Related papers: Tunneling dynamics of the relativistic Schrodinger…

Using a density matrix description in space we study the evolution of wavepackets in a fluctuating space-time background. We assume that space-time fluctuations manifest as classical fluctuations of the metric. From the non-relativistic…

The classical equation of motion of a charged point particle, including its radiation reaction, is described by the Lorentz-Dirac equation. We found a new class of solutions that describe tunneling (in a completely classical context!). For…

The "particle in a box" problem is investigated for a relativistic particle obeying the Klein-Gordon equation. To find the bound states, the standard methods known from elementary non-relativistic quantum mechanics can only be employed for…

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…

In this paper, we consider the existence and the asymptotic completeness of the wave operators for Schrodinger equations with time-dependent potentials which are short-range in space.

A semiclassical method of complex trajectories for the calculation of the tunneling exponent in systems with many degrees of freedom is further developed. It is supplemented with an easily implementable technique, which enables one to…

Wave-packet scattering from a stationary potential is significantly modified when the wave-packet is subject to an external time-dependent force during the interaction. In the semiclassical limit, wave--packet motion is simply described by…

A solution of the scattering problem is obtained for the Schr\"odinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident…

We study the total transmission of quantum particles satisfying the Klein-Gordon equation through a potential barrier based on the classical wave propagation theory. We deduce an analytical expression for the wave impedance for Klein-Gordon…

We derive dispersion estimates for solutions of a one-dimensional discrete Dirac equations with a potential. In particular, we improve our previous result, weakening the conditions on the potential. To this end we also provide new results…

We propose the quantum simulation of the Dirac equation with potentials, allowing the study of relativistic scaterring and the Klein tunneling. This quantum relativistic effect permits a positive-energy Dirac particle to propagate through a…

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…

In the context of nonrelativistic quantum mechanics, Gaussian wavepacket solutions of the time-dependent Schr\"odinger equation provide useful physical insight. This is not the case for relativistic quantum mechanics, however, for which…

Inspired by new trends in atomtronics, cold atoms devices and Bose-Einstein condensate dynamics, we apply a general technique of N=4 extended Supersymmetric Quantum Mechanics to isospectral Hamiltonians with triple-well potentials, i.e.…

We consider tunneling to the continuum in a multi-dimensional potential. It is demonstrate that this problem can be treated as two separate problems: a) a bound state and b) a non-resonance scattering problem, by a proper splitting of the…

We study a non-linear Schroedinger equation with a Hartree-type nonlinearity and a localized random time-dependent external potential. Sharp dispersive estimates for the linear Schroedinger equation with a random time-dependent potential…

We use the method of Laplace transformation to determine the dynamics of a wave packet that passes a barrier by tunneling. We investigate the transmitted wave packet and find that it can be resolved into a sequence of subsequent wave…

Process of quantum tunneling of particles in various physical systems can be effectively controlled even by a weak and slow varying in time electromagnetic signal if to adapt specially its shape to a particular system. During an…

Singularity of the potential function makes quantum tunneling problem mathematically underdetermined. To circumvent the difficulties it introduced in physics, a potential singularity cutoff is often used, followed by a reverse limit…

We set up a tunneling approach to the analogue Hawking effect in the case of models of analogue gravity which are affected by dispersive effects. An effective Schroedinger-like equation for the basic scattering phenomenon IN->P+N*, where IN…