Momentum-space decoherence of distinguishable and identical particles in the Caldeira-Leggett formalism

Abstract

In this work, momentum-space decoherence using minimum and nonminimum-uncertainty-product (stretched) Gaussian wave packets in the framework of Caldeira-Leggett formalism and under the presence of a linear potential is studied. As a dimensionless measure of decoherence, purity, a quantity appearing in the definition of the {\it linear entropy}, is studied taking into account the role of the stretching parameter. Special emphasis is on the open dynamics of the well-known cat states and bosons and fermions compared to distinguishable particles. For the cat state, while the stretching parameter speeds up the decoherence, the external linear potential strength does not affect the decoherence time; only the interference pattern is shifted. Furthermore, the interference pattern is not observed for minimum-uncertainty-product-Gaussian wave packets in the momentum space. Concerning bosons and fermions, the question we have addressed is how the symmetry of the wave functions of indistinguishable particles is manifested in the decoherence process, which is understood here as the loss of being indistinguishable due to the gradual emergence of classical statistics with time. We have observed that the initial bunching and anti-bunching character of bosons and fermions, respectively, in the momentum space are not preserved as a function of the environmental parameters, temperature and damping constant. However, fermionic distributions are slightly broader than the distinguishable ones and these similar to the bosonic distributions. This general behavior could be interpreted as a residual reminder of the symmetry of the wave functions in the momentum space for this open dynamics.