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  • 1. Aas, E.
    et al.
    Ayyer, A.
    Linusson, Svante
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Potka, Samu
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    The exact phase diagram for a semipermeable TASEP with nonlocal boundary jumps2019Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 52, nr 35, artikel-id 355001Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider a finite one-dimensional totally asymmetric simple exclusion process with four types of particles, {1, 0, 1, }, in contact with reservoirs. Particles of species 0 can neither enter nor exit the lattice, and those of species are constrained to lie at the first and last site. Particles of species 1 enter from the left reservoir into either the first or second site, move rightwards, and leave from either the last or penultimate site. Conversely, particles of species 1 enter from the right reservoir into either the last or penultimate site, move leftwards, and leave from either the first or last site. This dynamics is motivated by a natural random walk on the Weyl group of type D. We compute the exact nonequilibrium steady state distribution using a matrix ansatz building on earlier work of Arita. We then give explicit formulas for the nonequilibrium partition function as well as densities and currents of all species in the steady state, and derive the phase diagram.

  • 2. Arutyunov, Gleb
    et al.
    Heinze, Martin
    Medina-Rincon, Daniel
    KTH, Centra, Nordic Institute for Theoretical Physics NORDITA. Uppsala University, Sweden; Stockholm University, Sweden.
    Superintegrability of geodesic motion on the sausage model2017Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, nr 24, artikel-id 244002Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Reduction of the eta-deformed sigma model on AdS(5) x S-5 to the two-dimensional squashed sphere (S-2)eta can be viewed as a special case of the Fateev sausage model where the coupling constant v is imaginary. We show that geodesic motion in this model is described by a certain superintegrable mechanical system with four-dimensional phase space. This is done by means of explicitly constructing three integrals of motion which satisfy the sl(2) Poisson algebra relations, albeit being non-polynomial in momenta. Further, we find a canonical transformation which transforms the Hamiltonian of this mechanical system to the one describing the geodesic motion on the usual two-sphere. By inverting this transformation we map geodesics on this auxiliary two-sphere back to the sausage model.

  • 3.
    Aurell, Erik
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Beräkningsbiologi, CB. KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre. Aalto Univ.
    Zakrzewski, Jakub
    Zyczkowski, Karol
    Time reversals of irreversible quantum maps2015Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 48, nr 38, artikel-id 38FT01Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We propose an alternative notion of time reversal in open quantum systems as represented by linear quantum operations, and a related generalization of classical entropy production in the environment. This functional is the ratio of the probability to observe a transition between two states under the forward and the time reversed dynamics, and leads, as in the classical case, to fluctuation relations as tautological identities. As in classical dynamics in contact with a heat bath, time reversal is not unique, and we discuss several possibilities. For any bistochastic map its dual map preserves the trace and describes a legitimate dynamics reversed in time, in that case the entropy production in the environment vanishes. For a generic stochastic map we construct a simple quantum operation which can be interpreted as a time reversal. For instance, the decaying channel, which sends the excited state into the ground state with a certain probability, can be reversed into the channel transforming the ground state into the excited state with the same probability.

  • 4. Bombardelli, D.
    et al.
    Cagnazzo, Alessandra
    KTH, Centra, Nordic Institute for Theoretical Physics NORDITA. DESY Hamburg, Theory Group, Germany.
    Frassek, R.
    Levkovich-Maslyuk, F.
    Loebbert, F.
    Negro, S.
    Szecsenyi, I. M.
    Sfondrini, A.
    van Tongeren, S. J.
    Torrielli, A.
    An integrability primer for the gauge-gravity correspondence: an introduction Preface2016Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 49, nr 32, artikel-id 320301Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We introduce a series of articles reviewing various aspects of integrable models relevant to the anti-de Sitter (AdS)/conformal quantum field theory (CFT) correspondence. Topics covered in these reviews are: classical integrability, Yangian symmetry, factorized scattering, the Bethe ansatz, the thermodynamic Bethe ansatz, and integrable structures in (conformal) quantum field theory. In the present article we highlight how these concepts have found application in AdS/CFT, and provide a brief overview of the material contained in this series.

  • 5. Borsato, R.
    et al.
    Ohlsson Sax, Olof
    KTH, Centra, Nordic Institute for Theoretical Physics NORDITA.
    Sfondrini, A.
    Stefański, B.
    Torrielli, A.
    On the dressing factors, Bethe equations and Yangian symmetry of strings on AdS(3) x S-3 x T-42017Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, nr 2, artikel-id 024004Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Integrability is believed to underlie the correspondence with sixteen supercharges. We elucidate the role of massless modes within this integrable framework. Firstly, we find the dressing factors that enter the massless and mixed-mass worldsheet S matrix. Secondly, we derive a set of all-loop Bethe Equations for the closed strings, determine their symmetries and weak-coupling limit. Thirdly, we investigate the underlying Yangian symmetry in the massless sector and show that it fits into the general framework of Yangian integrability. In addition, we compare our S matrix in the near-relativistic limit with recent perturbative worldsheet calculations of Sundin and Wulff.

  • 6. Borsato, Riccardo
    et al.
    Ohlsson Sax, Olof
    Sfondrini, Alessandro
    Stefanski, Bogdan, Jr.
    On the spectrum of AdS(3) x S-3 x T-4 strings with Ramond-Ramond flux2016Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 49, nr 41, artikel-id 41LT03Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We analyze the spectrum of perturbative closed strings on AdS(3) x S-3 x T-4 with Ramond-Ramond flux using integrable methods. By solving the crossing equations we determine the massless and mixed-mass dressing factors of the worldsheet S matrix and derive the Bethe equations. Using these, we construct the underlying integrable spin chain and show that it reproduces the reducible spin chain conjectured at weak coupling in Olof Ohlsson S, Bogdan S Jr and Torrielli A 2013 (arXiv: 1211.1952). We find that the string-theory massless modes are described by gapless excitations of the spin chain. The resulting degeneracy of vacua matches precisely the protected supergravity spectrum found by de Boer.

  • 7.
    Borsato, Riccardo
    et al.
    KTH, Centra, Nordic Institute for Theoretical Physics NORDITA.
    Wulff, Linus
    Masaryk Univ, Dept Theoret Phys & Astrophys, Brno 61137, Czech Republic..
    Marginal deformations of WZW models and the classical Yang-Baxter equation2019Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 52, nr 22, artikel-id 225401Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We show how so-called Yang-Baxter (YB) deformations of sigma models, based on an R-matrix solving the classical Yang-Baxter equation (CYBE), give rise to marginal current-current deformations when applied to the Wess-Zumino-Witten (WZW) model. For non-compact groups these marginal deformations are more general than the ones usually considered, since they can involve a non-Abelian current subalgebra. We classify such deformations of the AdS(3) x S-3 string.

  • 8.
    Cagnazzo, Alessandra
    et al.
    KTH, Centra, Nordic Institute for Theoretical Physics NORDITA.
    Sorokin, Dmitri
    Tseytlin, Arkady A.
    Wulff, Linus
    Semiclassical equivalence of Green-Schwarz and pure-spinor/hybrid formulations of superstrings in AdS(5) x S-5 and AdS(2) x S-2 x T-62013Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 46, nr 6, s. 065401-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We demonstrate the equivalence between the worldsheet one-loop partition functions computed near classical string solutions in the Green-Schwarz and in the pure-spinor formulations of superstrings in AdS(5) x S-5. While their bosonic sectors are the same in the conformal gauge, their fermionic sectors superficially appear to be very different (first versus second-derivative kinetic terms, presence versus absence of fermionic gauge symmetry). Still, we show that the quadratic fluctuation spectrum of 16 fermionic modes of the pure-spinor formulation is the same as in the Green-Schwarz superstring and the contribution of the extra 'massless' fermionic modes cancels against that of the pure-spinor ghosts. We also provide evidence for a similar semiclassical equivalence between the Green-Schwarz and the hybrid formulations of superstrings in AdS(2) x S-2 x T-6 by studying several particular examples of string solutions.

  • 9.
    Caputa, P.
    et al.
    KTH, Centra, Nordic Institute for Theoretical Physics NORDITA.
    Rams, M. M.
    Quantum dimensions from local operator excitations in the Ising model2017Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, nr 5, artikel-id 055002Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We compare the time evolution of entanglement measures after local operator excitation in the critical Ising model with predictions from conformal field theory. For the spin operator and its descendants we find that Rényi entropies of a block of spins increase by a constant that matches the logarithm of the quantum dimension of the conformal family. However, for the energy operator we find a small constant contribution that differs from the conformal field theory answer equal to zero. We argue that the mismatch is caused by the subtleties in the identification between the local operators in conformal field theory and their lattice counterpart. Our results indicate that evolution of entanglement measures in locally excited states not only constraints this identification, but also can be used to extract non-trivial data about the conformal field theory that governs the critical point. We generalize our analysis to the Ising model away from the critical point, states with multiple local excitations, as well as the evolution of the relative entropy after local operator excitation and discuss universal features that emerge from numerics. © 2017 IOP Publishing Ltd.

  • 10.
    Caputa, Pawel
    et al.
    KTH, Centra, Nordic Institute for Theoretical Physics NORDITA. Stockholm University, Sweden; Kyoto University, Japan.
    Kusuki, Yuya
    Takayanagi, Tadashi
    Watanabe, Kento
    Evolution of entanglement entropy in orbifold CFTs2017Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, nr 24, artikel-id 244001Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this work we study the time evolution of the Renyi entanglement entropy for locally excited states created by twist operators in the cyclic orbifold (T-2)(n)/Z(n) and the symmetric orbifold (T-2)(n)/S-n. We find that when the square of its compactification radius is rational, the second Renyi entropy approaches a universal constant equal to the logarithm of the quantum dimension of the twist operator. On the other hand, in the non-rational case, we find a new scaling law for the Renyi entropies given by the double logarithm of time log log t for the cyclic orbifold CFT.

  • 11.
    Carmona, Philippe
    et al.
    Univ Nantes, Lab Math Jean Leray, UMR 6629, 2 Rue Houssiniere,BP 92208, F-44322 Nantes 03, France..
    Nguyen, Gia Bao
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Petrelis, Nicolas
    Univ Nantes, Lab Math Jean Leray, UMR 6629, 2 Rue Houssiniere,BP 92208, F-44322 Nantes 03, France..
    Torri, Niccolo
    CNRS, Campus Jussieu,4 Pl Jussieu, F-75252 Paris 5, France.;Univ Paris 06, Lab Probabil & Modeles Aleatoires, Campus Jussieu,4 Pl Jussieu, F-75252 Paris 5, France..
    Interacting partially directed self-avoiding walk: a probabilistic perspective2018Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 51, nr 15, artikel-id 153001Artikel, forskningsöversikt (Refereegranskat)
    Abstract [en]

    We review some recent results obtained in the framework of the 2D interacting self-avoiding walk (ISAW). After a brief presentation of the rigorous results that have been obtained so far for ISAW we focus on the interacting partially directed self-avoiding walk (IPDSAW), a model introduced in Zwanzig and Lauritzen (1968 J. Chem. Phys. 48 3351) to decrease the mathematical complexity of ISAW. In the first part of the paper, we discuss how a new probabilistic approach based on a random walk representation (see Nguyen and Petrelis (2013 J. Stat. Phys. 151 1099-120)) allowed for a sharp determination of the asymptotics of the free energy close to criticality (see Carmona et al (2016 Ann. Probab. 44 3234-90)). Some scaling limits of IPDSAW were conjectured in the physics literature (see e.g. Brak et al (1993 Phys. Rev. E 48 2386-96)). We discuss here the fact that all limits are now proven rigorously, i.e. for the extended regime in Carmona and Petrelis (2016 Electron. J. Probab. 21 1-52), for the collapsed regime in Carmona et al (2016 Ann. Probab. 44 3234-90) and at criticality in Carmona and Petrelis (2017b arxiv:1709.06448). The second part of the paper starts with the description of four open questions related to physically relevant extensions of IPDSAW. Among such extensions is the interacting prudent self-avoiding walk (IPSAW) whose configurations are those of the 2D prudent walk. We discuss the main results obtained in Petrelis and Torri (2016 Ann. Inst. Henri Poincare D) about IPSAW and in particular the fact that its collapse transition is proven to exist rigorously.

  • 12. Cooke, Michael
    et al.
    Dekel, Amit
    KTH, Centra, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, Sweden.
    Drukker, Nadav
    The Wilson loop CFT: insertion dimensions and structure constants from wavy lines2017Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, nr 33, artikel-id 335401Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study operator insertions into the 1/2 BPS Wilson loop in N = 4 SYM theory and determine their two-point coefficients, anomalous dimensions and structure constants. The calculation is done for the first few lowest dimension insertions and relies on known results for the expectation value of a smooth Wilson loop. In addition to the particular coefficients that we calculate, our study elucidates the connection between deformations of the line and operator insertions and between the vacuum expectation value of the line and the CFT data of the insertions.

  • 13. Fjelstad, Jens
    et al.
    Månsson, Teresia
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik.
    New symmetries of the chiral Potts model2012Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 45, nr 15, s. 155208-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper a hitherto unknown spectrum generating algebra, consisting of two coupled Temperley-Lieb algebras, is found in the three-state chiral Potts model. From this, we can construct new Onsager integrable models. One realization is in terms of a staggered isotropic XY spin chain. Further we investigate the importance of the algebra for the existence of mutually commuting conserved charges. This leads us to a natural generalization of the boost operator, which generates the charges.

  • 14. Fokas, A. S.
    et al.
    Lenells, Jonatan
    The unified method: I. Nonlinearizable problems on the half-line2012Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 45, nr 19, artikel-id 195201Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Boundary value problems for integrable nonlinear evolution PDEs formulated on the half-line can be analyzed by the unified method introduced by one of the authors and used extensively in the literature. The implementation of this general method to this particular class of problems yields the solution in terms of the unique solution of a matrix RiemannHilbert problem formulated in the complex k-plane (the Fourier plane), which has a jump matrix with explicit (x, t)-dependence involving four scalar functions of k, called the spectral functions. Two of these functions depend on the initial data, whereas the other two depend on all boundary values. The most difficult step of the new method is the characterization of the latter two spectral functions in terms of the given initial and boundary data, i.e. the elimination of the unknown boundary values. For certain boundary conditions, called linearizable, this can be achieved simply using algebraic manipulations. Here, we present an effective characterization of the spectral functions in terms of the given initial and boundary data for the general case of non-linearizable boundary conditions. This characterization is based on the analysis of the so-called global relation, on the analysis of the equations obtained from the global relation via certain transformations leaving the dispersion relation of the associated linearized PDE invariant and on the computation of the large k asymptotics of the eigenfunctions defining the relevant spectral functions. © 2012 IOP Publishing Ltd.

  • 15.
    Garjani, B. Majidzadeh
    et al.
    KTH, Centra, Nordic Institute for Theoretical Physics NORDITA.
    Ardonne, E.
    Anyon chains with pairing terms2017Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, nr 13, artikel-id 135201Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we introduce a one-dimensional model of su(2)(k) anyons in which the number of anyons can fluctuate by means of a pairing term. The model can be tuned to a point at which one can determine the exact zero-energy ground states, in close analogy to the spin-1 AKLT model. We also determine the points at which the model is integrable and determine the behavior of the model at these integrable points.

  • 16.
    Garjani, B. Majidzadeh
    et al.
    KTH, Centra, Nordic Institute for Theoretical Physics NORDITA.
    Estienne, B.
    Ardonne, E.
    On the particle entanglement spectrum of the Laughlin states2015Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 48, nr 28, artikel-id 285205Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The study of the entanglement entropy and entanglement spectrum has proven to be very fruitful in identifying topological phases of matter. Typically, one performs numerical studies of finite-size systems. However, there are few rigorous results in this regard. We revisit the problem of determining the rank of the 'particle entanglement spectrum' (PES) of the Laughlin states. We reformulate the problem into a problem concerning the ideal of symmetric polynomials that vanish under the formation of several clusters of particles. We introduce an explicit generating set of this ideal, and we prove that polynomials in this ideal have a total degree that is bounded from below. We discuss the difficulty in proving the same bound on the degree of any of the variables, which is necessary to determine the rank of the PES.

  • 17.
    Guica, Monica
    et al.
    KTH, Centra, Nordic Institute for Theoretical Physics NORDITA. CEA Saclay, Inst Phys Theor, F-91191 Gif Sur Yvette, France.;Stockholm Univ, NORDITA, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden.;Uppsala Univ, Dept Phys & Astron, SE-75108 Uppsala, Sweden..
    Maslyuk, Fedor Levkovich
    Stockholm Univ, NORDITA, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden.;KTH Royal Inst Technol, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden..
    Zarembo, Konstantin
    KTH, Centra, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, NORDITA, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden..;Uppsala Univ, Dept Phys & Astron, SE-75108 Uppsala, Sweden..
    Integrability in dipole-deformed N=4 super Yang-Mills2017Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, nr 39, artikel-id 394001Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study the null dipole deformation of N = 4 super Yang-Mills theory, which is an example of a potentially solvable 'dipole CFT': a theory that is non-local along a null direction, has non-relativistic conformal invariance along the remaining ones, and is holographically dual to a Schrodinger space-time. We initiate the field-theoretical study of the spectrum in this model by using integrability inherited from the parent theory. The dipole deformation corresponds to a nondiagonal Drinfeld-Reshetikhin twist in the spin chain picture, which renders the traditional Bethe ansatz inapplicable from the very beginning. We use instead the Baxter equation supplemented with nontrivial asymptotics, which gives the full 1-loop spectrum in the sl(2) sector. We show that anomalous dimensions of long gauge theory operators perfectly match the string theory prediction, providing a quantitative test of Schrodinger holography.

  • 18. Harland, Derek
    et al.
    Jäykkä, Juha
    KTH, Centra, Nordic Institute for Theoretical Physics NORDITA.
    Shnir, Yakov
    Speight, Martin
    Isospinning hopfions2013Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 46, nr 22, s. 225402-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The problem of constructing internally rotating solitons of fixed angular frequency omega in the Faddeev-Skyrme model is reformulated as a variational problem for an energy-like functional, called pseudoenergy, which depends parametrically on omega. This problem is solved numerically using a gradient descent method, without imposing any spatial symmetries on the solitons, and the dependence of the solitons' energy on omega, and on their conserved total isospin J, studied. It is found that, generically, the shape of a soliton is independent of omega, and that its size grows monotonically with omega. A simple elastic rod model of time-dependent hopfions is developed which, despite having only one free parameter, accounts well for most of the numerical results.

  • 19.
    Heinze, Martin
    et al.
    KTH, Centra, Nordic Institute for Theoretical Physics NORDITA. Humboldt-Universität zu Berlin, Germany.
    Jorjadze, G.
    Megrelidze, L.
    Isometry group orbit quantization of spinning strings in AdS3 × S32015Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 48, nr 12, artikel-id 125401Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Describing the bosonic AdS3 × S3 particle and string in SU(1,1) × SU(2) group variables, we provide a Hamiltonian treatment of the isometry group orbits of solutions via analysis of the pre-symplectic form. For the particle we obtain a one-parameter family of orbits parameterized by creation-annihilation variables, which leads to the HolsteinPrimakoff realization of the isometry group generators. The scheme is then applied to spinning string solutions characterized by one winding number in AdS3 and two winding numbers in S3. We find a two-parameter family of orbits, where quantization again provides the Holstein-Primakoff realization of the symmetry generators with an oscillator-type energy spectrum. Analyzing the minimal energy at strong coupling, we verify the spectrum of short strings at special values of winding numbers.

  • 20.
    Holmin, Samuel
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Kurlberg, Pär
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Månsson, Daniel
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Elektroteknisk teori och konstruktion.
    On the free path length distribution for linear motion in an n-dimensional box2018Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 51, nr 46, artikel-id 465201Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider the distribution of free path lengths, or the distance between consecutive bounces of random particles, in an n-dimensional rectangular box. If each particle travels a distance R, then, as R -> infinity the free path length coincides with the distribution of the length of the intersection of a random line with the box (for a natural ensemble of random lines) and we give an explicit formula (piecewise real analytic) for the probability density function in dimension two and three. In dimension two we also consider a closely related model where each particle is allowed to bounce N times, as N -> infinity, and give an explicit (again piecewise real analytic) formula for its probability density function. Further, in both models we can recover the side lengths of the box from the location of the discontinuities of the probability density functions.

  • 21.
    Hoppe, Jens
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Relativistic membranes2013Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 46, nr 2, s. 023001-Artikel, forskningsöversikt (Refereegranskat)
    Abstract [en]

    The classical dynamics of M-dimensional extended objects arising from stationary points of the world volume swept out in space time is discussed from various points of view. An introduction to the Hamiltonian mechanics of bosonic compact M(em)branes is given, emphasing the diversity of the different formulations and gauge choices. For moving hypersurfaces, a graph description-including its nonlinear realization of Lorentz invariance-and hydrodynamic formulations (in light-cone coordinates as well as when choosing the time coordinate of a Lorentz observer as the dependent variable) are presented. A matrix regularization for M = 2 (existing for all topologies) is explained in detail for the 2-sphere, as well as multilinear formulations for M > 2. The recently found dynamical symmetry that exists for all M and related reconstruction algebras are covered, just as some explicit solutions of the level-set equations.

  • 22.
    Lenells, Jonatan
    University of Cambridge, United Kingdom .
    Poisson structure of a modified Hunter-Saxton equation2008Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 41, nr 28, artikel-id 285207Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Both the well-known Korteweg-de Vries equation and the Hunter-Saxton equation with a linear wux-term, -utxx = -2ωu x + 2uxuxx + uuxxx, ω > 0, are bi-Hamiltonian in the sense that each equation is Hamiltonian with respect to two compatible, but distinct, Poisson brackets. We present a nonlinear change of variables which maps between the two bi-Poisson structures, giving a correspondence between the infinite hierarchies of conservation laws and commuting flows associated with the equations. In particular, under this change of variables this (modified) Hunter-Saxton equation can be viewed as a member of the KdV hierarchy.

  • 23.
    Lenells, Jonatan
    Baylor University, United States; University of Cambridge, United Kingdom .
    The KdV equation on the half-line: The Dirichlet to Neumann map2013Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 46, nr 34, artikel-id 345203Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider initial-boundary value problems for the KdV equation u t + ux + 6uux + uxxx = 0 on the half-line x 0. For a well-posed problem, the initial data u(x, 0) as well as one of the three boundary values {u(0, t), ux (0, t), uxx (0, t)} can be prescribed; the other two boundary values remain unknown. We provide a characterization of the unknown boundary values for the Dirichlet as well as the two Neumann problems in terms of a system of nonlinear integral equations. The characterizations are effective in the sense that the integral equations can be solved perturbatively to all orders in a well-defined recursive scheme.

  • 24.
    Lenells, Jonatan
    et al.
    Baylor University, United States .
    Fokas, A. S.
    The unified method: II. NLS on the half-line with t-periodic boundary conditions2012Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 45, nr 19, artikel-id 195202Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Boundary value problems for integrable nonlinear evolution PDEs formulated on the half-line can be analyzed by the unified method introduced by one of the authors and used extensively in the literature. The implementation of this general method to this particular class of problems yields the solution in terms of the unique solution of a matrix RiemannHilbert problem formulated in the complex k-plane (the Fourier plane), which has a jump matrix with explicit (x, t)-dependence involving four scalar functions of k, called spectral functions. Two of these functions depend on the initial data, whereas the other two depend on all boundary values. The most difficult step of the new method is the characterization of the latter two spectral functions in terms of the given initial and boundary data, i.e. the elimination of the unknown boundary values. For certain boundary conditions, called linearizable, this can be achieved by simply using algebraic manipulations. Here, we first present an effective characterization of the spectral functions in terms of the given initial and boundary data for the general case of non-linearizable boundary conditions. This characterization is based on the analysis of the so-called global relation and on the introduction of the so-called GelfandLevitanMarchenko representations of the eigenfunctions defining the spectral functions. We then concentrate on the physically significant case of t-periodic Dirichlet boundary data. After presenting certain heuristic arguments which suggest that the Neumann boundary values become periodic as t → , we show that for the case of the NLS with a sine-wave as Dirichlet data, the asymptotics of the Neumann boundary values can be computed explicitly at least up to third order in a perturbative expansion and indeed at least up to this order are asymptotically periodic.

  • 25.
    Lenells, Jonatan
    et al.
    Baylor University, United States .
    Fokas, A. S.
    The unified method: III. Nonlinearizable problems on the interval2012Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 45, nr 19, artikel-id 195203Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Boundary value problems for integrable nonlinear evolution PDEs formulated on the finite interval can be analyzed by the unified method introduced by one of the authors and extensively used in the literature. The implementation of this general method to this particular class of problems yields the solution in terms of the unique solution of a matrix RiemannHilbert problem formulated in the complex k-plane (the Fourier plane), which has a jump matrix with explicit (x, t)-dependence involving six scalar functions of k, called the spectral functions. Two of these functions depend on the initial data, whereas the other four depend on all boundary values. The most difficult step of the new method is the characterization of the latter four spectral functions in terms of the given initial and boundary data, i.e. the elimination of the unknown boundary values. Here, we present an effective characterization of the spectral functions in terms of the given initial and boundary data. We present two different characterizations of this problem. One is based on the analysis of the so-called global relation, on the analysis of the equations obtained from the global relation via certain transformations leaving the dispersion relation of the associated linearized PDE invariant and on the computation of the large k asymptotics of the eigenfunctions defining the relevant spectral functions. The other is based on the analysis of the global relation and on the introduction of the so-called GelfandLevitanMarchenko representations of the eigenfunctions defining the relevant spectral functions. We also show that these two different characterizations are equivalent and that in the limit when the length of the interval tends to infinity, the relevant formulas reduce to the analogous formulas obtained recently for the case of boundary value problems formulated on the half-line.

  • 26.
    Lundholm, Douglas
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Geometric extensions of many-particle Hardy inequalities2015Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 48, nr 17, artikel-id 175203Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Certain many-particle Hardy inequalities are derived in a simple and systematic way using the so-called ground state representation for the Laplacian on a subdomain of R^n. This includes geometric extensions of the standard Hardy inequalities to involve volumes of simplices spanned by a subset of points. Clifford/multilinear algebra is employed to simplify geometric computations. These results and the techniques involved are relevant for classes of exactly solvable quantum systems such as the Calogero-Sutherland models and their higher-dimensional generalizations, as well as for membrane matrix models, and models of more complicated particle interactions of geometric character.

  • 27.
    Mancarella, Francesco
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik. NORDITA.
    Trombettoni, Andrea
    Mussardo, Giuseppe
    Statistical interparticle potential of an ideal gas of non-Abelian anyons2013Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 46, nr 27, s. 275001-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We determine and study the statistical interparticle potential of an ideal system of non-Abelian Chern-Simons (NACS) particles, comparing our results with the corresponding results of an ideal gas of Abelian anyons. In the Abelian case, the statistical potential depends on the statistical parameter alpha; it has 'quasi-bosonic' behavior for 0 < alpha < 1/2 (non-monotonic with a minimum) and 'quasi-fermionic' behavior for 1/2 <= alpha < 1 (monotonically decreasing without a minimum). In the non-Abelian case, the behavior of the statistical potential depends on the Chern-Simons coupling and the isospin quantum number: as a function of these two parameters, a phase diagram with quasi-bosonic, quasi-fermionic and bosonic-like regions is obtained and investigated. Finally, using the obtained expression for the statistical potential, we compute the second virial coefficient of the NACS gas, which correctly reproduces the results available in the literature.

  • 28.
    Månsson, Teresia
    ax-Planck Institut für Gravitationsphysik.
    Is there a tower of charges to be discovered?2007Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 41, s. 194014-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We investigate higher-loop integrability for a q-deformation of the -sector of SYM theory. First we construct a generalization of the long-range spin chain, which for the lowest orders describes the non-deformed dilatation operator. This generalized model is built up from Temperley–Lieb algebra generators and describes the deformed theory to at least two loops. When constructing the model we have demanded the existence of one commuting charge, which puts strong constraints on the parameters to three-loop orders. We also write the five first charges for this model at two-loops order. Our main goal is to obtain an explicit expression for an infinite number of commuting charges, all commuting with the dilatation operator. This would imply integrability. As a step towards this goal we present in this paper an expression for a generic local charge of the one-loop dilatation operator, which happens to be a generator of the Temperley–Lieb algebra.

  • 29.
    Nissinen, Jaakko
    et al.
    KTH, Centra, Nordic Institute for Theoretical Physics NORDITA.
    Ardonne, Eddy
    KTH, Centra, Nordic Institute for Theoretical Physics NORDITA.
    Local height probabilities in a composite Andrews-Baxter-Forrester model2012Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 45, nr 43, s. 435001-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study the local height probabilities in a composite height model, derived from the restricted solid-on-solid model introduced by Andrews, Baxter and Forrester, and their connection with conformal field theory characters. The obtained conformal field theories also describe the critical behavior of the model at two different critical points. In addition, at criticality, the model is equivalent to a one-dimensional chain of anyons, subject to competing two- and three-body interactions. The anyonic-chain interpretation provided the original motivation to introduce the composite height model, and by obtaining the critical behavior of the composite height model, the critical behavior of the anyonic chains is established as well. Depending on the overall sign of the Hamiltonian, this critical behavior is described by a diagonal coset-model, generalizing the minimal models for one sign, and by Fateev-Zamolodchikov parafermions for the other.

  • 30. Pestun, Vasily
    et al.
    Zabzine, Maxim
    Benini, Francesco
    Dimofte, Tudor
    Dumitrescu, Thomas T.
    Hosomichi, Kazuo
    Kim, Seok
    Lee, Kimyeong
    Le Floch, Bruno
    Marino, Marcos
    Minahan, Joseph A.
    Morrison, David R.
    Pasquetti, Sara
    Qiu, Jian
    Rastelli, Leonardo
    Razamat, Shlomo S.
    Pufu, Silvu S.
    Tachikawa, Yuji
    Willett, Brian
    Zarembo, Konstantin
    KTH, Centra, Nordic Institute for Theoretical Physics NORDITA.
    Localization techniques in quantum field theories2017Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, nr 44, artikel-id 440301Artikel i tidskrift (Övrigt vetenskapligt)
    Abstract [en]

    This is the foreword to the special issue on localization techniques in quantum field theory. The summary of individual chapters is given and their interrelation is discussed.

  • 31. Shapiro, B.
    et al.
    Zarembo, K.
    KTH, Centra, Nordic Institute for Theoretical Physics NORDITA.
    Level crossing in random matrices: I. Random perturbation of a fixed matrix2017Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, nr 4, artikel-id 045201Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider level crossing in a matrix family H = H-0 + lambda V where H-0 is a fixed N x N matrix and V belongs to one of the standard Gaussian random matrix ensembles. We study the probability distribution of level crossing points in the complex plane of lambda, for which we obtain a number of exact, asymptotic and approximate formulas.

  • 32.
    Thylwe, Karl-Erik
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Hamzavi, Majid
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Light-heavy quark-type linear potential models with spin- and pseudospin-symmetric states2013Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 46, nr 8, s. 085305-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Possible spin- and pseudospin-symmetric states with positive energies of the Dirac equation with linear scalar and vector potentials are investigated. Two exact relativistic spin symmetries of linear quark-type potential models are shown to exist for positive energies. It is known that positive-energy states which still exist in the non-relativistic limit are always of the spin-symmetric type, like those described in the Schrodinger framework. However, if significant relativistic corrections to the Schrodinger theory are considered and also different possible signs of vector and scalar potentials, there exist two exact spin symmetries: a spin- symmetric energy spectrum that tends to the previously known spectrum obtained by the Schrodinger theory in the non-relativistic limit, and a pseudospin-symmetric energy spectrum that does not. The exact symmetries are perturbed by modifying the strengths of the relativistic linear vector and scalar potentials and introducing a tensor coupling. These perturbations may cancel each other.

  • 33.
    Thylwe, Karl-Erik
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    McCabe, P.
    Amplitude-phase calculations of Regge poles obtained from coupled radial Dirac equations2011Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 44, nr 27, s. 275305-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A recently developed amplitude-phase method for spinor-wave solutions is applied to the calculations of Regge pole positions and residues of Dirac particles. At a given energy the Dirac spin causes two sets of Regge poles that tend to coalesce in the non-relativistic limit. For the particular case of equal Lorentz-type vector and scalar potentials there is only one pole string, located very close to the non-relativistic pole string.

  • 34.
    Thylwe, Karl-Erik
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    McCabe, Patrick
    Coupled radial Schrodinger equations written as Dirac-type equations: application to an amplitude-phase approach2012Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 45, nr 13, s. 135302-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The classical amplitude-phase method due to Milne, Wilson, Young and Wheeler in the 1930s is known to be a powerful computational tool for determining phase shifts and energy eigenvalues in cases where a sufficiently slowly varying amplitude function can be found. The key for the efficient computations is that the original single-state radial Schrodinger equation is transformed to a nonlinear equation, the Milne equation. Such an equation has solutions that may or may not oscillate, depending on boundary conditions, which then requires a robust recipe for locating the (optimal) 'almost constant' solutions for its use in the method. For scattering problems the solutions of the amplitude equations always approach constants as the radial distance r tends to infinity, and there is no problem locating the 'optimal' amplitude functions from a low-order semiclassical approximation. In the present work, the amplitude-phase approach is generalized to two coupled Schrodinger equations similar to an earlier generalization to radial Dirac equations. The original scalar amplitude then becomes a vector quantity, and the original Milne equation is generalized accordingly. Numerical applications to resonant electron-atom scattering are illustrated.

  • 35.
    Zarembo, Konstantin
    KTH, Centra, Nordic Institute for Theoretical Physics NORDITA.
    Localization and AdS/CFT correspondence2017Ingår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, nr 44, artikel-id 443011Artikel, forskningsöversikt (Refereegranskat)
1 - 35 av 35
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