628,919 research outputs found
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
Sine-Gordon Theory for the Equation of State of Classical Hard-Core Coulomb systems. III Loopwise Expansion
We present an exact field theoretical representation of an ionic solution
made of charged hard spheres. The action of the field theory is obtained by
performing a Hubbard-Stratonovich transform of the configurational Boltzmann
factor. It is shown that the Stillinger-Lovett sum rules are satisfied if and
only if all the field correlation functions are short range functions. The mean
field, Gaussian and two-loops approximations of the theory are derived and
discussed. The mean field approximation for the free energy constitutes a
rigorous lower bound for the exact free energy, while the mean field pressure
is an upper bound. The one-loop order approximation is shown to be identical
with the random phase approximation of the theory of liquids. Finally, at the
two-loop order and in the pecular case of the restricted primitive model, one
recovers results obtained in the framework of the mode expansion theory.Comment: 35 pages, 3 figure
Integrating out the Dirac sea in the Walecka model
We derive a purely fermionic no-sea effective theory, featuring
positive-energy states only for the Walecka model. In contrast to the so-called
mean-field theory approach with the no-sea approximation, where the Dirac sea
is simply omitted from the outset, we turn to the relativistic Hartree
approximation and explicitly construct a no-sea effective theory from the
underlying quantum field theory. Several results obtained within these two
approaches are confronted with each other. This sheds new light on the
reliability of the mean-field theory with the no-sea approximation as well as
the role of the Dirac sea. Restricting to 1+1 dimensions, we obtain new
analytical insights into nonuniform nuclear matter.Comment: 15 pages, 8 figures, several points clarified, Fig.7 replaced,
references adde
Random Sequential Adsorption on a Line: Mean-Field Theory of Diffusional Relaxation
We develop a new fast-diffusion approximation for the kinetics of deposition
of extended objects on a linear substrate, accompanied by diffusional
relaxation. This new approximation plays the role of the mean-field theory for
such processes and is valid over a significantly larger range than an earlier
variant, which was based on a mapping to chemical reactions. In particular,
continuum-limit off-lattice deposition is described naturally within our
approximation. The criteria for the applicability of the mean-field theory are
derived. While deposition of dimers, and marginally, trimers, is affected by
fluctuations, we find that the k-mer deposition kinetics is asymptotically
mean-field like for all k=4,5,..., where the limit k->infinity, when properly
defined, describes deposition-diffusion kinetics in the continuum.Comment: 18 page
Model study of the sign problem in a mean-field approximation
We study the sign problem of the fermion determinant at nonzero baryon
chemical potential. For this purpose we apply a simple model derived from
Quantum Chromodynamics, in the limit of large chemical potential and mass. For
SU(2) color, there is no sign problem and the mean-field approximation is
similar to data from the lattice. For SU(3) color the sign problem is
unavoidable, even in a mean-field approximation. We apply a phase-reweighting
method, combined with the mean-field approximation, to estimate thermodynamic
quantities. We also investigate the mean-field free energy using a saddle-point
approximation.Comment: 7 pages, 2 figures, talk presented at the XXV International Symposium
on Lattice Field Theory, July 30 - August 4, 2007, Regensburg, German
Dynamics of Polymers: a Mean-Field Theory
We derive a general mean-field theory of inhomogeneous polymer dynamics; a
theory whose form has been speculated and widely applied, but not heretofore
derived. Our approach involves a functional integral representation of a
Martin-Siggia-Rose type description of the exact many-chain dynamics. A saddle
point approximation to the generating functional, involving conditions where
the MSR action is stationary with respect to a collective density field
and a conjugate MSR response field , produces the desired dynamical
mean-field theory. Besides clarifying the proper structure of mean-field theory
out of equilibrium, our results have implications for numerical studies of
polymer dynamics involving hybrid particle-field simulation techniques such as
the single-chain in mean-field method (SCMF)
Stochastic quantum dynamics beyond mean-field
Mean-field approaches where a complex fermionic many-body problem is replaced
by an ensemble of independent particles in a self-consistent mean-field can
describe many static and dynamical aspects. It generally provides a rather good
approximation for the average properties of one-body degrees of freedom.
However, the mean-field approximation generally fails to produce quantum
fluctuations of collective motion. To overcome this difficulty, noise can be
added to the mean-field theory leading to a stochastic description of the
many-body problem. In the present work, we summarize recent progress in this
field and discuss approaches where fluctuations have been added either to the
initial time, like in the Stochastic Mean-Field theory or continuously in time
as in the Stochastic Time-Dependent Hartree-Fock. In some cases, the initial
problem can even be re-formulated exactly by introducing Quantum Monte-Carlo
methods in real-time. The possibility to describe superfluid systems is also
invoked. Successes and shortcomings of the different beyond mean-field theories
are discussed and illustrated.Comment: 34 pages, submitted to EPJA-Review sectio
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