834 research outputs found
Non-perturbative Approach to Critical Dynamics
This paper is devoted to a non-perturbative renormalization group (NPRG)
analysis of Model A, which stands as a paradigm for the study of critical
dynamics. The NPRG formalism has appeared as a valuable theoretical tool to
investigate non-equilibrium critical phenomena, yet the simplest -- and
nontrivial -- models for critical dynamics have never been studied using NPRG
techniques. In this paper we focus on Model A taking this opportunity to
provide a pedagological introduction to NPRG methods for dynamical problems in
statistical physics. The dynamical exponent is computed in and
and is found in close agreement with results from other methods.Comment: 13 page
Reaction-diffusion processes and non-perturbative renormalisation group
This paper is devoted to investigating non-equilibrium phase transitions to
an absorbing state, which are generically encountered in reaction-diffusion
processes. It is a review, based on [Phys. Rev. Lett. 92, 195703; Phys. Rev.
Lett. 92, 255703; Phys. Rev. Lett. 95, 100601], of recent progress in this
field that has been allowed by a non-perturbative renormalisation group
approach. We mainly focus on branching and annihilating random walks and show
that their critical properties strongly rely on non-perturbative features and
that hence the use of a non-perturbative method turns out to be crucial to get
a correct picture of the physics of these models.Comment: 14 pages, submitted to J. Phys. A for the proceedings of the
conference 'Renormalization Group 2005', Helsink
Microscopics of disordered two-dimensional electron gases under high magnetic fields: Equilibrium properties and dissipation in the hydrodynamic regime
We develop in detail a new formalism [as a sequel to the work of T. Champel
and S. Florens, Phys. Rev. B 75, 245326 (2007)] that is well-suited for
treating quantum problems involving slowly-varying potentials at high magnetic
fields in two-dimensional electron gases. For an arbitrary smooth potential we
show that electronic Green's function is fully determined by closed recursive
expressions that take the form of a high magnetic field expansion in powers of
the magnetic length l_B. For illustration we determine entirely Green's
function at order l_B^3, which is then used to obtain quantum expressions for
the local charge and current electronic densities at equilibrium. Such results
are valid at high but finite magnetic fields and for arbitrary temperatures, as
they take into account Landau level mixing processes and wave function
broadening. We also check the accuracy of our general functionals against the
exact solution of a one-dimensional parabolic confining potential,
demonstrating the controlled character of the theory to get equilibrium
properties. Finally, we show that transport in high magnetic fields can be
described hydrodynamically by a local equilibrium regime and that dissipation
mechanisms and quantum tunneling processes are intrinsically included at the
microscopic level in our high magnetic field theory. We calculate microscopic
expressions for the local conductivity tensor, which possesses both transverse
and longitudinal components, providing a microscopic basis for the
understanding of dissipative features in quantum Hall systems.Comment: small typos corrected; published versio
Single-site approximation for reaction-diffusion processes
We consider the branching and annihilating random walk and with reaction rates and , respectively, and hopping rate
, and study the phase diagram in the plane. According
to standard mean-field theory, this system is in an active state for all
, and perturbative renormalization suggests that this mean-field
result is valid for ; however, nonperturbative renormalization predicts
that for all there is a phase transition line to an absorbing state in the
plane. We show here that a simple single-site
approximation reproduces with minimal effort the nonperturbative phase diagram
both qualitatively and quantitatively for all dimensions . We expect the
approach to be useful for other reaction-diffusion processes involving
absorbing state transitions.Comment: 15 pages, 2 figures, published versio
Nonâlinear explicit dynamic analysis of shells using the BST rotationâfree triangle
The paper describes the application of the simple rotationâfree basic shell triangle (BST) to the nonâlinear analysis of shell structures using an explicit dynamic formulation. The derivation of the BST element involving translational degrees of freedom only using a combined finite element–finite volume formulation is briefly presented. Details of the treatment of geometrical and material non linearities for the dynamic solution using an updated Lagrangian description and an hypoelastic constitutive law are given. The efficiency of the BST element for the non linear transient analysis of shells using an explicit dynamic integration scheme is shown in a number of examples of application including problems with frictional contact situations
Non Perturbative Renormalization Group, momentum dependence of -point functions and the transition temperature of the weakly interacting Bose gas
We propose a new approximation scheme to solve the Non Perturbative
Renormalization Group equations and obtain the full momentum dependence of
-point functions. This scheme involves an iteration procedure built on an
extension of the Local Potential Approximation commonly used within the Non
Perturbative Renormalization Group. Perturbative and scaling regimes are
accurately reproduced. The method is applied to the calculation of the shift
in the transition temperature of the weakly repulsive Bose gas, a
quantity which is very sensitive to all momenta intermediate between these two
regions. The leading order result is in agreement with lattice calculations,
albeit with a theoretical uncertainty of about 25%. The next-to-leading order
differs by about 10% from the best accepted result
Path integral evaluation of the one-loop effective potential in field theory of diffusion-limited reactions
The well-established effective action and effective potential framework from
the quantum field theory domain is adapted and successfully applied to
classical field theories of the Doi and Peliti type for diffusion controlled
reactions. Through a number of benchmark examples, we show that the direct
calculation of the effective potential in fixed space dimension to
one-loop order reduces to a small set of simple elementary functions,
irrespective of the microscopic details of the specific model. Thus the
technique, which allows one to obtain with little additional effort, the
potentials for a wide variety of different models, represents an important
alternative to the standard model dependent diagram-based calculations. The
renormalized effective potential, effective equations of motion and the
associated renormalization group equations are computed in spatial
dimensions for a number of single species field theories of increasing
complexity.Comment: Plain LaTEX2e, 32 pages and three figures. Submitted to Journal of
Statistical Physic
Non-Perturbative Renormalization Group for Simple Fluids
We present a new non perturbative renormalization group for classical simple
fluids. The theory is built in the Grand Canonical ensemble and in the
framework of two equivalent scalar field theories as well. The exact mapping
between the three renormalization flows is established rigorously. In the Grand
Canonical ensemble the theory may be seen as an extension of the Hierarchical
Reference Theory (L. Reatto and A. Parola, \textit{Adv. Phys.}, \textbf{44},
211 (1995)) but however does not suffer from its shortcomings at subcritical
temperatures. In the framework of a new canonical field theory of liquid state
developed in that aim our construction identifies with the effective average
action approach developed recently (J. Berges, N. Tetradis, and C. Wetterich,
\textit{Phys. Rep.}, \textbf{363} (2002))
Stable isotope geochemistry of the Ulldemolins Pb-Zn-Cu deposit (SW Catalonian Coastal Ranges, Spain)
The Pb-Zn-Cu deposit of Ulldemolins occurs within the Carboniferous sedimentary series of the southernmost
Catalonian Coastal Ranges. It consists of sulphide-bearing calc-silicate assemblages, with epidote, Ca-amphiboles
and Ca-garnet, which develop selectively along a dolomicrite bed near the contact with a granite porphyry.
Two mineralisation styles can be differentiated: a) banded and b) irregular. Fluid inclusions and stable isotope
compositions of sulphur in sulphides (sphalerite, galena and chalcopyrite) and carbon and oxygen in carbonates
(calcite and dolomite) were studied in order to constrain the genesis and the source of mineralizing fluids. Fluid
inclusions in sphalerite and calcite are aqueous, liquid+vapour and have a salinity between 1.2 and 7.2 wt%
NaCl eq. and homogenization temperatures in the range of 273Âș to 368ÂșC. The ÎŽ34S(V-CDT) values in the banded
mineralisation are mostly between â1.5 and +2.1â°, and those from the irregular mineralisation are between â1.1
and +20.5â°. These ÎŽ34S values of the banded mineralisation are in agreement with a magmatic origin of sulphur.
In addition, the ÎŽ18O(SMOW) values of hydrothermal calcite, from +6.9 to +12.5â°, are consistent with a magmatic
origin of the fluids that formed the banded ore deposit. Later, a new input of fluids interacted with the previously
formed mineral assemblages and modified part of the deposit, leading locally to an irregular skarn mineralisation
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