相关论文: Homogenization of the Schrodinger equation with a …
We present a Gedankenexperiment that leads to a violation of detailed balance if quantum mechanical transition probabilities are treated in the usual way by applying Fermi's "golden rule". This Gedankenexperiment introduces a collection of…
A closed-form solution to the energy-based stochastic Schrodinger equation with a time-dependent coupling is obtained. The solution is algebraic in character, and is expressed directly in terms of independent random data. The data consist…
In recent years, an increasing attention has been paid to quantum heterostructures with tailored functionalities, such as heterojunctions and quantum matematerials, in which quantum dynamics of electrons can be described by the…
Transport and scattering phenomena in open quantum-systems with a continuous energy spectrum are conveniently solved using the time-dependent Schrodinger equation. In the time-dependent picture, the evolution of an initially localized…
We consider nonlinear Schr\"odinger equations in $\R^3$. Assume that the linear Hamiltonians have two bound states. For certain finite codimension subset in the space of initial data, we construct solutions converging to the excited states…
The semiclassical Schr\"{o}dinger equation with multiscale and random potentials often appears when studying electron dynamics in heterogeneous quantum systems. As time evolves, the wavefunction develops high-frequency oscillations in both…
A 1-dimensional model for coherent quantum energy transfer through a complex of compressible boxes is investigated by numerical integration of the time-dependent Schr\"odinger equation. Energy is communicated from one box to the next by the…
We consider the description of a Fermi gas of free electrons given by the Boltzmann--Fermi--Dirac equation, and aim at providing a precise mathematical understanding of the Fermi ground state and its first-order approximation of excited…
We regard the real and imaginary parts of the Schrodinger wave function as canonical conjugate variables.With this pair of conjugate variables and some other 2n pairs, we construct a quadratic Hamiltonian density. We then show that the…
We consider a cubic nonlinear Schroedinger equation with periodic potential. In a semiclassical scaling the nonlinear interaction of modulated pulses concentrated in one or several Bloch bands is studied. The notion of closed mode systems…
We propose a nanodevice based on a typical planar semiconductor heterostructure with lateral confinement potential created by voltages applied to local electrodes. We show how to obtain near parabolical confinement along the nanodevice, and…
According to theorems of Shnirelman and followers, in the semiclassical limit the quantum wavefunctions of classically ergodic systems tend to the microcanonical density on the energy shell. We here develop a semiclassical theory that…
We calculate the shift, due to interatomic interactions, of an optical transition in an atomic Fermi gas trapped in an optical lattice, as in recent experiments of Campbell {\it et al.}, Science {\bf 324}, 360 (2009). Using a pseudospin…
In this paper we discuss a solution of the free particle Schrodinger equation in which the time and space dependence are not separable. The wavefunction is written as a product of exponential terms, Hermite polynomials and a phase. The…
Nonequilibrium quantum physics greatly simplifies in the case of time-periodic Hamiltonians, since Floquet theory provides an analogue to Bloch's theorem in the time domain. Still, the formal properties of Floquet many-body theory remain…
We predict phase-transitions in the quantum noise characteristics of systems described by the quantum nonlinear Schr\"odinger equation, showing them to be related to the solitonic field transition at half the fundamental soliton amplitude.…
The finite element method (FEM) and the boundary element method (BEM) can numerically solve the Helmholtz system for acoustic wave propagation. When an object with heterogeneous wave speed or density is embedded in an unbounded exterior…
In this paper, we investigate that the H\"older regularity of solutions to the time fractional Schr\"odinger equation of order $1<\alpha<2$, which interpolates between the Schr\"odinger and wave equations. This is inspired by Hirata and…
We show that by computing the electron-impurity scattering rate at the first order via Fermi's golden rule, and assuming that the localized impurity potential is of Yukawa form, one obtains a wave vector transfer distribution which is…
This paper concerns the homogenization problem of a parabolic equation with large, time-dependent, random potentials in high dimensions $d\geq 3$. Depending on the competition between temporal and spatial mixing of the randomness, the…