217 research outputs found
Instantaneous Pair Theory for High-Frequency Vibrational Energy Relaxation in Fluids
Notwithstanding the long and distinguished history of studies of vibrational
energy relaxation, exactly how it is that high frequency vibrations manage to
relax in a liquid remains somewhat of a mystery. Both experimental and
theoretical approaches seem to say that there is a natural frequency range
associated with intermolecular motions in liquids, typically spanning no more
than a few hundred cm^{-1}. Landau-Teller-like theories explain how a solvent
can absorb any vibrational energy within this "band", but how is it that
molecules can rid themselves of superfluous vibrational energies significantly
in excess of these values? We develop a theory for such processes based on the
idea that the crucial liquid motions are those that most rapidly modulate the
force on the vibrating coordinate -- and that by far the most important of
these motions are those involving what we have called the mutual nearest
neighbors of the vibrating solute. Specifically, we suggest that whenever there
is a single solvent molecule sufficiently close to the solute that the solvent
and solute are each other's nearest neighbors, then the instantaneous
scattering dynamics of the solute-solvent pair alone suffices to explain the
high frequency relaxation. The many-body features of the liquid only appear in
the guise of a purely equilibrium problem, that of finding the likelihood of
particularly effective solvent arrangements around the solute. These results
are tested numerically on model diatomic solutes dissolved in atomic fluids
(including the experimentally and theoretically interesting case of I_2 in Xe).
The instantaneous pair theory leads to results in quantitative agreement with
those obtained from far more laborious exact molecular dynamics simulations.Comment: 55 pages, 6 figures Scheduled to appear in J. Chem. Phys., Jan, 199
Relationship between quantum decoherence times and solvation dynamics in condensed phase chemical systems
A relationship between the time scales of quantum coherence loss and
short-time solvent response for a solute/bath system is derived for a Gaussian
wave packet approximation for the bath. Decoherence and solvent response times
are shown to be directly proportional to each other, with the proportionality
coefficient given by the ratio of the thermal energy fluctuations to the
fluctuations in the system-bath coupling. The relationship allows the
prediction of decoherence times for condensed phase chemical systems from well
developed experimental methods.Comment: 10 pages, no figures, late
Mean-atom-trajectory model for the velocity autocorrelation function of monatomic liquids
We present a model for the motion of an average atom in a liquid or
supercooled liquid state and apply it to calculations of the velocity
autocorrelation function and diffusion coefficient . The model
trajectory consists of oscillations at a distribution of frequencies
characteristic of the normal modes of a single potential valley, interspersed
with position- and velocity-conserving transits to similar adjacent valleys.
The resulting predictions for and agree remarkably well with MD
simulations of Na at up to almost three times its melting temperature. Two
independent processes in the model relax velocity autocorrelations: (a)
dephasing due to the presence of many frequency components, which operates at
all temperatures but which produces no diffusion, and (b) the transit process,
which increases with increasing temperature and which produces diffusion.
Because the model provides a single-atom trajectory in real space and time,
including transits, it may be used to calculate all single-atom correlation
functions.Comment: LaTeX, 8 figs. This is an updated version of cond-mat/0002057 and
cond-mat/0002058 combined Minor changes made to coincide with published
versio
A semiclassical trace formula for the canonical partition function of one dimensional systems
We present a semiclassical trace formula for the canonical partition function
of arbitrary one-dimensional systems. The approximation is obtained via the
stationary exponent method applied to the phase-space integration of the
density operator in the coherent state representation. The formalism is valid
in the low temperature limit, presenting accurate results in this regime. As
illustrations we consider a quartic Hamiltonian that cannot be split into
kinetic and potential parts, and a system with two local minima. Applications
to spin systems are also presented.Comment: 22 pages, 4 figures new section with applications to spin system
Global perspectives on the energy landscapes of liquids, supercooled liquids, and glassy systems: The potential energy landscape ensemble
In principle, all of the dynamical complexities of many-body systems are
encapsulated in the potential energy landscapes on which the atoms move - an
observation that suggests that the essentials of the dynamics ought to be
determined by the geometry of those landscapes. But what are the principal
geometric features that control the long-time dynamics? We suggest that the key
lies not in the local minima and saddles of the landscape, but in a more global
property of the surface: its accessible pathways. In order to make this notion
more precise we introduce two ideas: (1) a switch to a new ensemble that
removes the concept of potential barriers from the problem, and (2) a way of
finding optimum pathways within this new ensemble. The potential energy
landscape ensemble, which we describe in the current paper, regards the maximum
accessible potential energy, rather than the temperature, as a control
variable. We show here that while this approach is thermodynamically equivalent
to the canonical ensemble, it not only sidesteps the idea of barriers, it
allows us to be quantitative about the connectivity of a landscape. We
illustrate these ideas with calculations on a simple atomic liquid and on the
Kob-Andersen model of a glass-forming liquid, showing, in the process, that the
landscape of the Kob-Anderson model appears to have a connectivity transition
at the landscape energy associated with its mode-coupling transition. We turn
to the problem of finding the most efficient pathways through potential energy
landscapes in our companion paper.Comment: 43 pages, 7 figure
Entropy, Dynamics and Instantaneous Normal Modes in a Random Energy Model
It is shown that the fraction f of imaginary frequency instantaneous normal
modes (INM) may be defined and calculated in a random energy model(REM) of
liquids. The configurational entropy S and the averaged hopping rate among the
states R are also obtained and related to f, with the results R~f and
S=a+b*ln(f). The proportionality between R and f is the basis of existing INM
theories of diffusion, so the REM further confirms their validity. A link to S
opens new avenues for introducing INM into dynamical theories. Liquid 'states'
are usually defined by assigning a configuration to the minimum to which it
will drain, but the REM naturally treats saddle-barriers on the same footing as
minima, which may be a better mapping of the continuum of configurations to
discrete states. Requirements of a detailed REM description of liquids are
discussed
Nodal domains on quantum graphs
We consider the real eigenfunctions of the Schr\"odinger operator on graphs,
and count their nodal domains. The number of nodal domains fluctuates within an
interval whose size equals the number of bonds . For well connected graphs,
with incommensurate bond lengths, the distribution of the number of nodal
domains in the interval mentioned above approaches a Gaussian distribution in
the limit when the number of vertices is large. The approach to this limit is
not simple, and we discuss it in detail. At the same time we define a random
wave model for graphs, and compare the predictions of this model with analytic
and numerical computations.Comment: 19 pages, uses IOP journal style file
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