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 $\nu$ exist only for $|\nu|$ 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 $R^{1,d-3}\times T^2$ at finite temperature and fermion density. The Phase structure of the vacuum is presented for the case with $d=4$ 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)