Ehrenfest dynamics is purity non-preserving: a necessary ingredient for decoherence
Alonso, J. L.
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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 system, we choose to work in the statistical Ehrenfest formalism that we introduced in Alonso et al. [J. Phys. A: Math. Theor. 44, 396004 (2011)10.1088/1751-8113/44/39/395004]. From it, we develop a new framework to determine exactly the change in the purity of the quantum subsystem along with the evolution of a statistical Ehrenfest system. In a simple case, we verify how and to which extent Ehrenfest statistical dynamics makes a system with more than one classical trajectory, and an initial quantum pure state become a quantum mixed one. We prove this numerically showing how the evolution of purity depends on time, on the dimension of the quantum state space D, and on the number of classical trajectories N of the initial distribution. The results in this work open new perspectives for studying decoherence with Ehrenfest dynamics.
Is part ofJournal of Chemical Physics, 2012, vol. 137, núm. 5, p. 054106-1/13
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Alonso, J. L.; Castro, Alberto; Clemente-Gallardo, Jesús; Cuchí Oterino, J. C.; Echenique, Pablo; Falceto, Fernando (IOP Publishing, 2011)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 ...
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 ...
Alonso, J. L.; Bruscolini, P.; Castro, Alberto; Clemente-Gallardo, Jesús; Cuchí Oterino, J. C.; Jover-Galtier, J. A. (American Chemical Society, 2018-06-26)In previous works, we introduced a geometric route to define our Ehrenfest statistical dynamics (ESD) and we proved that, for a simple toy model, the resulting ESD does not preserve purity. We now take a step further: we ...