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Journals
Quantum Reports
Special Issues
Continuous and Discrete Phase-Space Methods and Their Applications
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Continuous and Discrete Phase-Space Methods and Their Applications

A special issue of Quantum Reports (ISSN 2624-960X).

Deadline for manuscript submissions: closed (31 March 2023) | Viewed by 9333

Special Issue Editors

Prof. Dr. Andrei Klimov

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Guest Editor
Departamento de Física, Universidad de Guadalajara, Guadalajara 44420, Jalisco, Mexico
Interests: discrete and continuous phase-space methods; fundaments of quantum mechanics; quantum optical models
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Luis L. Sánchez-Soto

E-Mail Website
Guest Editor
Departamento de Óptica, Facultad de Fisica, Universidad Complutense, 28040 Madrid, Spain
Interests: quantum optics; quantum information; polarization; tomography; discrete quantum systems; phase-space method
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Hubert de Guise

E-Mail Website
Guest Editor
Department of Physics, Lakehead University, Thunder Bay, ON P7B 5E1, Canada
Interests: fundamentals of quantum mechanics; phase-space methods

Special Issue Information

Dear Colleagues,

The phase-space description of quantum systems has provided a very useful description of quantum systems since it was introduced by Wigner in the 1930s. This approach is useful in practical calculations because its formulation does not depend on the number of particles, in stark contrast with situations where the overwhelming complexity of dynamics of macroscopic quantum states precludes finding exact solutions either analytically nor numerically.

One traditional area of application of phase-space methods includes the evolution of quantum systems under Hamiltonians invariant under different symmetry groups. Although attention is still principally focused on Heisenberg–Weyl symmetry, progress with the phase-space approach has also been achieved in systems with other types of symmetries. In addition, a class of discrete systems, e.g., those where the set of admissible operations is limited to the Clifford group, can also be analyzed using the general geometric ideas of phase-space representation. In spite of a comparably small number of reported applications of discrete phase-space methods, they open the possibility to a non-redundant description of the global properties of multipartite systems in the macroscopic limit.

This Special Issue will focus on modern problems, conceptual and practical, of phase-space representations beyond the more traditional areas of applications. We encourage authors to submit research or review articles in the general areas listed below:

  • Theory of quasidistribution functions for quantum systems with continuous symmetries
  • Phase-space evolution
  • Truncated Wigner approximations and beyond
  • Discrete phase-space methods
  • Evolution of finite systems in phase-space representation
  • Macroscopic and semiclassical limits

Prof. Dr. Andrei Klimov
Prof. Dr. Luis L. Sánchez-Soto
Prof. Dr. Hubert de Guise
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Quantum Reports is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • quasidistribution functions
  • phase-space evolution
  • semiclassical dynamics
  • discrete phase-space methods
  • macroscopic limit

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Published Papers (4 papers)

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Research

17 pages, 407 KiB  
Article
Asymptotic Quantization of a Particle on a Sphere
by José L. Romero and Andrei B. Klimov
Quantum Rep. 2023, 5(1), 294-310; https://doi.org/10.3390/quantum5010020 - 21 Mar 2023
Viewed by 2303
Abstract
Quantum systems whose states are tightly distributed among several invariant subspaces (variable spin systems) can be described in terms of distributions in a four-dimensional phase-space T∗S2 in the limit of large average angular momentum. The cotangent bundle [...] Read more.
Quantum systems whose states are tightly distributed among several invariant subspaces (variable spin systems) can be described in terms of distributions in a four-dimensional phase-space T∗S2 in the limit of large average angular momentum. The cotangent bundle T∗S2 is also the classical manifold for systems with E(3) symmetry group with appropriately fixed Casimir operators. This allows us to employ the asymptotic form of the star-product proper for variable (integer) spin systems to develop a deformation quantization scheme for a particle moving on the two-dimensional sphere, whose observables are elements of e(3) algebra and the corresponding phase-space is T∗S2. We show that the standard commutation relations of the e(3) algebra are recovered from the corresponding classical Poisson brackets and the explicit expressions for the eigenvalues and eigenfunctions of some quantized classical observables (such as the angular momentum operators and their squares) are obtained. Full article
(This article belongs to the Special Issue Continuous and Discrete Phase-Space Methods and Their Applications)
8 pages, 283 KiB  
Article
Energy Transition Density of Driven Chaotic Systems: A Compound Trace Formula
by Alfredo M. Ozorio de Almeida
Quantum Rep. 2022, 4(4), 558-565; https://doi.org/10.3390/quantum4040040 - 30 Nov 2022
Cited by 1 | Viewed by 1522
Abstract
Oscillations in the probability density of quantum transitions of the eigenstates of a chaotic Hamiltonian within classically narrow energy ranges have been shown to depend on closed compound orbits. These are formed by a pair of orbit segments, one in the energy shell [...] Read more.
Oscillations in the probability density of quantum transitions of the eigenstates of a chaotic Hamiltonian within classically narrow energy ranges have been shown to depend on closed compound orbits. These are formed by a pair of orbit segments, one in the energy shell of the original Hamiltonian and the other in the energy shell of the driven Hamiltonian, with endpoints that coincide. Viewed in the time domain, the same pair of trajectory segments arises in the semiclassical evaluation of the trace of a compound propagator: the product of the complex exponentials of the original Hamiltonian and of its driven image. It is shown here that the probability density is the double Fourier transform of this trace, and that the closed compound orbits emulate the role played by the periodic orbits in Gutzwiller’s trace formula in its semiclassical evaluation. The phase of the oscillations with the energies or the evolution parameters agree with those previously obtained, whereas the amplitude of the contribution of each closed compound orbit is more compact and independent of any feature of the Weyl–Wigner representation in which the calculation was carried out. Full article
(This article belongs to the Special Issue Continuous and Discrete Phase-Space Methods and Their Applications)
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14 pages, 577 KiB  
Article
Coherent Phase States in the Coordinate and Wigner Representations
by Miguel Citeli de Freitas and Viktor V. Dodonov
Quantum Rep. 2022, 4(4), 509-522; https://doi.org/10.3390/quantum4040036 - 8 Nov 2022
Cited by 2 | Viewed by 2316
Abstract
In this paper, we numerically study the coordinate wave functions and the Wigner functions of the coherent phase states (CPS), paying particular attention to their differences from the standard (Klauder–Glauber–Sudarshan) coherent states, especially in the case of the high mean values of the [...] Read more.
In this paper, we numerically study the coordinate wave functions and the Wigner functions of the coherent phase states (CPS), paying particular attention to their differences from the standard (Klauder–Glauber–Sudarshan) coherent states, especially in the case of the high mean values of the number operator. In this case, the CPS can possess a strong coordinate (or momentum) squeezing, which is roughly twice weaker than for the vacuum squeezed states. The Robertson–Schrödinger invariant uncertainty product in the CPS logarithmically increases with the mean value of the number operator (whereas it is constant for the standard coherent states). Some measures of the (non)Gaussianity of CPS are considered. Full article
(This article belongs to the Special Issue Continuous and Discrete Phase-Space Methods and Their Applications)
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18 pages, 391 KiB  
Article
Integral Quantization for the Discrete Cylinder
by Jean-Pierre Gazeau and Romain Murenzi
Quantum Rep. 2022, 4(4), 362-379; https://doi.org/10.3390/quantum4040026 - 21 Sep 2022
Cited by 5 | Viewed by 2287
Abstract
Covariant integral quantizations are based on the resolution of the identity by continuous or discrete families of normalized positive operator valued measures (POVM), which have appealing probabilistic content and which transform in a covariant way. One of their advantages is their ability to [...] Read more.
Covariant integral quantizations are based on the resolution of the identity by continuous or discrete families of normalized positive operator valued measures (POVM), which have appealing probabilistic content and which transform in a covariant way. One of their advantages is their ability to circumvent problems due to the presence of singularities in the classical models. In this paper, we implement covariant integral quantizations for systems whose phase space is Z×S1, i.e., for systems moving on the circle. The symmetry group of this phase space is the discrete & compact version of the Weyl–Heisenberg group, namely the central extension of the abelian group Z×SO(2). In this regard, the phase space is viewed as the right coset of the group with its center. The non-trivial unitary irreducible representation of this group, as acting on L2(S1), is square integrable on the phase space. We show how to derive corresponding covariant integral quantizations from (weight) functions on the phase space and resulting resolution of the identity. As particular cases of the latter we recover quantizations with de Bièvre-del Olmo–Gonzales and Kowalski–Rembielevski–Papaloucas coherent states on the circle. Another straightforward outcome of our approach is the Mukunda Wigner transform. We also look at the specific cases of coherent states built from shifted gaussians, Von Mises, Poisson, and Fejér kernels. Applications to stellar representations are in progress. Full article
(This article belongs to the Special Issue Continuous and Discrete Phase-Space Methods and Their Applications)
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