8,692 research outputs found
Non-ergodic transitions in many-body Langevin systems: a method of dynamical system reduction
We study a non-ergodic transition in a many-body Langevin system. We first
derive an equation for the two-point time correlation function of density
fluctuations, ignoring the contributions of the third- and fourth-order
cumulants. For this equation, with the average density fixed, we find that
there is a critical temperature at which the qualitative nature of the
trajectories around the trivial solution changes. Using a method of dynamical
system reduction around the critical temperature, we simplify the equation for
the time correlation function into a two-dimensional ordinary differential
equation. Analyzing this differential equation, we demonstrate that a
non-ergodic transition occurs at some temperature slightly higher than the
critical temperature.Comment: 8 pages, 1 figure; ver.3: Calculation errors have been fixe
Assembling strategies in extrinsic evolvable hardware with bi-directional incremental evolution
Bidirectional incremental evolution (BIE) has been proposed as a technique to overcome the âstallingâ effect in evolvable hardware applications. However preliminary results show perceptible dependence of performance of BIE and quality of evaluated circuit on assembling strategy applied during reverse stage of incremental evolution. The purpose of this paper is to develop assembling strategy that will assist BIE to produce relatively optimal solution with minimal computational effort (e.g. the minimal number of generations)
Photoabsorption spectra in the continuum of molecules and atomic clusters
We present linear response theories in the continuum capable of describing
photoionization spectra and dynamic polarizabilities of finite systems with no
spatial symmetry. Our formulations are based on the time-dependent local
density approximation with uniform grid representation in the three-dimensional
Cartesian coordinate. Effects of the continuum are taken into account either
with a Green's function method or with a complex absorbing potential in a
real-time method. The two methods are applied to a negatively charged cluster
in the spherical jellium model and to some small molecules (silane, acetylene
and ethylene).Comment: 13 pages, 9 figure
Nonadiabatic generation of coherent phonons
The time-dependent density functional theory (TDDFT) is the leading
computationally feasible theory to treat excitations by strong electromagnetic
fields. Here the theory is applied to coherent optical phonon generation
produced by intense laser pulses. We examine the process in the crystalline
semimetal antimony (Sb), where nonadiabatic coupling is very important. This
material is of particular interest because it exhibits strong phonon coupling
and optical phonons of different symmetries can be observed. The TDDFT is able
to account for a number of qualitative features of the observed coherent
phonons, despite its unsatisfactory performance on reproducing the observed
dielectric functions of Sb. A simple dielectric model for nonadiabatic coherent
phonon generation is also examined and compared with the TDDFT calculations.Comment: 19 pages, 11 figures. This is prepared for a special issue of Journal
of Chemical Physics on the topic of nonadiabatic processe
A universal form of slow dynamics in zero-temperature random-field Ising model
The zero-temperature Glauber dynamics of the random-field Ising model
describes various ubiquitous phenomena such as avalanches, hysteresis, and
related critical phenomena. Here, for a model on a random graph with a special
initial condition, we derive exactly an evolution equation for an order
parameter. Through a bifurcation analysis of the obtained equation, we reveal a
new class of cooperative slow dynamics with the determination of critical
exponents.Comment: 4 pages, 2 figure
Dynamics of k-core percolation in a random graph
We study the edge deletion process of random graphs near a k-core percolation
point. We find that the time-dependent number of edges in the process exhibits
critically divergent fluctuations. We first show theoretically that the k-core
percolation point is exactly given as the saddle-node bifurcation point in a
dynamical system. We then determine all the exponents for the divergence based
on a universal description of fluctuations near the saddle-node bifurcation.Comment: 16 pages, 4 figure
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