The random walk of a particle on an asymmetric chain in the presence of an attractive center, pos... more The random walk of a particle on an asymmetric chain in the presence of an attractive center, possibly trapping, is examined by means of the equivalent transfer rates technique. Both the situations of ordered and disordered hopping rates are studied. It is assumed that initially the particle is located on the attractive center. The (average) probability of presence of the particle at its initial point is computed as a function of time. In the ordered case this quantity decreases exponentially toward its limiting value (with in certain cases an inverse power-law prefactor), while in the presence of disorder it decreases according to a power law, with an exponent depending both on disorder and on asymmetry. When the possibility of trapping is taken into account, this model is relevant for the description of the transfer of energy in a photosynthetic system. The amount of energy conserved within the chain, as a function of time, and the average lifetime of the particle before it is captured by the trap are examined in both ordered and disordered situations.
Physica A: Statistical Mechanics and its Applications, 1992
We have investigated the kinetics of excitation in the frame of the conventional Pauli master equ... more We have investigated the kinetics of excitation in the frame of the conventional Pauli master equation for a molecular aggregate with a decay channel attached to one distinguished molecule (or site). As a principally new feature we assume the rate of probability flow through the decay channel to be a randomly modulated function of time. The modulation is described by a Markoff stochastic process and we do not invoke the white-noise assumption. An exact calculation is given for a broad family of stochastic processes which bridges (and includes) the asymmetric random telegraph signal and the Gaussian process. The general method is then applied in three physically relevant situations: one-molecule aggregate, cyclic-antenna system and infinite linear chain. In these models, we discuss the site-occupation probabilities, the aggregate-excitation function and the mean de-excitation time.
We investigate the distribution function Q(P) describing the survival probability on a comb consi... more We investigate the distribution function Q(P) describing the survival probability on a comb consisting of a backbone with lateral, randomly disconnected infinite branches. Two different regimes are analyzed in some detail: (i) at short times, Q(P) is shown to have a self-similar structure (devil's staircase); (ii) at large times, this function becomes smooth and tends toward a rather well-defined unit step function. The disorder-averaged survival probability (p0(t)) is expected to decrease as t-3/4 at large times, whereas the relative fluctuations of the sampledependent po(t) display a very slow decay in time, going to zero like t-~/s.
The random walk of a particle on an asymmetric chain in the presence of an attractive center, pos... more The random walk of a particle on an asymmetric chain in the presence of an attractive center, possibly trapping, is examined by means of the equivalent transfer rates technique. Both the situations of ordered and disordered hopping rates are studied. It is assumed that initially the particle is located on the attractive center. The (average) probability of presence of the particle at its initial point is computed as a function of time. In the ordered case this quantity decreases exponentially toward its limiting value (with in certain cases an inverse power-law prefactor), while in the presence of disorder it decreases according to a power law, with an exponent depending both on disorder and on asymmetry. When the possibility of trapping is taken into account, this model is relevant for the description of the transfer of energy in a photosynthetic system. The amount of energy conserved within the chain, as a function of time, and the average lifetime of the particle before it is captured by the trap are examined in both ordered and disordered situations.
The random walk of a particle on an asymmetric chain in the presence of an attractive center, pos... more The random walk of a particle on an asymmetric chain in the presence of an attractive center, possibly trapping, is examined by means of the equivalent transfer rates technique. Both the situations of ordered and disordered hopping rates are studied. It is assumed that initially the particle is located on the attractive center. The (average) probability of presence of the particle at its initial point is computed as a function of time. In the ordered case this quantity decreases exponentially toward its limiting value (with in certain cases an inverse power-law prefactor), while in the presence of disorder it decreases according to a power law, with an exponent depending both on disorder and on asymmetry. When the possibility of trapping is taken into account, this model is relevant for the description of the transfer of energy in a photosynthetic system. The amount of energy conserved within the chain, as a function of time, and the average lifetime of the particle before it is captured by the trap are examined in both ordered and disordered situations.
Physica A: Statistical Mechanics and its Applications, 1992
We have investigated the kinetics of excitation in the frame of the conventional Pauli master equ... more We have investigated the kinetics of excitation in the frame of the conventional Pauli master equation for a molecular aggregate with a decay channel attached to one distinguished molecule (or site). As a principally new feature we assume the rate of probability flow through the decay channel to be a randomly modulated function of time. The modulation is described by a Markoff stochastic process and we do not invoke the white-noise assumption. An exact calculation is given for a broad family of stochastic processes which bridges (and includes) the asymmetric random telegraph signal and the Gaussian process. The general method is then applied in three physically relevant situations: one-molecule aggregate, cyclic-antenna system and infinite linear chain. In these models, we discuss the site-occupation probabilities, the aggregate-excitation function and the mean de-excitation time.
We investigate the distribution function Q(P) describing the survival probability on a comb consi... more We investigate the distribution function Q(P) describing the survival probability on a comb consisting of a backbone with lateral, randomly disconnected infinite branches. Two different regimes are analyzed in some detail: (i) at short times, Q(P) is shown to have a self-similar structure (devil's staircase); (ii) at large times, this function becomes smooth and tends toward a rather well-defined unit step function. The disorder-averaged survival probability (p0(t)) is expected to decrease as t-3/4 at large times, whereas the relative fluctuations of the sampledependent po(t) display a very slow decay in time, going to zero like t-~/s.
The random walk of a particle on an asymmetric chain in the presence of an attractive center, pos... more The random walk of a particle on an asymmetric chain in the presence of an attractive center, possibly trapping, is examined by means of the equivalent transfer rates technique. Both the situations of ordered and disordered hopping rates are studied. It is assumed that initially the particle is located on the attractive center. The (average) probability of presence of the particle at its initial point is computed as a function of time. In the ordered case this quantity decreases exponentially toward its limiting value (with in certain cases an inverse power-law prefactor), while in the presence of disorder it decreases according to a power law, with an exponent depending both on disorder and on asymmetry. When the possibility of trapping is taken into account, this model is relevant for the description of the transfer of energy in a photosynthetic system. The amount of energy conserved within the chain, as a function of time, and the average lifetime of the particle before it is captured by the trap are examined in both ordered and disordered situations.
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