Journal of Mathematical Physics: Most Recent Articles
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Please follow the links to view the content.Coherent states, quantum gravity, and the Born- Oppenheimer approximation. II. Compact Lie groups
http://scitation.aip.org/content/aip/journal/jmp/57/7/10.1063/1.4954803?TRACK=RSS
<div><p>In this article, the second of three, we discuss and develop the basis of a Weyl quantisation for compact Lie groups aiming at loop quantum gravity-type models. This Weyl quantisation may serve as the main mathematical tool to implement the program of space adiabatic perturbation theory in such models. As we already argued in our first article, space adiabatic perturbation theory offers an ideal framework to overcome the obstacles that hinder the direct implementation of the conventional Born-Oppenheimer approach in the canonical formulation of loop quantum gravity. Additionally, we conjecture the existence of a new form of the Segal-Bargmann-Hall “coherent state” transform for compact Lie groups <span class="jp-italic">G</span>, which we prove for <span class="jp-italic">G</span> = <span class="jp-italic">U</span>(1)<sup xmlns="http://pub2web.metastore.ingenta.com/ns/"><span xmlns="" class="jp-italic">n</span></sup> and support by numerical evidence for <span class="jp-italic">G</span> = <span class="jp-italic">SU</span>(2). The reason for conjoining this conjecture with the main topic of this article originates in the observation that the coherent state transform can be used as a basic building block of a coherent state quantisation (Berezin quantisation) for compact Lie groups <span class="jp-italic">G</span>. But, as Weyl and Berezin quantisation for ℝ<sup xmlns="http://pub2web.metastore.ingenta.com/ns/">2<span xmlns="" class="jp-italic">d</span></sup> are intimately related by heat kernel evolution, it is natural to ask whether a similar connection exists for compact Lie groups as well. Moreover, since the formulation of space adiabatic perturbation theory requires a (deformation) quantisation as minimal input, we analyse the question to what extent the coherent state quantisation, defined by the Segal-Bargmann-Hall transform, can serve as basis of the former.</p></div>Fri, 01 Jul 2016 12:31:54 GMThttp://scitation.aip.org/content/aip/journal/jmp/57/7/10.1063/1.4954803?TRACK=RSSAlexander Stottmeister and Thomas Thiemann2016-07-01T12:31:54ZConsistency of multi-time Dirac equations with general interaction potentials
http://scitation.aip.org/content/aip/journal/jmp/57/7/10.1063/1.4954947?TRACK=RSS
<div><p>In 1932, Dirac proposed a formulation in terms of multi-time wave functions as candidate for relativistic many-particle quantum mechanics. A well-known consistency condition that is necessary for existence of solutions strongly restricts the possible interaction types between the particles. It was conjectured by Petrat and Tumulka that interactions described by multiplication operators are generally excluded by this condition, and they gave a proof of this claim for potentials without spin-coupling. Under suitable assumptions on the differentiability of possible solutions, we show that there are potentials which are admissible, give an explicit example, however, show that none of them fulfills the physically desirable Poincaré invariance. We conclude that in this sense, Dirac’s multi-time formalism does not allow to model interaction by multiplication operators, and briefly point out several promising approaches to interacting models one can instead pursue.</p></div>Fri, 01 Jul 2016 12:15:03 GMThttp://scitation.aip.org/content/aip/journal/jmp/57/7/10.1063/1.4954947?TRACK=RSSDirk-André Deckert and Lukas Nickel2016-07-01T12:15:03ZNovel isochronous N-body problems featuring N arbitrary rational coupling constants
http://scitation.aip.org/content/aip/journal/jmp/57/7/10.1063/1.4954851?TRACK=RSS
<div><p>A novel class of <span class="jp-italic">N</span>-body problems is identified, with <span class="jp-italic">N</span> an <span class="jp-italic">arbitrary</span> positive integer (<span class="jp-italic">N</span> ≥ 2). These <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">models</span> are characterized by Newtonian (“accelerations equal forces”) <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">equations of motion</span> describing <span class="jp-italic">N</span> equal point-particles moving in the complex <span class="jp-italic">z</span>-plane. These highly <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">nonlinear equations</span> feature <span class="jp-italic">N</span>
<span class="jp-italic">arbitrary</span> coupling constants, yet they can be <span class="jp-italic">solved</span> by <span class="jp-italic">algebraic</span> operations and if <span class="jp-italic">all</span> the <span class="jp-italic">N</span> coupling constants are <span class="jp-italic">real</span> and <span class="jp-italic">rational</span> the corresponding <span class="jp-italic">N</span>-body problem is <span class="jp-italic">isochronous</span>: its <span class="jp-italic">generic</span> solutions are <span class="jp-italic">all completely periodic</span> with an overall period <span class="jp-italic">T</span> independent of the initial data (but many solutions feature subperiods <span class="jp-italic">T</span>/<span class="jp-italic">p</span> with <span class="jp-italic">p</span>
<span class="jp-italic">integer</span>). It is moreover shown that these <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">models</span> are Hamiltonian.</p></div>Fri, 01 Jul 2016 12:14:55 GMThttp://scitation.aip.org/content/aip/journal/jmp/57/7/10.1063/1.4954851?TRACK=RSSF. Calogero2016-07-01T12:14:55ZParametric symmetries in exactly solvable real and PT symmetric complex potentials
http://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4954330?TRACK=RSS
<div><p>In this paper, we discuss the parametric symmetries in different exactly solvable systems characterized by real or complex <span class="jp-italic">PT</span> symmetric potentials. We focus our attention on the conventional potentials such as the generalized Pöschl Teller (GPT), Scarf-I, and <span class="jp-italic">PT</span> symmetric Scarf-II which are <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">invariant</span> under certain parametric transformations. The resulting set of potentials is shown to yield a completely different behavior of the <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">bound state</span> solutions. Further, the supersymmetric partner potentials acquire different forms under such parametric transformations leading to new sets of exactly solvable real and <span class="jp-italic">PT</span> symmetric complex potentials. These potentials are also observed to be shape <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">invariant</span> (SI) in nature. We subsequently take up a study of the newly discovered rationally extended SI potentials, corresponding to the above mentioned conventional potentials, whose <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">bound state</span> solutions are associated with the exceptional orthogonal <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">polynomials</span> (EOPs). We discuss the transformations of the corresponding Casimir operator employing the properties of the <span class="jp-italic">so</span>(2, 1) algebra.</p></div>Thu, 30 Jun 2016 12:33:20 GMThttp://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4954330?TRACK=RSSRajesh Kumar Yadav, Avinash Khare, Bijan Bagchi, Nisha Kumari and Bhabani Prasad Mandal2016-06-30T12:33:20ZHamiltonian analysis for linearly acceleration-dependent Lagrangians
http://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4954804?TRACK=RSS
<div><p>We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar features provided by the surface terms arising for this type of theories and we discuss some important properties for this kind of actions in order to pave the way for the construction of a well defined quantum counterpart by means of canonical methods. In particular, we analyse in detail the constraint structure for these theories and its relation to the inherent conserved quantities where the associated energies together with a Noether charge may be identified. The constraint structure is fully analyzed without the introduction of auxiliary variables, as proposed in recent works involving higher order Lagrangians. Finally, we also provide some examples where our approach is explicitly applied and emphasize the way in which our original arrangement results in propitious for the Hamiltonian formulation of covariant field theories.</p></div>Wed, 29 Jun 2016 13:49:20 GMThttp://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4954804?TRACK=RSSMiguel Cruz, Rosario Gómez-Cortés, Alberto Molgado and Efraín Rojas2016-06-29T13:49:20ZAdjoint affine fusion and tadpoles
http://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4954909?TRACK=RSS
<div><p>We study affine fusion with the adjoint representation. For simple Lie algebras, elementary and universal formulas determine the decomposition of a tensor product of an integrable highest-weight representation with the adjoint representation. Using the (refined) affine depth rule, we prove that equally striking results apply to adjoint affine fusion. For diagonal fusion, a coefficient equals the number of nonzero Dynkin labels of the relevant affine highest weight, minus 1. A nice lattice-polytope interpretation follows and allows the straightforward calculation of the genus-1 1-point adjoint Verlinde dimension, the adjoint affine fusion tadpole. Explicit formulas, (piecewise) polynomial in the level, are written for the adjoint tadpoles of all classical Lie algebras. We show that off-diagonal adjoint affine fusion is obtained from the corresponding tensor product by simply dropping non-dominant representations.</p></div>Wed, 29 Jun 2016 13:26:23 GMThttp://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4954909?TRACK=RSSAndrew Urichuk and Mark A. Walton2016-06-29T13:26:23ZClusters of eigenvalues for the magnetic Laplacian with Robin condition
http://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4954500?TRACK=RSS
<div><p>We study the Schrödinger operator with a constant magnetic field in the exterior of a compact domain in Euclidean space. Functions in the domain of the operator are subject to a boundary condition of the third type (a magnetic Robin condition). In addition to the Landau levels, we obtain that the spectrum of this operator consists of clusters of eigenvalues around the Landau levels and that they do accumulate to the Landau levels from below. We give a precise asymptotic formula for the rate of accumulation of eigenvalues in these clusters, which is independent of the boundary condition.</p></div>Tue, 28 Jun 2016 12:13:35 GMThttp://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4954500?TRACK=RSSMagnus Goffeng, Ayman Kachmar and Mikael Persson Sundqvist2016-06-28T12:13:35ZAlgebraic solutions of shape-invariant position-dependent effective mass systems
http://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4954283?TRACK=RSS
<div><p>Keeping in view the ordering ambiguity that arises due to the presence of position-dependent effective mass in the kinetic energy term of the Hamiltonian, a general scheme for obtaining algebraic solutions of quantum mechanical systems with position-dependent effective mass is discussed. We quantize the Hamiltonian of the pertaining system by using symmetric ordering of the operators concerning momentum and the spatially varying mass, initially proposed by von Roos and Lévy-Leblond. The algebraic method, used to obtain the solutions, is based on the concepts of supersymmetric quantum mechanics and shape invariance. In order to exemplify the general formalism a class of non-linear oscillators has been considered. This class includes the particular example of a one-dimensional oscillator with different position-dependent effective mass profiles. Explicit expressions for the eigenenergies and eigenfunctions in terms of generalized Hermite polynomials are presented. Moreover, properties of these modified Hermite polynomials, like existence of generating function and recurrence relations among the polynomials have also been studied. Furthermore, it has been shown that in the harmonic limit, all the results for the linear harmonic oscillator are recovered.</p></div>Mon, 27 Jun 2016 12:09:48 GMThttp://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4954283?TRACK=RSSNaila Amir and Shahid Iqbal2016-06-27T12:09:48ZCoherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations
http://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4954228?TRACK=RSS
<div><p>This article, as the first of three, aims at establishing the (time-dependent) Born-Oppenheimer approximation, in the sense of space adiabatic perturbation theory, for quantum systems constructed by techniques of the loop quantum gravity framework, especially the canonical formulation of the latter. The analysis presented here fits into a rather general framework and offers a solution to the problem of applying the usual Born-Oppenheimer ansatz for molecular (or structurally analogous) systems to more general quantum systems (e.g., spin-orbit models) by means of space adiabatic perturbation theory. The proposed solution is applied to a simple, finite dimensional model of interacting spin systems, which serves as a non-trivial, minimal model of the aforesaid problem. Furthermore, it is explained how the content of this article and its companion affect the possible extraction of quantum field theory on curved spacetime from loop quantum gravity (including matter fields).</p></div>Fri, 24 Jun 2016 12:08:56 GMThttp://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4954228?TRACK=RSSAlexander Stottmeister and Thomas Thiemann2016-06-24T12:08:56ZA generalized Jaynes-Cummings model: The relativistic parametric amplifier and a single trapped ion
http://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4954329?TRACK=RSS
<div><p>We introduce a generalization of the Jaynes-Cummings <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">model</span> and study some of its properties. We obtain the energy spectrum and eigenfunctions of this <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">model</span> by using the tilting transformation and the squeezed number states of the one-dimensional harmonic <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">oscillator.</span> As physical applications, we connect this new <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">model</span> to two important and novelty problems: the relativistic parametric <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">amplifier</span> and the quantum simulation of a single trapped ion.</p></div>Thu, 23 Jun 2016 12:11:58 GMThttp://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4954329?TRACK=RSSD. Ojeda-Guillén, R. D. Mota and V. D. Granados2016-06-23T12:11:58ZA functional realization of 𝔰𝔩(3, ℝ) providing minimal Vessiot–Guldberg–Lie algebras of nonlinear second-order ordinary differential equations as proper subalgebras
http://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4954255?TRACK=RSS
<div><p>A functional realization of the Lie algebra <span class="capture-id"><script xmlns="http://pub2web.metastore.ingenta.com/ns/" type="math/mml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mi mathvariant="fraktur">s</mml:mi><mml:mi mathvariant="fraktur">l</mml:mi><mml:mfenced close=")" open="(" separators=""><mml:mrow><mml:mn>3</mml:mn><mml:mo>,</mml:mo><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:mfenced></mml:math></script></span> as a Vessiot–Guldberg–Lie algebra of second order differential equation (SODE) Lie systems is proposed. It is shown that a minimal Vessiot–Guldberg–Lie algebra <span class="capture-id"><script xmlns="http://pub2web.metastore.ingenta.com/ns/" type="math/mml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:msub><mml:mrow><mml:mi mathvariant="script">L</mml:mi></mml:mrow><mml:mrow><mml:mi>V</mml:mi><mml:mi>G</mml:mi></mml:mrow></mml:msub></mml:math></script></span> is obtained from proper subalgebras of <span class="capture-id"><script xmlns="http://pub2web.metastore.ingenta.com/ns/" type="math/mml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mi mathvariant="fraktur">s</mml:mi><mml:mi mathvariant="fraktur">l</mml:mi><mml:mfenced close=")" open="(" separators=""><mml:mrow><mml:mn>3</mml:mn><mml:mo>,</mml:mo><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:mfenced></mml:math></script></span> for each of the SODE Lie systems of this type by particularization of one functional and two scalar parameters of the <span class="capture-id"><script xmlns="http://pub2web.metastore.ingenta.com/ns/" type="math/mml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mi mathvariant="fraktur">s</mml:mi><mml:mi mathvariant="fraktur">l</mml:mi><mml:mfenced close=")" open="(" separators=""><mml:mrow><mml:mn>3</mml:mn><mml:mo>,</mml:mo><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:mfenced></mml:math></script></span>-realization. The relation between the various Vessiot–Guldberg–Lie algebras by means of a limiting process in the scalar parameters further allows to define a notion of contraction of SODE Lie systems.</p></div>Thu, 23 Jun 2016 12:11:50 GMThttp://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4954255?TRACK=RSSR. Campoamor-Stursberg2016-06-23T12:11:50ZSecond-order asymptotics for quantum hypothesis testing in settings beyond i.i.d.—quantum lattice systems and more
http://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4953582?TRACK=RSS
<div><p>Quantum Stein’s lemma is a cornerstone of quantum statistics and concerns the problem of correctly identifying a quantum state, given the knowledge that it is one of two specific states (<span class="jp-italic">ρ</span> or <span class="jp-italic">σ</span>). It was originally derived in the asymptotic i.i.d. setting, in which arbitrarily many (say, <span class="jp-italic">n</span>) identical copies of the state (<span class="jp-italic">ρ</span>
<sup xmlns="http://pub2web.metastore.ingenta.com/ns/">⊗<span xmlns="" class="jp-italic">n</span></sup> or <span class="jp-italic">σ</span>
<sup xmlns="http://pub2web.metastore.ingenta.com/ns/">⊗<span xmlns="" class="jp-italic">n</span></sup>) are considered to be available. In this setting, the lemma states that, for any given upper bound on the probability <span class="jp-italic">α<span class="jp-sub">n</span></span> of erroneously inferring the state to be <span class="jp-italic">σ</span>, the probability <span class="jp-italic">β<span class="jp-sub">n</span></span> of erroneously inferring the state to be <span class="jp-italic">ρ</span> decays exponentially in <span class="jp-italic">n</span>, with the rate of decay converging to the relative entropy of the two states. The second order asymptotics for quantum hypothesis testing, which establishes the speed of convergence of this rate of decay to its limiting value, was derived in the i.i.d. setting independently by Tomamichel and Hayashi, and Li. We extend this result to settings beyond i.i.d. Examples of these include Gibbs states of quantum spin systems (with finite-range, translation-invariant interactions) at high temperatures, and quasi-free states of fermionic lattice gases.</p></div>Wed, 22 Jun 2016 12:46:59 GMThttp://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4953582?TRACK=RSSNilanjana Datta, Yan Pautrat and Cambyse Rouzé2016-06-22T12:46:59ZDissipative entanglement of quantum spin fluctuations
http://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4954072?TRACK=RSS
<div><p>We consider two non-interacting infinite quantum spin chains immersed in a common thermal environment and undergoing a local dissipative dynamics of Lindblad type. We study the time evolution of collective mesoscopic quantum spin fluctuations that, unlike macroscopic mean-field observables, retain a quantum character in the thermodynamical limit. We show that the microscopic dissipative dynamics is able to entangle these mesoscopic degrees of freedom, through a purely mixing mechanism. Further, the behaviour of the dissipatively generated quantum correlations between the two chains is studied as a function of temperature and dissipation strength.</p></div>Wed, 22 Jun 2016 12:46:52 GMThttp://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4954072?TRACK=RSSF. Benatti, F. Carollo and R. Floreanini2016-06-22T12:46:52ZOn the geometry of mixed states and the Fisher information tensor
http://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4954328?TRACK=RSS
<div><p>In this paper, we will review the co-adjoint orbit formulation of finite dimensional quantum mechanics, and in this framework, we will interpret the notion of quantum Fisher information index (and metric). Following previous work of part of the authors, who introduced the definition of Fisher information tensor, we will show how its antisymmetric part is the pullback of the natural Kostant–Kirillov–Souriau symplectic form along some natural diffeomorphism. In order to do this, we will need to understand the symmetric logarithmic derivative as a proper 1-form, settling the issues about its very definition and explicit computation. Moreover, the fibration of co-adjoint orbits, seen as spaces of mixed states, is also discussed.</p></div>Wed, 22 Jun 2016 12:46:44 GMThttp://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4954328?TRACK=RSSI. Contreras, E. Ercolessi and M. Schiavina2016-06-22T12:46:44ZLocal unitary equivalence of quantum states and simultaneous orthogonal equivalence
http://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4954230?TRACK=RSS
<div><p>The correspondence between local unitary equivalence of bipartite quantum states and simultaneous orthogonal equivalence is thoroughly investigated and strengthened. It is proved that local unitary equivalence can be studied through simultaneous similarity under projective orthogonal transformations, and four parametrization independent algorithms are proposed to judge when two density matrices on ℂ<sup xmlns="http://pub2web.metastore.ingenta.com/ns/"><span xmlns="" class="jp-italic">d</span><span xmlns="" class="jp-sub">1</span></sup> ⊗ ℂ<sup xmlns="http://pub2web.metastore.ingenta.com/ns/"><span xmlns="" class="jp-italic">d</span><span xmlns="" class="jp-sub">2</span></sup> are locally unitary equivalent in connection with trace identities, Kronecker pencils, Albert determinants and Smith normal forms.</p></div>Tue, 21 Jun 2016 12:10:22 GMThttp://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4954230?TRACK=RSSNaihuan Jing, Min Yang and Hui Zhao2016-06-21T12:10:22ZQuantum Max-flow/Min-cut
http://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4954231?TRACK=RSS
<div><p>The classical max-flow min-cut <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">theorem</span> describes transport through certain idealized classical networks. We consider the quantum analog for <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">tensor</span> networks. By associating an integral capacity to each edge and a <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">tensor</span> to each vertex in a flow network, we can also interpret it as a <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">tensor</span> network and, more specifically, as a linear map from the input space to the output space. The quantum max-flow is defined to be the maximal rank of this linear map over all choices of <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">tensors.</span> The quantum min-cut is defined to be the minimum product of the capacities of edges over all cuts of the <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">tensor</span> network. We show that unlike the classical case, the quantum max-flow=min-cut conjecture is not true in general. Under certain conditions, e.g., when the capacity on each edge is some power of a fixed integer, the quantum max-flow is proved to equal the quantum min-cut. However, concrete examples are also provided where the equality does not hold. We also found connections of quantum max-flow/min-cut with <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">entropy</span> of <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">entanglement</span> and the quantum satisfiability problem. We speculate that the phenomena revealed may be of interest both in spin systems in condensed matter and in quantum gravity.</p></div>Tue, 21 Jun 2016 12:08:32 GMThttp://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4954231?TRACK=RSSShawn X. Cui, Michael H. Freedman, Or Sattath, Richard Stong and Greg Minton2016-06-21T12:08:32ZThe Wentzel–Kramers–Brillouin approximation method applied to the Wigner function
http://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4954071?TRACK=RSS
<div><p>An adaptation of the Wentzel–Kramers–Brilluoin method in the deformation quantization formalism is presented with the aim to obtain an approximate technique of solving the eigenvalue problem for energy in the phase space quantum approach. A relationship between the phase <span class="capture-id"><script xmlns="http://pub2web.metastore.ingenta.com/ns/" type="math/mml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mi>σ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mover accent="true" class="vector"><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mo>→</mml:mo></mml:mover><mml:mo>)</mml:mo></mml:mrow></mml:math></script></span> of a wave function <span class="capture-id"><script xmlns="http://pub2web.metastore.ingenta.com/ns/" type="math/mml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mo>exp</mml:mo><mml:mfenced close=")" open="(" separators=""><mml:mrow><mml:mfrac><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">ħ</mml:mi></mml:mrow></mml:mfrac><mml:mi>σ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mover accent="true" class="vector"><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mo>→</mml:mo></mml:mover><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfenced></mml:math></script></span> and its respective Wigner function is derived. Formulas to calculate the Wigner function of a product and of a superposition of wave functions are proposed. Properties of a Wigner function of interfering states are also investigated. Examples of this quasi–classical approximation in deformation quantization are analysed. A strict form of the Wigner function for states represented by tempered generalised functions has been derived. Wigner functions of unbound states in the Poeschl–Teller potential have been found.</p></div>Mon, 20 Jun 2016 12:32:39 GMThttp://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4954071?TRACK=RSSJ. Tosiek, R. Cordero and F. J. Turrubiates2016-06-20T12:32:39ZEigenvalue asymptotics for Dirac–Bessel operators
http://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4953245?TRACK=RSS
<div><p>In this paper, we establish the eigenvalue asymptotics for non-self-adjoint Dirac–Bessel operators on (0, 1) with arbitrary real angular momenta and square integrable potentials, which gives the first step for solution of the related inverse problem. The approach is based on a careful examination of the corresponding characteristic functions and their zero distribution.</p></div>Mon, 20 Jun 2016 12:09:23 GMThttp://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4953245?TRACK=RSSRostyslav O. Hryniv and Yaroslav V. Mykytyuk2016-06-20T12:09:23ZQuantum and spectral properties of the Labyrinth model
http://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4953379?TRACK=RSS
<div><p>We consider the Labyrinth model, which is a two-dimensional <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">quasicrystal</span> model. We show that the spectrum of this model, which is known to be a product of two Cantor <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">sets,</span> is an interval for small values of the coupling constant. We also consider the <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">density of states</span>
<span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">measure</span> of the Labyrinth model and show that it is absolutely continuous with respect to Lebesgue <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">measure</span> for almost all values of coupling constants in the small coupling regime.</p></div>Thu, 16 Jun 2016 12:11:27 GMThttp://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4953379?TRACK=RSSYuki Takahashi2016-06-16T12:11:27ZAchieving the Holevo bound via a bisection decoding protocol
http://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4953690?TRACK=RSS
<div><p>We present a new decoding protocol to realize transmission of classical information through a quantum channel at asymptotically maximum capacity, achieving the Holevo bound and thus the optimal communication rate. At variance with previous proposals, our scheme recovers the message bit by bit, making use of a series of “yes-no” measurements, organized in bisection fashion, thus determining which codeword was sent in log<span class="jp-sub">2</span>
<span class="jp-italic">N</span> steps, <span class="jp-italic">N</span> being the number of codewords.</p></div>Wed, 15 Jun 2016 12:37:00 GMThttp://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4953690?TRACK=RSSMatteo Rosati and Vittorio Giovannetti2016-06-15T12:37:00ZOn a quantum entropy power inequality of Audenaert, Datta, and Ozols
http://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4953638?TRACK=RSS
<div><p>We give a short proof of a recent <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">inequality</span> of Audenaert, Datta, and Ozols, and determine cases of equality.</p></div>Tue, 14 Jun 2016 12:06:10 GMThttp://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4953638?TRACK=RSSEric A. Carlen, Elliott H. Lieb and Michael Loss2016-06-14T12:06:10ZStability estimate for the aligned magnetic field in a periodic quantum waveguide from Dirichlet-to-Neumann map
http://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4953687?TRACK=RSS
<div><p>In this article, we study the boundary inverse problem of determining the aligned magnetic field appearing in the magnetic Schrödinger equation in a periodic quantum cylindrical waveguide, by knowledge of the Dirichlet-to-Neumann map. We prove a Hölder stability estimate with respect to the Dirichlet-to-Neumann map, by means of the geometrical optics solutions of the magnetic Schrödinger equation.</p></div>Tue, 14 Jun 2016 12:06:03 GMThttp://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4953687?TRACK=RSSYoussef Mejri2016-06-14T12:06:03ZCoherent distributions for the rigid rotator
http://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4953369?TRACK=RSS
<div><p>
<span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">Coherent</span> solutions of the classical Liouville <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">equation</span> for the rigid rotator are presented as positive phase-space distributions localized on the <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">Lagrangian</span> submanifolds of Hamilton-Jacobi <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">theory.</span> These solutions become Wigner-type quasiprobability distributions by a formal discretization of the left-invariant <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">vector fields</span> from their <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">Fourier transform</span> in <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">angular momentum.</span> The results are consistent with the usual quantization of the anisotropic rotator, but the expected value of the Hamiltonian contains a finite “zero point” energy term. It is shown that during the time when a quasiprobability distribution evolves according to the Liouville <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">equation,</span> the related quantum <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">wave function</span> should satisfy the time-dependent Schrödinger <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">equation.</span>
</p></div>Tue, 14 Jun 2016 12:05:58 GMThttp://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4953369?TRACK=RSSMarius Grigorescu2016-06-14T12:05:58ZKato expansion in quantum canonical perturbation theory
http://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4953639?TRACK=RSS
<div><p>This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson’s ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. We compare the efficiency of the corresponding computational algorithm with the efficiencies of the Van Vleck and Magnus methods for high perturbative orders.</p></div>Mon, 13 Jun 2016 12:04:18 GMThttp://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4953639?TRACK=RSSAndrey Nikolaev2016-06-13T12:04:18ZGlobal solutions to the two-dimensional Riemann problem for a system of conservation laws
http://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4953450?TRACK=RSS
<div><p>We study the global solutions to the two-dimensional Riemann problem for a system of <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">conservation laws.</span> The initial data are three constant states separated by three rays emanating from the origin. Under the assumption that each ray in the initial data outside of the origin projects exactly one planar contact <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">discontinuity,</span> this problem is classified into five cases. By the self-similar transformation, the reduced system changes type from being elliptic near the origin to being hyperbolic far away in self-similar plane. Then in hyperbolic region, applying the generalized characteristic analysis method, a Goursat problem is solved to describe the interactions of planar contact <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">discontinuities.</span> While, in elliptic region, a <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">boundary value problem</span> arises. It is proved that this <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">boundary value problem</span> admits a unique solution. Based on these preparations, five explicit solutions and their corresponding criteria can be obtained in self-similar plane.</p></div>Mon, 13 Jun 2016 12:04:07 GMThttp://scitation.aip.org/content/aip/journal/jmp/57/6/10.1063/1.4953450?TRACK=RSSYicheng Pang, Shaohong Cai and Yuanying Zhao2016-06-13T12:04:07Z