465 research outputs found
Mapping quantum-classical Liouville equation: projectors and trajectories
The evolution of a mixed quantum-classical system is expressed in the mapping
formalism where discrete quantum states are mapped onto oscillator states,
resulting in a phase space description of the quantum degrees of freedom. By
defining projection operators onto the mapping states corresponding to the
physical quantum states, it is shown that the mapping quantum-classical
Liouville operator commutes with the projection operator so that the dynamics
is confined to the physical space. It is also shown that a trajectory-based
solution of this equation can be constructed that requires the simulation of an
ensemble of entangled trajectories. An approximation to this evolution equation
which retains only the Poisson bracket contribution to the evolution operator
does admit a solution in an ensemble of independent trajectories but it is
shown that this operator does not commute with the projection operators and the
dynamics may take the system outside the physical space. The dynamical
instabilities, utility and domain of validity of this approximate dynamics are
discussed. The effects are illustrated by simulations on several quantum
systems.Comment: 4 figure
Effective pair potentials for spherical nanoparticles
An effective description for spherical nanoparticles in a fluid of point
particles is presented. The points inside the nanoparticles and the point
particles are assumed to interact via spherically symmetric additive pair
potentials, while the distribution of points inside the nanoparticles is taken
to be spherically symmetric and smooth. The resulting effective pair
interactions between a nanoparticle and a point particle, as well as between
two nanoparticles, are then given by spherically symmetric potentials. If
overlap between particles is allowed, the effective potential generally has
non-analytic points, but for each effective potential the expressions for
different overlapping cases can be written in terms of one analytic auxiliary
potential. Effective potentials for hollow nanoparticles (appropriate e.g. for
buckyballs) are also considered, and shown to be related to those for solid
nanoparticles. Finally, explicit expressions are given for the effective
potentials derived from basic pair potentials of power law and exponential
form, as well as from the commonly used London-Van der Waals, Morse,
Buckingham, and Lennard-Jones potential. The applicability of the latter is
demonstrated by comparison with an atomic description of nanoparticles with an
internal face centered cubic structure.Comment: 27 pages, 12 figures. Unified description of overlapping and
nonoverlapping particles added, as well as a comparison with an idealized
atomic descriptio
Efficient algorithms for rigid body integration using optimized splitting methods and exact free rotational motion
Hamiltonian splitting methods are an established technique to derive stable
and accurate integration schemes in molecular dynamics, in which additional
accuracy can be gained using force gradients. For rigid bodies, a tradition
exists in the literature to further split up the kinetic part of the
Hamiltonian, which lowers the accuracy. The goal of this note is to comment on
the best combination of optimized splitting and gradient methods that avoids
splitting the kinetic energy. These schemes are generally applicable, but the
optimal scheme depends on the desired level of accuracy. For simulations of
liquid water it is found that the velocity Verlet scheme is only optimal for
crude simulations with accuracies larger than 1.5%, while surprisingly a
modified Verlet scheme (HOA) is optimal up to accuracies of 0.4% and a fourth
order gradient scheme (GIER4) is optimal for even higher accuracies.Comment: 2 pages, 1 figure. Added clarifying comments. Accepted for
publication in the Journal of Chemical Physic
An Extension of the Fluctuation Theorem
Heat fluctuations are studied in a dissipative system with both mechanical
and stochastic components for a simple model: a Brownian particle dragged
through water by a moving potential. An extended stationary state fluctuation
theorem is derived. For infinite time, this reduces to the conventional
fluctuation theorem only for small fluctuations; for large fluctuations, it
gives a much larger ratio of the probabilities of the particle to absorb rather
than supply heat. This persists for finite times and should be observable in
experiments similar to a recent one of Wang et al.Comment: 12 pages, 1 eps figure in color (though intelligible in black and
white
The Lyapunov spectrum of the many-dimensional dilute random Lorentz gas
For a better understanding of the chaotic behavior of systems of many moving
particles it is useful to look at other systems with many degrees of freedom.
An interesting example is the high-dimensional Lorentz gas, which, just like a
system of moving hard spheres, may be interpreted as a dynamical system
consisting of a point particle in a high-dimensional phase space, moving among
fixed scatterers. In this paper, we calculate the full spectrum of Lyapunov
exponents for the dilute random Lorentz gas in an arbitrary number of
dimensions. We find that the spectrum becomes flatter with increasing
dimensionality. Furthermore, for fixed collision frequency the separation
between the largest Lyapunov exponent and the second largest one increases
logarithmically with dimensionality, whereas the separations between Lyapunov
exponents of given indices not involving the largest one, go to fixed limits.Comment: 8 pages, revtex, 6 figures, submitted to Physical Review
Onsager-Machlup theory and work fluctuation theorem for a harmonically driven Brownian particle
We extend Tooru-Cohen analysis for nonequilirium steady state(NSS) of a
Brownian particle to nonequilibrium oscillatory state (NOS) of Brownian
particle by considering time dependent external drive protocol. We consider an
unbounded charged Brownian particle in the presence of an oscillating electric
field and prove work fluctuation theorem, which is valid for any initial
distribution and at all times. For harmonically bounded and constantly dragged
Brownian particle considered by Tooru and Cohen, work fluctuation theorem is
valid for any initial condition(also NSS), but only in large time limit. We use
Onsager-Machlup Lagrangian with a constraint to obtain frequency dependent work
distribution function, and describe entropy production rate and properties of
dissipation functions for the present system using Onsager-Machlup functional.Comment: 6 pages, 1 figur
Extended Heat-Fluctuation Theorems for a System with Deterministic and Stochastic Forces
Heat fluctuations over a time \tau in a non-equilibrium stationary state and
in a transient state are studied for a simple system with deterministic and
stochastic components: a Brownian particle dragged through a fluid by a
harmonic potential which is moved with constant velocity. Using a Langevin
equation, we find the exact Fourier transform of the distribution of these
fluctuations for all \tau. By a saddle-point method we obtain analytical
results for the inverse Fourier transform, which, for not too small \tau, agree
very well with numerical results from a sampling method as well as from the
fast Fourier transform algorithm. Due to the interaction of the deterministic
part of the motion of the particle in the mechanical potential with the
stochastic part of the motion caused by the fluid, the conventional heat
fluctuation theorem is, for infinite and for finite \tau, replaced by an
extended fluctuation theorem that differs noticeably and measurably from it. In
particular, for large fluctuations, the ratio of the probability for absorption
of heat (by the particle from the fluid) to the probability to supply heat (by
the particle to the fluid) is much larger here than in the conventional
fluctuation theorem.Comment: 23 pages, 6 figures. Figures are now in color, Eq. (67) was corrected
and a footnote was added on the d-dimensional cas
Lyapunov spectra of billiards with cylindrical scatterers: comparison with many-particle systems
The dynamics of a system consisting of many spherical hard particles can be
described as a single point particle moving in a high-dimensional space with
fixed hypercylindrical scatterers with specific orientations and positions. In
this paper, the similarities in the Lyapunov exponents are investigated between
systems of many particles and high-dimensional billiards with cylindrical
scatterers which have isotropically distributed orientations and homogeneously
distributed positions. The dynamics of the isotropic billiard are calculated
using a Monte-Carlo simulation, and a reorthogonalization process is used to
find the Lyapunov exponents. The results are compared to numerical results for
systems of many hard particles as well as the analytical results for the
high-dimensional Lorentz gas. The smallest three-quarters of the positive
exponents behave more like the exponents of hard-disk systems than the
exponents of the Lorentz gas. This similarity shows that the hard-disk systems
may be approximated by a spatially homogeneous and isotropic system of
scatterers for a calculation of the smaller Lyapunov exponents, apart from the
exponent associated with localization. The method of the partial stretching
factor is used to calculate these exponents analytically, with results that
compare well with simulation results of hard disks and hard spheres.Comment: Submitted to PR
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