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Abstract:

The relationship between the mean-field approximations in various interacting models of statistical physics and measures of classical and quantum correlations is explored. We present a method that allows us to find an upper bound for the total amount of correlations (and hence entanglement) in a physical system in thermal equilibrium at some temperature in terms of its free energy and internal energy. This method is first illustrated by using two qubits interacting through the Heisenberg coupling, where entanglement and correlations can be computed exactly. It is then applied to the one-dimensional (1D) Ising model in a transverse magnetic field, for which entanglement and correlations cannot be obtained by exact methods. We analyse the behaviour of correlations in various regimes and identify critical regions, comparing them with already known results. Finally, we present a general discussion of the effects of entanglement on the macroscopic, thermodynamical features of solid-state systems. In particular, we exploit the fact that a d-dimensional quantum system in thermal equilibrium can be made to correspond to a (d + 1)-dimensional classical system in equilibrium to substitute all entanglement for classical correlations.

Abstract:

We calculate the geometric phase of a spin-1/2 system driven by one and two mode quantum fields subject to decoherence. Using the quantum jump approach, we show that the corrections to the phase in the no-jump trajectory are different when considering adiabatic and nonadiabatic evolutions. We discuss the implications of our results from both fundamental as well as quantum computational perspectives.

Abstract:

A method to simulate the dynamics of anyons through the Jaynes-Cummings model is presented. The simulation of anyons with m/2, m/3, m/4 statistics and transmution of statistics of the system from Fermi to Bose, through the anyonics statistics was also shown. The entanglement of the system eigenstates which provides a two-dimensional confinement in the effective evolution of the system plays an important role. It is also shown that it is possible to transmute the statistics of the system continuall7 from ferminons to bosons for particular parameters.