Related papers: Sharp Tunneling Estimates for a Double-Well Model …
Here we consider stationary states for nonlinear Schrodinger equations with symmetric double well potentials. These stationary states may bifurcate as the strength of the nonlinear term increases and we observe two different pictures…
Recently, a class of PT-invariant quantum mechanical models described by the non-Hermitian Hamiltonian $H=p^2+x^2(ix)^\epsilon$ was studied. It was found that the energy levels for this theory are real for all $\epsilon\geq0$. Here, the…
We study the dynamics of multi-dimensional quantum tunneling by introducing a complex absorbing potential to a two-dimensional model for spontaneous fission. We fist diagonalize the Hamiltonian with the complex potential to determine a…
The WKB and instanton answers for the tunnel splitting of the ground state in a symmetric double well potential are both reduced to an expression involving only the functionals of the potential, without the need for solving any auxilliary…
We construct a variety of new exactly-solvable quantum systems, the potentials of which are given in terms of Lambert-W functions. In particular, we generate Schr\"odinger models with energy-dependent potentials, conventional Schr\"odinger…
In this paper we discuss a family of models of particle and energy diffusion on a one-dimensional lattice, related to those studied previously in [Sasamoto-Wadati], [Barraquand-Corwin] and [Povolotsky] in the context of KPZ universality…
We employ the tight-binding propagation method to study Klein tunneling and quantum interference in large graphene systems. With this efficient numerical scheme, we model the propagation of a wave packet through a potential barrier and…
We study the focusing intercritical NLS \begin{align}\label{abstract_nls} i\pt_t u+\Delta_{x,y}u=-|u|^\alpha u\tag{NLS} \end{align} on the semiperiodic waveguide manifold $\R^d_x\times \T_y$ with $d\geq 5$ and…
The double-well problem for the two-dimensional Dirac equation is solved for a family of quasi-one-dimensional potentials in terms of confluent Heun functions. We demonstrate that for a double well separated by a barrier, both the energy…
We study and simulate N=2 supersymmetric Wess-Zumino models in one and two dimensions. For any choice of the lattice derivative, the theories can be made manifestly supersymmetric by adding appropriate improvement terms corresponding to…
The chiral Luttinger liquid model for the edge dynamics of a two-dimensional electron gas in a strong magnetic field is derived from coarse-graining and a lowest Landau level projection procedure at arbitrary filling factors $\nu<1$ --…
We have derived and analyzed the wavefunctions and energy states for an asymmetric double quantum wells, broadened due to static interface disorder effects, within well known discreet variable representation approach for solving the…
The formation of codimension-one interfaces for multiwell gradient-driven problems is well-known and established in the scalar case, where the equation is often referred to as the Allen-Cahn equation. The vectorial case in contrast is quite…
In the semiclassical limit h to 0, we analyze a class of self-adjoint Schr\"odinger operators H_h = h^2 L + h W + V id_E acting on sections of a vector bundle E over an oriented Riemannian manifold M where L is a Laplace type operator, W is…
We derive a model-independent expression for finite-volume matrix elements. Specifically, we present a relativistic, non-perturbative analysis of the matrix element of an external current between a one-scalar in-state and a two-scalar…
New sharp Strichartz estimates for the Maxwell system in two dimensions with rough permittivity and non-trivial charges are proved. We use the FBI transform to carry out the analysis in phase space. For this purpose, the Maxwell equations…
We study quasi-one-dimensional scattering of one and two particles with short-range interactions on a discrete lattice model in two dimensions. One of the directions is tightly confined by an arbitrary trapping potential. We obtain the…
We consider tunneling between symmetric wells for a 2-D semi-classical Schr\"odinger operator for energies close to the quadratic minimum of the potential V in two cases: (1) excitations of the lowest frequency in the harmonic oscillator…
We report on numerical procedures for, and preliminary results on the search for, tunnelling centres in Lennard-Jones clusters, seen as simple model systems of glasses. Several of the double-well potentials identified are good candidates to…
Localization of a particle in the wells of an asymmetric double-well (DW) potential is investigated here. Information entropy-based uncertainty measures, such as Shannon entropy, Fisher information, Onicescu energy, etc., and phasespace…