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arXiv:cond-mat/9712067 · Journal of Physics A Mathematical and General

Effective potential, Mori product and quantum dynamics

Alessandro Cuccoli, R Giachetti, V Tognetti, Ruggero Vaia

Published Jun 5, 1998• 4 citations
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Abstract

We present a method that permits the calculation of the dynamical correlation functions for quantum systems. These are obtained by evaluating the generating functionals of the static moments of the relaxation functions in a self-consistent approximation that can be obtained by an appropriate extension of the effective potential theory.
DOI
10.1088/0305-4470/31/22/003

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A method for calculating quantum averages and static correlation functions of configurational observables is introduced, by extending a variational method, which permits the reduction of the problem to the computation of classical-like averages. This approach opens the possibility of obtaining novel results in many fields, and strongly shortens the computer time needed for numerical calculations. As an example, the well-known sine-Gordon model is considered, and its relevant quantum correlation functions are calculated on the whole temperature range.
The spin dynamics of two dimensional XY ferromagnet are reexamined at low temperatures in the framework of the Mori continued fraction formalism using the Gaussian approximation. In this formalism, the terms on denominators for the Laplace transform of the relaxation function R(t) are related to the frequency moments of the relaxation shape function R(q,w). In the Gaussian approximation scheme, we truncate the continued fraction for R(t) on the second stage. Adopting this approximation, we calculated up to the sixth moment. The moments are writing in terms the static spin correlation functions. In the estimation of the fourth and sixth moment at finite temperature, the four and six-spin correlation functions may be approximated by a sum of products of appropriate pair correlation functions(mode-mode decoupling). In this work we calculated the static spin correlation functions for the expressions to the fourth and sixth moments, needed in the study of the dynamics.
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Superfluidity properties of heated finite Fermi systems are studied in the static fluctuation approximation, which is an original method. This method relies on a single and controlled approximation, which permits taking correctly into account quasiparticle correlations and thereby going beyond the independent-quasiparticle model. A closed self-consistent set of equations for calculating correlation functions at finite temperature is obtained for a finite Fermi system described by the Bardeen–Cooper–Schrieffer Hamiltonian. An equation for the energy gap is found with allowance for fluctuation effects. It is shown that the phase transition to the supefluid state is smeared upon the inclusion of fluctuations.