220 research outputs found
A Variational Procedure for Time-Dependent Processes
A simple variational Lagrangian is proposed for the time development of an
arbitrary density matrix, employing the "factorization" of the density. Only
the "kinetic energy" appears in the Lagrangian. The formalism applies to pure
and mixed state cases, the Navier-Stokes equations of hydrodynamics, transport
theory, etc. It recaptures the Least Dissipation Function condition of
Rayleigh-Onsager {\bf and in practical applications is flexible}. The
variational proposal is tested on a two level system interacting that is
subject, in one instance, to an interaction with a single oscillator and, in
another, that evolves in a dissipative mode.Comment: 25 pages, 4 figure
A methodology for determining amino-acid substitution matrices from set covers
We introduce a new methodology for the determination of amino-acid
substitution matrices for use in the alignment of proteins. The new methodology
is based on a pre-existing set cover on the set of residues and on the
undirected graph that describes residue exchangeability given the set cover.
For fixed functional forms indicating how to obtain edge weights from the set
cover and, after that, substitution-matrix elements from weighted distances on
the graph, the resulting substitution matrix can be checked for performance
against some known set of reference alignments and for given gap costs. Finding
the appropriate functional forms and gap costs can then be formulated as an
optimization problem that seeks to maximize the performance of the substitution
matrix on the reference alignment set. We give computational results on the
BAliBASE suite using a genetic algorithm for optimization. Our results indicate
that it is possible to obtain substitution matrices whose performance is either
comparable to or surpasses that of several others, depending on the particular
scenario under consideration
Systematic model behavior of adsorption on flat surfaces
A low density film on a flat surface is described by an expansion involving
the first four virial coefficients. The first coefficient (alone) yields the
Henry's law regime, while the next three correct for the effects of
interactions. The results permit exploration of the idea of universal
adsorption behavior, which is compared with experimental data for a number of
systems
Studies of Phase Turbulence in the One Dimensional Complex Ginzburg-Landau Equation
The phase-turbulent (PT) regime for the one dimensional complex
Ginzburg-Landau equation (CGLE) is carefully studied, in the limit of large
systems and long integration times, using an efficient new integration scheme.
Particular attention is paid to solutions with a non-zero phase gradient. For
fixed control parameters, solutions with conserved average phase gradient
exist only for less than some upper limit. The transition from phase to
defect-turbulence happens when this limit becomes zero. A Lyapunov analysis
shows that the system becomes less and less chaotic for increasing values of
the phase gradient. For high values of the phase gradient a family of
non-chaotic solutions of the CGLE is found. These solutions consist of
spatially periodic or aperiodic waves travelling with constant velocity. They
typically have incommensurate velocities for phase and amplitude propagation,
showing thereby a novel type of quasiperiodic behavior. The main features of
these travelling wave solutions can be explained through a modified
Kuramoto-Sivashinsky equation that rules the phase dynamics of the CGLE in the
PT phase. The latter explains also the behavior of the maximal Lyapunov
exponents of chaotic solutions.Comment: 16 pages, LaTeX (Version 2.09), 10 Postscript-figures included,
submitted to Phys. Rev.
Band-gaps in long Josephson junctions with periodic phase-shifts
We investigate analytically and numerically a long Josephson junction on an infnite domain, having arbitrary periodic phase shift of k, that is, the so-called 0-k long Josephson junction. The system is described by a one-dimensional sine-Gordon equation and has relatively recently been proposed as artificial atom lattices. We discuss the existence of periodic solutions of the system and investigate their stability both in the absence and presence of an applied bias current. We find critical values of the phase-discontinuity and the applied bias current beyond which a solution switches to its complementary counterpart. Due to the periodic discontinuity in the phase, the system admits regions of allowed and forbidden bands. We perturbatively investigate the Arnold tongues that separate the region of allowed and forbidden bands, and discuss the effect of an applied bias current on the band-gap structure. We present numerical simulations to support our analytical results
Recurrent dynamical symmetry breaking and restoration by Wilson lines at finite densities on a torus
In this paper we derive the general expression of a one-loop effective
potential of the nonintegrable phases of Wilson lines for an SU(N) gauge theory
with a massless adjoint fermion defined on the spactime manifold
at finite temperature and fermion density. The Phase
structure of the vacuum is presented for the case with and N=2 at zero
temperature. It is found that gauge symmetry is broken and restored alternately
as the fermion density increases, a feature not found in the Higgs mechanism.
It is the manifestation of the quantum effects of the nonintegrable phases.Comment: 17 pages, 2 figure
Some aspects of the Liouville equation in mathematical physics and statistical mechanics
This paper presents some mathematical aspects of Classical Liouville theorem
and we have noted some mathematical theorems about its initial value problem.
Furthermore, we have implied on the formal frame work of Stochastic Liouville
equation (SLE)
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