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Pseudo-fermion formalism applied to nonequilibrium Kondo-type problems

Omar Morandi, Paul-Antoine Hervieux, Giovanni Manfredi

Published Jan 1, 2010• 2 citations
Publisher

Abstract

A straightforward limit procedure is developed for evaluating the expectation value of a generic many-particle operator defined in the Abrikosov-Coleman’s pseudo-fermion formalism. It can be useful for the study of nonequilibrium \nKondo-type problems.
DOI
10.1393/ncc/i2010-10577-1

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We present a new non-perturbative method to deal with the time-dependent quantum many-body problem, which is an extension of Wegner's flow equations to time-dependent Hamiltonians. The formalism provides a scaling procedure for the set of time-dependent interaction constants. We apply these ideas to a Kondo model with a ferromagnetic exchange coupling switched on over a time scale τ. We show that the asymptotic expectation value of the impurity spin interpolates continuously between its quenched and adiabatic value.
Cluster development may furnish a powerful device for the calculation of the expectation values of the observables of a many-fermion system with respect to dynamically correlated state vectors. The generalized normalization integral, a generating function for the required expectation values, is defined, and four of the many possible decompositions of this function into cluster integrals are explored. Two of these decompositions are slight extensions of the conventional ones of Iwamoto and Yamada and Aviles, Hartogh, and Tolhoek. The other two are product decompositions, leading to new ``factor-cluster'' formalisms. A factor-cluster expansion is applied to the evaluation of the n-particle spatial distribution function.
The problem of measuring the charge contained in a finite volume for the theory of free fermions is discussed. The expectation values of Q/sub V/ (an operator for total charge contained in a volume V) are calculated for localized one-particle solutions of the Dirac equation in both 2 and 4 dimensional space time. This measurement procedure is well-defined and leads to physically reasonable results. Two-particle states are considered to determine whether or not the measurement of the charge of one of the particles can be carried out. This measurement procedure is found to be well-defined and leads to physically reasonable results. (GHT)