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A Themed Issue in Honor of Professor Viktor Dodonov—55 Years...
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A Themed Issue in Honor of Professor Viktor Dodonov—55 Years in Quantum Physics

A special issue of Physics (ISSN 2624-8174). This special issue belongs to the section "Quantum Mechanics and Quantum Systems".

Deadline for manuscript submissions: 31 December 2025 | Viewed by 5067

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

Special Issue Information

Dear Colleagues,

Fifty-five years ago, in September of 1969, Viktor Dodonov [then a 4th-year student at Moscow Institute of Physics and Technology (MIPT)] began to study the course of Quantum Mechanics as a part of the theoretical physics program of that institute. The weekly seminars in his group were conducted by a young assistant professor of the Theoretical Physics Department of MIPT and a researcher at Lebedev Physics Institute of the Academy of Sciences of USSR (LPI), Dr. Vladimir Man'ko. One year later, Viktor started to perform scientific research under the informal supervision of Vladimir Man'ko and Ilya Malkin [who also worked at the Theoretical Physics Department of MIPT]. Their first joint paper, entitled "Coherent states of a charged particle in a time-dependent uniform electromagnetic field of a plane current", was finished in 1971 and published in Physica (Amsterdam) in 1972 [vol. 59, p. 241]. Since then, various problems related to the motion of charged particles (non-relativistic and relativistic) have been one of the favorite subjects of Viktor's studies.

One of his recent papers in this field, "Giant diamagnetism of a quantum charged particle after inversion of the magnetic field", written with his son Alexandre, was published in Physical Review A in 2022 [vol. 105, art. 062201]. The new concept of even/odd coherent states was introduced by Dodonov, Malkin, and Man'ko in the paper "Even and odd coherent states and excitations of a singular oscillator" [Physica, v.72, p.597 (1974)]. Currently, these states are considered the simplest model of the famous "Schroedinger cat" states.

Properties of different kinds of "squeezed" and other "nonclassical" states were the subjects of studies performed by Viktor through the decades. His famous review "`Nonclassical' states in quantum optics: a “squeezed' review of the first 75 years” [Journal of Optics B, v.4, p.R1-R33 (2002)] contained more than 800 references; it was cited more than 700 times by now. In his PhD thesis, defended in MIPT in 1976 (under the supervision of Vladimir Man'ko and Prof. Vladimir Berestetskiy), Viktor developed an elegant method of time-dependent linear quantum invariants, which enables one to solve the dynamics of quantum systems with general time-dependent quadratic Hamiltonians most simply. These initial results were acknowledged by the Lenin Komsomol Prize for young scientists of the Moscow Region in 1981. Since that period, Viktor has published (with many collaborators and students) more than 300 papers cited more than 6000 times. From 1972 to 1996, he was the assistant/associate professor at MIPT and researcher at LPI. Since 2003, he has been a full professor at the University of Brasilia in Brazil. Among various lines of research conducted by Viktor, a distinguished role belongs to the so-called Dynamical Casimir Effect. His first paper in this direction was published with Andrei Klimov and Vladimir Man'ko in 1989 ["Nonstationary Casimir effect and oscillator energy level shift", Physics Letters A, v.142, p.511]. Since that time, he has published dozens of well-cited papers and several reviews in this field [the first review, "Nonstationary Casimir Effect and analytical solutions for quantum fields in cavities with moving boundaries" with 333 references, was published in 2001; the most recent review "Fifty years of the Dynamical Casimir Effect" was published in Physics, vol. 2, pp. 67-105 (2020); it contained more than 555 references]. Another area that always attracted Viktor's attention was the uncertainty relations and their generalizations in different parts of physics and information theory. Here, he also published several original papers and reviews.

Celebrating the 55 years journey of Viktor Dodonov through the Quantum World, we invite all colleagues to submit papers related to the following large areas where Viktor made significant contributions:

  • Dynamical Casimir Effect and quantum systems with moving (nonstationary) boundaries;
  • Time-dependent quantum invariants and their applications;
  • Uncertainty relations, their generalizations, and applications;
  • "Nonclassical" states in quantum optics, quantum information, and other areas;
  • Quantum particles in magnetic fields;
  • Motion (evolution) of quantum packets;
  • Dynamics of closed and open quantum systems;
  • Master equations and their solutions;
  • Adiabatic and fast dynamics;
  • Jaynes-Cummings model, its generalizations and applications;
  • Wigner function and quantum dynamics in phase space;
  • Nonlinear generalizations of the Schroedinger equation;
  • Decoherence, damping, relaxation, and thermalization in quantum systems;
  • Quantum systems with time-dependent parameters.

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

Manuscript Submission Information

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Keywords

  • Nonstationary Casimir effect
  • phase-space methods
  • uncertainty relations
  • decoherence
  • nonclassicality
  • nonlinear and time-dependent quantum evolution

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Published Papers (7 papers)

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Research

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11 pages, 319 KB  
Article
Non-Linear Quantum Dynamics in Coupled Double-Quantum- Dot-Cavity Systems
by Tatiana Mihaescu, Mihai A. Macovei and Aurelian Isar
Physics 2025, 7(4), 47; https://doi.org/10.3390/physics7040047 - 14 Oct 2025
Viewed by 158
Abstract
The steady-state quantum dynamics of a compound sample consisting of a semiconductor double-quantum-dot (DQD) system, non-linearly coupled with a leaking superconducting transmission line resonator, is theoretically investigated. Particularly, the transition frequency of the DQD is taken to be equal to the doubled resonator [...] Read more.
The steady-state quantum dynamics of a compound sample consisting of a semiconductor double-quantum-dot (DQD) system, non-linearly coupled with a leaking superconducting transmission line resonator, is theoretically investigated. Particularly, the transition frequency of the DQD is taken to be equal to the doubled resonator frequency, whereas the inter-dot Coulomb interaction is considered weak. As a consequence, the steady-state quantum dynamics of this complex non-linear system exhibit sudden changes in its features, occurring at a critical DQD-cavity coupling strength, suggesting perspectives for designing on-chip microwave quantum switches. Furthermore, we show that, above the threshold, the electrical current through the double-quantum dot follows the mean photon number into the microwave mode inside the resonator. This might not be the case any more below that critical coupling strength. Lastly, the photon quantum correlations vary from super-Poissonian to Poissonian photon statistics, i.e., towards single-qubit lasing phenomena at microwave frequencies. Full article
(This article belongs to the Special Issue A Themed Issue in Honor of Professor Viktor Dodonov—55 Years in Quantum Physics)
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17 pages, 692 KB  
Article
Disentanglement of a Bipartite System Portrayed in a (3+1)D Compact Minkowski Manifold: Quadridistances and Quadrispeeds
by Salomon S. Mizrahi
Physics 2025, 7(4), 45; https://doi.org/10.3390/physics7040045 - 28 Sep 2025
Viewed by 319
Abstract
In special relativity, particle trajectories, whether mass-bearing or not, can be traced on the Minkowski spacetime manifold in (3+1)D. Meantime, in quantum mechanics, trajectories in the phase space are not strictly outlined because coordinate and linear momentum cannot be measured simultaneously with arbitrary [...] Read more.
In special relativity, particle trajectories, whether mass-bearing or not, can be traced on the Minkowski spacetime manifold in (3+1)D. Meantime, in quantum mechanics, trajectories in the phase space are not strictly outlined because coordinate and linear momentum cannot be measured simultaneously with arbitrary precision since they do not commute within the Hilbert space formalism. However, from the density matrix representing a quantum system, the extracted information still produces an imperative description of its properties and, furthermore, by appropriately reordering the matrix entries, additional information can be obtained from the same content. Adhering to this line of work, the paper investigates the definition and the meaning of velocity and speed in a typical quantum phenomenon, the disentanglement for a bipartite system when dynamical evolution is displayed in a (3+1)D pseudo-spacetime whose coordinates are constructed from combinations of entries to the density matrix. The formalism is based on the definition of a Minkowski manifold with compact support, where trajectories are defined following the same reasoning and formalism present in the Minkowski manifold of special relativity. The space-like and time-like regions acquire different significations referred to entangled-like and separable-like, respectively. The definition and the sense of speed and velocities of disentanglement follow naturally from the formalism. Depending on the dynamics of the physical state of the system, trajectories may meander between regions of entanglement and separability in the space of new coordinates defined on the Minkowski manifold. Full article
(This article belongs to the Special Issue A Themed Issue in Honor of Professor Viktor Dodonov—55 Years in Quantum Physics)
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25 pages, 1706 KB  
Article
A Comparison of Quantum and Semiclassical Rabi Models Near Multiphoton Resonances in the Presence of Parametric Modulation
by Marcos V. S. de Paula, Marco A. Damasceno Faustino and Alexandre V. Dodonov
Physics 2025, 7(3), 42; https://doi.org/10.3390/physics7030042 - 16 Sep 2025
Viewed by 398
Abstract
We compare the semiclassical and quantum predictions for the unitary dynamics of a two-level atom interacting with a single-mode electromagnetic field under parametric modulation of the atomic parameters in the regime of multiphoton atom–field resonances. We derive approximate analytic solutions for the semiclassical [...] Read more.
We compare the semiclassical and quantum predictions for the unitary dynamics of a two-level atom interacting with a single-mode electromagnetic field under parametric modulation of the atomic parameters in the regime of multiphoton atom–field resonances. We derive approximate analytic solutions for the semiclassical Rabi model when the atomic transition frequency and the atom–field coupling strength undergo harmonic external modulations. These solutions are compared to the predictions of the quantum Rabi model, which we solve numerically for an initial coherent state with a large average photon number (on the order of 104), in the regime of three-photon resonance. We show that, for short enough times and sufficiently intense coherent states, the semiclassical dynamics agrees quite well with the quantum dynamics, although it inevitably fails at longer times due to the absence of collapse–revival behavior. Furthermore, we describe how the field state evolves throughout the interaction, presenting numerical results for the average photon number, entropies (related to atom–field entanglement), and other quantities characterizing the photon number statistics of the electromagnetic field. Full article
(This article belongs to the Special Issue A Themed Issue in Honor of Professor Viktor Dodonov—55 Years in Quantum Physics)
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21 pages, 347 KB  
Article
The Classical Geometry of Chaotic Green Functions and Wigner Functions
by Alfredo M. Ozorio de Almeida
Physics 2025, 7(3), 35; https://doi.org/10.3390/physics7030035 - 5 Aug 2025
Viewed by 479
Abstract
Semiclassical (SC) approximations for various representations of a quantum state are constructed on a single (Lagrangian) surface in the phase space but such surface is not available for chaotic systems. An analogous evolution surface underlies SC representations of the evolution operator, albeit in [...] Read more.
Semiclassical (SC) approximations for various representations of a quantum state are constructed on a single (Lagrangian) surface in the phase space but such surface is not available for chaotic systems. An analogous evolution surface underlies SC representations of the evolution operator, albeit in a doubled phase space. Here, it is shown that corresponding to the Fourier transform on a unitary operator, represented as a Green function or spectral Wigner function, a Legendre transform generates a resolvent surface as the classical basis for SC representations of the resolvent operator in the double-phase space, independently of the integrable or chaotic nature of the system. This surface coincides with derivatives of action functions (or generating functions) depending on the choice of appropriate coordinates, and its growth departs from the energy shell following trajectories in the double-phase space. In an initial study of the resolvent surface based on its caustics, its complex nature is revealed to be analogous to a multidimensional sponge. Resummation of the trace of the resolvent in terms of linear combinations of periodic orbits, known as pseudo orbits or composite orbits, provides a cutoff to the SC sum at the Heisenberg time. Here, it is shown that the corresponding actions for higher times can be approximately included within true secondary periodic orbits, in which heteroclinic orbits join multiple windings of relatively short periodic orbits into larger circuits. Full article
(This article belongs to the Special Issue A Themed Issue in Honor of Professor Viktor Dodonov—55 Years in Quantum Physics)
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31 pages, 410 KB  
Article
The Time-Dependent Schrödinger Equation, Riccati Equation, and Airy Functions
by Nathan A. Lanfear and Sergei K. Suslov
Physics 2025, 7(2), 19; https://doi.org/10.3390/physics7020019 - 29 May 2025
Viewed by 1377
Abstract
We construct the Green functions (or Feynman’s propagators) for the Schrödinger equations of the form iψt+14ψxx±tx2ψ=0 (for the wave function ψ and its time (t) and [...] Read more.
We construct the Green functions (or Feynman’s propagators) for the Schrödinger equations of the form iψt+14ψxx±tx2ψ=0 (for the wave function ψ and its time (t) and x-space derivatives) in terms of Airy functions and solve the Cauchy initial value problem in the coordinate and momentum representations. Particular solutions of the corresponding nonlinear Schrödinger equations with variable coefficients are also found. A special case of the quantum parametric oscillator is studied in detail first. The Green function is explicitly given in terms of Airy functions and the corresponding transition amplitudes are found in terms of a hypergeometric function. The general case of the quantum parametric oscillator is considered then in a similar fashion. A group theoretical meaning of the transition amplitudes and their relation with Bargmann’s functions is established. The relevant bibliography, to the best of our knowledge, is addressed. Full article
(This article belongs to the Special Issue A Themed Issue in Honor of Professor Viktor Dodonov—55 Years in Quantum Physics)
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11 pages, 475 KB  
Article
Stability of Bi-Partite Correlations in Symmetric N-Qubit States Under Deterministic Measurements
by Carlos Muñoz, Luis Roa and Andrei B. Klimov
Physics 2025, 7(2), 12; https://doi.org/10.3390/physics7020012 - 9 Apr 2025
Viewed by 741
Abstract
In this paper, we analyze the distribution of bi-partite correlations in pure symmetric N-qubit states during local deterministic measurements, which ensure the same value of the reduced purities in the outcome states. It is analytically shown that all reduced purities grow in [...] Read more.
In this paper, we analyze the distribution of bi-partite correlations in pure symmetric N-qubit states during local deterministic measurements, which ensure the same value of the reduced purities in the outcome states. It is analytically shown that all reduced purities grow in the process of deterministic measurements. This allows us to characterize the stability of bi-partite entanglement during the optimal correlation transfer under single-qubit measurements in the asymptotic limit N≫1. Full article
(This article belongs to the Special Issue A Themed Issue in Honor of Professor Viktor Dodonov—55 Years in Quantum Physics)
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Review

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24 pages, 495 KB  
Review
Dynamical Transitions in Trapped Superfluids Excited by Alternating Fields
by Vyacheslav I. Yukalov and Elizaveta P. Yukalova
Physics 2025, 7(3), 41; https://doi.org/10.3390/physics7030041 - 12 Sep 2025
Viewed by 366
Abstract
The paper presents a survey of some dynamical transitions in nonequilibrium trapped Bose-condensed systems subject to the action of alternating fields. Nonequilibrium states of trapped systems can be implemented in two ways: resonant and nonresonant. Under resonant excitation, several coherent modes are generated [...] Read more.
The paper presents a survey of some dynamical transitions in nonequilibrium trapped Bose-condensed systems subject to the action of alternating fields. Nonequilibrium states of trapped systems can be implemented in two ways: resonant and nonresonant. Under resonant excitation, several coherent modes are generated by external alternating fields with the frequencies been tuned to resonance with some transition frequencies of the trapped system. A Bose system of trapped atoms with Bose–Einstein condensate can display two types of the Josephson effect, the standard one, when the system is separated into two or more parts in different locations, or the internal Josephson effect, when there are no any separation barriers but the system becomes nonuniform due to the coexistence of several coherent modes interacting one with another. The mathematics in both these cases is similar. We focus on the internal Josephson effect. Systems with nonlinear coherent modes demonstrate rich dynamics, including Rabi oscillations, the Josephson effect, and chaotic motion. Under the Josephson effect, there exist dynamic transitions that are similar to phase transitions in equilibrium systems. The bosonic Josephson effect is shown to be implementable not only for quite weakly interacting systems, but also in superfluids with not necessarily as weak interactions. Sufficiently strong nonresonant excitation can generate several types of nonequilibrium states comprising vortex germs, vortex rings, vortex lines, vortex turbulence, droplet turbulence, and wave turbulence. Nonequilibrium states are shown to be characterized and distinguished by effective temperature, effective Fresnel number, and dynamic scaling laws. Full article
(This article belongs to the Special Issue A Themed Issue in Honor of Professor Viktor Dodonov—55 Years in Quantum Physics)
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