Unitary Approaches to Dissipative Quantum Dynamics

Abstract

We describe in detail a general system-bath strategy for investigating the quantum behavior of small systems interacting with complex environments. In this approach, a simplified heat bath is used as a surrogate for realistic environments, and explicit, unitary quantum simulations of the "universe" (the system plus the bath) are performed by means of high-dimensional wave-packet techniques. In this chapter, we describe the underlying Hamiltonians and the related reduced dynamical descriptions, show how to recast real-world problems into this form, introduce some of the methods currently used to deal with high-dimensional quantum dynamics, and present the results of this strategy when applied to numerous problems of physicochemical interest.

Sticking of atomic hydrogen on graphene

“…In our work (Bonfanti et al 2015a) the starting point was the equilibrium autocorrelation function for the hydrogen displacement (or velocity) during its oscillatory motion in the chemisorbed state, since such information is in principle experimentally available through several vibrational spectroscopies. Furthermore, such choice does not require any a priori knowledge of the system potential (Bonfanti et al 2015a, 2015c, Bonfanti and Martinazzo 2016b, Gottwald et al 2016, hence suits well to an ab initio molecular dynamics (AIMD) approach. The resulting model, though derived from an equilibrium situation, proved to be robust enough to accurately describe the non-equilibrium sticking dynamics up to collision energies well above the height of the barrier (Bonfanti et al 2015b).…”

Smolyak Algorithm Adapted to a System–Bath Separation: Application to an Encapsulated Molecule with Large-Amplitude Motions

“…The study of quantum systems coupled to a complex host, for instance, the guest–host complexes, − has attracted strong interest in recent years, − spanning the fields of fundamental quantum physics, physical chemistry, quantum optics, etc. Some of these problems go beyond a structureless environment description, leading to the emergence of more accurate non-Markovian quantum models based on a system–bath approach. − Given the well-known exponential scaling of the problem, the bath is usually described using effective approaches, e.g., a collection of harmonic oscillators, with a reconstructed effective system–bath coupling, e.g., the spectral density formulation. ,− These approaches are limited, to some extent, to specifically tailored systems. Meanwhile, a variety of multiconfigurational quantum dynamics methods have been proposed, for example, the well-known multiconfiguration time-dependent Hartree (MCTDH) method, , the variational multiconfigurational Gaussian (vMCG) method, and their extended versions. , These methods have been shown to be highly efficient, although MCTDH normally requires a sum-of-product expression for the potentials to cover specific problems.…”

A Smolyak algorithm adapted to a system-bath separation: application to an encapsulated molecule with large amplitude motions

“…a collection of harmonic oscillators, with a reconstructed effective system-bath coupling, e.g. the spectral density formulation [5,7,8]. These approaches are limited, to some extent, to specifically tailored systems.…”