Related papers: Sharp Tunneling Estimates for a Double-Well Model …
Time analysis of oscillations of a particle between wells in the one-dimensional double-well potential with infinite high outside walls, based on wave packet use and energy spectrum analysis, is presented. For the double-well potential of…
By using the WKB quantization we deduce an analytical formula for the energy splitting in a double-well potential which is the usual Landau formula with additional quantum corrections. Then we analyze the accuracy of our formula for the…
The classical square well potential is smoothed with a finite range smoothing function in order to get a new simple strictly finite range form for the phenomenological nuclear potential. The smoothed square well form becomes exactly zero…
Numerical Stochastic Perturbation Theory (NSPT) has over the years proved to be a valuable tool, in particular being able to reach unprecedented orders for Lattice Gauge Theories, whose perturbative expansions are notoriously cumbersome.…
This article analyzes an explicit temporal splitting numerical scheme for the stochastic Allen-Cahn equation driven by additive noise, in a bounded spatial domain with smooth boundary in dimension $d\le 3$. The splitting strategy is…
We present a study of a general spin Hamiltonian with terms up to fourth order. With the coherent states the semiclassical potential is obtained and with catastrophe theory its parameter space is constructed. When the fourth order…
In this article we are interested in the microscopic modeling of a two-dimensional two-well problem which arises from the square-to-rectangular transformation in (two-dimensional) shape-memory materials. In this discrete set-up, we focus on…
Initially, we derive a nonlinear integral equation for the vacuum counting function of the spin 1/2-XYZ chain in the {\it disordered regime}, thus paralleling similar results by Kl\"umper \cite{KLU}, achieved through a different technique…
The description of number of dual (quasy)-exactly solvable models with its hidden symmetry algebra has been given at different levels of analysis within the framework of generalized Kustaanheimo-Stiefel (KS)-transformations. It's shown that…
We establish an optimal strong convergence rate of a fully discrete numerical scheme for second order parabolic stochastic partial differential equations with monotone drifts, including the stochastic Allen-Cahn equation, driven by an…
This paper deals with semiclassical asymptotics of the three-dimensional magnetic Laplacian in presence of magnetic confinement. Using generic assumptions on the geometry of the confinement, we exhibit three semiclassical scales and their…
We prove spectral properties for random Landau Schr\"odinger operators on $L^2(\mathbb{R}^2)$ with bounded, random potentials supported in a square $\Lambda_L \subset \mathbb{R}^2$ of side length $L>0$, using semiclassical…
Using a recent reformulation of quantum mechanics where the potential function is not required, we are able to obtain the energy spectrum and wave function associated with the infinite square well analytically. Therefore, this work…
We establish a quantitative rigidity estimate for two-well frame-indifferent nonlinear energies, in the case in which the two wells have exactly one rank-one connection. Building upon this novel rigidity result, we then analyze solid-solid…
The purpose of this article is to construct global solutions, in a probabilistic sense, for the nonlinear Schr{\"o}dinger equation posed on $\mathbb{R}^d$, in a supercritical regime. Firstly, we establish Bourgain type bilinear estimates…
Using the formalism of extended $N=4$ supersymmetric quantum mechanics we consider the procedure of the construction of multi--well potentials. We demostrate the form--invariance of Hamiltonians entering the supermultiplet, using the…
We study the intra-planar tunneling between quantum Hall samples separated by a quasi one-dimensional barrier, induced through the interaction of edge degrees of freedom with the charge density waves of a Hall crystal defined in a parallel…
Numerical studies are presented to assess error estimates for a separable (Hartree) approximation for dynamically evolving composite quantum systems which exhibit distinct scales defined by their mass and frequency ratios. The relevant…
The fractional quantum Hall (FQH) effect provides a paradigmatic example of a topological phase of matter. FQH edges are theoretically described via models belonging to the class of chiral Luttinger liquid (CLL) theories [1 (Wen, 2007)].…
Using canonical (Schrodinger) quantization of spherically symetric gravitational dust systems, we find the quasi-classical (coherent) state, |\alpha^{(s)}>, that corresponds to the classical Schwarzschild solution. We calculate the…