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Kinetic theory provides modeling of open quantum systems subject to Markovian noise via the Wigner–Fokker–Planck equation, which is an alternate of the Lindblad master equation setting, having the advantage of great physical intuition as it is the quantum equivalent of the classical phase space description. We perform a numerical inspection of the Wehrl entropy for the benchmark problem of a harmonic potential, since the existence of a steady state and its analytical formula have been proven theoretically in this case. When there is friction in the noise terms, no theoretical results on the monotonicity of absolute entropy are available. We provide numerical results of the time evolution of the entropy in the case with friction using a stochastic (Euler–Maruyama-based Monte Carlo) numerical solver. For all the chosen initial conditions studied (all of them Gaussian states), up to the inherent numerical error of the method, one cannot disregard the possibility of monotonic behavior even in the case under study, where the noise includes friction terms. [ABSTRACT FROM AUTHOR]

We investigate the asymptotic relation between the inverse problems relying on the Helmholtz equation and the radiative transfer equation (RTE) as physical models in the high-frequency limit. In particular, we evaluate the asymptotic convergence of a generalized version of the inverse scattering problem based on the Helmholtz equation, to the inverse scattering problem of the Liouville equation (a simplified version of RTE). The two inverse problems are connected through the Wigner transform that translates the wave-type description on the physical space to the kinetic-type description on the phase space, and the Husimi transform that models data localized both in location and direction. The finding suggests that impinging tightly concentrated monochromatic beams can indeed provide stable reconstruction of the medium, asymptotically in the high-frequency regime. This fact stands in contrast with the unstable reconstruction for the classical inverse scattering problem when the probing signals are plane waves. [ABSTRACT FROM AUTHOR]

We consider a recently developed method to analyze the angular structure of pulsed acoustic fields in an underwater sound channel. The method is based on the Husimi transform that allows us to approximately link a wave field with the corresponding ray arrivals. The advantage of the method lies in the possibility of its practical realization by a vertical hydrophone array crossing only a small part of the oceanic depth. The main aim of the present work is to find the optimal parameter values of the array that ensure good angular accuracy and sufficient reliability of the algorithm to calculate the arrival angles. Broadband pulses with central frequencies of 80 and 240 Hz are considered. It is shown that an array with a length of several hundred meters allows measuring the angular spectrum with an accuracy of up to 1 degree. The angular resolution is lowered with an increase of the sound wavelength due to the fundamental limitations imposed by the uncertainty relation. [ABSTRACT FROM AUTHOR]

We will show that Liouville and quantum Liouville operators L and Lħ generate two C0-groups etL and etLħ of isometries in L²(ℝ2n) and etLħ converges ultraweakly to etL. As a consequence we show that the Gaussian mollifier of the Wigner function, called Husimi function, converges in L¹(ℝ2n) to the solution of the Liouville equation. [ABSTRACT FROM AUTHOR]

Abstract: Smoothed Wigner transforms have been used in signal processing, as a regularized version of the Wigner transform, and have been proposed as an alternative to it in the homogenization and/or semiclassical limits of wave equations. We derive explicit, closed formulations for the coarse-scale representation of the action of pseudodifferential operators. The resulting “smoothed operators” are in general of infinite order. The formulation of an appropriate framework, resembling the Gelfand–Shilov spaces, is necessary. Similarly we treat the “smoothed Wigner calculus”. In particular this allows us to reformulate any linear equation, as well as certain nonlinear ones (e.g., Hartree and cubic nonlinear Schrödinger), as coarse-scale phase-space equations (e.g., smoothed Vlasov), with spatial and spectral resolutions controlled by two free parameters. Finally, it is seen that the smoothed Wigner calculus can be approximated, uniformly on phase-space, by differential operators in the semiclassical regime. This improves the respective weak-topology approximation result for the Wigner calculus. [Copyright &y& Elsevier]

A global existence, uniqueness and regularity theorem is proved for the simplest Markovian Wigner–Poisson–Fokker–Planck model incorporating friction and dissipation mechanisms. The proof relies on Green function and energy estimates under mild formulation, making essential use of the Husimi function and the elliptic regularization of the Fokker–Planck operator. [Copyright &y& Elsevier]