Related papers: Semiclassical wave-packets emerging from interacti…
Quantum collision models allow for the dynamics of open quantum systems to be described by breaking the environment into small segments, typically consisting of non-interacting harmonic oscillators or two-level systems. This work introduces…
We study the particle creation process in the Schwinger model coupled with an external classical source. One can approach the problem by taking advantage that the full quantized model is solvable and equivalent to a (massive) gauge field…
For closed quantum systems driven away from equilibrium, work is often defined in terms of projective measurements of initial and final energies. This definition leads to statistical distributions of work that satisfy nonequilibrium work…
We consider a Schr\"{o}dinger particle placed in an external electromagnetic field of the form typical for scattering settings in the field theory: $F=F^\mathrm{ret}+F^\mathrm{in}=F^\mathrm{adv}+F^\mathrm{out}$, where the current producing…
I discuss a formalism for computing quantum scattering amplitudes using a semiclassical expansion of a functional integral representation for the S-matrix. The classical background for the expansion is determined by solving the equations of…
The quantum dynamics of an electron in a uniform magnetic field is studied for geometries corresponding to integrable cases. We obtain the uniform asymptotic approximation of the WKB energies and wavefunctions for the semi-infinite plane…
Localized scattering phenomena may result in the formation of stationary matter waves originating from a compact region in physical space. Mathematically, such waves are advantageously expressed in terms of quantum sources that are…
By using a test-function method, we construct $n$ exact solutions of a quantum harmonic oscillator with a time-dependent "spring constant". Any $n$-th solution describes a wave-packet train consisting of $n+1$ packets. Its center oscillates…
We present a new hydrodynamic analogy of nonrelativistic quantum particles in potential wells. Similarities between a real variant of the Schr\"odinger equation and gravity-capillary shallow water waves are reported and analyzed. We show…
We develop a system of non-linear stochastic evolution equations that describes the continuous measurements of quantum systems with mixed initial state. We address quantum systems with unbounded Hamiltonians and unbounded interaction…
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…
Although quantum mechanics is a mature theory, fundamental problems discussed during its time of foundation have remained with us to this day. These problems are centered on the problematic relation between the quantum and classical worlds.…
The numerical prediction, theoretical analysis, and experimental verification of the phenomenon of wave packet revivals in quantum systems has flourished over the last decade and a half. Quantum revivals are characterized by initially…
This work continues our studies of nonlinear evolution of a system of wavepackets. We study a wave propagation governed by a nonlinear system of hyperbolic PDE's with constant coefficients with the initial data being a multi-wavepacket. By…
The three-dimensional Schredinger's equation is analyzed with the help of the correspondence principle between classical and quantum-mechanical quantities. Separation is performed after reduction of the original equation to the form of the…
We take up the idea of Nelson's stochastic processes, the aim of which was to deduce Schr\"odinger's equation. We make two major changes here. The first one is to consider deterministic processes which are pseudo-random but which have the…
A simple and explicit technique for the numerical solution of the two-particle, time-dependent Schr\"{o}dinger equation is assembled and tested. The technique can handle interparticle potentials that are arbitrary functions of the…
We derive stochastic master equation for a quantum system interacting with an environment prepared in a continuous-mode $N$-photon state. To determine the conditional evolution of the quantum system depending on continuous in time…
We employ a self consistent framework to study the backreaction effects of particle creation in the coupled semiclassical dynamics of a quantum complex scalar field and a classical electric field in both (1 + 1) and (1 + 3) dimensional…
The dynamics of states representing arbitrary N-level quantum systems, including dissipative systems, can be modelled exactly by the dynamics of classical coupled oscillators. There is a direct one-to-one correspondence between the quantum…