A mechanical model of normal and anomalous diffusion

The overdamped dynamics of a charged particle driven by an uniform electric field through a random sequence of scatterers in one dimension is investigated. Analytic expressions of the mean velocity and of the velocity power spectrum are presented. These show that above a threshold value of the field normal diffusion is superimposed to ballistic motion. The diffusion constant can be given explicitly. At the threshold field the transition between conduction and localization is accompanied by an anomalous diffusion. Our results exemplify that, even in the absence of time-dependent stochastic forces, a purely mechanical model equipped with a quenched disorder can exhibit normal as well as anomalous diffusion, the latter emerging as a critical property.Comment: 16 pages, no figure

Quantum entanglement in photosynthetic light harvesting complexes

Light harvesting components of photosynthetic organisms are complex, coupled, many-body quantum systems, in which electronic coherence has recently been shown to survive for relatively long time scales despite the decohering effects of their environments. Within this context, we analyze entanglement in multi-chromophoric light harvesting complexes, and establish methods for quantification of entanglement by presenting necessary and sufficient conditions for entanglement and by deriving a measure of global entanglement. These methods are then applied to the Fenna-Matthews-Olson (FMO) protein to extract the initial state and temperature dependencies of entanglement. We show that while FMO in natural conditions largely contains bipartite entanglement between dimerized chromophores, a small amount of long-range and multipartite entanglement exists even at physiological temperatures. This constitutes the first rigorous quantification of entanglement in a biological system. Finally, we discuss the practical utilization of entanglement in densely packed molecular aggregates such as light harvesting complexes.Comment: 14 pages, 7 figures. Improved presentation, published versio

Hierarchical Equations of Motion Approach to Quantum Thermodynamics

We present a theoretical framework to investigate quantum thermodynamic processes under non-Markovian system-bath interactions on the basis of the hierarchical equations of motion (HEOM) approach, which is convenient to carry out numerically "exact" calculations. This formalism is valuable because it can be used to treat not only strong system-bath coupling but also system-bath correlation or entanglement, which will be essential to characterize the heat transport between the system and quantum heat baths. Using this formalism, we demonstrated an importance of the thermodynamic effect from the tri-partite correlations (TPC) for a two-level heat transfer model and a three-level autonomous heat engine model under the conditions that the conventional quantum master equation approaches are failed. Our numerical calculations show that TPC contributions, which distinguish the heat current from the energy current, have to be take into account to satisfy the thermodynamic laws.Comment: 9 pages, 4 figures. As a chapter of: F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso (eds.), "Thermodynamics in the quantum regime - Recent Progress and Outlook", (Springer International Publishing

Excitation Dynamics and Relaxation in a Molecular Heterodimer

The exciton dynamics in a molecular heterodimer is studied as a function of differences in excitation and reorganization energies, asymmetry in transition dipole moments and excited state lifetimes. The heterodimer is composed of two molecules modeled as two-level systems coupled by the resonance interaction. The system-bath coupling is taken into account as a modulating factor of the energy gap of the molecular excitation, while the relaxation to the ground state is treated phenomenologically. Comparison of the description of the excitation dynamics modeled using either the Redfield equations (secular and full forms) or the Hierarchical quantum master equation (HQME) is demonstrated and discussed. Possible role of the dimer as an excitation quenching center in photosynthesis self-regulation is discussed. It is concluded that the system-bath interaction rather than the excitonic effect determines the excitation quenching ability of such a dimer

Electronic Coherence Dephasing in Excitonic Molecular Complexes: Role of Markov and Secular Approximations

We compare four different types of equations of motion for reduced density matrix of a system of molecular excitons interacting with thermodynamic bath. All four equations are of second order in the linear system-bath interaction Hamiltonian, with different approximations applied in their derivation. In particular we compare time-nonlocal equations obtained from so-called Nakajima-Zwanzig identity and the time-local equations resulting from the partial ordering prescription of the cummulant expansion. In each of these equations we alternatively apply secular approximation to decouple population and coherence dynamics from each other. We focus on the dynamics of intraband electronic coherences of the excitonic system which can be traced by coherent two-dimensional spectroscopy. We discuss the applicability of the four relaxation theories to simulations of population and coherence dynamics, and identify features of the two-dimensional coherent spectrum that allow us to distinguish time-nonlocal effects.Comment: 14 pages, 8 figure

Suppression of quantum oscillations and the dependence on site energies in electronic excitation transfer in the Fenna-Matthews-Olson trimer

Energy transfer in the photosynthetic complex of the Green Sulfur Bacteria known as the Fenna-Matthews-Olson (FMO) complex is studied theoretically taking all three subunits (monomers) of the FMO trimer and the recently found eighth bacteriochlorophyll (BChl) molecule into account. We find that in all considered cases there is very little transfer between the monomers. Since it is believed that the eighth BChl is located near the main light harvesting antenna we look at the differences in transfer between the situation when BChl 8 is initially excited and the usually considered case when BChl 1 or 6 is initially excited. We find strong differences in the transfer dynamics, both qualitatively and quantitatively. When the excited state dynamics is initialized at site eight of the FMO complex, we see a slow exponential-like decay of the excitation. This is in contrast to the oscillations and a relatively fast transfer that occurs when only seven sites or initialization at sites 1 and 6 is considered. Additionally we show that differences in the values of the electronic transition energies found in the literature lead to a large difference in the transfer dynamics

Focal Contacts as Mechanosensors: Externally Applied Local Mechanical Force Induces Growth of Focal Contacts by an Mdia1-Dependent and Rock-Independent Mechanism

The transition of cell–matrix adhesions from the initial punctate focal complexes into the mature elongated form, known as focal contacts, requires GTPase Rho activity. In particular, activation of myosin II–driven contractility by a Rho target known as Rho-associated kinase (ROCK) was shown to be essential for focal contact formation. To dissect the mechanism of Rho-dependent induction of focal contacts and to elucidate the role of cell contractility, we applied mechanical force to vinculin-containing dot-like adhesions at the cell edge using a micropipette. Local centripetal pulling led to local assembly and elongation of these structures and to their development into streak-like focal contacts, as revealed by the dynamics of green fluorescent protein–tagged vinculin or paxillin and interference reflection microscopy. Inhibition of Rho activity by C3 transferase suppressed this force-induced focal contact formation. However, constitutively active mutants of another Rho target, the formin homology protein mDia1 (Watanabe, N., T. Kato, A. Fujita, T. Ishizaki, and S. Narumiya. 1999. Nat. Cell Biol. 1:136–143), were sufficient to restore force-induced focal contact formation in C3 transferase-treated cells. Force-induced formation of the focal contacts still occurred in cells subjected to myosin II and ROCK inhibition. Thus, as long as mDia1 is active, external tension force bypasses the requirement for ROCK-mediated myosin II contractility in the induction of focal contacts. Our experiments show that integrin-containing focal complexes behave as individual mechanosensors exhibiting directional assembly in response to local force

Non-Markovian stochastic description of quantum transport in photosynthetic systems

We analyze several aspects of the transport dynamics in the LH1-RC core of purple bacteria, which consists basically in a ring of antenna molecules that transport the energy into a target molecule, the reaction center, placed in the center of the ring. We show that the periodicity of the system plays an important role to explain the relevance of the initial state in the transport efficiency. This picture is modified, and the transport enhanced for any initial state, when considering that molecules have different energies, and when including their interaction with the environment. We study this last situation by using stochastic Schr{\"o}dinger equations, both for Markovian and non-Markovian type of interactions.Comment: 21 pages, 5 figure