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Journal of Surface Investigation X-ray Synchrotron and Neutron Techniques

Features of Quantum-Particle Propagation through Porous Structures

Г. М. Филиппов, A. S. Sabirov, В. А. Александров, Anatoly Viktorovich Stepanov

Published Nov 1, 2020• 2 citations
Publisher

Abstract

Abstrtact The propagation of wave packets of quantum particles through porous structures in thin semi-transparent films is studied. Numerical solution of the nonstationary Schrödinger equation is used in two-dimensional (for slits) and three-dimensional (round holes) cases. The transmission coefficient of quantum particles is compared with that of classical particles with the same density distribution. The vortex motion of the flux density having a hydrodynamic analog is studied. A variant of the “quantum caustic” is considered upon scattering of the particle wave packet at an obstacle.

DOI
10.1134/s1027451020050262

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Abstrtact The propagation of wave packets of quantum particles through porous structures in thin semi-transparent films is studied. Numerical solution of the nonstationary Schrödinger equation is used in two-dimensional (for slits) and three-dimensional (round holes) cases. The transmission coefficient of quantum particles is compared with that of classical particles with the same density distribution. The vortex motion of the flux density having a hydrodynamic analog is studied. A variant of the “quantum caustic” is considered upon scattering of the particle wave packet at an obstacle.
Scattering of a quantum particle with internal structure is fundamentally different from that of a point particle and shows quantum effects such as the modification of transmission due to tunnelling and trapping of the particle. As in a preceding paper (Shore et al 2014 New J. Phys. 17 013046 ) we consider a model of a symmetric, rigid rotor travelling through an aperture in a thin but impenetrable screen which is perpendicular to both the direction of motion and the rotation axis. We determine the quantum mechanical properties of this two-dimensional geometrical model using a quasi one-dimensional scattering problem with unconventional boundaries. Our calculations rely on finding the Green's function, which has a direct connection to the scattering matrix. Evaluated on a discrete lattice the Hamiltonian is 'dressed' by a self-energy correction that takes into account the open boundary conditions in an exact way. We find that the passage through the aperture can be suppressed or enhanced as a result of the rotational motion. These effects manifest themselves through resonances in the transmission probability as a function of incident energy and symmetry of the incident wavefunction. We determine the density-of-states to reveal the mode structure of resonant states and to exhibit the lifetimes of temporary trapping within the aperture.
A method for the solution of the time-dependent Schrödinger equation in two dimensions is presented which is based on the hydrodynamic analogy to quantum mechanics. The continuum introduced in that analogy is approximated by a finite number of particles, whose trajectories are computed. The procedure is applied here to the dynamics of a Gaussian wave packet on a two-dimensional quadratic potential surface containing a saddle point. Comparison with the known analytical solution indicates that the method is capable of accurate results with substantially less computer time required than in methods previously employed.
The tunneling of a quantum system with an internal degree of freedom through a potential barrier is considered. Based on the exact numerical solution to the nonstationary Schrödinger equation, the tunneling of a model two-particle system through a potential barrier is studied and the dependences of the tunneling transparency of the barrier on the parameters of the wave packet that describes the system at the initial moment are obtained. A sharp increase in the tunneling probability related to the formation of a long-lived quasibound state of the system in the barrier region is demonstrated. A simple analytical model of the tunneling of a system with an internal degree of freedom that allows for a qualitative interpretation of the main features of the tunneling is constructed.