Environmental dynamics, correlations, and the emergence of noncanonical equilibrium states in open quantum systems

Abstract

Quantum systems are invariably open, evolving under surrounding influences rather than in isolation. Standard open quantum system methods eliminate all information on the environmental state to yield a tractable description of the system dynamics. By incorporating a collective coordinate of the environment into the system Hamiltonian, we circumvent this limitation. Our theory provides straightforward access to important environmental properties that would otherwise be obscured, allowing us to quantify the evolving system-environment correlations. As a direct result, we show that the generation of robust system-environment correlations that persist into equilibrium (heralded also by the emergence of non-Gaussian environmental states) renders the canonical system steady-state almost always incorrect. The resulting equilibrium states deviate markedly from those predicted by standard perturbative techniques and are instead fully characterised by thermal states of the mapped system-collective coordinate Hamiltonian. We outline how noncanonical system states could be investigated experimentally to study deviations from canonical thermodynamics, with direct relevance to molecular and solid-state nanosystems.

Energy transfer in structured and unstructured environments: Master equations beyond the Born-Markov approximations

“…18, which we shall summarise here for completeness. To move beyond the weakcoupling limit appropriate to Born-Markov (e.g., Redfield) master equations, we apply a normal mode transformation to Eq.…”

“…Strong coupling between the system and its environment leads to the accumulation of significant system-environment correlations that may be present even a) Electronic mail: Jakeilessmith@gmail.com b) Electronic mail: ahsan.nazir@manchester.ac.uk within the steady-state. [16][17][18][19] In addition to the (often low frequency) continuum, the environmental spectral densities of pigment-protein complexes are generally structured; that is, there are specific underdamped vibrational modes of the environment that couple strongly to the excitonic degrees of freedom. There is now increasing evidence to suggest that these underdamped modes are an important contributing factor to the long-lived coherences observed in photosynthetic systems, [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] as well as links between the quantum mechanical nature of these vibrational modes and enhanced transfer rates.…”

“…Apart from its conceptual simplicity, the reaction coordinate master equation (RCME) is attractive due to the additional insight that it provides beyond the system, into both the environmental dynamics and the generation of systemenvironment correlations. 18 In this work, we shall employ the RCME to investigate EET in a molecular dimer system beyond weak systemenvironment coupling. We shall show that over the broad regimes considered, the RC model captures all important system-environment correlations for EET in the presence of both underdamped and overdamped environments, agreeing perfectly with numerically exact data generated using the HEOM.…”

“…1) was introduced to describe the dynamical behaviour of a system coupled to an environment with strong low-frequency components, leading to long environmental correlation times. 18 Here, a collective coordinate of the bath [67][68][69][70][71][72][73][74][75][76] is incorporated into an enlarged effective system Hamiltonian. This allows for the derivation of a second-order master equation for the dynamics of the reduced system and RC, accurately describing the system dynamics even in the presence of strong system-environment correlations and extended environmental memory.…”

Analysis of the non-Markovianity for electron transfer reactions in an oligothiophene-fullerene heterojunction

“…The mixture is nearly composed of a single state so one observes an increase of purity towards nearly 1. In the third case R = 3.5 Å, the final value different from one can be taken as a sign of the strong correlation between the system and the bath resulting in a noncanonical distribution in the system [67]. Fig.…”