78 research outputs found
The Work-Hamiltonian Connection and the Usefulness of the Jarzynski Equality for Free Energy Calculations
The connection between work and changes in the Hamiltonian for a system with
a time-dependent Hamiltonian has recently been called into question, casting
doubt on the usefulness of the Jarzynski equality for calculating free energy
changes. In this paper, we discuss the relationship between two possible
definitions of free energy and show how some recent disagreements regarding the
applicability of the Jarzynski equality are the result of different authors
using different definitions of free energy. Finally, in light of the recently
raised doubts, we explicitly demonstrate that it is indeed possible to obtain
physically relevant free energy profiles from molecular pulling experiments by
using the Jarzynski equality and the results of Hummer and Szabo.Comment: 3 page
Variational Treatment of a Harmonic Oscillator Coupled to a Dissipative Heat Bath
We consider the problem of a single quantum oscillator coupled linearly to a heat bath of independent harmonic modes. An exact solution is presented for the system-oscillator observables of interest. The exact results are then used to evaluate the utility of a variational approach to the problem that has proven useful recently in elucidating the dynamics of dissipatively coupled systems. We find that the variational approach does provide a good description for most, but not all, observables of interest. Both the exact and the variational treatment demonstrate the important role played by the low-frequency bath modes in determining qualitative features of the dynamical behavior
Low Temperature Tunneling Dynamics in Condensed Media
There has been considerable interest recently in the low temperature dynamics of condensed phase tunneling phenomena. In this paper we consider the interplay between quasiparticle transport and vibrational relaxation; the former taking place via tunneling in a double well potential, and the latter occurring due to interactions of the tunneling system with a harmonic bath. Taking the system-bath interactions to be linear in the bath coordinates, and explicitly allowing for a vibrationally excited well, we present a unified treatment of the weak and strong coupling regimes and obtain reduced equations of motion for the tunneling particle position operator. Solutions are obtained for several important limiting cases. In particular, we find that at sufficiently low temperatures, the dynamical behavior strongly resembles that of multisite spin jump model
Correlated interaction fluctuations in photosynthetic complexes
The functioning and efficiency of natural photosynthetic complexes is
strongly influenced by their embedding in a noisy protein environment, which
can even serve to enhance the transport efficiency. Interactions with the
environment induce fluctuations of the transition energies of and interactions
between the chlorophyll molecules, and due to the fact that different
fluctuations will partially be caused by the same environmental factors,
correlations between the various fluctuations will occur. We argue that
fluctuations of the interactions should in general not be neglected, as these
have a considerable impact on population transfer rates, decoherence rates and
the efficiency of photosynthetic complexes. Furthermore, while correlations
between transition energy fluctuations have been studied, we provide the first
quantitative study of the effect of correlations between interaction
fluctuations and transition energy fluctuations, and of correlations between
the various interaction fluctuations. It is shown that these additional
correlations typically lead to changes in interchromophore transfer rates,
population oscillations and can lead to a limited enhancement of the light
harvesting efficiency
Electrodynamics of Amorphous Media at Low Temperatures
Amorphous solids exhibit intrinsic, local structural transitions, that give
rise to the well known quantum-mechanical two-level systems at low
temperatures. We explain the microscopic origin of the electric dipole moment
of these two-level systems: The dipole emerges as a result of polarization
fluctuations between near degenerate local configurations, which have nearly
frozen in at the glass transition. An estimate of the dipole's magnitude, based
on the random first order transition theory, is obtained and is found to be
consistent with experiment. The interaction between the dipoles is estimated
and is shown to contribute significantly to the Gr\"{u}neisen parameter anomaly
in low glasses. In completely amorphous media, the dipole moments are
expected to be modest in size despite their collective origin. In partially
crystalline materials, however, very large dipoles may arise, possibly
explaining the findings of Bauer and Kador, J. Chem. Phys. {\bf 118}, 9069
(2003).Comment: Submitted for publication; April 27, 2005 versio
Single-file dynamics with different diffusion constants
We investigate the single-file dynamics of a tagged particle in a system
consisting of N hardcore interacting particles (the particles cannot pass each
other) which are diffusing in a one-dimensional system where the particles have
different diffusion constants. For the two particle case an exact result for
the conditional probability density function (PDF) is obtained for arbitrary
initial particle positions and all times. The two-particle PDF is used to
obtain the tagged particle PDF. For the general N-particle case (N large) we
perform stochastic simulations using our new computationally efficient
stochastic simulation technique based on the Gillespie algorithm. We find that
the mean square displacement for a tagged particle scales as the square root of
time (as for identical particles) for long times, with a prefactor which
depends on the diffusion constants for the particles; these results are in
excellent agreement with very recent analytic predictions in the mathematics
literature.Comment: 9 pages, 5 figures. Journal of Chemical Physics (in press
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