Statistics and Nosé formalism for Ehrenfest dynamics
Alonso, J. L.
MetadataShow full item record
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.
Is part ofJournal of Physics A: Mathematical and Theoretical, 2011, vol. 44:395004
Showing items related by title, author, creator and subject.
Alonso, J. L.; Clemente-Gallardo, Jesús; Cuchí Oterino, J. C.; Echenique, Pablo; Falceto, Fernando (American Institute of Physics, 2012)We discuss the evolution of purity in mixed quantum/classical approaches to electronic nonadiabatic dynamics in the context of the Ehrenfest model. As it is impossible to exactly determine initial conditions for a realistic ...
Alonso, J. L.; Castro, Alberto; Clemente-Gallardo, Jesús; Cuchí Oterino, J. C.; Echenique, Pablo; Esteve, J. G.; Falceto, Fernando (American Physical Society, 2015)Schrödinger suggested that thermodynamical functions cannot be based on the gratuitous allegation that quantum-mechanical levels (typically the orthogonal eigenstates of the Hamiltonian operator) are the only allowed states ...
Nogareda, Carmina; López Gatius, Fernando; Santolaria Blasco, Pilar; García Ispierto, Irina; Bech Sàbat, Gregori; Pabón, M.; Mezo, M.; Gonzalez-Warleta, M.; Castro Hermida, J. A.; Yániz Pérez de Albéniz, Jesús; Almería, S. (Elsevier, 2007)The dynamics of antibody production against Neospora caninum during the gestation period was examined in chronically infected dairy cows. Data were obtained from 86 pregnant parous dairy cows, 21 of which had suffered ...