Stochastic solution to quantum dynamics

Details Stochastic solution to quantum dynamics Stochastic solution to quantum dynamics

Feb 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994stin...9426550j&link_type=abstract

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Physics

Liouville Equations, Monte Carlo Method, Quantum Mechanics, Stochastic Processes, Algorithms, Momentum, Transport Theory

Scientific paper

The quantum Liouville equation in the Wigner representation is solved numerically by using Monte Carlo methods. For incremental time steps, the propagation is implemented as a classical evolution in phase space modified by a quantum correction. The correction, which is a momentum jump function, is simulated in the quasi-classical approximation via a stochastic process. The technique, which is developed and validated in two- and three- dimensional momentum space, extends an earlier one-dimensional work. Also, by developing a new algorithm, the application to bound state motion in an anharmonic quartic potential shows better agreement with exact solutions in two-dimensional phase space.

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