相关论文: Semi-classical determination of exponentially smal…
The asymptotic behavior of some semilinear parabolic PDEs is analyzed by means of a "mean value" property. This property allows us to determine, by means of appropriate {\em{a priori}} estimates, some exponential decay results for suitable…
We explore the quantization of classical models with position-dependent mass (PDM) terms constrained to a bounded interval in the canonical position. This is achieved through the Weyl-Heisenberg covariant integral quantization by properly…
We consider a pair of parallel straight quantum waveguides coupled laterally through a window of a width $ \ell $ in the common boundary. We show that such a system has at least one bound state for any $ \ell>0 $. We find the corresponding…
We prove that the scattering matrix at a fixed quasi--energy determines uniquely a time--periodic potential that decays exponentially at infinity. We consider potentials that for each fixed time belong to $L^{3/2}$ in space. The exponent…
We study the transitions between neighboring energy levels in a quasi-one-dimensional semiconductor quantum dot with two interacting electrons in it, when it is subject to a linearly time-dependent electric field. We analyze the…
We develop a method based on tensor networks to create localized single particle excitations on top of strongly-correlated quantum spin chains. In analogy to the problem of creating localized Wannier modes, this is achieved by optimizing…
The usual approach on electrostatic wave decay process for a weak beam-plasma system considers two different wave modes interplaying, the Langmuir and ion-sound mode. In the present paper, a single-mode approach is shown to be feasible for…
Semiclassical mechanics of systems with first-class constraints is developed. Starting from the quantum theory, one investigates such objects as semiclassical states and observables, semiclassical inner product, semiclassical gauge…
We study the time behavior of wave functions involved in tunneling through a smooth potential barrier in one dimension in the semiclassical limit. We determine the leading order component of the wave function that tunnels. It is…
The time dependent density matrix of a system with potential barrier is studied using path integrals. The characterization of the initial state, which is assumed to be restricted to one side of the barrier, and the time evolution of the…
In this paper, we derive general theorems for controlling (vector-valued) first order ordinary differential equations such that its solutions stop at a finite time $T>0$ and apply them to relaxation and dissipative oscillation processes. We…
We consider Markov models of large-scale networks where nodes are characterized by their local behavior and by a mobility model over a two-dimensional lattice. By assuming random walk, we prove convergence to a system of partial…
We solve the Klein-Gordon equation in the presence of a spatially one-dimensional cusp potential. The scattering solutions are obtained in terms of Whittaker functions and the condition for the existence of transmission resonances is…
Theory of scattering by many small bodies is developed under various assumptions concerning the ratio $\frac{a}{d}$, where $a$ is the characteristic dimension of a small body and $d$ is the distance between neighboring bodies $d =…
This article is devoted to the construction of numerical methods which remain insensitive to the smallness of the semiclassical parameter for the linear Schr{\"o}dinger equation in the semiclassical limit. We specifically analyse the…
This paper concerns time-dependent scattering theory and in particular the concept of time delay for a class of one-dimensional anisotropic quantum systems. These systems are described by a Schr\"{o}dinger Hamiltonian $H = -\Delta + V$ with…
We present a detailed study of scattering by an amplitude-modulated potential barrier using three distinct physical frameworks: quantum, classical, and semiclassical. Classical physics gives bounds on the energy and momentum of the…
There has been much success in describing the limiting spatial fluctuations of growth models in the Kardar-Parisi-Zhang (KPZ) universality class. A proper rescaling of time should introduce a non-trivial temporal dimension to these limiting…
We study the diffusion of monochromatic classical waves in a disordered acoustic medium by scattering theory. In order to avoid artifacts associated with mathematical point scatterers, we model the randomness by small but finite insertions.…
We calculate the Landauer conductance through chaotic ballistic devices in the semiclassical limit, to all orders in the inverse number of scattering channels without and with a magnetic field. Families of pairs of entrance-to-exit…