Quantum biology, as introduced in the previous chapter, mainly studies the dynamical influence of quantum effects in biological systems. In processes such as exciton transport in photosynthetic complexes, radical pair spin dynamics in magnetoreception, and photo-induced retinal isomerization in the rhodopsin protein, a quantum description is a necessity rather than an option. The quantum modelling of biological processes is not limited to solving the Schrödinger equation for an isolated molecular structure. Natural systems are open to the exchange of particles, energy or information with their surrounding environments that often have complex structures. Therefore the theory of open quantum systems plays a key role in dynamical modelling of quantum-biological systems. Research in quantum biology and open quantum system theory have found a bilateral relationship. Quantum biology employs open quantum system methods to a great extent while serving as a new paradigm for development of advanced formalisms for non-equilibrium biological processes.

In this chapter, we overview the basic concepts of quantum mechanics and approaches to open quantum system (or decoherence) dynamics. Here, we do not intend to discuss all aspects of about a century-old theory of open quantum systems that dates back to the original work of Paul Dirac on atomic radiative emission and absorption (Dirac, 1927). Instead, we mainly focus on the integro-differential equations that are commonly used for modelling quantum-biological systems. Interested readers can learn more about open quantum systems in various books and review articles in both physics and chemistry literature, including the references (Kraus, 1983; Breuer and Petruccione, 2002; Kubo et al., 2003; Weiss, 2008; May and Kühn, 2011).

Recent progress in science and technology has led to the revival of an old question concerning the relevance of quantum effects in biological systems. Indeed Pascual Jordan's 1943 book, Die Physik und das Geheimnis des Lebens had already posed the question “Sind die Gesetze der Atomphysik und Quantenphysik für die Lebensvorgänge von wesentlicher Bedeutung?” (Are the laws of atomic and quantum physics of essential importance for life?) and coined the term Quanten-Biologie (quantum biology). At the time this question was essentially of a theoretical nature as the technology did not yet exist to pursue it in experiment.

Indeed quantum biology has been benefiting considerably from the refinement in experimental tools which is beginning to provide direct access to the observation of quantum dynamics in biological systems. Indeed, we are increasingly gaining sensitivity towards quantum phenomena at short lengths and timescales. In recent years, these newly found technological capabilities have helped to elevate the study of quantum biology from a mainly theoretical endeavour to a field in which theoretical questions, concepts and hypotheses may be tested experimentally and thus verified or disproved. We should stress here that experiments are essential to verify theoretical models because biological systems already have a complexity and structural variety that prevents us from knowing and controlling all of the aspects. Results obtained using these refined experimental techniques lead to new theoretical challenges and thus stimulate the development of novel theoretical approaches. It is this mutually beneficial interplay between experiment and theory that promises accelerated developments within the field.

Transport phenomena at the nanoscale exhibit both quantum (coherent) and classical (noisy) behaviour. Coherent and incoherent transfer are normally viewed as limiting cases of a certain underlying dynamics. However, there exist parameter regimes where an intricate interplay between environmental noise and quantum coherence emerges, and whose net effect is an increase in the efficiency of the transport process. In this chapter we illustrate this phenomenon in the context of excitation transport across quantum networks. These are model systems for the description of energy transfer within molecular complexes and, in particular, photosynthetic pigment–protein molecules, a type of biologically relevant structures whose dynamics has been recently shown to exhibit quantum coherent features. We show that nearly perfect transport efficiency is achieved in a regime that utilizes both coherent and noisy features, and argue that Nature may have chosen this intermediate regime to operate optimally.

Introduction

The dynamical behaviour of a quantum system can be substantially affected by interaction with a fluctuating environment and one might initially be led to expect a negative effect on quantum transport involving coherent hopping of a (quasi-) particle between localized sites. In this section, however, we demonstrate that quantum transport efficiency can be enhanced by a dynamical interplay of the quantum dynamics imposed by the system Hamiltonian with the pure dephasing induced by a fluctuating environment.