718 research outputs found
Calculation of semiclassical free energy differences along non-equilibrium classical trajectories
We have derived several relations, which allow the evaluation of the system
free energy changes in the leading order in along classically
generated trajectories. The results are formulated in terms of purely classical
Hamiltonians and trajectories, so that semiclassical partition functions can be
computed, e.g., via classical molecular dynamics simulations. The Hamiltonians,
however, contain additional potential-energy terms, which are proportional to
and are temperature-dependent. We discussed the influence of
quantum interference on the nonequilibrium work and problems with unambiguous
definition of the semiclassical work operator
Molecular reorientation in hydrogen-bonding liquids: through algebraic relaxation toward exponential decay
We present a model for the description of orientational relaxation in
hydrogen-bonding liquids. The model contains two relaxation parameters which
regulate the intensity and efficiency of dissipation, as well as the memory
function which is responsible for the short-time relaxation effects. It is
shown that the librational portion of the orientational relaxation is described
by an algebraic contribution, on top of which more rapid and
non-monotonous decays caused by the memory effects are superimposed. The
long-time behavior of the orientational relaxation is exponential, although
non-diffusional. It is governed by the rotational energy relaxation. We apply
the model to interpret recent molecular dynamic simulations and polarization
pump-probe experiments on in liquid [C. J. Fecko et al, J. Chem.
Phys. 122, 054506 (2005)]
Microscopic origin of the jump diffusion model
The present paper is aimed at studying the microscopic origin of the jump
diffusion. Starting from the -body Liouville equation and making only the
assumption that molecular reorientation is overdamped, we derive and solve the
new (hereafter generalized diffusion) equation. This is the most general
equation which governs orientational relaxation of an equilibrium molecular
ensemble in the hindered rotation limit and in the long time limit. The
generalized diffusion equation is an extension of the small-angle diffusion
equation beyond the impact approximation. We establish the conditions under
which the generalized diffusion equation can be identified with the jump
diffusion equation, and also discuss the similarities and differences between
the two approaches
Velocity dependence of friction and Kramers relaxation rates
We study the influence of the velocity dependence of friction on the escape
of a Brownian particle from the deep potential well (,
is the barrier height, is the Boltzmann constant, is the
bath temperature). The bath-induced relaxation is treated within the Rayleigh
model (a heavy particle of mass in the bath of light particles of mass
) up to the terms of the order of ,
. The term is equivalent to the Fokker-Planck
dissipative operator, and the term is responsible for the
velocity dependence of friction. As expected, the correction to the Kramers
escape rate in the overdamped limit is proportional to and is
small. The corresponding correction in the underdamped limit is proportional to
and is not necessarily small. We thus suggest that
the effects due to the velocity-dependent friction may be of considerable
importance in determining the rate of escape of an under- and moderately damped
Brownian particle from a deep potential well, while they are of minor
importance for an overdamped particle
Self-similarity of single-channel transmission for electron transport in nanowires
We demonstrate that the single-channel transmission in the resonance
tunneling regime exhibits self-similarity as a function of the nanowire length
and the energy of incident electrons. The self-similarity is used to design the
nonlinear transformation of the nanowire length and energy which, on the basis
of known values of transmission for a certain region on the energy-length
plane, yields transmissions for other regions on this plane. Test calculations
with a one-dimensional tight-binding model illustrate the described
transformations. Density function theory based transport calculations of Na
atomic wires confirm the existence of the self-similarity in the transmission
Calculations of canonical averages from the grand canonical ensemble
Grand canonical and canonical ensembles become equivalent in the
thermodynamic limit, but when the system size is finite the results obtained in
the two ensembles deviate from each other. In many important cases, the
canonical ensemble provides an appropriate physical description but it is often
much easier to perform the calculations in the corresponding grand canonical
ensemble. We present a method to compute averages in canonical ensemble based
on calculations of the expectation values in grand canonical ensemble. The
number of particles, which is fixed in the canonical ensemble, is not
necessarily the same as the average number of particles in the grand canonical
ensemble
Directed motion and useful work from an isotropic nonequilibrium distribution
We demonstrate that a gas of classical particles trapped in an external
asymmetric potential undergoes a quasiperiodic motion, if the temperature of
its initial velocity distribution differs from the equilibrium
temperature, . The magnitude of the effect is determined by the value
of , and the direction of the motion is determined by the sign
of this expression. The "loading'' and "unloading'' of the gas particles change
directions of their motion, thereby creating a possibility of shuttle-like
motion. The system works as a Carnot engine where the heat flow between kinetic
and potential parts of the nonequilibrium distribution produces the useful
work
A model for dynamical solvent control of molecular junction electronic properties
Experimental measurements of electron transport properties of molecular
junctions are often performed in solvents. Solvent-molecule coupling and
physical properties of the solvent can be used as the external stimulus to
control electric current through a molecule. In this paper, we propose a model,
which includes dynamical effects of solvent-molecule interaction in the
non-equilibrium Green's function calculations of electric current. The solvent
is considered as a macroscopic dipole moment that reorients stochastically and
interacts with the electrons tunnelling through the molecular junction. The
Keldysh-Kadanoff-Baym equations for electronic Green's functions are solved in
time-domain with subsequent averaging over random realisations of rotational
variables using Furutsu-Novikov method for exact closure of infinite hierarchy
of stochastic correlation functions. The developed theory requires the use of
wide-band approximation as well as classical treatment of solvent degrees of
freedom. The theory is applied to a model molecular junction. It is
demonstrated that not only electrostatic interaction between molecular junction
and solvent but also solvent viscosity can be used to control electrical
properties of the junction. Aligning of the rotating dipole moment breaks
particle-hole symmetry of the transmission favouring either hole or electron
transport channels depending upon the aligning potential
What can be learned about molecular reorientation from single molecule polarization microscopy?
We have developed a general approach for the calculation of the single
molecule polarization correlation function C(t), which delivers a correlation
of the emission dichroisms at time 0 and t. The approach is model independent
and valid for general asymmetric top molecules. The key dynamic quantities of
our analysis are the even-rank orientational correlation functions, the
weighted sum of which yields C(t). We have demonstrated that the use of
non-orthogonal schemes for the detection of the single molecule polarization
responses makes it possible to manipulate the weighting coefficients in the
expansion of C(t). Thus valuable information about the orientational
correlation functions of the rank higher than second can be extracted from
C(t)
First-passage time theory of activated rate chemical processes in electronic molecular junctions
Confined nanoscale spaces, electric fields and tunneling currents make the
molecular electronic junction an experimental device for the discovery of new,
out-of-equilibrium chemical reactions. Reaction-rate theory for
current-activated chemical reactions is developed by combining a Keldysh
nonequilibrium Green's functions treatment of electrons, Fokker-Planck
description of the reaction coordinate, and Kramers' first-passage time
calculations. The NEGF provide an adiabatic potential as well as a diffusion
coefficient and temperature with local dependence on the reaction coordinate.
Van Kampen's Fokker-Planck equation, which describes a Brownian particle moving
in an external potential in an inhomogeneous medium with a position-dependent
friction and diffusion coefficient, is used to obtain an analytic expression
for the first-passage time. The theory is applied to several transport
scenarios: a molecular junction with a single, reaction coordinate dependent
molecular orbital, and a model diatomic molecular junction. We demonstrate the
natural emergence of Landauer's blowtorch effect as a result of the interplay
between the configuration dependent viscosity and diffusion coefficients. The
resultant localized heating in conjunction with the bond-deformation due to
current-induced forces are shown to be the determining factors when considering
chemical reaction rates; each of which result from highly tunable parameters
within the system
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