10,136 research outputs found
Modelling a Bistable System Strongly Coupled to a Debye Bath: A Quasiclassical Approach Based on the Generalised Langevin Equation
Bistable systems present two degenerate metastable configurations separated
by an energy barrier. Thermal or quantum fluctuations can promote the
transition between the configurations at a rate which depends on the dynamical
properties of the local environment (i.e., a thermal bath). In the case of
classical systems, strong system-bath interaction has been successfully
modelled by the Generalised Langevin Equation (GLE) formalism. Here we show
that the efficient GLE algorithm introduced in Phys. Rev. B 89, 134303 (2014)
can be extended to include some crucial aspects of the quantum fluctuations. In
particular, the expected isotopic effect is observed along with the convergence
of the quantum and classical transition rates in the strong coupling limit.
Saturation of the transition rates at low temperature is also retrieved, in
qualitative, yet not quantitative, agreement with the analytic predictions. The
discrepancies in the tunnelling regime are due to an incorrect sampling close
to the barrier top. The domain of applicability of the quasiclassical GLE is
also discussed.Comment: 21 pages, 5 figures. Presented at the NESC16 conference: Advances in
theory and simulation of non-equilibrium system
Applications of the Generalised Langevin Equation: towards a realistic description of the baths
The Generalised Langevin Equation (GLE) method, as developed in Ref. [Phys.
Rev. B 89, 134303 (2014)], is used to calculate the dissipative dynamics of
systems described at the atomic level. The GLE scheme goes beyond the commonly
used bilinear coupling between the central system and the bath, and permits us
to have a realistic description of both the dissipative central system and its
surrounding bath. We show how to obtain the vibrational properties of a
realistic bath and how to convey such properties into an extended Langevin
dynamics by the use of the mapping of the bath vibrational properties onto a
set of auxiliary variables. Our calculations for a model of a Lennard-Jones
solid show that our GLE scheme provides a stable dynamics, with the
dissipative/relaxation processes properly described. The total kinetic energy
of the central system always thermalises toward the expected bath temperature,
with appropriate fluctuation around the mean value. More importantly, we obtain
a velocity distribution for the individual atoms in the central system which
follows the expected canonical distribution at the corresponding temperature.
This confirms that both our GLE scheme and our mapping procedure onto an
extended Langevin dynamics provide the correct thermostat. We also examined the
velocity autocorrelation functions and compare our results with more
conventional Langevin dynamics.Comment: accepted for publication in PR
Power law tails of time correlations in a mesoscopic fluid model
In a quenched mesoscopic fluid, modelling transport processes at high
densities, we perform computer simulations of the single particle energy
autocorrelation function C_e(t), which is essentially a return probability.
This is done to test the predictions for power law tails, obtained from mode
coupling theory. We study both off and on-lattice systems in one- and
two-dimensions. The predicted long time tail ~ t^{-d/2} is in excellent
agreement with the results of computer simulations. We also account for finite
size effects, such that smaller systems are fully covered by the present theory
as well.Comment: 11 pages, 12 figure
Ricci Collineations of the Bianchi Type II, VIII, and IX Space-times
Ricci and contracted Ricci collineations of the Bianchi type II, VIII, and IX
space-times, associated with the vector fields of the form (i) one component of
is different from zero and (ii) two components of are
different from zero, for , are presented. In subcase (i.b), which
is , some known solutions are found, and in subcase
(i.d), which is , choosing ,
the Bianchi type II, VIII, and IX space-times is reduced to the
Robertson-Walker metric.Comment: 12 Pages, LaTeX, 1 Table, no figure
Nonequilibrium Generalised Langevin Equation for the calculation of heat transport properties in model 1D atomic chains coupled to two 3D thermal baths
We use a Generalised Langevin Equation (GLE) scheme to study the thermal
transport of low dimensional systems. In this approach, the central classical
region is connected to two realistic thermal baths kept at two different
temperatures [H. Ness et al., Phys. Rev. B {\bf 93}, 174303 (2016)]. We
consider model Al systems, i.e. one-dimensional atomic chains connected to
three-dimensional baths. The thermal transport properties are studied as a
function of the chain length and the temperature difference
between the baths. We calculate the transport properties both in the linear
response regime and in the non-linear regime. Two different laws are obtained
for the linear conductance versus the length of the chains. For large
temperatures ( K) and temperature differences ( K), the chains, with atoms, present a diffusive transport regime
with the presence of a temperature gradient across the system. For lower
temperatures( K) and temperature differences ( K), a regime similar to the ballistic regime is observed. Such a
ballistic-like regime is also obtained for shorter chains (). Our
detailed analysis suggests that the behaviour at higher temperatures and
temperature differences is mainly due to anharmonic effects within the long
chains.Comment: Accepted for publication in J. Chem. Phy
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