Particle Monte Carlo simulation of Wigner function tunneling

Vladimir S. Filinov, Pavel R. Levashov, Alexander S. Larkin

John W. Negele

Jean Michel Sellier, Ivan Dimov

Alexander S. Larkin, Vladimir S. Filinov, В. Е. Фортов

Abstract Quantum effects can affect the shape of the particle kinetic energy distribution function, as the interaction of a particle with its surroundings restricts the volume of configuration space, which, due to the uncertainty relation, results in an increase in the volume of the momentum space, i.e., in a rise in the fraction of particles with higher momenta. Allowing for quantum effects at calculations of the equilibrium rate constants of inelastic processes is important in consideration of such phenomena as the transition of combustion into detonation, flame propagation, vibrational relaxation, and even thermonuclear fusion at high pressure and low temperatures. Quantum effects are also important in treatment of transport properties of the strongly interacting systems of many particles. In this work the new path integral representation of the quantum Wigner function in the phase space has been developed for canonical ensemble. Explicit analytical expression of the Wigner function has been obtained in harmonic approximation. New quantum Monte‐Carlo method for ab initio calculations of the average values of quantum operators, Wigner function, momentum and position distributions and wave functions of the ground state has been developed and tested. Obtained results are in a very good agreement with available analytical results and results of usual path‐integral Monte‐Carlo method. The developed approach allows simulation of thermodynamic and kinetic properties of quantum systems and calculation average values of quantum operators, when the usual path integral Monte Carlo methods in configurational space failed. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Damien Querlioz, Jérôme Saint-Martin, Arnaud Bournel +1 more

This paper examines the phonon-induced electron decoherence in semiconductor nanostructures and nanodevices within the Wigner transport equation, solved using a particle Monte Carlo technique. The Wigner-Boltzmann formalism is first established as a relevant and original approach to modeling electron quantum decoherence in semiconductors. The simulation of the time evolution of a free wave-packet then allows analyzing the competition between decoherence and wave-packet expansion in a semiconductor. It is additionally argued that decoherence occurs faster than in the widely studied case of quantum Brownian motion. The simulation of a wave packet interacting with a tunnel barrier allows studying the electron localization induced by decoherence. The case of a wave packet interacting with a double barrier puts forward the mechanism of decoherence-induced transition from resonant to sequential transport through a bound state. Finally the simulation of resonant tunneling devices shows how these phenomena take place in nanodevices and highlights the transition from the quantum transport regime to the semiclassical transport regime induced by phonon scattering.