the moments of its negative eigenvalues we prove the estimate

    tr H--(gamma) <= C-gamma,C-d integral(Rd) (V(x) - (d-2)(2)/4\x\(2))(gamma+d/2) dx, gamma > 0.

    Similar estimates hold for the one-dimensional operator with a Dirichlet condition at the origin and for the two-dimensional Aharonov-Bohm operator.

  • 14.
    Frank, Rupert L.
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Siedentop, Heinz
    Warzel, Simone
    The ground state energy of heavy atoms: Relativistic lowering of the leading energy correction2008Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 278, nr 2, s. 549-566Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We describe atoms by a pseudo-relativistic model that has its origin in the work of Chandrasekhar. We prove that the leading energy correction for heavy atoms, the Scott correction, exists. It turns out to be lower than in the non-relativistic description of atoms. Our proof is valid up to and including the critical coupling constant. It is based on a renormalization of the energy whose zero level we adjust to be the ground-state energy of the corresponding non-relativistic problem. This allows us to roll the proof back to results for the Schrodinger operator.

  • 15.
    Frank, Rupert
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Lieb, Elliott H.
    Departments of Mathematics and Physics, Princeton University.
    Seiringer, Robert
    Department of Physics, Princeton University.
    Stability of relativistic matter with magnetic fields for nuclear charges up to the critical value2007Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 275, nr 2, s. 479-489Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We give a proof of stability of relativistic matter with magnetic fields all the way up to the critical value of the nuclear charge Z alpha = 2/pi.

  • 16. Froehlich, Juerg
    et al.
    Jonsson, B. Lars G.
    KTH, Skolan för elektro- och systemteknik (EES), Elektroteknisk teori och konstruktion.
    Lenzmann, Enno
    Boson stars as solitary waves2007Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 274, nr 1, s. 1-30Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study the nonlinear equation i theta t psi = (root-Delta+m(2) - m) psi - (vertical bar x vertical bar(-1) * vertical bar psi vertical bar(2)) psi on R-3, which is known to describe the dynamics of pseudo-relativistic boson stars in the meanfield limit. For positive mass parameters, m > 0, we prove existence of travelling solitary waves, psi(t, x) = ei t mu phi(v)(x - vt), for some mu is an element of R and with speed vertical bar v vertical bar < 1, where c = 1 corresponds to the speed of light in our units. Due to the lack of Lorentz covariance, such travelling solitary waves cannot be obtained by applying a Lorentz boost to a solitary wave at rest (with v = 0). To overcome this difficulty, we introduce and study an appropriate variational problem that yields the functions phi(v) H-1/2(R-3) as minimizers, which we call boosted ground states. Our existence proof makes extensive use of concentration-compactness-type arguments. In addition to their existence, we prove orbital stability of travelling solitary waves psi(t, x) = e i t mu(v)(x - vt) and pointwise exponential decay of phi(v)(x) in x.

  • 17. Frohlich, J.
    et al.
    Gustafson, S.
    Jonsson, B. Lars G.
    KTH, Tidigare Institutioner, Teoretisk elektroteknik.
    Sigal, I. M.
    Solitary wave dynamics in an external potential2004Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 250, nr 3, s. 613-642Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study the behavior of solitary-wave solutions of some generalized nonlinear Schrodinger equations with an external potential. The equations have the feature that in the absence of the external potential, they have solutions describing inertial motions of stable solitary waves. We consider solutions of the equations with a non-vanishing external potential corresponding to initial conditions close to one of these solitary wave solutions and show that, over a large interval of time, they describe a solitary wave whose center of mass motion is a solution of Newton's equations of motion for a point particle in the given external potential, up to small corrections corresponding to radiation damping.

  • 18. Gicquaud, Romain
    et al.
    Sakovich, Anna
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    A Large Class of Non-Constant Mean Curvature Solutions of the Einstein Constraint Equations on an Asymptotically Hyperbolic Manifold2012Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 310, nr 3, s. 705-763Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We construct solutions of the constraint equation with non constant mean curvature on an asymptotically hyperbolic manifold by the conformal method. Our approach consists in decreasing a certain exponent appearing in the equations, constructing solutions of these sub-critical equations and then in letting the exponent tend to its true value. We prove that the solutions of the sub-critical equations remain bounded which yields solutions of the constraint equation unless a certain limit equation admits a non-trivial solution. Finally, we give conditions which ensure that the limit equation admits no non-trivial solution.

  • 19.
    Gustafsson, Björn
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Tkachev, Vladimir
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    The Resultant on Compact Riemann Surfaces2009Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 286, nr 1, s. 313-358Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We introduce a notion of the resultant of two meromorphic functions on a compact Riemann surface and demonstrate its usefulness in several respects. For example, we exhibit several integral formulas for the resultant, relate it to potential theory and give explicit formulas for the algebraic dependence between two meromorphic functions on a compact Riemann surface. As a particular application, the exponential transform of a quadrature domain in the complex plane is expressed in terms of the resultant of two meromorphic functions on the Schottky double of the domain.

  • 20. Günaydin, Murat
    et al.
    Volin, Dmytro
    KTH, Centra, Nordic Institute for Theoretical Physics NORDITA.
    The Complete Unitary Dual of Non-compact Lie Superalgebra su(p,q|m) via the Generalised Oscillator Formalism, and Non-compact Young Diagrams2019Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 367, nr 3, s. 873-939Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study the unitary representations of the non-compact real forms of the complex Lie superalgebra sl(n|m). Among them, only the real form su(p,q|m) with (p+q=n) admits nontrivial unitary representations, and all such representations are of the highest-weight type (or the lowest-weight type). We extend the standard oscillator construction of the unitary representations of non-compact Lie superalgebras over standard Fock spaces to generalised Fock spaces which allows us to define the action of oscillator determinants raised to non-integer powers. We prove that the proposed construction yields all the unitary representations including those with continuous labels. The unitary representations can be diagrammatically represented by non-compact Young diagrams. We apply our general results to the physically important case of four-dimensional conformal superalgebra su(2,2|4) and show how it yields readily its unitary representations including those corresponding to supermultiplets of conformal fields with continuous (anomalous) scaling dimensions.

  • 21.
    Hedenmalm, Håkan
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Wennman, Aron
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Off-Spectral Analysis of Bergman Kernels2020Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 373, nr 3, s. 1049-1083Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The asymptotic analysis of Bergman kernels with respect to exponentially varying measures near emergent interfaces has attracted recent attention. Such interfaces typically occur when the associated limiting Bergman density function vanishes on a portion of the plane, the off-spectral region. This type of behavior is observed when the metric is negatively curved somewhere, or when we study partial Bergman kernels in the context of positively curved metrics. In this work, we cover these two situations in a unified way, for exponentially varying weights on the complex plane. We obtain a uniform asymptotic expansion of the coherent state of depthn rooted at an off-spectral point, which we also refer to as the root function at the point in question. The expansion is valid in the entire off-spectral component containing the root point, and protrudes into the spectrum as well. This allows us to obtain error function transition behavior of the density of states along the smooth interface. Previous work on asymptotic expansions of Bergman kernels is typically local, and valid only in the bulk region of the spectrum, which contrasts with our non-local expansions.

  • 22.
    Hekmati, Pedram
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
    Mickelsson, Jouko
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
    Fractional Loop Group and Twisted K-theory2010Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 299, nr 3, s. 741-763Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study the structure of abelian extensions of the group L (q) G of q-differentiable loops (in the Sobolev sense), generalizing from the case of the central extension of the smooth loop group. This is motivated by the aim of understanding the problems with current algebras in higher dimensions. Highest weight modules are constructed for the Lie algebra. The construction is extended to the current algebra of the supersymmetric Wess-Zumino-Witten model. An application to the twisted K-theory on G is discussed.

  • 23.
    Johansson, Kurt
    KTH, Tidigare Institutioner, Matematik.
    Determinantal processes with number variance saturation2004Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 252, nr 3-Jan, s. 111-148Artikel i tidskrift (Refereegranskat)
  • 24.
    Johansson, Kurt
    KTH, Tidigare Institutioner                               , Matematik.
    Discrete polynuclear growth and determinantal processes2003Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 242, nr 2-Jan, s. 277-329Artikel i tidskrift (Refereegranskat)
  • 25.
    Johansson, Kurt
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Non-colliding Brownian Motions and the Extended Tacnode Process2013Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 319, nr 1, s. 231-267Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider non-colliding Brownian motions with two starting points and two endpoints. The points are chosen so that the two groups of Brownian motions just touch each other, a situation that is referred to as a tacnode. The extended kernel for the determinantal point process at the tacnode point is computed using new methods and given in a different form from that obtained for a single time in previous work by Delvaux, Kuijlaars and Zhang. The form of the extended kernel is also different from that obtained for the extended tacnode kernel in another model by Adler, Ferrari and van Moerbeke. We also obtain the correlation kernel for a finite number of non-colliding Brownian motions starting at two points and ending at arbitrary points.

  • 26.
    Johansson, Kurt
    KTH, Tidigare Institutioner                               , Matematik.
    Shape fluctuations and random matrices2000Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 209, nr 2, s. 437-476Artikel i tidskrift (Refereegranskat)
  • 27.
    Johansson, Kurt
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Two Time Distribution in Brownian Directed Percolation2016Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, s. 1-52Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In the zero temperature Brownian semi-discrete directed polymer we study the joint distribution of two last-passage times at positions ordered in the time-like direction. This is the situation when we have the slow de-correlation phenomenon. We compute the limiting joint distribution function in a scaling limit. This limiting distribution is given by an expansion in determinants that is not a Fredholm expansion. A somewhat similar looking formula was derived non-rigorously in a related model by Dotsenko.

  • 28.
    Johansson, Kurt
    KTH, Tidigare Institutioner                               , Matematik.
    Universality of the local spacing distribution in certain ensembles of hermitian Wigner matrices2001Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 215, nr 3, s. 683-705Artikel i tidskrift (Refereegranskat)
  • 29. Kaloshin, Vadim
    et al.
    Saprykina, Maria
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    An Example of a Nearly Integrable Hamiltonian System with a Trajectory Dense in a Set of Maximal Hausdorff Dimension2012Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 315, nr 3, s. 643-697Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The famous ergodic hypothesis suggests that for a typical Hamiltonian on a typical energy surface nearly all trajectories are dense. KAM theory disproves it. Ehrenfest (The Conceptual Foundations of the Statistical Approach in Mechanics. Ithaca, NY: Cornell University Press, 1959) and Birkhoff (Collected Math Papers. Vol 2, New York: Dover, pp 462-465, 1968) stated the quasi-ergodic hypothesis claiming that a typical Hamiltonian on a typical energy surface has a dense orbit. This question is wide open. Herman (Proceedings of the International Congress of Mathematicians, Vol II (Berlin, 1998). Doc Math 1998, Extra Vol II, Berlin: Int Math Union, pp 797-808, 1998) proposed to look for an example of a Hamiltonian near with a dense orbit on the unit energy surface. In this paper we construct a Hamiltonian which has an orbit dense in a set of maximal Hausdorff dimension equal to 5 on the unit energy surface.

  • 30.
    Kreiss, Heinz -Otto
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Reula, O.
    Sarbach, O.
    Winicour, J.
    Boundary Conditions for Coupled Quasilinear Wave Equations with Application to Isolated Systems2009Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 289, nr 3, s. 1099-1129Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider the initial-boundary value problem for systems of quasilinear wave equations on domains of the form [0, T] x I pound, where I pound is a compact manifold with smooth boundaries a,I pound. By using an appropriate reduction to a first order symmetric hyperbolic system with maximal dissipative boundary conditions, well posedness of such problems is established for a large class of boundary conditions on a,I pound. We show that our class of boundary conditions is sufficiently general to allow for a well posed formulation for different wave problems in the presence of constraints and artificial, nonreflecting boundaries, including Maxwell's equations in the Lorentz gauge and Einstein's gravitational equations in harmonic coordinates. Our results should also be useful for obtaining stable finite-difference discretizations for such problems.

  • 31.
    Kurlberg, Pär
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Rosenzweig, Lior
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Superscars for arithmetic toral point scatterers2016Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 349, nr 1, s. 329-360Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We investigate eigenfunctions of the Laplacian perturbed by a delta potential on the standard tori in dimensions . Despite quantum ergodicity holding for the set of "new" eigenfunctions we show that superscars occur-there is phase space localization along families of closed orbits, in the sense that some semiclassical measures contain a finite number of Lagrangian components of the form , for uniformly bounded from below. In particular, for both and , eigenfunctions fail to equidistribute in phase space along an infinite subsequence of new eigenvalues. For , we also show that some semiclassical measures have both strongly localized momentum marginals and non-uniform quantum limits (i.e., the position marginals are non-uniform). For , superscarred eigenstates are quite rare, but for we show that the phenomenon is quite common-with denoting the counting function for the new eigenvalues below x, there are eigenvalues with the property that any semiclassical limit along these eigenvalues exhibits superscarring.

  • 32. Kurlberg, Pär
    et al.
    Rudnick, Z.
    On quantum ergodicity for linear maps of the torus2001Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 222, nr 1, s. 201-227Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We prove a strong version of quantum ergodicity for linear hyperbolic maps of the torus (cat maps). We show that there is a density one sequence of integers so that as N tends to infinity along this sequence., all eigenfunctions of the quantum propagator at inverse Planck constant N are uniformly distributed. A key step in the argument is to show that for a hyperbolic matrix in the modular group. there is a density one sequence of integers N for which its order (or period) modulo N is somewhat larger than rootN.

  • 33.
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Matematisk fysik. KTH, Skolan för teknikvetenskap (SCI), Fysik, Kondenserade materiens teori.
    Fermion Current Algebras and Schwinger Terms in 3+1 Dimensions1994Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 162, s. 1-32Artikel i tidskrift (Refereegranskat)
  • 34.
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Fysik, Matematisk fysik. KTH, Skolan för teknikvetenskap (SCI), Fysik, Kondenserade materiens teori.
    Loop groups, anyons and the Calogero-Sutherland model1999Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 201, s. 1-34Artikel i tidskrift (Refereegranskat)
  • 35.
    Langmann, Edwin
    KTH, Tidigare Institutioner, Fysik.
    Second quantization of the elliptic Calogero-Sutherland model2004Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 247, nr 2, s. 321-351Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We construct a quantum field theory model of anyons on a circle and at finite temperature. We find an anyon Hamiltonian providing a second quantization of the elliptic Calogero-Sutherland model. This allows us to prove a remarkable identity which is a starting point for an algorithm to construct eigenfunctions and eigenvalues of the elliptic Calogero-Sutherland Hamiltonian.

  • 36.
    Langmann, Edwin
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
    Lebowitz, Joel L.
    Departments of Mathematics and Physics, Rutgers University.
    Mastropietro, Vieri
    Dipartimento di Matematica, Università degli Studi di Milano.
    Moosavi, Per
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik.
    Steady states and universal conductance in a quenched Luttinger model2016Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, s. 1-32Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We obtain exact analytical results for the evolution of a 1+1-dimensional Luttinger model prepared in a domain wall initial state, i.e., a state with different densities on its left and right sides. Such an initial state is modeled as the ground state of a translation invariant Luttinger Hamiltonian (Formula presented.) with short range non-local interaction and different chemical potentials to the left and right of the origin. The system evolves for time t > 0 via a Hamiltonian (Formula presented.) which differs from (Formula presented.) by the strength of the interaction. Asymptotically in time, as (Formula presented.), after taking the thermodynamic limit, the system approaches a translation invariant steady state. This final steady state carries a current I and has an effective chemical potential difference (Formula presented.) between right- (+) and left- (−) moving fermions obtained from the two-point correlation function. Both I and (Formula presented.) depend on (Formula presented.) and (Formula presented.). Only for the case (Formula presented.) does (Formula presented.) equal the difference in the initial left and right chemical potentials. Nevertheless, the Landauer conductance for the final state, (Formula presented.), has a universal value equal to the conductance quantum (Formula presented.) for the spinless case.

  • 37.
    Laptev, Ari
    et al.
    KTH, Tidigare Institutioner                               , Matematik.
    Naboko, S.
    Safronov, O.
    On new relations between spectral properties of Jacobi matrices and their coefficients2003Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 241, nr 1, s. 91-110Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study the spectral properties of Jacobi matrices. By using ``higher order'' trace formulae we obtain a result relating the properties of the elements of Jacobi matrices and the corresponding spectral measures. Complicated expressions for traces of some operators can be magically simplified allowing us to apply induction arguments. Our theorems are generalizations of a recent result of R. Killip and B. Simon [17].

  • 38.
    Laptev, Ari
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Naboko, S.
    Safronov, Oleg
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Absolutely continuous spectrum of Schrödinger operators with slowly decaying and oscillating potentials2005Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 253, nr 3, s. 611-631Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The aim of this paper is to extend a class of potentials for which the absolutely continuous spectrum of the corresponding multidimensional Schrodinger operator is essentially supported by [0, infinity). Our main theorem states that this property is preserved for slowly decaying potentials provided that there are some oscillations with respect to one of the variables.

  • 39. Laptev, Ari
    et al.
    Safronov, Oleg
    Eigenvalue Estimates for Schrodinger Operators with Complex Potentials2009Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 292, nr 1, s. 29-54Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We discuss properties of eigenvalues of non-self-adjoint Schrodinger operators with complex-valued potential V. Among our results are estimates of the sum of powers of imaginary parts of eigenvalues by the L-p-norm of JV.

  • 40.
    Lenells, Jonatan
    Baylor University, United States .
    Boundary Value Problems for the Stationary Axisymmetric Einstein Equations: A Disk Rotating Around a Black Hole2011Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 304, nr 3, s. 585-635Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We solve a class of boundary value problems for the stationary axisymmetric Einstein equations involving a disk rotating around a central black hole. The solutions are given explicitly in terms of theta functions on a family of hyperelliptic Riemann surfaces of genus 4. In the absence of a disk, they reduce to the Kerr black hole. In the absence of a black hole, they reduce to the Neugebauer-Meinel disk.

  • 41.
    Lenells, Jonatan
    et al.
    Leibniz Universität Hannover, Germany .
    Misiołek, G.
    Tiǧlay, F.
    Integrable evolution equations on spaces of tensor densities and their peakon solutions2010Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 299, nr 1, s. 129-161Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study a family of equations defined on the space of tensor densities of weight λ on the circle and introduce two integrable PDE. One of the equations turns out to be closely related to the inviscid Burgers equation while the other has not been identified in any form before. We present their Lax pair formulations and describe their bihamiltonian structures. We prove local wellposedness of the corresponding Cauchy problem and include results on blow-up as well as global existence of solutions. Moreover, we construct "peakon" and "multi-peakon" solutions for all λ ≠ 0, 1, and "shock-peakons" for λ = 3. We argue that there is a natural geometric framework for these equations that includes other well-known integrable equations and which is based on V. Arnold's approach to Euler equations on Lie groups.

  • 42.
    Lester, Stephen
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Rudnick, Zeev
    Small Scale Equidistribution of Eigenfunctions on the Torus2017Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 350, nr 1, s. 279-300Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study the small scale distribution of the L-2 mass of eigenfunctions of the Laplacian on the flat torus T-d. Given an orthonormal basis of eigenfunctions, we show the existence of a density one subsequence whose L-2 mass equidistributes at small scales. In dimension two our result holds all the way down to the Planck scale. For dimensions d = 3, 4 we can restrict to individual eigenspaces and show small scale equidistribution in that context. We also study irregularities of quantum equidistribution: We construct eigenfunctions whose L-2 mass does not equidistribute at all scales above the Planck scale. Additionally, in dimension d = 4 we show the existence of eigenfunctions for which the proportion of L-2 mass in small balls blows up at certain scales.

  • 43.
    Lundholm, Douglas
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Portmann, Fabian
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Solovej, Jan Philip
    University of Copenhagen, Denmark.
    Lieb-Thirring Bounds for Interacting Bose Gases2015Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 335, nr 2, s. 1019-1056Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study interacting Bose gases and prove lower bounds for the kinetic plus interaction energy of a many-body wave function in terms of its particle density. These general estimates are then applied to various types of interactions, including hard sphere (in 3D) and hard disk (in 2D) as well as a general class of homogeneous potentials.

  • 44.
    Lundholm, Douglas
    et al.
    University of Copenhagen.
    Solovej, Jan Philip
    University of Copenhagen.
    Hardy and Lieb-Thirring Inequalities for Anyons2013Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 322, nr 3, s. 883-908Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider the many-particle quantum mechanics of anyons, i.e. identical particles in two space dimensions with a continuous statistics parameter α∈[0,1] ranging from bosons (α = 0) to fermions (α = 1). We prove a (magnetic) Hardy inequality for anyons, which in the case that α is an odd numerator fraction implies a local exclusion principle for the kinetic energy of such anyons. From this result, and motivated by Dyson and Lenard’s original approach to the stability of fermionic matter in three dimensions, we prove a Lieb-Thirring inequality for these types of anyons.

  • 45. Martens, Marco
    et al.
    Winckler, Björn
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    On the Hyperbolicity of Lorenz Renormalization2014Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 325, nr 1, s. 185-257Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider infinitely renormalizable Lorenz maps with real critical exponent alpha > 1 of certain monotone combinatorial types. We prove the existence of periodic points of the renormalization operator, and that each map in the limit set of renormalization has an associated two-dimensional strong unstable manifold. For monotone families of Lorenz maps we prove that each infinitely renormalizable combinatorial type has a unique representative within the family. We also prove that each infinitely renormalizable map has no wandering intervals, is ergodic, and has a uniquely ergodic minimal Cantor attractor of measure zero.

  • 46.
    Mickelsson, Jouko
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
    Pellonpää, Juha-Pekka
    Families index theorem in supersymmetric WZW model and twisted K-theory: The SU(2) case2007Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 271, nr 3, s. 775-789Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The construction of twisted K-theory classes on a compact Lie group is reviewed using the supersymmetric Wess-Zumino-Wittenmodel on a cylinder. The Quillen superconnection is introduced for a family of supercharges parametrized by a compact Lie group and the Chern character is explicitly computed in the case of SU( 2). For large euclidean time, the character form is localized on a D-brane.

  • 47.
    Olofsson, Rikard
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Large Supremum Norms and Small Shannon Entropy for Hecke Eigenfunctions of Quantized Cat Maps2009Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 286, nr 3, s. 1051-1072Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper concerns the behavior of eigenfunctions of quantized cat maps and in particular their supremum norm. We observe that for composite integer values of N, the inverse of Planck's constant, some of the desymmetrized eigenfunctions have very small support and hence very large supremum norm. We also prove an entropy estimate and show that our functions satisfy equality in this estimate. In the case when N is a prime power with even exponent we calculate the supremum norm for a large proportion of all desymmetrized eigenfunctions and we find that for a given N there is essentially at most four different values these assume.

  • 48.
    Ringström, Hans
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    A Unified Approach to the Klein-Gordon Equation on Bianchi Backgrounds2019Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 372, nr 2, s. 599-656Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we study solutions to the Klein-Gordon equation on Bianchi backgrounds. In particular, we are interested in the asymptotic behaviour of solutions in the direction of silent singularities. The main conclusion is that, for a given solution u to the Klein-Gordon equation, there are smooth functions u(i), i = 0, 1, on the Lie group under consideration, such that u(sigma) (. , sigma) - u(1) and u(. , sigma) - u(1)sigma - u(0) asymptotically converge to zero in the direction of the singularity (where s is a geometrically defined time coordinate such that the singularity corresponds to sigma -> -infinity). Here u(i), i = 0, 1, should be thought of as data on the singularity. Interestingly, it is possible to prove that the asymptotics are of this form for a large class of Bianchi spacetimes. Moreover, the conclusion applies for singularities that arematter dominated; singularities that are vacuum dominated; and even when the asymptotics of the underlying Bianchi spacetime are oscillatory. To summarise, there seems to be a universality as far as the asymptotics in the direction of silent singularities are concerned. In fact, it is tempting to conjecture that as long as the singularity of the underlying Bianchi spacetime is silent, then the asymptotics of solutions are as described above. In order to contrast the above asymptotics with the non-silent setting, we, by appealing to known results, provide a complete asymptotic characterisation of solutions to the Klein-Gordon equation on a flat Kasner background. In that setting, us does, generically, not converge.

  • 49.
    Ringström, Hans
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Instability of Spatially Homogeneous Solutions in the Class of T-2-Symmetric Solutions to Einstein's Vacuum Equations2015Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 334, nr 3, s. 1299-1375Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In the subject of cosmology, spatially homogeneous solutions are often used to model the universe. It is therefore of interest to ask what happens when perturbing into the spatially inhomogeneous regime. To this end, we, in the present paper, study the future asymptotics of solutions to Einstein's vacuum equations in the case of T-2-symmetry. It turns out that in this setting, whether the solution is spatially homogeneous or not can be characterized in terms of the asymptotics of one variable appearing in the equations; there is a monotonic function such that if its limit is finite, then the solution is spatially homogeneous and if the limit is infinite, then the solution is spatially inhomogeneous. In particular, regardless of how small the initial perturbation away from spatial homogeneity is, the resulting asymptotics are very different. Using spatially homogeneous solutions as models is therefore, in this class, hard to justify.

  • 50. Ringström, Hans
    On curvature decay in expanding cosmological models2006Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 264, nr 3, s. 613-630Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Consider a globally hyperbolic cosmological spacetime. Topologically, the spacetime is then a compact 3-manifold in cartesian product with an interval. Assuming that there is an expanding direction, is there any relation between the topology of the 3-manifold and the asymptotics? In fact, there is a result by Michael Anderson, where he obtains relations between the long-time evolution in General Relativity and the geometrization of 3-manifolds. In order to obtain conclusions however, he makes assumptions concerning the rate of decay of the curvature as proper time tends to infinity. It is thus of interest to find out if such curvature decay conditions are always fulfilled. We consider here the Gowdy spacetimes, for which we prove that the decay condition holds. However, we observe that for general Bianchi VIII spacetimes, the curvature decay condition does not hold, but that some aspects of the expected asymptotic behaviour are still true.

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