515 research outputs found
Structural and ultrametric properties of twenty(L-alanine)
We study local energy minima of twenty(L-alanine). The minima are generated
using high-temperature Molecular Dynamics and Chain-Growth Monte Carlo
simulations, with subsequent minimization. We find that the lower-energy
configurations are -helices for a wide range of dielectric constant
values and that there is no noticeable difference
between the distribution of energy minima in space for different
values of Ultrametricity tests show that lower-energy -helical) configurations form a set which is ultrametric to a
certain degree, providing evidence for the presence of fine structure among
those minima. We put forward a heuristic argument for this fine structure. We
also find evidence for ultrametricity of a different kind among and energy minima. We analyze the distribution of lengths of
-helical portions among the minimized configurations and find a
persistence phenomenon for the ones, in qualitative agreement
with previous studies of critical lengths. Email contact:
[email protected]: Saclay-T93/025 Email: [email protected]
A Mean Field Approximation to the Worldsheet Model of Planar phi^3 Field Theory
We develop an approximation scheme for our worldsheet model of the sum of
planar diagrams based on mean field theory. At finite coupling the mean field
equations show a weak coupling solution that resembles the perturbative
diagrams and a strong coupling solution that seems to represent a tensionless
soup of field quanta. With a certain amount of fine-tuning, we find a solution
of the mean field equations that seems to support string formation.Comment: 27 pages, 10 figures, typos corrected, appendix on slowly varying
mean fields adde
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
Topological Wilson-loop area law manifested using a superposition of loops
We introduce a new topological effect involving interference of two meson
loops, manifesting a path-independent topological area dependence. The effect
also draws a connection between quark confinement, Wilson-loops and topological
interference effects. Although this is only a gedanken experiment in the
context of particle physics, such an experiment may be realized and used as a
tool to test confinement effects and phase transitions in quantum simulation of
dynamic gauge theories.Comment: Superceding arXiv:1206.2021v1 [quant-ph
Directed polymers and interfaces in random media : free-energy optimization via confinement in a wandering tube
We analyze, via Imry-Ma scaling arguments, the strong disorder phases that
exist in low dimensions at all temperatures for directed polymers and
interfaces in random media. For the uncorrelated Gaussian disorder, we obtain
that the optimal strategy for the polymer in dimension with
involves at the same time (i) a confinement in a favorable tube of radius with (ii) a superdiffusive behavior with for the wandering of the best favorable
tube available. The corresponding free-energy then scales as with and the left tail of the probability
distribution involves a stretched exponential of exponent .
These results generalize the well known exact exponents ,
and in , where the subleading transverse length is known as the typical distance between two replicas in the Bethe
Ansatz wave function. We then extend our approach to correlated disorder in
transverse directions with exponent and/or to manifolds in dimension
with . The strategy of being both confined and
superdiffusive is still optimal for decaying correlations (), whereas
it is not for growing correlations (). In particular, for an
interface of dimension in a space of total dimension with
random-bond disorder, our approach yields the confinement exponent . Finally, we study the exponents in the presence of an
algebraic tail in the disorder distribution, and obtain various
regimes in the plane.Comment: 19 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
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
Field theoretic approach to the counting problem of Hamiltonian cycles of graphs
A Hamiltonian cycle of a graph is a closed path that visits each site once
and only once. I study a field theoretic representation for the number of
Hamiltonian cycles for arbitrary graphs. By integrating out quadratic
fluctuations around the saddle point, one obtains an estimate for the number
which reflects characteristics of graphs well. The accuracy of the estimate is
verified by applying it to 2d square lattices with various boundary conditions.
This is the first example of extracting meaningful information from the
quadratic approximation to the field theory representation.Comment: 5 pages, 3 figures, uses epsf.sty. Estimates for the site entropy and
the gamma exponent indicated explicitl
Hamiltonian Cycles on a Random Three-coordinate Lattice
Consider a random three-coordinate lattice of spherical topology having 2v
vertices and being densely covered by a single closed, self-avoiding walk, i.e.
being equipped with a Hamiltonian cycle. We determine the number of such
objects as a function of v. Furthermore we express the partition function of
the corresponding statistical model as an elliptic integral.Comment: 10 pages, LaTeX, 3 eps-figures, one reference adde
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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