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The algebra of generalized linear quantum canonical transformations is examined in the prespective of Schwinger's unitary-canonical basis. Formulation of the quantum phase problem within the theory of quantum canonical transformations and…
We analyse some features of the class of discrete Wigner functions that was recently introduced by Gibbons et al. to represent quantum states of systems with power-of-prime dimensional Hilbert spaces [Phys. Rev. A 70, 062101 (2004)]. We…
A direct comparison of quantum and classical dynamical systems can be accomplished through the use of distribution functions. This is useful for both fundamental investigations such as the nature of the quantum-classical transition as well…
We suggest an extension of the Hilbert Phase Space formalism, which appears to be naturally suited for application to the dissipative (open) quantum systems, such as those described by the non-stationary (time-dependent) Hamiltonians…
The integral Wigner - Liouwille equation describing time evolution of the semi-relativistic quantum 1D harmonic oscillator have been exactly solved by combination of the Monte-Carlo procedure and molecular dynamics methods. The strong…
The relation that exists in quantum mechanics among action variables, angle variables and the phases of quantum states is clarified, by referring to the system of a generalized oscillator. As a by-product, quantum-mechanical meaning of the…
The interplay between classical and quantum mechanical evolution in the optical centrifuge (OC) is discussed. The analysis is based on the quantum mechanical formalism starting from either the ground state or a thermal ensemble. Two…
Using linear invariant operators in a constructive way we find the most general thermal density operator and Wigner function for time-dependent generalized oscillators. The general Wigner function has five free parameters and describes the…
Using a nonlinear Schr\"{o}dinger equation for the wave function of all systems, continuous transitions between quantum and classical motions are demonstrated for (i) the double-slit set up, (ii) the 2D harmonic oscillator and (iii) the…
The presence of negative values in the Wigner quasiprobability distribution is deemed one of the hallmarks of nonclassical phenomena in quantum systems. Here we demonstrate a classical model of squeezed light that, when combined with…
Egorov's theorem on the classical propagation of quantum observables is related to prominent quasi-classical descriptions of quantum molecuar dynamics as the linearized semiclassical initial value representation (LSC-IVR), the Wigner phase…
In this paper, we study the classical limit and unitary evolution of quantum cosmology by applying the Weyl--Wigner--Groenewold--Moyal formalism of deformation quantization to quantum cosmology of a homogeneous and isotropic universe with…
We review the problem of state reconstruction in classical and in quantum physics, which is rarely considered at the textbook level. We review a method for retrieving a classical state in phase space, similar to that used in medical imaging…
The density operator for a quantum system in thermal equilibrium with its environment depends on Planck's constant, as well as the temperature. At high temperatures, the Weyl representation, that is, the thermal Wigner function, becomes…
Time dependence for barrier penetration is considered in the phase space. An asymptotic phase-space propagator for nonrelativistic scattering on a one - dimensional barrier is constructed. The propagator has a form universal for various…
Quantum mechanics has been formulated in phase space, with the Wigner function as the representative of the quantum density operator, and classical mechanics has been formulated in Hilbert space, with the Groenewold operator as the…
A quantum phase space with Wannier basis is constructed: (i) classical phase space is divided into Planck cells; (ii) a complete set of Wannier functions are constructed with the combination of Kohn's method and L\"owdin method such that…
We consider a two-dimensional (2D) generalization of the standard kicked-rotor (KR) and show that it is an excellent model for the study of 2D quantum systems with underlying diffusive classical dynamics. First we analyze the distribution…
A quantum manifestation of chaotic classical dynamics is found in the framework of oscillatory numbers statistics for the model of nonlinear dissipative oscillator. It is shown by numerical simulation of an ensemble of quantum trajectories…
Gaussian quantum systems exhibit many explicitly quantum effects but can be simulated classically. Using both the Hilbert space (Koopman) and the phase-space (Moyal) formalisms we investigate how robust this classicality is. We find…