Quantum statistical approach to extended mean-field theory

G. A. Raggio, Reinhard F. Werner

R. Rossignoli, Angel Ricardo Plastino

An extended mean-field approximation for statistical operators is derived within the context of information theory. The ensuing scheme is applied to (many) boson mean-field approaches within a completely general statistical framework. Numerical examples are given within the context of the finite-temperature anharmonic oscillator problem. Fluctuations are also discussed.

Best, Christoph, Schaefer, Andreas

We investigate the description of statistical field theories using Daubechies' orthonormal compact wavelets on a lattice. A simple variational approach is used to extend mean field theory and make predictions for the fluctuation strengths of wavelet coefficients and thus for the correlation function. The results are compared to Monte Carlo simulations. We find that wavelets provide a reasonable description of critical phenomena with only a small number of variational parameters. This lets us hope for an implementation of the renormalization group in wavelet space.

Andreas Wipf

M. D. Johnson, Claudius Gros, S. M. Girvin +1 more

Giorgio Parisi A

I present here some results on the mean field theory approach to the statistical mechanics of a D-dimensional array of Josephson junctions in the presence of a magnetic field. The mean field theory equations are obtained by computing the thermodynamical properties. In the high temperature region in the limit D→∞, where the problem is simplified, this limit defines the mean field approximation. Close to the transition point the system behaves very similar to a particular form of spin glasses, i.e., to gauge glasses. We have noticed that in this limit the evaluation of the coefficients of the high temperature expansion may be mapped onto the computation of some matrix elements for the q-deformed harmonic oscillator. The same arguments can be used to predict the thermodynamical properties in the mean field limit. These results can be extended to the low temperature phase using a conjecture on the equivalence of some system without disorder with appropriate random systems.