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  • 1.
    Arnlind, Joakim
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Representation theory of C-algebras for a higher order class of spheres and tori2008In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 49, no 5, p. 053502-1-053502-13Article in journal (Refereed)
    Abstract [en]

    We construct C-algebras for a class of surfaces that are inverse images of certain polynomials of arbitrary degree. By using the directed graph associated with a matrix, the representation theory can be understood in terms of "loop" and "string" representations, which are closely related to the dynamics of an iterated map in the plane. As a particular class of algebras, we introduce the "Henon algebras," for which the dynamical map is a generalized Henon map, and give an example where irreducible representations of all dimensions exist.

  • 2.
    Atai, Farrokh
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Deformed Calogero-Sutherland model and fractional quantum Hall effect2017In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 58, no 1, article id 011902Article in journal (Refereed)
    Abstract [en]

    The deformed Calogero-Sutherland (CS) model is a quantum integrable system with arbitrary numbers of two types of particles and reducing to the standard CS model in special cases. We show that a known collective field description of the CS model, which is based on conformal field theory (CFT), is actually a collective field description of the deformed CS model. This provides a natural application of the deformed CS model in Wen's effective field theory of the fractional quantum Hall effect (FQHE), with the two kinds of particles corresponding to electrons and quasi-hole excitations. In particular, we use known mathematical results about super-Jack polynomials to obtain simple explicit formulas for the orthonormal CFT basis proposed by van Elburg and Schoutens in the context of the FQHE.

  • 3. Bach, V.
    et al.
    Frohlich, J.
    Jonsson, B. Lars G.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Bogolubov-Hartree-Fock mean field theory for neutron stars and other systems with attractive interactions2009In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 50, no 10Article in journal (Refereed)
    Abstract [en]

    A simplification of the Bogolubov-Hartree-Fock theory, which is a natural generalization of the traditional Hartree-Fock theory, is derived. This simplification allows to express the pairing interaction in terms of the one-particle density matrix for systems interacting by attractive pair potentials, such as the Newtonian gravitational potential.

  • 4.
    Bjerklöv, Kristian
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Positive Lyapunov exponents for continuous quasiperiodic Schrodinger equations2006In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 47, no 2Article in journal (Refereed)
    Abstract [en]

    We prove that the continuous one-dimensional Schrodinger equation with an analytic quasi-periodic potential has positive Lyapunov exponents in the bottom of the spectrum for large couplings.

  • 5.
    Blennow, Mattias
    et al.
    KTH, Superseded Departments, Physics.
    Ohlsson, Tommy
    KTH, Superseded Departments, Physics.
    Exact series solution to the two flavor neutrino oscillation problem in matter2004In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 45, no 11, p. 4053-4063Article in journal (Refereed)
    Abstract [en]

    In this paper, we present a real nonlinear differential equation for the two flavor neutrino oscillation problem in matter with an arbitrary density profile. We also present an exact series solution to this nonlinear differential equation. In addition, we investigate numerically the convergence of this solution for different matter density profiles such as constant and linear profiles as well as the Preliminary Reference Earth Model describing the Earth's matter density profile. Finally, we discuss other methods used for solving the neutrino flavor evolution problem.

  • 6. Boscain, Ugo
    et al.
    Grönberg, Fredrik
    KTH, School of Engineering Sciences (SCI), Physics.
    Long, Ruixing
    Rabitz, Herschel
    Minimal time trajectories for two-level quantum systems with two bounded controls2014In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 55, no 6, p. 062106-Article in journal (Refereed)
    Abstract [en]

    In this paper we consider the minimum time population transfer problem for a two level quantum system driven by two external fields with bounded amplitude. The controls are modeled as real functions and we do not use the Rotating Wave Approximation. After projection on the Bloch sphere, we treat the time-optimal control problem with techniques of optimal synthesis on 2D manifolds. Based on the Pontryagin Maximum Principle, we characterize a restricted set of candidate optimal trajectories. Properties on this set, crucial for complete optimal synthesis, are illustrated by numerical simulations. Furthermore, when the two controls have the same bound and this bound is small with respect to the difference of the two energy levels, we get a complete optimal synthesis up to a small neighborhood of the antipodal point of the initial condition.

  • 7.
    Boscain, Ugo
    et al.
    CMAP Ecole Polytech, CNRS, Palaiseau, France.;INRIA Saclay, Team GECO, Saclay, France..
    Grönberg, Fredrik
    KTH, School of Engineering Sciences (SCI), Physics, Physics of Medical Imaging. Linköping Univ, Dept Elect Engn ISY, Linkoping, Sweden..
    Long, Ruixing
    Gen Motors Canada, Oshawa, ON, Canada..
    Rabitz, Herschel
    Princeton Univ, Dept Chem, Princeton, NJ 08544 USA..
    Minimal time trajectories for two-level quantum systems with two bounded controls (vol 55, 062106, 2014)2014In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 55, no 8, article id 089901Article in journal (Refereed)
  • 8. Calogero, F.
    et al.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Goldfishing by gauge theory2006In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 47, no 8Article in journal (Refereed)
    Abstract [en]

    A new solvable many-body problem of goldfish type is identified and used to revisit the connection between two different approaches to solvable dynamical systems. An isochronous variant of this model is identified and investigated. Alternative versions of these models are presented. The behavior of the alternative isochronous model near its equilibrium configurations is investigated, and a remarkable Diophantine result, as well as related Diophantine conjectures, are thereby obtained.

  • 9. De Sole, A.
    et al.
    Hekmati, Pedram
    School of Mathematical Sciences, University of Adelaide.
    Kac, Victor G.
    Calculus structure on the Lie conformal algebra complex and the variational complex2011In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 52, no 5Article in journal (Refereed)
    Abstract [en]

    We construct a calculus structure on the Lie conformal algebra cochain complex. By restricting to degree one chains, we recover the structure of a g-complex introduced in [A. De Sole and V. G. Kac, Commun. Math. Phys. 292, 667 (2009)]. A special case of this construction is the variational calculus, for which we provide explicit formulas.

  • 10. Dejak, S. I.
    et al.
    Jonsson, B. Lars G.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Long-time dynamics of variable coefficient modified Korteweg-de Vries solitary waves2006In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 47, no 7Article in journal (Refereed)
    Abstract [en]

    We study the long-time behavior of solutions to the Korteweg-de Vries-type equation partial derivative(t)u=-partial derivative(x)(partial derivative(2)(x)u+f(u)-b(t,x)u), with initial conditions close to a stable, b=0 solitary wave. The coefficient b is a bounded and slowly varying function, and f is a nonlinearity. For a restricted class of nonlinearities, we prove that for long time intervals, such solutions have the form of the solitary wave, whose center and scale evolve according to a certain dynamical law involving the function b(t,x), plus an H-1(R)-small fluctuation. The result is stronger than those previously obtained for general nonlinearities f.

  • 11.
    Ekholm, Tomas
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Portmann, Fabian
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    A magnetic contribution to the Hardy inequality2014In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 55, no 2, p. 022101-Article in journal (Refereed)
    Abstract [en]

    We study the quadratic form associated to the kinetic energy operator in the presence of an external magnetic field in d = 3. We show that if the radial component of the magnetic field does not vanish identically, then the classical lower bound given by Hardy is improved by a non-negative potential term depending on properties of the magnetic field.

  • 12. Forger, M
    et al.
    Paufler, Cornelius
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Romer, H
    Hamiltonian multivector fields and Poisson forms in multisymplectic field theory2005In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 46, no 11, p. 112903-Article in journal (Refereed)
    Abstract [en]

    We present a general classification of Hamiltonian multivector fields and of Poisson forms on the extended multiphase space appearing in the geometric formulation of first order classical field theories. This is a prerequisite for computing explicit expressions for the Poisson bracket between two Poisson forms.

  • 13. Fredenhagen, Stefan
    et al.
    Hoppe, Jens
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Hynek, Mariusz
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    The Lorentz anomaly via operator product expansion2015In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 56, no 10, article id 102302Article in journal (Refereed)
    Abstract [en]

    The emergence of a critical dimension is one of the most striking features of string theory. One way to obtain it is by demanding closure of the Lorentz algebra in the light-cone gauge quantisation, as discovered for bosonic strings more than forty years ago. We give a detailed derivation of this classical result based on the operator product expansion on the Lorentzian world-sheet.

  • 14.
    Gordon, James
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Semenoff, Gordon W.
    World-line instantons and the Schwinger effect as a Wentzel-Kramers-Brillouin exact path integral2015In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 56, no 2, article id 022111Article in journal (Refereed)
    Abstract [en]

    A detailed study of the semiclassical expansion of the world line path integral for a charged relativistic particle in a constant external electric field is presented. We show that the Schwinger formula for charged particle pair production is reproduced exactly by the semiclassical expansion around classical instanton solutions when the leading order of fluctuations is taken into account. We prove that all corrections to this leading approximation vanish and that the WKB approximation to the world line path integral is exact.

  • 15.
    Hallnäs, Martin
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Exact solutions of two complementary one-dimensional quantum many-body systems on the half-line2005In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 46, no 5Article in journal (Refereed)
    Abstract [en]

    We consider two particular one-dimensional quantum many-body systems with local interactions related to the root system C-N. Both models describe identical particles moving on the half-line with nontrivial boundary conditions at the origin, but in the first model the particles interact with the delta interaction while in the second via a particular momentum dependent interaction commonly known as delta-prime interaction. We show that the Bethe ansatz solution of the delta-interaction model is consistent even for the general case where the particles are distinguishable, whereas for the delta-prime interaction it only is consistent and nontrivial in the fermion case. We also establish a duality between the bosonic delta- and the fermionic delta-prime model, and we elaborate on the physical interpretations of these models.

  • 16.
    Hoppe, Jens
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Lundholm, Douglas
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Trzetrzelewski, Maciej
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Spin(9) average of SU(N) matrix models2009In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 50, no 4, p. 043510-1-043510-7Article in journal (Refereed)
    Abstract [en]

    We apply a method of group averaging to states and operators appearing in (truncations of) the Spin(9)xSU(N) invariant matrix models. We find that there is an exact correspondence between the standard supersymmetric Hamiltonian and the Spin (9) average of a relatively simple lower-dimensional model.

  • 17.
    Jonsson, B. Lars G.
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Ovchinnikov, Yu. N.
    Sigal, I. M.
    Ting, F. S. T.
    Dynamics of breakup of multiple vortices in Gross-Pitaevskii equations of superfluids2011In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 52, no 9Article in journal (Refereed)
    Abstract [en]

    In this paper we study the Gross-Pitaevskii equation of the theory of superfluidity, i.e., the nonlinear Schroumldinger equation of the Ginzburg-Landau type. We investigate the dynamics of the breakup of the double vortex. More specifically, we prove instability of the double vortex, compute the complex eigenvalue responsible for this instability, and derive the dynamical equation of motion of (centers of) single vortices resulting from splitting of the double vortex. We expect that our analysis can be extended to vortices of higher degree and to magnetic and Chern-Simmons vortices. (C) 2011 American Institute of Physics. [doi:10.1063/1.3629473]

  • 18. Kurasov, P.
    et al.
    Garjani, B. Majidzadeh
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Quantum graphs: PT -symmetry and reflection symmetry of the spectrum2017In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 58, no 2, article id 023506Article in journal (Refereed)
    Abstract [en]

    Not necessarily self-adjoint quantum graphs-differential operators on metric graphs-are considered. Assume in addition that the underlying metric graph possesses an automorphism (symmetry) P. If the differential operator is PT -symmetric, then its spectrum has reflection symmetry with respect to the real line. Our goal is to understand whether the opposite statement holds, namely, whether the reflection symmetry of the spectrum of a quantum graph implies that the underlying metric graph possesses a non-trivial automorphism and the differential operator is PT symmetric. We give partial answer to this question by considering equilateral stargraphs. The corresponding Laplace operator with Robin vertex conditions possesses reflection-symmetric spectrum if and only if the operator is PT -symmetric with P being an automorphism of the metric graph.

  • 19.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    A superversion of quasifree second quantization. I. Charged particles1992In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 3, no 3, p. 1032-1046Article in journal (Refereed)
  • 20.
    Langmann, Edwin
    KTH, Superseded Departments, Physics.
    Algorithms to solve the (quantum) Sutherland model2001In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 42, no 9, p. 4148-4157Article in journal (Refereed)
    Abstract [en]

    We give a self-contained presentation and comparison of two different algorithms to explicitly solve quantum many body models of indistinguishable particles moving on a circle and interacting with two-body potentials of 1/sin(2)-type. The first algorithm is due to Sutherland and well-known; the second one is a limiting case of a novel algorithm to solve the elliptic generalization of the Sutherland model. These two algorithms are different in several details. We show that they are equivalent, i.e., they yield the same solution and are equally simple.

  • 21.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Cocycles for Boson and Fermion Bogoliubov Transformations1994In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 35, p. 96-112Article in journal (Refereed)
  • 22.
    Langmann, Edwin
    KTH, Superseded Departments, Physics.
    Generalized Yang-Mills actions from Dirac operator determinants2001In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 42, no 11, p. 5238-5256Article in journal (Refereed)
    Abstract [en]

    We consider the quantum effective action of Dirac fermions on four-dimensional flat Euclidean space coupled to external vector- and axial Yang-Mills fields, i.e., the logarithm of the (regularized) determinant of a Dirac operator on flat R-4 twisted by generalized Yang-Mills fields. According to physics folklore, the logarithmic divergent part of this effective action in the pure vector case is proportional to the Yang-Mills action. We present a simple explicit computation proving this fact and extending it to the chiral case. We use an efficient computation method for quantum effective actions which is based on calculation rules for pseudo-differential operators and which yields an expansion of the logarithm of Dirac operators in local and quasi-gauge invariant polynomials of decreasing scaling dimension.

  • 23.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Non-commutative Integration Calculus1995In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 36, p. 3822-3835Article in journal (Refereed)
  • 24.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Remarkable identities related to the (quantum) elliptic Calogero-Sutherland model2006In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 47, no 2Article in journal (Refereed)
    Abstract [en]

    We present remarkable functional identities related to the elliptic Calogero-Sutherland (eCS) system. We derive them from a second quantization of the eCS model within a quantum field theory model of anyons on a circle and at finite temperature. The identities involve two eCS Hamiltonians with arbitrary and, in general, different particle numbers N and M, and a particular function of N+M variables arising as anyon correlation function of N particles and M antiparticles. In addition to identities obtained from anyons with the same statistics parameter lambda, we also obtain dual relations involving mixed correlation functions of anyons with two different statistics parameters lambda and 1/lambda. We also give alternative, elementary proofs of these identities by direct computations.

  • 25.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Scattering matrix in external field problems1996In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 37, p. 3933-3953Article in journal (Refereed)
  • 26.
    Langmann, Edwin
    et al.
    KTH, Superseded Departments, Physics.
    Mickelsson, J.
    Rydh, S.
    Anomalies and Schwinger terms in NCG field theory models2001In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 42, no 10, p. 4779-4801Article in journal (Refereed)
    Abstract [en]

    We study the quantization of chiral fermions coupled to generalized Dirac operators arising in NCG Yang-Mills theory. The cocycles describing chiral symmetry breaking are calculated. In particular, we introduce a generalized locality principle for the cocycles. Local cocycles are by definition expressions which can be written as generalized traces of operator commutators. In the case of pseudodifferential operators, these traces lead in fact to integrals of ordinary local de Rham forms. As an application of the general ideas we discuss the case of noncommutative tori. We also develop a gerbe theoretic approach to the chiral anomaly in the Hamiltonian quantization of NCG field theory.

  • 27.
    Langmann, Edwin
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Moosavi, Per
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Construction by bosonization of a fermion-phonon model2015In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 56, no 9, article id 091902Article in journal (Refereed)
    Abstract [en]

    We discuss an extension of the (massless) Thirring model describing interacting fermions in one dimension which are coupled to phonons and where all interactions are local. This fermion-phonon model can be solved exactly by bosonization.We present a construction and solution of this model which is mathematically rigorous by treating it as a continuum limit of a Luttinger-phonon model. A self-contained account of the mathematical results underlying bosonization is included, together with complete proofs.

  • 28.
    Langmann, Edwin
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Takemura, Kouichi
    Source identity and kernel functions for Inozemtsev-type systems2012In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 53, no 8, p. 082105-Article in journal (Refereed)
    Abstract [en]

    The Inozemtsev Hamiltonian is an elliptic generalization of the differential operator defining the BCN trigonometric quantum Calogero-Sutherland model, and its eigenvalue equation is a natural many-variable generalization of the Heun differential equation. We present kernel functions for Inozemtsev Hamiltonians and Chalykh-Feigin-Veselov-Sergeev-type deformations thereof. Our main result is a solution of a heat-type equation for a generalized Inozemtsev Hamiltonian which is the source of all these kernel functions. Applications are given, including a derivation of simple exact eigenfunctions and eigenvalues of the Inozemtsev Hamiltonian.

  • 29.
    Lenells, Jonatan
    et al.
    Leibniz Universität Hannover, Germany .
    Fokas, A. S.
    On a novel integrable generalization of the sine-Gordon equation2010In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 51, no 2, article id 055912JMPArticle in journal (Refereed)
    Abstract [en]

    We consider an integrable generalization of the sine-Gordon (sG) equation that was earlier derived by one of the authors using bi-Hamiltonian methods. This equation is related to the sG equation in the same way that the Camassa-Holm equation is related to the Korteweg-de Vries equation. In this paper we (a) derive a Lax pair, (b) use the Lax pair to solve the initial-value problem on the line, (c) analyze solitons, (d) show that the generalized sG and sG equations are related by a Liouville transformation, (e) derive conservation laws, and (f) analyze traveling-wave solutions.

  • 30.
    Lenells, Jonatan
    et al.
    University of Cambridge, United Kingdom.
    Lechtenfeld, O.
    On the N=2 supersymmetric Camassa-Holm and Hunter-Saxton equations2009In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 50, no 1, article id 012704Article in journal (Refereed)
    Abstract [en]

    We consider N=2 supersymmetric extensions of the Camassa-Holm and Hunter-Saxton equations. We show that they admit geometric interpretations as Euler equations on the superconformal algebra of contact vector fields on the 1∫2 -dimensional supercircle. We use the bi-Hamiltonian formulation to derive Lax pairs. Moreover, we present some simple examples of explicit solutions. As a by-product of our analysis, we obtain a description of the bounded traveling-wave solutions for the two-component Hunter-Saxton equation.

  • 31.
    Linnaeus, Staffan
    KTH, School of Technology and Health (STH), Basic Science and Biomedicine.
    Phase-integral method for the radial Dirac equation2014In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 55, p. 092303-Article in journal (Refereed)
    Abstract [en]

    A phase-integral (WKB) solution of the radial Dirac equation is calculated up to the third order of approximation, retaining perfect symmetry between the two components of the wave function and introducing no singularities except at the zeroth-order transition points. The potential is allowed to be of scalar, vector, or tensor type, or any combination of these. The connection problem is investigated in detail. Explicit formulas are given for single-turning-point phase shifts and single-well energy levels.

  • 32.
    Loikkanen, Juha
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Paufler, Cornelius
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Yang-Mills action from minimally coupled bosons on R-4 and on the four-dimensional Moyal plane2005In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 46, no 3, p. 032301-Article in journal (Refereed)
    Abstract [en]

    We consider bosons on (Euclidean) R-4 that are minimally coupled to an external Yang-Mills field. We compute the logarithmically divergent part of the cutoff regularized quantum effective action of this system. We confirm the known result that this term is proportional to the Yang-Mills action. We use pseudodifferential operator methods throughout to prepare the ground for a generalization of our calculation to the noncommutative four-dimensional Moyal plane R-theta(4) We also include a detailed comparison of our cutoff regularization to heat kernel techniques. In the case of the noncommutative space, we complement the usual technique of asymptotic expansion in the momentum variable with operator theoretic arguments in order to keep separated quantum from noncommutativity effects. We show that the result from the commutative space R-4 still holds if one replaces all pointwise products by the noncommutative Moyal product.

  • 33.
    Lundholm, Douglas
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    On the geometry of supersymmetric quantum mechanical systems2008In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 49, no 6, p. 062101-1-062101-15Article in journal (Refereed)
    Abstract [en]

    We consider some simple examples of supersymmetric quantum mechanical systems and explore their possible geometric interpretation with the help of geometric aspects of real Clifford algebras. This leads to natural extensions of the considered systems to higher dimensions and more complicated potentials.

  • 34. Marinucci, Domenico
    et al.
    Wigman, Igor
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    On the area of excursion sets of spherical Gaussian eigenfunctions2011In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 52, no 9, p. 093301-Article in journal (Refereed)
    Abstract [en]

    The high frequency behaviour for random eigenfunctions of the spherical Laplacian has been recently the object of considerable interest, also because of strong motivation arising from physics and cosmology. In this paper, we are concerned with the high frequency behaviour of excursion sets; in particular, we establish a uniform central limit theorem for the empirical measure, i.e., the proportion of spherical surface, where spherical Gaussian eigenfunctions lie below a level z. Our proofs borrow some techniques from the literature on stationary long memory processes; in particular, we expand the empirical measure into Hermite polynomials, and establish a uniform weak reduction principle, entailing that the asymptotic behaviour is asymptotically dominated by a single term in the expansion. As a result, we establish a functional central limit theorem; the limiting process is fully degenerate. (C) 2011 American Institute of Physics. [doi:10.1063/1.3624746]

  • 35.
    Nagel, Bengt
    KTH, Superseded Departments, Physics.
    Confluence expansions of the generalized hypergeometric function2004In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 45, no 1, p. 495-508Article in journal (Refereed)
    Abstract [en]

    By confluencing a subset of upper and lower parameters in the generalized hypergeometric function F-P(Q)(a(1,),...,a(P),c(1),...,c(Q);z) with the variable z one obtains a lower-order hypergeometric function in the limit when the confluence parameters go to infinity. It is shown that this function is the first term in a convergent expansion in terms of functions of the same type with parameters increasing stepwise by integers nu and coefficients which are polynomials in the reciprocals of the confluence parameters. These polynomials have nonvanishing lowest degree terms whose power increases with nu. The expansion can hence be used to derive asymptotic expansions for large but finite absolute values of the confluence parameters.

  • 36.
    Ohlsson, Tommy
    et al.
    KTH, Superseded Departments, Physics.
    Snellman, Håkan
    KTH, Superseded Departments, Physics.
    Three flavor neutrino oscillations in matter2000In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 41, no 5, p. 2768-2788Article in journal (Refereed)
    Abstract [en]

    We derive analytic expressions for three flavor neutrino oscillations in the presence of matter in the plane wave approximation using the Cayley-Hamilton formalism. Especially, we calculate the time evolution operator in both flavor and mass bases. Furthermore, we find the transition probabilities, matter mass squared differences, and matter mixing angles all expressed in terms of the vacuum mass squared differences, the vacuum mixing angles, and the matter density. The conditions for resonance in the presence of matter are also studied in some examples.

  • 37.
    Rodrigues, Ana
    et al.
    Department of Mathematical Sciences, IUPUI, 402 N. Blackford Street, Indianapolis, Indiana 46202-3216, USA and CMUP, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal .
    Llibre, Jaume
    Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, 08193 Barcelona, Spain .
    On the periodic orbits of Hamiltonian systems2010In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 51, no 4Article in journal (Refereed)
    Abstract [en]

    We show how to apply to Hamiltonian differential systems recent results for studying the periodic orbits of a differential system using the averaging theory. We have chosen two classical integrable Hamiltonian systems, one with the Hooke potential and the other with the Kepler potential, and we study the periodic orbits which bifurcate from the periodic orbits of these integrable systems, first perturbing the Hooke Hamiltonian with a nonautonomous potential, and second perturbing the Kepler problem with an autonomous potential.

  • 38.
    Rubensson, Emanuel H.
    et al.
    KTH, School of Biotechnology (BIO), Theoretical Chemistry.
    Rudberg, Elias
    KTH, School of Biotechnology (BIO), Theoretical Chemistry.
    Salek, Pawel
    KTH, School of Biotechnology (BIO), Theoretical Chemistry.
    Rotations of occupied invariant subspaces in self-consistent field calculations2008In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 49, no 3, p. 032103-Article in journal (Refereed)
    Abstract [en]

    In this article, the self-consistent field (SCF) procedure as used in Hartree-Fock and Kohn-Sham calculations is viewed as a sequence of rotations of the so-called occupied invariant subspace of the potential and density matrices. Computational approximations are characterized as erroneous rotations of this subspace. Differences between subspaces are measured and controlled by the canonical angles between them. With this approach, a first step is taken toward a method where errors from computational approximations are rigorously controlled and threshold values are directly related to the accuracy of the current trial density, thus eliminating the use of ad hoc threshold values. Then, the use of computational resources can be kept down as much as possible without impairment of the SCF convergence. (C) 2008 American Institute of Physics.

  • 39.
    Ryan, Paul
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Trinity Coll Dublin, Sch Math, Dublin 2, Ireland.;Trinity Coll Dublin, Hamilton Math Inst, Dublin 2, Ireland..
    Volin, Dmytro
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Trinity Coll Dublin, Sch Math, Dublin 2, Ireland.;Trinity Coll Dublin, Hamilton Math Inst, Dublin 2, Ireland.;Uppsala Univ, Dept Phys & Astron, POB 516, SE-75120 Uppsala, Sweden..
    Separated variables and wave functions for rational gl(N) spin chains in the companion twist frame2019In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 60, no 3, article id 032701Article in journal (Refereed)
    Abstract [en]

    We propose a basis for rational gl(N) spin chains in an arbitrary rectangular representation (S-A) that factorises the Bethe vectors into products of Slater determinants in Baxter Q-functions. This basis is constructed by repeated action of fused transfer matrices on a suitable reference state. We prove that it diagonalises the so-called B-operator; hence, the operatorial roots of the latter are the separated variables. The spectrum of the separated variables is also explicitly computed, and it turns out to be labeled by Gelfand-Tsetlin patterns. Our approach utilises a special choice of the spin chain twist which substantially simplifies derivations. 

  • 40.
    Thylwe, Karl-Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    McCabe, Patrick
    Bohr-Sommerfeld quantization condition for Dirac states derived from an Ermakov-type invariant2013In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 54, no 5, p. 052301-Article in journal (Refereed)
    Abstract [en]

    It is shown that solutions of the second-order decoupled radial Dirac equations satisfy Ermakov-type invariants. These invariants lead to amplitude-phase-type representations of the radial spinor solutions, with exact relations between their amplitudes and phases. Implications leading to a Bohr-Sommerfeld quantization condition for bound states, and a few particular atomic/ionic and nuclear/hadronic bound-state situations are discussed.

  • 41.
    Thylwe, Karl-Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Yngve, Staffan
    Froman, Per Olof
    Study of the validity of the phase-integral connection formula for potential barriers of arbitrary thickness2006In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 47, no 7Article in journal (Refereed)
    Abstract [en]

    The validity of the phase-integral connection matrix for potential barriers is discussed in a concrete way for a particular parabolic barrier, for the symmetric Eckart-Epstein barrier, and for the inverted Morse potential, when the first-order phase-integral approximation is used.

  • 42. Weston, V. H.
    et al.
    Jonsson, B. Lars G.
    KTH, Superseded Departments, Electromagnetic Theory.
    Wave front layer stripping approach to inverse scattering for the wave equation2002In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 43, no 10, p. 5045-5059Article in journal (Refereed)
    Abstract [en]

    The inverse problem involving a point pulse source exterior to a scattering medium, where the velocity c(x) is continuous, is considered. The layer stripping approach is applied to thin curvilinear layers whose surfaces are the primary wave fronts [with c(x) continuous, the reflected wave fronts will be secondary, i.e., of lower order singularity]. It is shown that the layer stripping approach can be used in the time-domain inverse problem without employing the added complexity of having to perform wave splitting. Furthermore the procedure to determine the normal derivative of c from the asymptotic short time behavior of the field quantities on an adjacent wave front surface has been simplified compared to earlier wave splitting methods. Uniqueness results are given.

1 - 42 of 42
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