Statistics and Nosé formalism for Ehrenfest dynamics

Alonso, J. L.; Castro, Alberto; Clemente-Gallardo, Jesús; Cuchí Oterino, J. C.; Echenique, Pablo; Falceto, Fernando

doi:https://doi.org/10.1088/1751-8113/44/39/395004

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Issue date

2011

Author

Alonso, J. L.

Castro, Alberto

Clemente-Gallardo, Jesús

Cuchí Oterino, J. C.

Echenique, Pablo

Falceto, Fernando

Suggested citation

Alonso, J. L.; Castro, Alberto; Clemente-Gallardo, Jesús; Cuchí Oterino, J. C.; Echenique, Pablo; Falceto, Fernando; . (2011) . Statistics and Nosé formalism for Ehrenfest dynamics. Journal of Physics A: Mathematical and Theoretical, 2011, vol. 44:395004. https://doi.org/10.1088/1751-8113/44/39/395004.

Abstract

Quantum dynamics (e.g., the Schrödinger equation) and classical dynamics (e.g., Hamilton equations) can both be formulated in equal geometric terms: a Poisson bracket defined on a manifold. The difference between both worlds is due to the presence of extra structure in the quantum case, that leads to

the appearance of the probabilistic nature of the measurements and the indetermination and superposition principles. In this paper we first show that the quantum-classical dynamics prescribed by the Ehrenfest equations can also be formulated within this general framework, what has been used in the literature to construct propagation schemes for Ehrenfest dynamics. Then, the existence of a well defined Poisson bracket allows to arrive to a Liouville equation for a statistical ensemble of Ehrenfest systems. The study of a generic toy model shows that the evolution produced by Ehrenfest dynamics is ergodic and therefore the only constants of motion are functions of the Hamiltonian. The emergence of the canonical ensemble characterized by the Boltzmann's distribution follows after an appropriate application of the principle of equal a priori probabilities to this case. This work provides the basis for extending stochastic methods to Ehrenfest dynamics.

URI

http://hdl.handle.net/10459.1/57789

DOI

https://doi.org/10.1088/1751-8113/44/39/395004

Is part of

Journal of Physics A: Mathematical and Theoretical, 2011, vol. 44:395004