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Recent Progress in Many-Body Theories

EVOLUTION OF FERMIONIC SYSTEMS AS AN EXPECTATION OVER POISSON PROCESSES

Matteo Beccaria A, Carlo Presilla A, Gian Fabrizio De Angelis, Giovanni Jona-Lasinio

Published Sep 1, 2000• 0 citations
Publisher
DOI
10.1142/9789812792754_0053

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We derive an exact probabilistic representation for the evolution of a Hubbard model with site- and spin-dependent hopping coefficients and site-dependent interactions in terms of an associated stochastic dynamics of a collection of Poisson processes. In a recent paper 1 we provided an exact probabilistic expression for the real time or the imaginary time evolution of a Fermi system, in particular a Hubbard model, in terms of an associated stochastic dynamics of a collection of Poisson processes. Here, we generalize the result 1 to the case of a Hubbard model with site- and spin-dependent hopping coefficients and site-dependent interactions. This situation is of interest if disorder is present 2. Let us consider the Hubbard Hamiltonian
The time that a given initial quantum state requires to evolve to an orthogonal state is used to explore the role played by entanglement in the dynamical evolution of composite fermionic systems. We study two different applications of free spin fermions in a four site cluster. It is shown that through selection of the hopping matrix elements, the relationship between entanglement and speed of quantum evolution can be controlled. Consequently, the result recently pointed out [J. Batle et al., Phys. Rev. A72 (2005) 032337] represents only a particular choice of the energy spectrum of the system.