Related papers: Generalised escape paths for dynamical tunneling i…
Numerical solutions of the time-dependent Schr\"odinger equation based on the variational principle may offer physical insight that cannot be gained by a solution using fixed grids in position and momentum space. Here we focus on the…
It is shown how the time-dependent Schr\"{o}dinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics.…
We analyze tunnel ionization of a single atom based on the Wigner function over the classical phase space which inspires improved classical electron trajectories: these start with exit momenta based on the quantum momentum function and…
The solution of the time-dependent Schr\"odinger equation is discussed for a particle confined in half-space $x>0$ with a linear potential $V(x)=Kx$ in the following situations: (a) sudden removal of the wall and switching on the linear…
The Schr\"{o}dinger equation admits smooth and finite solutions that spontaneously evolve into a singularity, even for a free particle. This blowup is generally ascribed to the intrinsic dispersive character of the associated time…
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…
We develop the semiclassical method of complex trajectories in application to chaotic dynamical tunneling. First, we suggest a systematic numerical technique for obtaining complex tunneling trajectories by the gradual deformation of the…
We compare Hawking radiation in a collapse background with Schwinger pair creation in an electric field. The comparison is driven by the presence of an analogue horizon in the Schwinger case, which causally divides spacetime for classical…
Trajectories are a central concept in our understanding of classical phenomena and also in rationalizing quantum mechanical effects. In this work we provide a way to determine semiclassical paths, approximations to quantum averages in phase…
Quantum particles interacting with potential barriers are ubiquitous in physics, and the question of how much time they spend inside classically forbidden regions has attracted interest for many decades. Recent developments of new…
The escape problem is defined in the context of quantum field theory. The escape rate is explicitly derived for a scalar field governed by fluctuation-dissipation dynamics, through generalizing the standard Kramers problem. In the presence…
Quantum mechanical tunneling across smooth double barrier potentials modeled using Gaussian functions, is analyzed numerically and by using the WKB approximation. The transmission probability, resonances as a function of incident particle…
Tunneling ionization in static or slowly varying electric fields is a cornerstone of strong-field physics and provides the entry point for semiclassical descriptions of above-threshold ionization and high-harmonic generation. In…
We develop a quantitative semiclassical theory for the resosnant tunneling through a quantum well in a tilted magnetic field. It is shown, that in the leading semiclassical approximation the tunneling current depends only on periodic orbits…
It is shown that the time-dependent equations (Schr\"odinger and Dirac) for a quantum system can be always derived from the time-independent equation for the larger object of the system interacting with its environment, in the limit that…
We use path-integrals to derive a general expression for the semiclassical approximation to the partition function of a one-dimensional quantum-mechanical system. Our expression depends solely on ordinary integrals which involve the…
This paper is concerned with the efficient numerical treatment of 1D stationary Schr\"odinger equations in the semi-classical limit when including a turning point of first order. For the considered scattering problems we show that the wave…
In this paper, we present quantum algorithms for a class of highly-oscillatory transport equations, which arise in semiclassical computation of surface hopping problems and other related non-adiabatic quantum dynamics, based on the…
In this paper we have generalized the quantum mechanics on fractal time-space. The time is changing on Cantor-set like but space is considered as fractal curve like Von-Koch curve. The Feynman path method in quantum mechanics has been…
Using the simplest but fundamental example, the problem of the infinite potential well, this paper makes an ideological attempt (supported by rigorous mathematical proofs) to approach the issue of…