Stochastic unraveling of Redfield master equations and its application to electron transfer problems

A method for stochastic unraveling of general time-local quantum master equations (QMEs) is proposed. The present kind of jump algorithm allows a numerically efficient treatment of QMEs which are not in Lindblad form, i.e. are not positive semidefinite by definition. The unraveling can be achieved by allowing for trajectories with negative weights. Such a property is necessary, e.g. to unravel the Redfield QME and to treat various related problems with high numerical efficiency. The method is successfully tested on the damped harmonic oscillator and on electron transfer models including one and two reaction coordinates. The obtained results are compared to those from a direct propagation of the reduced density matrix (RDM) as well as from the standard quantum jump method. Comparison of the numerical efficiency is performed considering both the population dynamics and the RDM in the Wigner phase space representation.Comment: accepted in J. Chem. Phys.; 26 pages, 6 figures; the order of authors' names on the title page correcte

Comparison of two models for bridge-assisted charge transfer

Based on the reduced density matrix method, we compare two different approaches to calculate the dynamics of the electron transfer in systems with donor, bridge, and acceptor. In the first approach a vibrational substructure is taken into account for each electronic state and the corresponding states are displaced along a common reaction coordinate. In the second approach it is assumed that vibrational relaxation is much faster than the electron transfer and therefore the states are modeled by electronic levels only. In both approaches the system is coupled to a bath of harmonic oscillators but the way of relaxation is quite different. The theory is applied to the electron transfer in ${\rm H_2P}-{\rm ZnP}-{\rm Q}$ with free-base porphyrin (${\rm H_2P}$) being the donor, zinc porphyrin (${\rm ZnP}$) being the bridge and quinone (${\rm Q}$) the acceptor. The parameters are chosen as similar as possible for both approaches and the quality of the agreement is discussed.Comment: 12 pages including 4 figures, 1 table, 26 references. For more info see http://eee.tu-chemnitz.de/~kili

Energetics of the primary electron transfer reaction revealed by ultrafast spectroscopy on modified bacterial reaction centers

The modification of reaction centers from Rhodobacter sphaeroides by the introduction of pheophytins instead of bacteriopheophytins leads to interesting changes in the primary photosynthetic reaction: long-living populations of the excited electronic state of the special pair P* and the bacteriochlorophyll anion B−A show up. The data allow the determination of the energetics in the reaction center. The free energy of the first intermediate P+B−A, where the electron has reached the accessory bacteriochlorophyll BA lies ≈ 450 cm−1 below the initially excited special pair P*

Cooperative Dynamics in Unentangled Polymer Fluids

We present a Generalized Langevin Equation for the dynamics of interacting semiflexible polymer chains, undergoing slow cooperative dynamics. The calculated Gaussian intermolecular center-of-mass and monomer potentials, wich enter the GLE, are in quantitative agreement with computer simulation data. The experimentally observed, short-time subdiffusive regime of the polymer mean-square displacements, emerges here from the competition between the intramolecular and the intermolecular mean-force potentials.Comment: 9 pages, latex, 3 figure

Loschmidt echo and stochastic-like quantum dynamics of nano-particles

We investigate time evolution of prepared vibrational state (system) coupled to a reservoir with dense spectrum of its vibrational states. We assume that the reservoir has an equidistant spectrum, and the system - reservoir coupling matrix elements are independent of the reservoir states. The analytical solution manifests three regimes of the evolution for the system: (I) weakly damped oscillations; (II) multicomponent Loschmidt echo in recurrence cycles; (III) overlapping recurrence cycles. We find the characteristic critical values of the system - reservoir coupling constant for the transitions between these regimes. Stochastic dynamics occurs in the regime (III) due to inevoidably in any real system coarse graining of time or energy measurements, or initial condition uncertainty. Even though a specific toy model is investigated here, when properly interpreted it yields quite reasonable description for a variety of physically relevant phenomena.Comment: 8 pages, 3 figure

Fluctuations from dissipation in a hot non-Abelian plasma

We consider a transport equation of the Boltzmann-Langevin type for non-Abelian plasmas close to equilibrium to derive the spectral functions of the underlying microscopic fluctuations from the entropy. The correlator of the stochastic source is obtained from the dissipative processes in the plasma. This approach, based on classical transport theory, exploits the well-known link between a linearized collision integral, the entropy and the spectral functions. Applied to the ultra-soft modes of a hot non-Abelian (classical or quantum) plasma, the resulting spectral functions agree with earlier findings obtained from the microscopic theory. As a by-product, it follows that B\"odeker's effective theory is consistent with the fluctuation-dissipation theorem.Comment: 9 pages, revtex, no figures, identical to published versio

Rate-equation calculations of the current flow through two-site molecular device and DNA-based junction

Here we present the calculations of incoherent current flowing through the two-site molecular device as well as the DNA-based junction within the rate-equation approach. Few interesting phenomena are discussed in detail. Structural asymmetry of two-site molecule results in rectification effect, which can be neutralized by asymmetric voltage drop at the molecule-metal contacts due to coupling asymmetry. The results received for poly(dG)-poly(dC) DNA molecule reveal the coupling- and temperature-independent saturation effect of the current at high voltages, where for short chains we establish the inverse square distance dependence. Besides, we document the shift of the conductance peak in the direction to higher voltages due to the temperature decrease.Comment: 12 pages, 6 figure

The Origins of Phase Transitions in Small Systems

The identification and classification of phases in small systems, e.g. nuclei, social and financial networks, clusters, and biological systems, where the traditional definitions of phase transitions are not applicable, is important to obtain a deeper understanding of the phenomena observed in such systems. Within a simple statistical model we investigate the validity and applicability of different classification schemes for phase transtions in small systems. We show that the whole complex temperature plane contains necessary information in order to give a distinct classification.Comment: 3 pages, 4 figures, revtex 4 beta 5, for further information see http://www.smallsystems.d

Theory of Adiabatic fluctuations : third-order noise

We consider the response of a dynamical system driven by external adiabatic fluctuations. Based on the `adiabatic following approximation' we have made a systematic separation of time-scales to carry out an expansion in $\alpha |\mu|^{-1}$, where $\alpha$ is the strength of fluctuations and $|\mu|$ is the damping rate. We show that probability distribution functions obey the differential equations of motion which contain third order terms (beyond the usual Fokker-Planck terms) leading to non-Gaussian noise. The problem of adiabatic fluctuations in velocity space which is the counterpart of Brownian motion for fast fluctuations, has been solved exactly. The characteristic function and the associated probability distribution function are shown to be of stable form. The linear dissipation leads to a steady state which is stable and the variances and higher moments are shown to be finite.Comment: Plain Latex, no figures, 28 pages; to appear in J. Phys.