4,175 research outputs found
Nonlinear Kinetics on Lattices based on the Kinetic Interaction Principle
Master equations define the dynamics that govern the time evolution of
various physical processes on lattices. In the continuum limit, master
equations lead to Fokker-Planck partial differential equations that represent
the dynamics of physical systems in continuous spaces. Over the last few
decades, nonlinear Fokker-Planck equations have become very popular in
condensed matter physics and in statistical physics. Numerical solutions of
these equations require the use of discretization schemes. However, the
discrete evolution equation obtained by the discretization of a Fokker-Planck
partial differential equation depends on the specific discretization scheme. In
general, the discretized form is different from the master equation that has
generated the respective Fokker-Planck equation in the continuum limit.
Therefore, the knowledge of the master equation associated with a given
Fokker-Planck equation is extremely important for the correct numerical
integration of the latter, since it provides a unique, physically motivated
discretization scheme. This paper shows that the Kinetic Interaction Principle
(KIP) that governs the particle kinetics of many body systems, introduced in
[G. Kaniadakis, Physica A, 296, 405 (2001)], univocally defines a very simple
master equation that in the continuum limit yields the nonlinear Fokker-Planck
equation in its most general form.Comment: 26 page
Physics with Coherent Matter Waves
This review discusses progress in the new field of coherent matter waves, in
particular with respect to Bose-Einstein condensates. We give a short
introduction to Bose-Einstein condensation and the theoretical description of
the condensate wavefunction. We concentrate on the coherence properties of this
new type of matter wave as a basis for fundamental physics and applications.
The main part of this review treats various measurements and concepts in the
physics with coherent matter waves. In particular we present phase manipulation
methods, atom lasers, nonlinear atom optics, optical elements, interferometry
and physics in optical lattices. We give an overview of the state of the art in
the respective fields and discuss achievements and challenges for the future
Properties of discrete breathers in graphane from ab initio simulations
A density functional theory (DFT) study of the discrete breathers (DBs) in
graphane (fully hydrogenated graphene) was performed. To the best of our
knowledge, this is the first demonstration of the existence of DBs in a
crystalline body from the first-principle simulations. It is found that the DB
is a robust, highly localized vibrational mode with one hydrogen atom
oscillating with a large amplitude along the direction normal to the graphane
plane with all neighboring atoms having much smaller vibration amplitudes. DB
frequency decreases with increase in its amplitude, and it can take any value
within the phonon gap and can even enter the low-frequency phonon band. The
concept of DB is then used to propose an explanation to the recent experimental
results on the nontrivial kinetics of graphane dehydrogenation at elevated
temperatures.Comment: 20.07.14 Submitted to PhysRev
Dynamics of Ordering in Alloys with Modulated Phases
This paper presents a theoretical model for studying the dynamics of ordering
in alloys which exhibit modulated phases. The model is different from the
standard time-dependent Ginzburg-Landau description of the evolution of a
non-conserved order parameter and resembles the Swift-Hohenberg model. The
early-stage growth kinetics is analyzed and compared to the Cahn-Hilliard
theory of continuous ordering. The effects of non-linearities on the growth
kinetics are discussed qualitatively and it is shown that the presence of an
underlying elastic lattice introduces qualitatively new effects. A lattice
Hamiltonian capable of describing these effects and suitable for carrying out
simulations of the growth kinetics is also constructed.Comment: 18 pages, 3 figures (postscript files appended), Brandeis-BC9
Macroscopic dynamics of incoherent soliton ensembles: soliton-gas kinetics and direct numerical modeling
We undertake a detailed comparison of the results of direct numerical
simulations of the integrable soliton gas dynamics with the analytical
predictions inferred from the exact solutions of the relevant kinetic equation
for solitons. We use the KdV soliton gas as a simplest analytically accessible
model yielding major insight into the general properties of soliton gases in
integrable systems. Two model problems are considered: (i) the propagation of a
`trial' soliton through a one-component `cold' soliton gas consisting of
randomly distributed solitons of approximately the same amplitude; and (ii)
collision of two cold soliton gases of different amplitudes (soliton gas shock
tube problem) leading to the formation of an incoherend dispersive shock wave.
In both cases excellent agreement is observed between the analytical
predictions of the soliton gas kinetics and the direct numerical simulations.
Our results confirm relevance of the kinetic equation for solitons as a
quantitatively accurate model for macroscopic non-equilibrium dynamics of
incoherent soliton ensembles.Comment: 20 pages, 8 figures, 34 references. Other author's papers can be
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