664 research outputs found
The explicit expression of the fugacity for weakly interacting Bose and Fermi gases
In this paper, we calculate the explicit expression for the fugacity for two-
and three-dimensional weakly interacting Bose and Fermi gases from their
equations of state in isochoric and isobaric processes, respectively, based on
the mathematical result of the boundary problem of analytic functions --- the
homogeneous Riemann-Hilbert problem. We also discuss the Bose-Einstein
condensation phase transition of three-dimensional hard-sphere Bose gases.Comment: 24 pages, 9 figure
Limiting Laws of Linear Eigenvalue Statistics for Unitary Invariant Matrix Models
We study the variance and the Laplace transform of the probability law of
linear eigenvalue statistics of unitary invariant Matrix Models of
n-dimentional Hermitian matrices as n tends to infinity. Assuming that the test
function of statistics is smooth enough and using the asymptotic formulas by
Deift et al for orthogonal polynomials with varying weights, we show first that
if the support of the Density of States of the model consists of two or more
intervals, then in the global regime the variance of statistics is a
quasiperiodic function of n generically in the potential, determining the
model. We show next that the exponent of the Laplace transform of the
probability law is not in general 1/2variance, as it should be if the Central
Limit Theorem would be valid, and we find the asymptotic form of the Laplace
transform of the probability law in certain cases
Integral equations of a cohesive zone model for history-dependent materials and their numerical solution
A nonlinear history-dependent cohesive zone (CZ) model of quasi-static crack propagation in
linear elastic and viscoelastic materials is presented. The viscoelasticity is described by a linear
Volterra integral operator in time. The normal stress on the CZ satisfies the history-dependent yield
condition, given by a nonlinear Abel-type integral operator. The crack starts propagating, breaking
the CZ, when the crack tip opening reaches a prescribed critical value. A numerical algorithm for
computing the evolution of the crack and CZ in time is discussed along with some numerical
results
On the applicability of the equations-of-motion technique for quantum dots
The equations-of-motion (EOM) hierarchy satisfied by the Green functions of a
quantum dot embedded in an external mesoscopic network is considered within a
high-order decoupling approximation scheme. Exact analytic solutions of the
resulting coupled integral equations are presented in several limits. In
particular, it is found that at the particle-hole symmetric point the EOM Green
function is temperature-independent due to a discontinuous change in the
imaginary part of the interacting self-energy. However, this imaginary part
obeys the Fermi liquid unitarity requirement away from this special point, at
zero temperature. Results for the occupation numbers, the density of states and
the local spin susceptibility are compared with exact Fermi liquid relations
and the Bethe ansatz solution. The approximation is found to be very accurate
far from the Kondo regime. In contrast, the description of the Kondo effect is
valid on a qualitative level only. In particular, we find that the Friedel sum
rule is considerably violated, up to 30%, and the spin susceptibility is
underestimated. We show that the widely-used simplified version of the EOM
method, which does not account fully for the correlations on the network, fails
to produce the Kondo correlations even qualitatively.Comment: 16 pages, 5 figure
Conformal Dynamics of Precursors to Fracture
An exact integro-differential equation for the conformal map from the unit
circle to the boundary of an evolving cavity in a stressed 2-dimensional solid
is derived. This equation provides an accurate description of the dynamics of
precursors to fracture when surface diffusion is important. The solution
predicts the creation of sharp grooves that eventually lead to material failure
via rapid fracture. Solutions of the new equation are demonstrated for the
dynamics of an elliptical cavity and the stability of a circular cavity under
biaxial stress, including the effects of surface stress.Comment: 4 pages, 3 figure
Asymptotic form of two-point correlation function of the XXZ spin chain
Correlation functions of the XXZ spin chain in the critical regime is studied
at zero-temperature. They are exactly represented in the Fredholm determinant
form and are related with an operator-valued Riemann-Hilbert problem. Analyzing
this problem we prove that a two-point correlation function consisting of
sufficiently separated spin operators is expressed by power-functions of the
distance between those operators.Comment: 9 pages, LaTeX2e (+ amssymb, amsthm); Proof of Lemma 1 is revise
Generalized kinetic equations for charge carriers in graphene
A system of generalized kinetic equations for the distribution functions of
two-dimensional Dirac fermions scattered by impurities is derived in the Born
approximation with respect to short-range impurity potential. It is proven that
the conductivity following from classical Boltzmann equation picture, where
electrons or holes have scattering amplitude reduced due chirality, is
justified except for an exponentially narrow range of chemical potential near
the conical point. When in this range, creation of infinite number of
electron-hole pairs related to quasi-relativistic nature of electrons in
graphene results in a renormalization of minimal conductivity as compared to
the Boltzmann term and logarithmic corrections in the conductivity similar to
the Kondo effect.Comment: final version, Phys. Rev. B, accepte
Eigenvalue correlations on Hyperelliptic Riemann surfaces
In this note we compute the functional derivative of the induced charge
density, on a thin conductor, consisting of the union of g+1 disjoint
intervals, with respect to an external
potential. In the context of random matrix theory this object gives the
eigenvalue fluctuations of Hermitian random matrix ensembles where the
eigenvalue density is supported on J.Comment: latex 2e, seven pages, one figure. To appear in Journal of Physics
Bi-Laplacian Growth Patterns in Disordered Media
Experiments in quasi 2-dimensional geometry (Hele Shaw cells) in which a
fluid is injected into a visco-elastic medium (foam, clay or
associating-polymers) show patterns akin to fracture in brittle materials, very
different from standard Laplacian growth patterns of viscous fingering. An
analytic theory is lacking since a pre-requisite to describing the fracture of
elastic material is the solution of the bi-Laplace rather than the Laplace
equation. In this Letter we close this gap, offering a theory of bi-Laplacian
growth patterns based on the method of iterated conformal maps.Comment: Submitted to PRL. For further information see
http://www.weizmann.ac.il/chemphys/ander
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