Related papers: \'Echelles de temps pour l'\'evolution quantique \…
We propose a new variant of the semiclassical quantisation with two independent parameters. The first one is proportional to the Planck constant as usually and the second one is connected with a deviation of the given potential from a very…
We propose and simulate a protocol to evolve a quantum particle forward in time such that its trajectory closely matches that of the particle's Newtonian counterpart. Using short bursts of Schr\"odinger time-evolution interleaved with…
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…
Multi-time equations are evolution equations involving several time variables, one for each particle. Such equations have been considered for the purpose of making theories manifestly Lorentz invariant. We compare their status and…
A certain modification of the semiclassical quantization condition based on the summarization of the known power expansion in the squared Planck constant is proposed. Corresponding deviation from exact spectra arises only together with the…
We present a time dependent quantum perturbation result, uniform in the Planck constant, for perturbations of potentials whose gradients are Lipschitz continuous by potentials whose gradients are only bounded a.e.. Though this low…
This paper focuses on finding an approximate solution of a kind of Fokker-Planck equation with time-dependent perturbations. A formulation of the approximate solution of the equation is constructed, and then the existence of the formulation…
We show how to approximate a solution of the first order linear evolution equation, together with its possible analytic continuation, using a solution of the time-fractional equation of order $\delta >1$, where $\delta \to 1+0$.
Within the framework of Weyl calculus we establish a quantum-classical correspondence for the time evolution of observables generated by a Dirac-Hamiltonian. This includes a semiclassical separation of particles and antiparticles. We then…
A method for numerical approximation of a new class of fractional parabolic stochastic evolution equations is introduced and analysed. This class of equations has recently been proposed as a space-time extension of the SPDE-method in…
We consider the links between consistent and approximate descriptions of the quantum-classical systems, i.e. systems are composed of two interacting subsystems, one of which behaves almost classically while the other requires a quantum…
In this paper we first observe some interesting parallels between Planck scale considerations and elementary particle Compton wavelength scale considerations, particularly in the context of Wheeler's space time foam and a space time arising…
We consider the nonlinear Schr{\"o}dinger equation with a short-range external potential, in a semi-classical scaling. We show that for fixed Planck constant, a com-plete scattering theory is available, showing that both the potential and…
Mathematical and phenomenological arguments in favor of asymmetric time evolution of micro-physical states are presented.
A temporally discrete Schroedinger time evolution equation is proposed for isotropic quantum cosmology coupled to a massless scalar source. The approach employs dynamically determined intrinsic time and produces the correct semiclassical…
We consider systems of stochastic evolutionary equations of the $p$-Laplace type. We establish convergence rates for a finite-element based space-time approximation, where the error is measured in a suitable quasi-norm. Under natural…
We introduce a method of approximate nonclassical Lie-B\"acklund symmetries for partial differential equations with a small parameter and discuss applications of this method to finding of approximate solutions both integrable and…
The periods after the end of the "primary" nucleation are considered. The approximate analytical description is given. The process is split into several periods which form the loop of evolution.
The semiclassical long-time limit of free evolution of quantum wave packets on the torus is under consideration. Despite of simplicity of this system, there are still open questions concerning the detailed description of the evolution on…
Last year I talked at this meeting about a possible time dependence of the QCD coupling constant $\alpha_s$. This year I shall look into the problem once more, without fully repeating the arguments given last year. Astrophysical indications…