1,179 research outputs found
Non-adiabatic dynamics of electrons and atoms under non-equilibrium conditions
An approach to non-adiabatic dynamics of atoms in molecular and condensed
matter systems under general non-equilibrium conditions is proposed. In this
method interaction between nuclei and electrons is considered explicitly up to
the second order in atomic displacements defined with respect to the mean
atomic trajectory. This method enables one to consider movement of atoms beyond
their simple vibrations. Both electrons and nuclei are treated fully
quantum-mechanically using a combination of path integrals applied to nuclei
and non-equilibrium Green's functions (NEGF) to elections. Our method is
partition-less: initially, the entire system is coupled and assumed to be at
thermal equilibrium. Then, the exact application of the Hubbard-Stratanovich
transformation in mixed real and imaginary times enables us to obtain, without
doing any additional approximations, an exact expression for the reduced
density matrix for nuclei and hence an effective quantum Liouville equation for
them, both containing Gaussian noises. It is shown that the time evolution of
the expectation values for atomic positions is described by an infinite
hierarchy of stochastic differential equations for atomic positions and momenta
and their various fluctuations. The actual dynamics is obtained by sampling all
stochastic trajectories. It is expected that applications of the method may
include photo-induced chemical reactions (e.g. dissociation), electromigration,
atomic manipulation in scanning tunneling microscopy, to name just a few.Comment: 30 pages, 1 fugur
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
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
Nonequilibrium processes from Generalised Langevin Equations: realistic nanoscale systems connected to two thermal baths
We extend the Generalised Langevin Equation (GLE) method [Phys. Rev. B 89,
134303 (2014)] to model a central classical region connected to two realistic
thermal baths at two different temperatures. In such nonequilibrium conditions
a heat flow is established, via the central system, in between the two baths.
The GLE-2B (GLE two baths) scheme permits us to have a realistic description of
both the dissipative central system and its surrounding baths. Following the
original GLE approach, the extended Langevin dynamics scheme is modified to
take into account two sets of auxiliary degrees of freedom corresponding to the
mapping of the vibrational properties of each bath. These auxiliary variables
are then used to solve the non-Markovian dissipative dynamics of the central
region. The resulting algorithm is used to study a model of a short Al nanowire
connected to two baths. The results of the simulations using the GLE-2B
approach are compared to the results of other simulations that were carried out
using standard thermostatting approaches (based on Markovian Langevin and
Nose-Hoover thermostats). We concentrate on the steady state regime and study
the establishment of a local temperature profile within the system. The
conditions for obtaining a flat profile or a temperature gradient are examined
in detail, in agreement with earlier studies. The results show that the GLE-2B
approach is able to treat, within a single scheme, two widely different thermal
transport regimes, i.e. ballistic systems, with no temperature gradient, and
diffusive systems with a temperature gradient.Comment: present version accepted for publication in Phys. Rev. B (Apr 2016
Non-equilibrium statistical mechanics of classical nuclei interacting with the quantum electron gas
Kinetic equations governing time evolution of positions and momenta of atoms
in extended systems are derived using quantum-classical ensembles within the
Non-Equilibrium Statistical Operator Method (NESOM). Ions are treated
classically, while their electrons quantum mechanically; however, the
statistical operator is not factorised in any way and no simplifying
assumptions are made concerning the electronic subsystem. Using this method, we
derive kinetic equations of motion for the classical degrees of freedom (atoms)
which account fully for the interaction and energy exchange with the quantum
variables (electrons). Our equations, alongside the usual Newtonian-like terms
normally associated with the Ehrenfest dynamics, contain additional terms,
proportional to the atoms velocities, which can be associated with the
electronic friction. Possible ways of calculating the friction forces which are
shown to be given via complicated non-equilibrium correlation functions, are
discussed. In particular, we demonstrate that the correlation functions are
directly related to the thermodynamic Matsubara Green's functions, and this
relationship allows for the diagrammatic methods to be used in treating
electron-electron interaction perturbatively when calculating the correlation
functions. This work also generalises previous attempts, mostly based on model
systems, of introducing the electronic friction into Molecular Dynamics
equations of atoms.Comment: 18 page
Calculation of electron density of periodic systems using non-orthogonal localised orbitals
Methods for calculating an electron density of a periodic crystal constructed
using non-orthogonal localised orbitals are discussed. We demonstrate that an
existing method based on the matrix expansion of the inverse of the overlap
matrix into a power series can only be used when the orbitals are highly
localised (e.g. ionic systems). In other cases including covalent crystals or
those with an intermediate type of chemical bonding this method may be either
numerically inefficient or fail altogether. Instead, we suggest an exact and
numerically efficient method which can be used for orbitals of practically
arbitrary localisation. Theory is illustrated by numerical calculations on a
model system.Comment: 12 pages, 4 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
Fr\'echet frames, general definition and expansions
We define an {\it -frame} with Banach spaces , , and a -space (\Theta, \snorm[\cdot]).
Then by the use of decreasing sequences of Banach spaces
and of sequence spaces , we define a general Fr\'
echet frame on the Fr\' echet space . We give
frame expansions of elements of and its dual , as well of some of
the generating spaces of with convergence in appropriate norms. Moreover,
we give necessary and sufficient conditions for a general pre-Fr\' echet frame
to be a general Fr\' echet frame, as well as for the complementedness of the
range of the analysis operator .Comment: A new section is added and a minor revision is don
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