Dynamics of indistinguishable free particles driven by a quantum bath

The time evolution of correlations for two indistinguishable free particles, in a one-dimensional lattice interacting with a quantum bath, is studied in the Born-Markov approximation. The analytical solution for the density matrix is obtained, for bosons and fermions, in the second quantization formalism. The time evolution of the negativity of indistinguishable particles is analyzed for quantum mixed states. Quantum correlations heavily depend on the selected bipartition; in return, a small difference between the statistics of the particles is noted, due to the Pauli exclusion principle. In the presence of dissipation, the negativity (a nonclassical correlation) shows a time-oscillatory behavior for a particular geometrical bipartition. The total probability of finding one particle in each subsystem is also calculated and shows consistent behavior.

Figure 1

Quantum correlation for two bosons (negativity) as a function of the dimensionless time $t^{\prime }$ for several values of the dissipative parameter $r_D=0,0.25,0.5,1.0,2.0$. The inset shows the bipartition used in (20).

Figure 2

Quantum correlation for two fermions (negativity) as function of dimensionless time $t^{\prime }$ and the same values of $r_D$ and bipartition as in Fig. 1. It decreases with increasing $t^{\prime }$ or $r_D$.

Figure 3

Negativity for two bosons as a function of the dimensionless time $t^{\prime }$ for the same values of the dissipative parameter $r_D$ as in Fig. 1. The studied bipartition is represented in the inset.

Figure 4

Negativity of indistinguishable particles (two fermions) as function of dimensionless time $t^{\prime }$ and the same values of $r_D$ and bipartition as in Fig. 3.

Figure 5

(a) Probability of finding one particle $P_{1,1}$ in $A$ and $B$ as a function of dimensionless time $t^{\prime }$ and several values of $r_D$. (b) Probability of finding two particles in $A$. (c) Probability of finding two particles in $B$. The bipartition is at left and right sites with respect to the origin of the lattice.

Figure 6

Probability (a) $P_{1,1}$, (b) $P_{2,0}$, and (c) $P_{0,2}$ as a function of dimensionless time $t^{\prime }$ and $r_D=0,0.25,0.5,1.0,2.0$ for the mirror-alternative bipartition (see the inset in Fig. 3).