Abstract
Nanoscale devices - either biological or artificial - operate in a regime where the usual assumptions of a structureless, Markovian, bath do not hold. Being able to predict and study the dynamics of such systems is crucial and is usually done by tracing out the bath degrees of freedom, which implies losing information about the environment. To go beyond these approaches we use a numerically exact method relying on a Matrix Product State representation of the quantum state of a system and its environment to keep track of the bath explicitly. This method is applied to a specific example of interaction that depends on the spatial structure of the system. The result is that we predict a non-Markovian dynamics where long-range couplings induce correlations into the environment. The environment dynamics can be naturally extracted from our method and shine a light on long time feedback effects that are responsible for the observed non-Markovian recurrences in the eigen-populations of the system.
Highlights
Real-life quantum systems are never truly isolated from the rest of the universe and are typically exposed to a macroscopic number of fluctuating degrees of freedom that constitute their often unobservable environments [1,2]
The pigment-protein complexes (PPCs) that perform the electron transfers at the core of photosynthesis are composed of photoactive pigments in interaction with a highly structured environment made of a protein scaffold that tunes the electronic and vibrational properties of the molecular network
As in most models of open systems, the environment is noninteracting, this allows the tensor network approach to be a computationally powerful method for exploring multisite dynamics where nonMarkovian environmental feedback could lead to functionally relevant nonequilibrium states and/or transient effects that could materially alter the outcome of a process, if a certain set of events precedes it
Summary
Real-life quantum systems are never truly isolated from the rest of the universe and are typically exposed to a macroscopic number of fluctuating degrees of freedom that constitute their often unobservable (and invariably uncontrollable) environments [1,2]. The evolution of the system’s density matrix can be described, for example, by an approximate weak-coupling master equation [1] or exactly using a process tensor [17] or a tensor network representation of the influence functional as in the time-evolving matrix product operator (TEMPO) method [18,19]. The multilayer multiconfiguration time-dependent Hartree method [23] relies on a description of the environmental degrees of freedom with so-called time-dependent single-particle functions Both the reduced density matrix and wave-function approaches have gained numerical efficiency by using tensor network Ansätze as their fundamental objects and exploiting efficient contractions and compression techniques. III we demonstrate regimes of the model where long-time and even periodic communication between the sites is mediated by the environment
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