Partition-free approach to open quantum systems in harmonic environments: An exact stochastic Liouville equation

Abstract

We present a partition-free approach to the evolution of density matrices for open quantum systems coupled to a harmonic environment. The influence functional for-

Exactly thermalized quantum dynamics of the spin-boson model coupled to a dissipative environment

“…This began with the development of the Feynman-Vernon influence functional formalism where the response of a linear bath is expressed as a path integral over an infinite number of displaced harmonic oscillators [3]. Several techniques have since been developed, including hierarchical equations of motion [4,5], stochastic Liouville-von Neumann equations [6][7][8][9][10], stochastic Schrödinger equations [11], and quasiadiabatic path integrals [12]. Importantly, none of these methods make the Markov assumption, where environment correlation times are taken to be negligibly short compared to the characteristic timescales of the system of interest.…”

“…This is fundamentally unphysical, especially for driven systems where a partitioned state is certainly not a good approximation of the correct initial thermal state and leads to incorrect transient dynamics with the possibility of the wrong asymptotic behavior. This is not the case for the recently proposed extended stochastic Liouville-von Neumann equation (ESLN) method [10], which builds on the earlier work of Graber, Schramm, and Ingold [13] and allows one to derive the equations of motion for the reduced density matrix of an open quantum system without assuming a partitioned initial state. The theory considers a formally exact solution of the Liouville equation for the density matrix of the combined system, consisting of the open system and a harmonic (bosonic) environment (bath).…”

Semi-classical generalized Langevin equation for equilibrium and nonequilibrium molecular dynamics simulation

“…Classical GLEs derived from Newtonian equation of motion can also be extended to the quantum mechanical regime, using the Heisenberg equation of motion [57], the influence functional approach of Feynman & Vernon [58], and the density matrix method [59,60]. Caldeira and Leggett successfully used the influence functional approach to study quantum tunneling in macroscopic systems and dynamics of quantum Brownian motion [61,62].…”

Driving spin-boson models from equilibrium using exact quantum dynamics

“…As was demonstrated in our previous work [47], instead of the aforementioned partitioned approximation, the initial state of the system may be described by a preparation of the canonical density matrix for the extended system [10]:…”

“…With some elementary manipulations, it is possible to derive an exact evolution of the reduced density matrix ρ(t) describing the open system. The set of equations governing this evolution constitutes the ESLE (for full details see [47]). The ESLE consists of two stochastic operator evolutions, which, upon averaging over realisations of the Gaussian stochastic noises it contains (see below), give the exact open system (i.e.…”