4,265 research outputs found
Two-dimensional one-component plasma in a quadrupolar field
The classical two-dimensional one-component plasma is an exactly solvable
model, at some special temperature, even when the one-body potential acting on
the particles has a quadrupolar term. As a supplement to a recent work of Di
Francesco, Gaudin, Itzykson, and Lesage [{\it Int. J. Mod. Phys.} {\bf A9},
4257 (1994)] about an -particle system ( large but finite), a macroscopic
argument is given for confirming that the particles form an elliptical blob,
the analogy between the classical plasma and a quantum -fermion system in a
magnetic field is used for the microscopic approach, and a microscopic
calculation of the surface charge-surface charge correlation function is
performed; an expected universal form is shown to be realized by this
correlation function.Comment: 11 pages,TE
The Ideal Conductor Limit
This paper compares two methods of statistical mechanics used to study a
classical Coulomb system S near an ideal conductor C. The first method consists
in neglecting the thermal fluctuations in the conductor C and constrains the
electric potential to be constant on it. In the second method the conductor C
is considered as a conducting Coulomb system the charge correlation length of
which goes to zero. It has been noticed in the past, in particular cases, that
the two methods yield the same results for the particle densities and
correlations in S. It is shown that this is true in general for the quantities
which depend only on the degrees of freedom of S, but that some other
quantities, especially the electric potential correlations and the stress
tensor, are different in the two approaches. In spite of this the two methods
give the same electric forces exerted on S.Comment: 19 pages, plain TeX. Submited to J. Phys. A: Math. Ge
Exact and asymtotic formulas for overdamped Brownian dynamics
Exact and asymptotic formulas relating to dynamical correlations for
overdamped Brownian motion are obtained. These formulas include a
generalization of the -sum rule from the theory of quantum fluids, a formula
relating the static current-current correlation to the static density-density
correlation, and an asymptotic formula for the small- behaviour of the
dynamical structure factor. Known exact evaluations of the dynamical
density-density correlation in some special models are used to illustrate and
test the formulas.Comment: 18 pages,LaTe
The averaged characteristic polynomial for the Gaussian and chiral Gaussian ensembles with a source
In classical random matrix theory the Gaussian and chiral Gaussian random
matrix models with a source are realized as shifted mean Gaussian, and chiral
Gaussian, random matrices with real , complex ( and
real quaternion ) elements. We use the Dyson Brownian motion model
to give a meaning for general . In the Gaussian case a further
construction valid for is given, as the eigenvalue PDF of a
recursively defined random matrix ensemble. In the case of real or complex
elements, a combinatorial argument is used to compute the averaged
characteristic polynomial. The resulting functional forms are shown to be a
special cases of duality formulas due to Desrosiers. New derivations of the
general case of Desrosiers' dualities are given. A soft edge scaling limit of
the averaged characteristic polynomial is identified, and an explicit
evaluation in terms of so-called incomplete Airy functions is obtained.Comment: 21 page
Derivation of an eigenvalue probability density function relating to the Poincare disk
A result of Zyczkowski and Sommers [J.Phys.A, 33, 2045--2057 (2000)] gives
the eigenvalue probability density function for the top N x N sub-block of a
Haar distributed matrix from U(N+n). In the case n \ge N, we rederive this
result, starting from knowledge of the distribution of the sub-blocks,
introducing the Schur decomposition, and integrating over all variables except
the eigenvalues. The integration is done by identifying a recursive structure
which reduces the dimension. This approach is inspired by an analogous approach
which has been recently applied to determine the eigenvalue probability density
function for random matrices A^{-1} B, where A and B are random matrices with
entries standard complex normals. We relate the eigenvalue distribution of the
sub-blocks to a many body quantum state, and to the one-component plasma, on
the pseudosphere.Comment: 11 pages; To appear in J.Phys
Another Derivation of a Sum Rule for the Two-Dimensional Two-Component Plasma
In a two-dimensional two-component plasma, the second moment of the number
density correlation function has the simple value , where is the dimensionless coupling
constant. This result is derived directly by using diagrammatic methods.Comment: 10 pages, uses axodraw.sty, elsart.sty, elsart12.sty, subeq.sty;
accepted for publication in Physica A, May 200
Algorithms to solve the Sutherland model
We give a self-contained presentation and comparison of two different
algorithms to explicitly solve quantum many body models of indistinguishable
particles moving on a circle and interacting with two-body potentials of
-type. The first algorithm is due to Sutherland and well-known; the
second one is a limiting case of a novel algorithm to solve the elliptic
generalization of the Sutherland model. These two algorithms are different in
several details. We show that they are equivalent, i.e., they yield the same
solution and are equally simple.Comment: 15 pages, LaTe
Two-component plasma in a gravitational field: Thermodynamics
We revisit the model of the two-component plasma in a gravitational field,
which mimics charged colloidal suspensions. We concentrate on the computation
of the grand potential of the system. Also, a special sum rule for this model
is presented.Comment: 7 pages, LaTeX2
A Combinatorial Interpretation of the Free Fermion Condition of the Six-Vertex Model
The free fermion condition of the six-vertex model provides a 5 parameter
sub-manifold on which the Bethe Ansatz equations for the wavenumbers that enter
into the eigenfunctions of the transfer matrices of the model decouple, hence
allowing explicit solutions. Such conditions arose originally in early
field-theoretic S-matrix approaches. Here we provide a combinatorial
explanation for the condition in terms of a generalised Gessel-Viennot
involution. By doing so we extend the use of the Gessel-Viennot theorem,
originally devised for non-intersecting walks only, to a special weighted type
of \emph{intersecting} walk, and hence express the partition function of
such walks starting and finishing at fixed endpoints in terms of the single
walk partition functions
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