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The European Physical Journal B

Quantum spherical model in a random field: coherent state path integral approach

Yu‐qiang Ma, W. Figueiredo

Published Jan 1, 1998• 0 citations
Publisher
DOI
10.1007/s100510050157

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A coherent state path integral is considered for bosons with an ensemble average of a random potential and with an additional, repulsive interaction in the context of BEC under inclusion of specially prepared disorder. The essential normalization of the coherent state path integral, as a generating function of observables, is obtained from the non-equilibrium time contour for 'forward' and 'backward' propagation so that a time contour metric has to be taken into account in the ensemble average with the random potential. Therefore, the respective symmetries for the derivation of a nonlinear sigma model follow from the involved time contour metric which leads to a coset decomposition Sp(4)/U(2) x U(2) of the symplectic group Sp(4) with the subgroup U(2) for the unitary invariance of the density-related vacuum or ground state; the corresponding spontaneous symmetry breaking gives rise to anomalous- or 'Nambu'-doubled field degrees of freedom within self-energy matrices which are finally regarded by remaining coset matrices. The notion of a 'return probability', according to the original 'Anderson-localization', is thus naturally contained within coherent state path integrals of a non-equilibrium contour time for equivalent 'forward' and 'backward' propagation.
The spin depolarization of a quantum particle in random magnetic field is treated in terms of a path integral in the spin states as well as the translational motion. The path integral of the spin operator, represented in terms of Fermion operators, is performed in the Fermion coherent state representation. An expression for the spin depolarization is obtained for an arbitrary magnetic field distribution. A particular case, in which the magnetic field is oriented in the z -direction and the magnitude is Gaussianly distributed, is considered and the spin decays exponentially in time.