450 research outputs found
Lattice QCD-2+1
We consider a 2+1-dimensional SU(N) lattice gauge theory in an axial gauge
with the link field U in the 1-direction set to one. The term in the
Hamiltonian containing the square of the electric field in the 1-direction is
non-local. Despite this non-locality, we show that weak-coupling perturbation
theory in this term gives a finite vacuum-energy density to second order, and
suggest that this property holds to all orders. Heavy quarks are confined, the
spectrum is gapped, and the space-like Wilson loop has area decay.Comment: Still Latex, 18 pages, no figures, with some further typographical
errors corrected. Version to appear in Phys. Rev.
Adsorption of polymers on a fluctuating surface
We study the adsorption of polymer chains on a fluctuating surface. Physical
examples are provided by polymer adsorption at the rough interface between two
non-miscible liquids, or on a membrane. In a mean-field approach, we find that
the self--avoiding chains undergo an adsorption transition, accompanied by a
stiffening of the fluctuating surface. In particular, adsorption of polymers on
a membrane induces a surface tension and leads to a strong suppression of
roughness.Comment: REVTEX, 9 pages, no figure
Gauge-Invariant Coordinates on Gauge-Theory Orbit Space
A gauge-invariant field is found which describes physical configurations,
i.e. gauge orbits, of non-Abelian gauge theories. This is accomplished with
non-Abelian generalizations of the Poincare'-Hodge formula for one-forms. In a
particular sense, the new field is dual to the gauge field. Using this field as
a coordinate, the metric and intrinsic curvature are discussed for Yang-Mills
orbit space for the (2+1)- and (3+1)-dimensional cases. The sectional, Ricci
and scalar curvatures are all formally non-negative. An expression for the new
field in terms of the Yang-Mills connection is found in 2+1 dimensions. The
measure on Schroedinger wave functionals is found in both 2+1 and 3+1
dimensions; in the former case, it resembles Karabali, Kim and Nair's measure.
We briefly discuss the form of the Hamiltonian in terms of the dual field and
comment on how this is relevant to the mass gap for both the (2+1)- and
(3+1)-dimensional cases.Comment: Typos corrected, more about the non-Abelian decomposition and inner
products, more discussion of the mass gap in 3+1 dimensions. Now 23 page
Integrable Models and Confinement in (2+1)-Dimensional Weakly-Coupled Yang-Mills Theory
We generalize the (2+1)-dimensional Yang-Mills theory to an anisotropic form
with two gauge coupling constants and . In an axial gauge, a
regularized version of the Hamiltonian of this gauge theory is
, where is the Hamiltonian of a set of
(1+1)-dimensional principal chiral nonlinear sigma models. We treat as
the interaction Hamiltonian. For gauge group SU(2), we use form factors of the
currents of the principal chiral sigma models to compute the string tension for
small , after reviewing exact S-matrix and form-factor methods. In
the anisotropic regime, the dependence of the string tension on the coupling
constant is not in accord with generally-accepted dimensional arguments.Comment: Now 37 pages, Section 5 moved to an appendix, more motivation given
in the introduction, a few more typos correcte
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.
Spin-Charge Separation and the Pauli Electron
The separation between the spin and the charge converts the quantum
mechanical Pauli Hamiltonian into the Hamiltonian of the non-Abelian
Georgi-Glashow model, notorious for its magnetic monopoles and confinement. The
independent spin and charge fluctuations both lead to the Faddeev model,
suggesting the existence of a deep duality structure and indicating that the
fundamental carriers of spin and charge are knotted solitons.Comment: 7 pages; v2: new results added, references update
Mean field and corrections for the Euclidean Minimum Matching problem
Consider the length of the minimum matching of N points in
d-dimensional Euclidean space. Using numerical simulations and the finite size
scaling law , we obtain
precise estimates of for . We then consider
the approximation where distance correlations are neglected. This model is
solvable and gives at an excellent ``random link'' approximation to
. Incorporation of three-link correlations further improves
the accuracy, leading to a relative error of 0.4% at d=2 and 3. Finally, the
large d behavior of this expansion in link correlations is discussed.Comment: source and one figure. Submitted to PR
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
Metastable configurations of spin models on random graphs
One-flip stable configurations of an Ising-model on a random graph with
fluctuating connectivity are examined. In order to perform the quenched average
of the number of stable configurations we introduce a global order-parameter
function with two arguments. The analytical results are compared with numerical
simulations.Comment: 11 pages Revtex, minor changes, to appear in Phys. Rev.
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