arXiv subjects

Jianshu Cao

Publications and source records attributed to Jianshu Cao.

At least 73 records · Page 4Linked to original sources

arXiv2014

Spectrins in Axonal Cytoskeletons: Dynamics Revealed by Extensions and Fluctuations

The macroscopic properties, the properties of individual components and how those components interact with each other are three important aspects of a composited structure. An understanding of the interplay between them is essential in the study of complex systems. Using axonal cytoskeleton as an example system, here we perform a theoretical study of slender structures that can be coarse-grained as a simple smooth 3-dimensional curve. We first present a generic model for such systems based on the fundamental theorem of curves. We use this generic model to demonstrate the applicability of the well-known worm-like chain (WLC) model to the network level and investigate the situation when the system is stretched by strong forces (weakly bending limit). We specifically studied recent experimental observations that revealed the hitherto unknown periodic cytoskeleton structure of axons and measured the longitudinal fluctuations. Instead of focusing on single molecules, we apply analytical results from the WLC model to both single molecule and network levels and focus on the relations between extensions and fluctuations. We show how this approach introduces constraints to possible local dynamics of the spectrin tetramers in the axonal cytoskeleton and finally suggests simple but self-consistent dynamics of spectrins in which the spectrins in one spatial period of axons fluctuate in-sync.

cond-mat.soft↗

arXiv2014

Förster resonance energy transfer, absorption and emission spectra in multichromophoric systems: I. Cumulant expansions

We study the Förster resonant energy transfer (FRET) rate in multichromophoric systems. The multichromophoric FRET rate is determined by the overlap integral of the donor's emission and acceptor's absorption spectra, which are obtained via 2nd-order cumulant expansion techniques developed in this work. We calculate the spectra and multichromophoric FRET rate for both localized and delocalized systems. (i) The role of the initial entanglement between the donor and its bath is found to be crucial in both the emission spectrum and the multichromophoric FRET rate. (ii) The absorption spectra obtained by the cumulant expansion method are quite close to the exact one for both localized and delocalized systems, even when the system-bath coupling is far from the perturbative regime. (iii) For the emission spectra, the cumulant expansion can give very good results for the localized system, but fail to obtain reliable spectra of the high excitations of a delocalized system, when the system-bath coupling is large and the thermal energy is small. (iv) Even though, the multichromophoric FRET rate is good enough since it is determined by the overlap integral of the spectra.

physics.bio-ph↗

arXiv2013

Shape transition of unstrained flattest single-walled carbon nanotubes under pressure

Single walled carbon nanotube's cross section can be flattened under hydrostatic pressure. One example is the cross section of a single walled carbon nanotube successively deforms from the original round shape to oval shape, then to peanut-like shape. At the transition point of reversible deformation between convex shape and concave shape, the side wall of nanotube is flattest. This flattest tube has many attractive properties. In the present work, an approximate approach is developed to determine the equilibrium shape of this unstrained flattest tube and the curvature distribution of this tube. Our results are in good agreement with recent numerical results, and can be applied to the study of pressure controlled electric properties of single walled carbon nanotubes. The present method can also be used to study other deformed inorganic and organic tube-like structures.

cond-mat.mes-hall↗

arXiv2013

Optimal tunneling enhances quantum photovoltaic effect in double quantum dots

We investigate quantum photovoltaic effect in double quantum dots by applying nonequilibrium quantum master equation. The drastic suppression of the photovoltaic current is observed near the open circuit voltage, which leads to the large filling factor. We find that there always exists an optimal inter-dot tunneling that significantly enhances the photovoltaic current. The maximal output power will also be obtained around the optimal inter-dot tunneling. Moreover, the open circuit voltage approximately behaves as the product of the eigen-level gap and the Carnot efficiency. These results suggest a great potential for double quantum dots as efficient photovoltaic devices.

cond-mat.mes-hall↗

arXiv2013

Correlated local bending of DNA double helix and its effect on the cyclization of short DNA fragments

We report a theoretical study of DNA flexibility and quantitatively predict the ring closure probability as a function of DNA contour length. Recent experimental studies show that the flexibility of short DNA fragments (as compared to the persistence length of DNA l_P~150 base pairs) cannot be described by the traditional worm-like chain (WLC) model, e.g., the observed ring closure probability is much higher than predicted. To explain these observations, DNA flexibility is investigated with explicit considerations of a new length scale l_D~10 base pairs, over which DNA local bend angles are correlated. In this correlated worm-like chain (C-WLC) model, a finite length correction term is analytically derived and the persistence length is found to be contour length dependent. While our model reduces to the traditional worm-like chain model when treating long DNA at length scales much larger than l_P, it predicts that DNA becomes much more flexible at shorter sizes, which helps explain recent cyclization measurements of short DNA fragments around 100 base pairs.

cond-mat.soft↗

arXiv2013

A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems

The hierarchical equations of motion technique has found widespread success as a tool to generate the numerically exact dynamics of non-Markovian open quantum systems. However, its application to low temperature environments remains a serious challenge due to the need for a deep hierarchy that arises from the Matsubara expansion of the bath correlation function. Here we present a hybrid stochastic hierarchical equation of motion (sHEOM) approach that alleviates this bottleneck and leads to a numerical cost that is nearly independent of temperature. Additionally, the sHEOM method generally converges with fewer hierarchy tiers allowing for the treatment of larger systems. Benchmark calculations are presented on the dynamics of two level systems at both high and low temperatures to demonstrate the efficacy of the approach. Then the hybrid method is used to generate the exact dynamics of systems that are nearly impossible to treat by the standard hierarchy. First, exact energy transfer rates are calculated across a broad range of temperatures revealing the deviations from the Forster rates. This is followed by computations of the entanglement dynamics in a system of two qubits at low temperature spanning the weak to strong system-bath coupling regimes.

physics.chem-ph↗

arXiv2013

Coherent quantum transport in disordered systems I: The influence of dephasing on the transport properties and absorption spectra on one-dimensional systems

Excitonic transport in static disordered one dimensional systems is studied in the presence of thermal fluctuations that are described by the Haken-Strobl-Reineker model. For short times, non-diffusive behavior is observed that can be characterized as the free-particle dynamics in the Anderson localized system. Over longer time scales, the environment-induced dephasing is sufficient to overcome the Anderson localization caused by the disorder and allow for transport to occur which is always seen to be diffusive. In the limiting regimes of weak and strong dephasing quantum master equations are developed, and their respective scaling relations imply the existence of a maximum in the diffusion constant as a function of the dephasing rate that is confirmed numerically. In the weak dephasing regime, it is demonstrated that the diffusion constant is proportional to the square of the localization length which leads to a significant enhancement of the transport rate over the classical prediction. Finally, the influence of noise and disorder on the absorption spectrum is presented and its relationship to the transport properties is discussed.

cond-mat.mes-hall↗

arXiv2013

A Novel Construction of Complex-valued Gaussian Processes with Arbitrary Spectral Densities and its Application to Excitation Energy Transfer

The recent experimental discoveries about excitation energy transfer (EET) in light harvesting antenna (LHA) attract a lot of interest. As an open non-equilibrium quantum system, the EET demands more rigorous theoretical framework to understand the interaction between system and environment and therein the evolution of reduced density matrix. A phonon is often used to model the fluctuating environment and convolutes the reduced quantum system temporarily. In this paper, we propose a novel way to construct complex-valued Gaussian processes to describe thermal quantum phonon bath exactly by converting the convolution of influence functional into the time correlation of complex Gaussian random field. Based on the construction, we propose a rigorous and efficient computational method, the covariance decomposition (CD) and conditional propagation scheme, to simulate the temporarily entangled reduced system. The new method allows us to study the non-Markovian effect without perturbation under the influence of different spectral densities of the linear system-phonon coupling coefficients. Its application in the study of EET in the Fenna-Matthews-Olson (FMO) model Hamiltonian under four different spectral densities is discussed. Since the scaling of our algorithm is linear due to its Monte Carlo nature, the future application of the method for large LHA systems is attractive. In addition, this method can be used to study the effect of correlated initial condition on the reduced dynamics in the future.

cond-mat.stat-mech↗

arXiv2013

Higher-Order Kinetic Expansion of Quantum Dissipative Dynamics: Mapping Quantum Networks to Kinetic Networks

We apply a new formalism to derive the higher-order quantum kinetic expansion (QKE) for studying dissipative dynamics in a general quantum network coupled with an arbitrary thermal bath. The dynamics of system population is described by a time-convoluted kinetic equation, where the time-nonlocal rate kernel is systematically expanded on the order of off-diagonal elements of the system Hamiltonian. In the second order, the rate kernel recovers the expression of the noninteracting-blip approximation (NIBA) method. The higher-order corrections in the rate kernel account for the effects of the multi-site quantum coherence and the bath relaxation. In a quantum harmonic bath, the rate kernels of different orders are analytically derived. As demonstrated by four examples, the higher-order QKE can reliably predict quantum dissipative dynamics, comparing well with the hierarchic equation approach. More importantly, the higher-order rate kernels can distinguish and quantify distinct nontrivial quantum coherent effects, such as long-range energy transfer from quantum tunneling and quantum interference arising from the phase accumulation of interactions.

physics.chem-ph↗

arXiv2012

Efficient Energy Transfer in Light-Harvesting Systems, II: Quantum-Classical Comparison, Flux Network, and Robustness Analysis

Following the calculation of optimal energy transfer in thermal environment in our first paper (Wu et al., New J. Phys., 2010, 12, 105012), full quantum dynamics and leading-order `classical' hopping kinetics are compared in the seven-site Fenna-Matthews-Olson (FMO) protein complex. The difference between these two dynamic descriptions is due to higher-order quantum corrections. Two thermal bath models, classical white noise (the Haken-Strobl-Reineker model) and quantum Debye model, are considered. In the seven-site FMO model, we observe that higher-order corrections lead to negligible changes in the trapping time or in energy transfer efficiency around the optimal and physiological conditions (2% in the HSR model and 0.1% in the quantum Debye model for the initial site at BChl 1). However, using the concept of integrated flux, we can identify significant differences in branching probabilities of the energy transfer network between hopping kinetics and quantum dynamics (26% in the HSR model and 32% in the quantum Debye model for the initial site at BChl 1). This observation indicates that the quantum coherence can significantly change the distribution of energy transfer pathways in the flux network with the efficiency nearly the same. The quantum-classical comparison of the average trapping time with the removal of the bottleneck site, BChl 4, demonstrates the robustness of the efficient energy transfer by the mechanism of multi-site quantum coherence. To reconcile with the latest eight-site FMO model, the quantum-classical comparison with the flux network analysis is summarized in the appendix. The eight-site FMO model yields similar trapping time and network structure as the seven-site FMO model but leads to a more disperse distribution of energy transfer pathways.

physics.chem-ph↗

arXiv2012

Non-Canonical Statistics of a Spin-Boson Model: Theory and Exact Monte-Carlo Simulations

Equilibrium canonical distribution in statistical mechanics assumes weak system-bath coupling (SBC). In real physical situations this assumption can be invalid and equilibrium quantum statistics of the system may be non-canonical. By exploiting both polaron transformation and perturbation theory in a spin-boson model, an analytical treatment is advocated to study non-canonical statistics of a two-level system at arbitrary temperature and for arbitrary SBC strength, yielding theoretical results in agreement with exact Monte-Carlo simulations. In particular, the eigen-representation of system's reduced density matrix is used to quantify non-canonical statistics as well as the quantumness of the open system. For example, it is found that irrespective of SBC strength, non-canonical statistics enhances as temperature decreases but vanishes at high temperature.

quant-ph↗

arXiv2012

Generic Mechanism of Optimal Energy Transfer Efficiency: A Scaling Theory of the Mean First Passage Time in Exciton Systems

An asymptotic scaling theory is presented using the conceptual basis of trapping-free subspace (i.e., orthogonal subspace) to establish the generic mechanism of optimal efficiency of excitation energy transfer (EET) in light-harvesting systems. Analogous to Kramers' turnover in classical rate theory, the enhanced efficiency in the weak damping limit and the suppressed efficiency in the strong damping limit define two asymptotic scaling regimes, which are interpolated to predict the functional form of optimal efficiency of the trapping-free subspace. In the presence of static disorder, the scaling law of transfer time with respect to dephasing rate changes from linear to square root, suggesting a weaker dependence on the environment. Though formulated in the context of EET, the analysis and conclusions apply in general to open quantum processes, including electron transfer, fluorescence emission, and heat conduction.

quant-ph↗

arXiv2012

Excitonic energy transfer in light-harvesting complexes in purple bacteria

Two distinct approaches, the Frenkel-Dirac time-dependent variation and the Haken-Strobl model, are adopted to study energy transfer dynamics in single-ring and double-ring light-harvesting systems in purple bacteria. It is found that inclusion of long-range dipolar interactions in the two methods results in significant increases in intra- or inter-ring exciton transfer efficiency. The dependence of exciton transfer efficiency on trapping positions on single rings of LH2 (B850) and LH1 is similar to that in toy models with nearest-neighbor coupling only. However, owing to the symmetry breaking caused by the dimerization of BChls and dipolar couplings, such dependence has been largely suppressed. In the studies of coupled-ring systems, both methods reveal interesting role of dipolar interaction in increasing energy transfer efficiency by introducing multiple intra/inter-ring transfer paths. Importantly, the time scale (~4ps) of inter-ring exciton transfer obtained from polaron dynamics is in good agreement with previous studies. In a double-ring LH2 system, dipole-induced symmetry breaking leads to global minima and local minima of the average trapping time when there is a finite value of non-zero dephasing rate, suggesting that environment plays a role in preserving quantum coherent energy transfer. In contrast, dephasing comes into play only when the perfect cylindrical symmetry in the hypothetic system is broken. This study has revealed that dipolar interaction between chromophores may play an important part in the high energy transfer efficiency in the LH2 system and many other natural photosynthetic systems.

physics.chem-ph↗

arXiv2012

An exact equilibrium reduced density matrix formulation I: The influence of noise, disorder, and temperature on localization in excitonic systems

An exact method to compute the entire equilibrium reduced density matrix for systems characterized by a system-bath Hamiltonian is presented. The approach is based upon a stochastic unraveling of the influence functional that appears in the imaginary time path integral formalism of quantum statistical mechanics. This method is then applied to study the effects of thermal noise, static disorder, and temperature on the coherence length in excitonic systems. As representative examples of biased and unbiased systems, attention is focused on the well-characterized light harvesting complexes of FMO and LH2, respectively. Due to the bias, FMO is completely localized in the site basis at low temperatures, whereas LH2 is completely delocalized. In the latter, the presence of static disorder leads to a plateau in the coherence length at low temperature that becomes increasingly pronounced with increasing strength of the disorder. The introduction of noise, however, precludes this effect. In biased systems, it is shown that the environment may increase the coherence length, but only decrease that of unbiased systems. Finally it is emphasized that for typical values of the environmental parameters in light harvesting systems, the system and bath are entangled at equilibrium in the single excitation manifold. That is, the density matrix cannot be described as a product state as is often assumed, even at room temperature. The reduced density matrix of LH2 is shown to be in precise agreement with the steady state limit of previous exact quantum dynamics calculations.

cond-mat.mes-hall↗

arXiv2012

Accuracy of Second Order Perturbation theory in the Polaron and Variational Polaron Frames

In the study of open quantum systems, the polaron transformation has recently attracted a renewed interest as it offers the possibility to explore the strong system-bath coupling regime. Despite this interest, a clear and unambiguous analysis of the regimes of validity of the polaron transformation is still lacking. Here we provide such a benchmark, comparing second order perturbation theory results in the original untransformed frame, the polaron frame and the variational extension with numerically exact path integral calculations of the equilibrium reduced density matrix. Equilibrium quantities allow a direct comparison of the three methods without invoking any further approximations as is usually required in deriving master equations. It is found that the second order results in the original frame are accurate for weak system-bath coupling, the full polaron results are accurate in the opposite regime of strong coupling, and the variational method is capable of interpolating between these two extremes. As the bath becomes more non-Markovian (slow bath), all three approaches become less accurate.

quant-ph↗

arXiv2011

Efficient energy transfer in light-harvesting systems, III: The influence of the eighth bacteriochlorophyll on the dynamics and efficiency in FMO

The most recent crystal structure of the Fenna-Matthews-Olson (FMO) protein complex indicates that each subunit contains an additional eighth chromophore. It has been proposed that this extra site functions as a link between the chlorosome antenna complex and the remaining seven chromophores in FMO [Schmidt am Busch et al, J. Phys. Chem. Lett., {\bf 2}, 93 (2011)]. Here, we investigate the implications of this scenario through numerical calculations with the generalized Bloch-Redfield (GBR) equation and the non-interacting blip approximation (NIBA). Three key insights into the population dynamics and energy transfer efficiency in FMO are provided. First, it is shown that the oscillations that are often observed in the population relaxation of the dimer composed of sites one and two may be completely suppressed in the eight site model. The presence of the coherent oscillations is shown to depend upon the particular initial preparation of the dimer state. Secondly it is demonstrated that while the presence of the eighth chromophore does not cause a dramatic change in the energy transfer efficiency, it does however lead to a dominant energy transfer pathway which can be characterized by an effective three site system arranged in an equally spaced downhill configuration. Such a configuration leads to an optimal value of the site energy of the eighth chromophore which is shown to be near to its suggested value. Finally we confirm that the energy transfer process in the eight site FMO complex remains efficient and robust. The optimal values of the bath parameters are computed and shown to be closer to the experimentally fitted values than those calculated previously for the seven site system.

physics.bio-ph↗

arXiv2010

Optimal Efficiency of Self-Assembling Light-Harvesting Arrays

Using a classical master equation that describes energy transfer over a given lattice, we explore how energy transfer efficiency along with the photon capturing ability depends on network connectivity, on transfer rates, and on volume fractions - the numbers and relative ratio of fluorescence chromophore components, e.g., donor (D), acceptor (A), and bridge (B) chromophores. For a one-dimensional AD array, the exact analytical expression for efficiency shows a steep increase with a D-to-A transfer rate when a spontaneous decay is sufficiently slow. This result implies that the introduction of B chromophores can be a useful method for improving efficiency for a two-component AD system with inefficient D-to-A transfer and slow spontaneous decay. Analysis of this one-dimensional system can be extended to higher-dimensional systems with chromophores arranged in structures such as a helical or stacked-disk rod, which models the self-assembling monomers of the tobacco mosaic virus coat protein. For the stacked-disk rod, we observe the following: (1) With spacings between sites fixed, a staggered conformation is more efficient than an eclipsed conformation. (2) For a given ratio of A and D chromophores, the uniform distribution of acceptors that minimizes the mean first passage time to acceptors is a key point to designing the optimal network for a donor-acceptor system with a relatively small D-to-A transfer rate. (3) For a three-component ABD system with a large B-to-A transfer rate, a key design strategy is to increase the number of the pathways in accordance with the directional energy flow from D to B to A chromophores.

cond-mat.stat-mech↗

arXiv2010

Efficient energy transfer in light-harvesting systems, I: optimal temperature, reorganization energy, and spatial-temporal correlations

Understanding the mechanisms of efficient and robust energy transfer in light-harvesting systems provides new insights for the optimal design of artificial systems. In this paper, we use the Fenna-Matthews-Olson (FMO) protein complex and phycocyanin 645 (PC 645) to explore the general dependence on physical parameters that help maximize the efficiency and maintain its stability. With the Haken-Strobl model, the maximal energy transfer efficiency (ETE) is achieved under an intermediate optimal value of dephasing rate. To avoid the infinite temperature assumption in the Haken-Strobl model and the failure of the Redfield equation in predicting the Forster rate behavior, we use the generalized Bloch-Redfield (GBR) equation approach to correctly describe dissipative exciton dynamics and find that maximal ETE can be achieved under various physical conditions, including temperature, reorganization energy, and spatial-temporal correlations in noise. We also identify regimes of reorganization energy where the ETE changes monotonically with temperature or spatial correlation and therefore cannot be optimized with respect to these two variables.

physics.chem-ph↗