Recovery of Purity in Dissipative Tunneling Dynamics

Abstract

The time evolution of purity for an initially localized state of a symmetric two-level system coupled to a dissipative bath is investigated using numerically exact real-time path integral methods. With strong system-bath coupling and high temperature, the purity decays monotonically to its fully mixed value, with a short-time Gaussian behavior, which is subsequently followed by exponential evolution. However, under low-temperature and weak coupling conditions, a substantial recovery of purity is observed. A simple theoretical analysis reveals three contributions that correspond to a completely incoherent, eigenstate population difference and rate terms. The last two of these terms can counter the early drop of purity and are responsible for its rebound. These findings caution against using purity as a measure of decoherence in the dynamics of quantum dissipative systems.

Relaxation of antiferromagnetic order and growth of Rényi entropy in a generalized Heisenberg star

“…In addition, P (t) experiences nearly perfect periodic recoveries for large enough J ′ /J. These behaviors seem qualitatively consistent with those for a bosonic bath [38].…”

“…It is known that for J ′ /J > −1 the ground state of H B is nondegenerate and possesses magnetization l z = 0; while for J ′ /J < −1 the bath is ferromagnetic and has two degenerate ground states, i.e., the two fully polarized states | ↑ • • • ↑ and | ↓ • • • ↓ [37]. Below we focus on the case of J ′ /J > 0, so that the initial bath state Recently, the purity dynamics of a qubit coupled to a bosonic bath has been studied and the long-time recovery of purity under low-temperature and weak system-bath coupling conditions is observed [38]. It is therefore interesting to study the purity dynamics of a central spin coupled to an interacting spin bath at zero temperature.…”

Quantum State-to-State Rates for Multistate Processes from Coherences

“…Since exp­(− k 1 t p – k –1 t p ) ≃ 1, the nonequilibrium flux quickly grows from zero to the value given by the right-hand side of eq at the onset t p of the plateau regime, after which it decays exponentially over a time that is very long compared to t p . Assuming, as usual, that the exponential factor is very close to unity at this time, we recover the result …”

“…Equation is completely general and exact, regardless of the form of the bath Hamiltonian, as long as the system-bath coupling is diagonal in the system basis. It generalizes the expression obtained earlier for a symmetric two-level system (TLS) and shows that, in the absence of imaginary components in the coherences, populations remain stationary. This is always the situation at long times, when the process has reached equilibrium and the RDM elements are given by Boltzmann matrix elements, which are purely real-valued.…”

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

“…More recently, decoherence in momentum space has been studied in the context of suppression of quantum-mechanical reflection [20] using a master equation resembling the CL equation [10,17] in the negligible dissipation limit; and for a non-relativistic charged particle described by a wave packet under the presence of linear interaction with the electromagnetic field in equilibrium at a certain temperature [21]. Recently, in the chemical physics community, studies about purity are also found questioning this quantity as a measure of decoherence in the dynamics of quantum dissipative systms [22][23][24].…”