Adiabatic-Nonadiabatic Transition in the Diffusive Hamiltonian Dynamics of a Classical Holstein Polaron

We study the Hamiltonian dynamics of a free particle injected onto a chain containing a periodic array of harmonic oscillators in thermal equilibrium. The particle interacts locally with each oscillator, with an interaction that is linear in the oscillator coordinate and independent of the particle's position when it is within a finite interaction range. At long times the particle exhibits diffusive motion, with an ensemble averaged mean-squared displacement that is linear in time. The diffusion constant at high temperatures follows a power law D ~ T^{5/2} for all parameter values studied. At low temperatures particle motion changes to a hopping process in which the particle is bound for considerable periods of time to a single oscillator before it is able to escape and explore the rest of the chain. A different power law, D ~ T^{3/4}, emerges in this limit. A thermal distribution of particles exhibits thermally activated diffusion at low temperatures as a result of classically self-trapped polaronic states.Comment: 15 pages, 4 figures Submitted to Physical Review

Resonance Effects in the Nonadiabatic Nonlinear Quantum Dimer

The quantum nonlinear dimer consisting of an electron shuttling between the two sites and in weak interaction with vibrations, is studied numerically under the application of a DC electric field. A field-induced resonance phenomenon between the vibrations and the electronic oscillations is found to influence the electronic transport greatly. For initially delocalization of the electron, the resonance has the effect of a dramatic increase in the transport. Nonlinear frequency mixing is identified as the main mechanism that influences transport. A characterization of the frequency spectrum is also presented.Comment: 7 pages, 6 figure

A Study of The Formation of Stationary Localized States Due to Nonlinear Impurities Using The Discrete Nonlinear Schr\"odinger Equation

The Discrete Nonlinear Schr$\ddot{o}$dinger Equation is used to study the formation of stationary localized states due to a single nonlinear impurity in a Caley tree and a dimeric nonlinear impurity in the one dimensional system. The rotational nonlinear impurity and the impurity of the form $-\chi \mid C \mid^{\sigma}$ where $\sigma$ is arbitrary and $\chi$ is the nonlinearity parameter are considered. Furthermore, $\mid C \mid$ represents the absolute value of the amplitude. Altogether four cases are studies. The usual Greens function approach and the ansatz approach are coherently blended to obtain phase diagrams showing regions of different number of states in the parameter space. Equations of critical lines separating various regions in phase diagrams are derived analytically. For the dimeric problem with the impurity $-\chi \mid C \mid^{\sigma}$, three values of $\mid \chi_{cr} \mid$, namely, $\mid \chi_{cr} \mid = 2$, at $\sigma = 0$ and $\mid \chi_{cr} \mid = 1$ and $\frac{8}{3}$ for $\sigma = 2$ are obtained. Last two values are lower than the existing values. Energy of the states as a function of parameters is also obtained. A model derivation for the impurities is presented. The implication of our results in relation to disordered systems comprising of nonlinear impurities and perfect sites is discussed.Comment: 10 figures available on reques

Periodically Varying Externally Imposed Environmental Effects on Population Dynamics

Effects of externally imposed periodic changes in the environment on population dynamics are studied with the help of a simple model. The environmental changes are represented by the temporal and spatial dependence of the competition terms in a standard equation of evolution. Possible applications of the analysis are on the one hand to bacteria in Petri dishes and on the other to rodents in the context of the spread of the Hantavirus epidemic. The analysis shows that spatio-temporal structures emerge, with interesting features which depend on the interplay of separately controllable aspects of the externally imposed environmental changes.Comment: 7 pages, 8 figures, include

Effects of disorder in location and size of fence barriers on molecular motion in cell membranes

The effect of disorder in the energetic heights and in the physical locations of fence barriers encountered by transmembrane molecules such as proteins and lipids in their motion in cell membranes is studied theoretically. The investigation takes as its starting point a recent analysis of a periodic system with constant distances between barriers and constant values of barrier heights, and employs effective medium theory to treat the disorder. The calculations make possible, in principle, the extraction of confinement parameters such as mean compartment sizes and mean intercompartmental transition rates from experimentally reported published observations. The analysis should be helpful both as an unusual application of effective medium theory and as an investigation of observed molecular movements in cell membranes.Comment: 9 pages, 5 figure

Phase transitions in systems of self-propelled agents and related network models

An important characteristic of flocks of birds, school of fish, and many similar assemblies of self-propelled particles is the emergence of states of collective order in which the particles move in the same direction. When noise is added into the system, the onset of such collective order occurs through a dynamical phase transition controlled by the noise intensity. While originally thought to be continuous, the phase transition has been claimed to be discontinuous on the basis of recently reported numerical evidence. We address this issue by analyzing two representative network models closely related to systems of self-propelled particles. We present analytical as well as numerical results showing that the nature of the phase transition depends crucially on the way in which noise is introduced into the system.Comment: Four pages, four figures. Submitted to PR

Stationary Localized States Due to a Nonlinear Dimeric Impurity Embedded in a Perfect 1-D Chain

The formation of Stationary Localized states due to a nonlinear dimeric impurity embedded in a perfect 1-d chain is studied here using the appropriate Discrete Nonlinear Schr$\ddot{o}$dinger Equation. Furthermore, the nonlinearity has the form, $\chi |C|^\sigma$ where $C$ is the complex amplitude. A proper ansatz for the Localized state is introduced in the appropriate Hamiltonian of the system to obtain the reduced effective Hamiltonian. The Hamiltonian contains a parameter, $\beta = \phi_1/\phi_0$ which is the ratio of stationary amplitudes at impurity sites. Relevant equations for Localized states are obtained from the fixed point of the reduced dynamical system. $|\beta|$ = 1 is always a permissible solution. We also find solutions for which $|\beta| \ne 1$. Complete phase diagram in the $(\chi, \sigma)$ plane comprising of both cases is discussed. Several critical lines separating various regions are found. Maximum number of Localized states is found to be six. Furthermore, the phase diagram continuously extrapolates from one region to the other. The importance of our results in relation to solitonic solutions in a fully nonlinear system is discussed.Comment: Seven figures are available on reques

Excitonic - vibronic coupled dimers: A dynamic approach

The dynamical properties of exciton transfer coupled to polarization vibrations in a two site system are investigated in detail. A fixed point analysis of the full system of Bloch - oscillator equations representing the coupled excitonic - vibronic flow is performed. For overcritical polarization a bifurcation converting the stable bonding ground state to a hyperbolic unstable state which is basic to the dynamical properties of the model is obtained. The phase space of the system is generally of a mixed type: Above bifurcation chaos develops starting from the region of the hyperbolic state and spreading with increasing energy over the Bloch sphere leaving only islands of regular dynamics. The behaviour of the polarization oscillator accordingly changes from regular to chaotic.Comment: uuencoded compressed Postscript file containing text and figures. In case of questions, please, write to [email protected]

On a random walk with memory and its relation to Markovian processes

We study a one-dimensional random walk with memory in which the step lengths to the left and to the right evolve at each step in order to reduce the wandering of the walker. The feedback is quite efficient and lead to a non-diffusive walk. The time evolution of the displacement is given by an equivalent Markovian dynamical process. The probability density for the position of the walker is the same at any time as for a random walk with shrinking steps, although the two-time correlation functions are quite different.Comment: 10 pages, 4 figure