47 research outputs found
Helicity modulus in the two-dimensional Hubbard model
The helicity modulus, which is the stiffness associated with a twisted order parameter, for the two-dimensional Hubbard model is calculated for the equivalent cases of (i) attractive on-site interaction (negative U) with arbitrary strength, arbitrary electron density, and zero magnetic field and (ii) repulsive on-site interaction (positive U) with arbitrary strength, at half-filling and in an arbitrary magnetic field. An explicit formula for the helicity modulus is derived using the Bogoliubov-Hartree-Fock approximation. An improved value for the helicity modulus is obtained by performing variational Monte Carlo calculations using a Gutzwiller projected trial wave function. To within a small correction term the helicity modulus is found to be given by -1/8 the average kinetic energy. The variational Monte Carlo calculation is found to increase the value of the helicity modulus by a small amount (about 5% for intermediate values of the interaction strength) compared to the results from the Bogoliubov-Hartree-Fock approximation. In the case of attractive interaction, from a comparison with the Kosterlitz-Thouless relation between critical temperature and helicity modulus, the critical temperature for a Kosterlitz-Thouless transition is calculated and a phase diagram is obtained. An optimal critical temperature is found for an intermediate value of U. We discuss connections of our results with results in the literature on the Hubbard model using the random-phase approximation and quantum Monte Carlo calculations.Theoretical Physic
Conductivity of the classical two-dimensional electron gas
We discuss the applicability of the Boltzmann equation to the classical
two-dimensional electron gas. We show that in the presence of both the
electron-impurity and electron-electron scattering the Boltzmann equation can
be inapplicable and the correct result for conductivity can be different from
the one obtained from the kinetic equation by a logarithmically large factor.Comment: Revtex, 3 page
Thermodynamic instabilities in one dimensional particle lattices: a finite-size scaling approach
One-dimensional thermodynamic instabilities are phase transitions not
prohibited by Landau's argument, because the energy of the domain wall (DW)
which separates the two phases is infinite. Whether they actually occur in a
given system of particles must be demonstrated on a case-by-case basis by
examining the (non-) analyticity properties of the corresponding transfer
integral (TI) equation. The present note deals with the generic Peyrard-Bishop
model of DNA denaturation. In the absence of exact statements about the
spectrum of the singular TI equation, I use Gauss-Hermite quadratures to
achieve a single-parameter-controlled approach to rounding effects; this allows
me to employ finite-size scaling concepts in order to demonstrate that a phase
transition occurs and to derive the critical exponents.Comment: 5 pages, 6 figures, subm. to Phys. Rev.
Stochastic lattice models for the dynamics of linear polymers
Linear polymers are represented as chains of hopping reptons and their motion
is described as a stochastic process on a lattice. This admittedly crude
approximation still catches essential physics of polymer motion, i.e. the
universal properties as function of polymer length. More than the static
properties, the dynamics depends on the rules of motion. Small changes in the
hopping probabilities can result in different universal behavior. In particular
the cross-over between Rouse dynamics and reptation is controlled by the types
and strength of the hoppings that are allowed. The properties are analyzed
using a calculational scheme based on an analogy with one-dimensional spin
systems. It leads to accurate data for intermediately long polymers. These are
extrapolated to arbitrarily long polymers, by means of finite-size-scaling
analysis. Exponents and cross-over functions for the renewal time and the
diffusion coefficient are discussed for various types of motion.Comment: 60 pages, 19 figure
Diffusion in a generalized Rubinstein-Duke model of electrophoresis with kinematic disorder
Using a generalized Rubinstein-Duke model we prove rigorously that kinematic
disorder leaves the prediction of standard reptation theory for the scaling of
the diffusion constant in the limit for long polymer chains
unaffected. Based on an analytical calculation as well as Monte Carlo
simulations we predict kinematic disorder to affect the center of mass
diffusion constant of an entangled polymer in the limit for long chains by the
same factor as single particle diffusion in a random barrier model.Comment: 29 pages, 3 figures, submitted to PR
Nonequilibrium wetting
When a nonequilibrium growing interface in the presence of a wall is
considered a nonequilibrium wetting transition may take place. This transition
can be studied trough Langevin equations or discrete growth models. In the
first case, the Kardar-Parisi-Zhang equation, which defines a very robust
universality class for nonequilibrium moving interfaces, with a soft-wall
potential is considered. While in the second, microscopic models, in the
corresponding universality class, with evaporation and deposition of particles
in the presence of hard-wall are studied. Equilibrium wetting is related to a
particular case of the problem, it corresponds to the Edwards-Wilkinson
equation with a potential in the continuum approach or to the fulfillment of
detailed balance in the microscopic models. In this review we present the
analytical and numerical methods used to investigate the problem and the very
rich behavior that is observed with them.Comment: Review, 36 pages, 16 figure
The Einstein relation in the Rubinstein-Duke reptation model
The Einstein relation between the friction coefficient and the diffusion coefficient is proven for the Rubinstein-Duke reptation model