Dissipative quantum systems modeled by a two-level-reservoir coupling

Abstract

The coupling between a quantum dynamical system and a two-level system reservoir is analysed within the framework of the Feynman-Vernon theory.We stress the differences between this new reservoir and the well-known bath of oscillators and show that, in order to obtain the Langevin equation for the system of interest in the high temperature regime, we have to choose a spectral distribution function J(ω) which is finite for ω = 0.

Dissipative quantum dynamics with the surrogate Hamiltonian approach. A comparison between spin and harmonic baths

“…To overcome such difficulties in the dynamics of molecules that are in intimate interaction with an environment, an alternative approach termed the Surrogate Hamiltonian [4] has been developed. The Surrogate Hamiltonian method employs a bath composed of two-level systems that acts as a spin bath [5,6,7,8,9].…”

“…In the limit of weak system-bath coupling, it has been shown that the two baths are equivalent. For finite temperature the equivalence requires a rescaling of the spectral density function which determines the coupling of the primary system to the different bath modes [5,6,7]. The limiting coupling strength where the dynamics induced by the two baths differ has not yet been characterized.…”

Effects of a nonlinear bath at low temperatures

“…24. For higher coupling g we expect deviations to the nonlinear bath even in the thermodynamic limit N → ∞ due to, e.g., the non-separable structure 25 of our nonlinear bath model.…”

“…Higher-order correlation functions are important to understand the behavior of a nonlinear bath. For small enough system-bath coupling strength, the nonlinear bath is identical to a linear one 24 . In this limit, the two-time bath correlation function plays a crucial role.…”

QUANTUM ENVIRONMENTS: SPINS BATHS, OSCILLATOR BATHS, and applications to QUANTUM MAGNETISM

“…The second environment is the "spin bath" model, which has been developed recently by myself and Prokof'ev [14,15,16,17,18] (see also refs. [19,21,20,22]), stimulated particularly by problems in quantum nanomagnetism (although it can be applied outside this domain [21,22,23,24]; to illustrate this, brief space is given to superconducting SQUIDs and spin chains). It describes environmental modes like paramagnetic or nuclear spins, or other similar cases in which each environmental mode has only a few (often only two) levels of interest, and where they are very weakly coupled.…”