Vlasov scaling for the Glauber dynamics in continuum

We consider Vlasov-type scaling for the Glauber dynamics in continuum with a positive integrable potential, and construct rescaled and limiting evolutions of correlation functions. Convergence to the limiting evolution for the positive density system in infinite volume is shown. Chaos preservation property of this evolution gives a possibility to derive a non-linear Vlasov-type equation for the particle density of the limiting system.Comment: 32 page

Longitudinal patterns in an Arkansas River Valley stream: an Application of the River Continuum Concept

The River Continuum Concept (RCC) provides the framework for studying how lotic ecosystems vary from headwater streams to large rivers. The RCC was developed in streams in eastern deciduous forests of North America, but watershed characteristics and land uses differ across ecoregions, presenting unique opportunities to study how predictions of the RCC may differ across regions. Additionally, RCC predictions may vary due to the influence of fishes, but few studies have used fish taxa as a metric for evaluating predictions of the RCC. Our goal was to determine if RCC predictions for stream orders 1 through 5 were supported by primary producer, macroinvertebrate, and fish communities in Cadron Creek of the Arkansas River Valley. We sampled chlorophyll a, macroinvertebrates, and fishes at five stream reaches across a gradient of watershed size. Contrary to RCC predictions, chlorophyll a did not increase in concentration with catchment size. As the RCC predicts, fish and macroinvertebrate diversity increased with catchment size. Shredding and collecting macroinvertebrate taxa supported RCC predictions, respectively decreasing and increasing in composition as catchment area increased. Herbivorous and predaceous fish did not follow RCC predictions; however, surface-water column feeding fish were abundant at all sites as predicted. We hypothesize some predictions of the RCC were not supported in headwater reaches of this system due to regional differences in watershed characteristics and altered resource availability due to land use surrounding sampling sites

Integral operators with the generalized sine-kernel on the real axis

The asymptotic properties of integral operators with the generalized sine kernel acting on the real axis are studied. The formulas for the resolvent and the Fredholm determinant are obtained in the large x limit. Some applications of the results obtained to the theory of integrable models are considered.Comment: 17 pages, 2 Postscript figures, submitted to Theor. Math. Phy

Vortices in a cylinder: Localization after depinning

Edge effects in the depinned phase of flux lines in hollow superconducting cylinder with columnar defects and electric current along the cylinder are investigated. Far from the ends of the cylinder vortices are distributed almost uniformly (delocalized). Nevertheless, near the edges these free vortices come closer together and form well resolved dense bunches. A semiclassical picture of this localization after depinning is described. For a large number of vortices their density $\rho(x)$ has square root singularity at the border of the bunch ($\rho(x)$ is semicircle in the simplest case). However, by tuning the strength of current, the various singular regimes for $\rho(x)$ may be reached. Remarkably, this singular behaviour reproduces the phase transitions discussed during the past decade within the random matrix regularization of 2d-Gravity.Comment: 4 pages, REVTEX, 2 eps figure

Three-coloring statistical model with domain wall boundary conditions. I. Functional equations

In 1970 Baxter considered the statistical three-coloring lattice model for the case of toroidal boundary conditions. He used the Bethe ansatz and found the partition function of the model in the thermodynamic limit. We consider the same model but use other boundary conditions for which one can prove that the partition function satisfies some functional equations similar to the functional equations satisfied by the partition function of the six-vertex model for a special value of the crossing parameter.Comment: 16 pages, notations changed for consistency with the next part, appendix adde

Bosons in cigar-shape traps: Thomas-Fermi regime, Tonks-Girardeau regime, and between

We present a quantitative analysis of the experimental accessibility of the Tonks-Girardeau gas in the current day experiments with cigar-trapped alkalis. For this purpose we derive, using a Bethe anzats generated local equation of state, a set of hydrostatic equations describing one-dimensional delta-interacting Bose gases trapped in a harmonic potential. The resulting solutions cover the_entire range_ of atomic densities.Comment: 4 pages, 4 figure

Exact Dynamical Correlation Functions of Calogero-Sutherland Model and One-Dimensional Fractional Statistics

One-dimensional model of non-relativistic particles with inverse-square interaction potential known as Calogero-Sutherland Model (CSM) is shown to possess fractional statistics. Using the theory of Jack symmetric polynomial the exact dynamical density-density correlation function and the one-particle Green's function (hole propagator) at any rational interaction coupling constant $\lambda = p/q$ are obtained and used to show clear evidences of the fractional statistics. Motifs representing the eigenstates of the model are also constructed and used to reveal the fractional {\it exclusion} statistics (in the sense of Haldane's ``Generalized Pauli Exclusion Principle''). This model is also endowed with a natural {\it exchange } statistics (1D analog of 2D braiding statistics) compatible with the {\it exclusion} statistics. (Submitted to PRL on April 18, 1994)Comment: Revtex 11 pages, IASSNS-HEP-94/27 (April 18, 1994

Many-body solitons in a one-dimensional condensate of hard core bosons

A mapping theorem leading to exact many-body dynamics of impenetrable bosons in one dimension reveals dark and gray soliton-like structures in a toroidal trap which is phase-imprinted. On long time scales revivals appear that are beyond the usual mean-field theory

Ground state properties of a one-dimensional condensate of hard core bosons in a harmonic trap

The exact N-particle ground state wave function for a one-dimensional condensate of hard core bosons in a harmonic trap is employed to obtain accurate numerical results for the one-particle density matrix, occupation number distribution of the natural orbitals, and momentum distribution. Our results show that the occupation of the lowest orbital varies as N^{0.59}, in contrast to N^{0.5} for a spatially uniform system, and N for a true BEC.Comment: 10 pages, 6 figures, submitted to Phys. Rev.

Remarks on Shannon's Statistical Inference and the Second Law in Quantum Statistical Mechanics

We comment on a formulation of quantum statistical mechanics, which incorporates the statistical inference of Shannon. Our basic idea is to distinguish the dynamical entropy of von Neumann, $H = -k Tr \hat{\rho}\ln\hat{\rho}$, in terms of the density matrix $\hat{\rho}(t)$, and the statistical amount of uncertainty of Shannon, $S= -k \sum_{n}p_{n}\ln p_{n}$, with $p_{n}=$ in the representation where the total energy and particle numbers are diagonal. These quantities satisfy the inequality $S\geq H$. We propose to interprete Shannon's statistical inference as specifying the {\em initial conditions} of the system in terms of $p_{n}$. A definition of macroscopic observables which are characterized by intrinsic time scales is given, and a quantum mechanical condition on the system, which ensures equilibrium, is discussed on the basis of time averaging. An interesting analogy of the change of entroy with the running coupling in renormalization group is noted. A salient feature of our approach is that the distinction between statistical aspects and dynamical aspects of quantum statistical mechanics is very transparent.Comment: 16 pages. Minor refinement in the statements in the previous version. This version has been published in Journal of Phys. Soc. Jpn. 71 (2002) 6