Related papers: A simple semiclassical approach to Kramers' proble…
We consider the semiclassical limit of nonlinear Schr\"odinger equations with wavepacket initial data. We recover the Wigner measure of the problem, a macroscopic phase-space density which controls the propagation of the physical…
An initial coherent state is propagated exactly by a kicked quantum Hamiltonian and its associated classical stroboscopic map. The classical trajectories within the initial state are regular for low kicking strengths, then bifurcate and…
Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and…
Building on the discussion in PRA 93, 042510 (2016), we present a systematic derivation of gradient corrections to the kinetic-energy functional and the one-particle density, in particular for two-dimensional systems. We derive the leading…
The Lindblad master equation for an open quantum system with a Hamiltonian containing an arbitrary potential is written as an equation for the Wigner distribution function in the phase space representation. The time derivative of this…
We develop a modified semi-classical approach to the approximate solution of Schrodinger's equation for certain nonlinear quantum oscillations problems. At lowest order, the Hamilton-Jacobi equation of the conventional semi-classical…
Starting from the density-matrix equation of motion, we derive a semiclassical kinetic equation for a general two-band electronic Hamiltonian, systematically including quantum-mechanical corrections up to second order in space-time…
We obtain analytic solutions to various models of dissipation of the quantum harmonic oscillator, employing a simple method in the Wigner function Fourier transform description of the system; and study as an exemplification, the driven open…
We derive the functional Schrodinger equation for quantum fields in curved spacetime in the semiclassical limit of quantum geometrodynamics with a Gaussian incoherent dust acting as a clock field. We perform the semiclassical limit using a…
The relativistic semi-classical approximation for a free massive particle is studied using the Wigner-Weyl formalism. A non-covariant Wigner function is proposed using the Newton-Wigner position operator. The perturbative solution for the…
A gauge-invariant Wigner quasi-distribution function for charged particles in classical electromagnetic fields is derived in a rigorous way. Its relation to the axial gauge is discussed, as well as the relation between the kinetic and…
We propose a Wigner quasiprobability distribution function for Hamiltonian systems in spaces of constant curvature --in this paper on hyperboloids--, which returns the correct marginals and has the covariance of the Shapiro functions under…
We investigate photon emission from a moving particle in an expanding universe. This process is analogous to the radiation from an accelerated charge in the classical electromagnetic theory. Using the framework of quantum field theory in…
The basics of the Wigner formulation of Quantum-Mechanics and few related interpretational issues are presented in a simple language. This formulation has extensive applications in Quantum Optics and in Mixed Quantum-Classical formulations.
The original perturbative Kramers' method (starting from the phase space coordinates) (Kramers, 1940) of determining the energy-controlled-diffusion equation for Newtonian particles with separable and additive Hamiltonians is generalized to…
In this paper, we reformulate the semi-classical Schr\"odinger equation in the presence of electromagnetic field by the Gaussian wave packets transform. With this approach, the highly oscillatory Schr\"odinger equation is equivalently…
Using a perturbative approach, we investigate the parametric down-conversion process without the semi-classical approximation. A Wigner functional formalism, which incorporates both the spatiotemproal degrees of freedom and the…
We consider the process of diffusion scattering of a wave function given on the phase space. In this process the heat diffusion is considered only along momenta. We write down the modified Kramers equation describing this situation. In this…
Kramers escape from a metastable state in the presence of both thermal and quantum fluctuations under strong damping is treated as a thermally activated process in a quantum modified semiclassical potential. Dirac's time-dependent…
To solve the quantum-mechanical problem the procedure of mapping onto linear space $W$ of generators of the (sub)group violated by given classical trajectory is formulated. The formalism is illustrated by the plane H-atom model. The problem…