Related papers: Semiclassical approximation with zero velocity tra…
We have developed a semiclassical approach to solving the Bogoliubov - de Gennes equations for superconductors. It is based on the study of classical orbits governed by an effective Hamiltonian corresponding to the quasiparticles in the…
In this work, we investigate stochastic quasi-Newton methods for minimizing a finite sum of cost functions over a decentralized network. In Part I, we develop a general algorithmic framework that incorporates stochastic quasi-Newton…
A novel approach is suggested for the statistical description of quantum systems of interacting particles. The key point of this approach is that a typical eigenstate in the energy representation (shape of eigenstates, SE) has a well…
The problem of inter-band tunneling in a semiconductor (Zener breakdown) in a nonstationary and homogeneous electric field is solved exactly. Using the exact analytical solution, the approximation based on classical trajectories is studied.…
Consider any stationary Schroedinger wave equation (SWE) solution $psi (x)$ for a particle. The corresponding PDF on position QTR{em}{x} of the particle is QTR{em}{p}$_{X}(x)=|psi (x)|^{2}$. There is a classical trajectory QTR{em}{x(t)} for…
The path integral approach to the quantization of one degree-of-freedom Newtonian particles is considered within the discrete time-slicing approach, as in Feynman's original development. In the time-slicing approximation the quantum…
We study tunneling in one-dimensional quantum mechanics using the path integral in real time, where solutions of the classical equation of motion live in the complex plane. Analyzing solutions with small (complex) energy, relevant for…
We consider a semiclassical random walk with respect to a probability measure associated to a potential with a finite number of critical points. We recover the spectral results from [1] on the corresponding operator in a more general…
We construct a class of systems for which quantum dynamics can be expanded around a mean field approximation with essentially classical content. The modulus of the quantum overlap of mean field states naturally introduces a classical…
Semiclassical Mechanics allows for a description of quantum systems which preserves their phase information, while using only the system's classical dynamics as an input. Over the time an identification has been developed between stationary…
This paper studies a method, which has been proposed in the Physics literature by [8, 7, 10], for estimating the quasi-stationary distribution. In contrast to existing methods in eigenvector estimation, the method eliminates the need for…
Following the semiclassical formalism of Strutinsky et al., we have obtained the complete eigenvalue spectrum for a particle enclosed in an infinitely high spheroidal cavity. Our spheroidal trace formula also reproduces the results of a…
An approach is developed for constructing simple analytical formulae accurately approximating solutions to eigenvalue problems of quantum mechanics. This approach is based on self-similar approximation theory. In order to derive…
Semidiscrete optimal transport is a challenging generalization of the classical transportation problem in linear programming. The goal is to design a joint distribution for two random variables (one continuous, one discrete) with fixed…
In a recent letter [Phys. Rev. Lett. {\bf 100}, 164101 (2008)] and within the context of quantized chaotic billiards, random plane wave and semiclassical theoretical approaches were applied to an example of a relatively new class of…
The damped nonlinear wave equation, also known as the nonlinear telegraph equation, is studied within the framework of semigroups and eigenfunction approximation. The linear semigroup assumes a central role: it is bounded on the domain of…
We describe a novel approach for computing wave correlation functions inside finite spatial domains driven by complex and statistical sources. By exploiting semiclassical approximations, we provide explicit algorithms to calculate the local…
A "quasiclassical" approximation to the quantum spectrum of the Schroedinger equation is obtained from the trace of a quasiclassical evolution operator for the "hydrodynamical" version of the theory, in which the dynamical evolution takes…
Electronic transport through chaotic quantum dots exhibits universal behaviour which can be understood through the semiclassical approximation. Within the approximation, transport moments reduce to codifying classical correlations between…
We present brief, to great extent pedagogical review on renormalization in curved space-time and of some recent results on the derivation and better understanding of quantum corrections to the action of gravity. The paper is mainly devoted…