287 research outputs found
Field theory fo charged fluids and colloids
A systematic field theory is presented for charged systems. The one-loop
level corresponds to the classical Debye-H\"uckel (DH) theory, and exhibits the
full hierarchy of multi-body correlations determined by pair-distribution
functions given by the screened DH potential. Higher-loop corrections can lead
to attractive pair interactions between colloids in asymmetric ionic
environments. The free energy follows as a loop-wise expansion in half-integer
powers of the density; the resulting two-phase demixing region shows pronounced
deviations from DH theory for strongly charged colloids.Comment: 4 pages, 2 ps figs; new version corrects some minor typo
The string model of the Cooper pair in the anisotropic superconductor
The analogy between the Cooper pair in high temperature superconductor and
the quark-antiquark pair in quantum chromodynamics (QCD) is proposed. In QCD
the nonlinear chromodynamical field between a quark and an antiquark is
confined to a tube. So we assume that there is the strong interaction between
phonons which can confine them to some tube too. This tube is described using
the nonlinear Schr\"odinger equation. We show that it has an infinite spectrum
of axially symmetric (string) solutions with negative finite linear energy
density. The one-dimensional nonlinear Schr\"odinger equation has a finite
spectrum (hence, it has a steady-state) which describes the Cooper pair
squezeed between anisotropy planes in the superconductor. It is shown that in
this model the transition temperature is approximately 45 K.Comment: final version, Latex, 9p, to be published in Phys. Rev.
Near-integrability and confinement for high-energy hadron-hadron collisions
We investigate an effective Hamiltonian for QCD at large s, in which
longitudinal gauge degrees of freedom are suppressed, but not eliminated. In an
axial gauge the effective field theory is a set of coupled (1+1)-dimensional
principal-chiral models, which are completely integrable. The confinement
problem is solvable in this context, and we find the longitudinal and
transverse string tensions with techniques already used for a similar
Hamiltonian in (2+1)-dimensions. We find some a posteriori justification for
the effective Hamiltonian as an eikonal approximation. Hadrons in this
approximation consist of partons, which are quarks and soliton-like excitations
of the sigma models. Diffractive hadron-hadron scattering appears primarily due
to exchange of longitudinal flux between partons.Comment: Typographical errors corrected, language improved, reference adde
A Soluble Free-Fermion Model in d Dimensions
We consider a vertex model in d dimensions characterized by lines which run
in a preferred direction. We show that this vertex model is soluble if the
weights of vertices with intersecting lines are given by a free-fermion
condition, and that a fugacity -1 is associated to each loop of lines. The
solution is obtained by mapping the model into a dimer problem and by
evaluating a Pfaffian. We also determine the critical point and the singular
behavior of the free energy.Comment: 19 pages, REVTEX, 6 figure
A meaningful expansion around detailed balance
We consider Markovian dynamics modeling open mesoscopic systems which are
driven away from detailed balance by a nonconservative force. A systematic
expansion is obtained of the stationary distribution around an equilibrium
reference, in orders of the nonequilibrium forcing. The first order around
equilibrium has been known since the work of McLennan (1959), and involves the
transient irreversible entropy flux. The expansion generalizes the McLennan
formula to higher orders, complementing the entropy flux with the dynamical
activity. The latter is more kinetic than thermodynamic and is a possible
realization of Landauer's insight (1975) that, for nonequilibrium, the relative
occupation of states also depends on the noise along possible escape routes. In
that way nonlinear response around equilibrium can be meaningfully discussed in
terms of two main quantities only, the entropy flux and the dynamical activity.
The expansion makes mathematical sense as shown in the simplest cases from
exponential ergodicity.Comment: 19 page
Steric Effects in Electrolytes: A Modified Poisson-Boltzmann Equation
The adsorption of large ions from solution to a charged surface is
investigated theoretically. A generalized Poisson--Boltzmann equation, which
takes into account the finite size of the ions is presented. We obtain
analytical expressions for the electrostatic potential and ion concentrations
at the surface, leading to a modified Grahame equation. At high surface charge
densities the ionic concentration saturates to its maximum value. Our results
are in agreement with recent experiments.Comment: 4 pages, 2 figure
Confinement in the Abelian-Higgs-type theories: string picture and field correlators
Field correlators and the string representation are used as two complementary
approaches for the description of confinement in the SU(N)-inspired dual
Abelian-Higgs-type model. In the London limit of the simplest, SU(2)-inspired,
model, bilocal electric field-strength correlators have been derived with
accounting for the contributions to these averages produced by closed dual
strings. The Debye screening in the plasma of such strings yields a novel
long-range interaction between points lying on the contour of the Wilson loop.
This interaction generates a Luescher-type term, even when one restrics oneself
to the minimal surface, as it is usually done in the bilocal approximation to
the stochastic vacuum model. Beyond the London limit, it has been shown that a
modified interaction appears, which becomes reduced to the standard Yukawa one
in the London limit. Finally, a string representation of the SU(N)-inspired
model with the theta-term, in the London limit, can be constructed.Comment: 17 pages, no figures, REVTeX 4; Invited contribution to the
collection of articles devoted to the 70th birthday of Yu.A. Simono
Optimisation problems and replica symmetry breaking in finite connectivity spin-glasses
A formalism capable of handling the first step of hierarchical replica
symmetry breaking in finite-connectivity models is introduced. The emerging
order parameter is claimed to be a probability distribution over the space of
field distributions (or, equivalently magnetisation distributions) inside the
cluster of states. The approach is shown to coincide with the previous works in
the replica symmetric case and in the two limit cases m=0,1 where m is Parisi's
break-point. As an application to the study of optimization problems, the
ground-state properties of the random 3-Satisfiability problem are investigated
and we present a first RSB solution improving replica symmetric results.Comment: 16 pages Revtex file, 1 figure; amended version with two new
appendices; to be published in J.Phys.
On the Topological Term in the String Representation of the Wilson Loop in the Dilute Instanton Gas
A topological term related to the number of self-intersections of the string
world-sheet is shown to emerge in the string representation of the Wilson loop
in the dilute instanton gas. The coupling constant of this term occurs to be
proportional to the topological charge of the instanton gas under
consideration.Comment: 4 pages, LaTeX, no figure
QCD as a Quantum Link Model
QCD is constructed as a lattice gauge theory in which the elements of the
link matrices are represented by non-commuting operators acting in a Hilbert
space. The resulting quantum link model for QCD is formulated with a fifth
Euclidean dimension, whose extent resembles the inverse gauge coupling of the
resulting four-dimensional theory after dimensional reduction. The inclusion of
quarks is natural in Shamir's variant of Kaplan's fermion method, which does
not require fine-tuning to approach the chiral limit. A rishon representation
in terms of fermionic constituents of the gluons is derived and the quantum
link Hamiltonian for QCD with a U(N) gauge symmetry is expressed in terms of
glueball, meson and constituent quark operators. The new formulation of QCD is
promising both from an analytic and from a computational point of view.Comment: 27 pages, including three figures. ordinary LaTeX; Submitted to Nucl.
Phys.
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