50,422 research outputs found
Comments on the Gauge Fixed BRST Cohomology and the Quantum Noether Method
We discuss in detail the relation between the gauge fixed and gauge invariant
BRST cohomology. We showed previously that in certain gauges some cohomology
classes of the gauge-fixed BRST differential do not correspond to gauge
invariant observables. We now show that in addition ``accidental'' conserved
currents may appear. These correspond one-to-one to observables that become
trivial in this gauge. We explicitly show how the gauge-fixed BRST cohomology
appears in the context of the Quantum Noether Method.Comment: 24 pages, example section improved, short version without background
material will appear in Physics Letters
Effects of turbulent mixing on critical behaviour: Renormalization group analysis of the Potts model
Critical behaviour of a system, subjected to strongly anisotropic turbulent
mixing, is studied by means of the field theoretic renormalization group.
Specifically, relaxational stochastic dynamics of a non-conserved
multicomponent order parameter of the Ashkin-Teller-Potts model, coupled to a
random velocity field with prescribed statistics, is considered. The velocity
is taken Gaussian, white in time, with correlation function of the form
, where is
the component of the wave vector, perpendicular to the distinguished direction
("direction of the flow") --- the -dimensional generalization of the
ensemble introduced by Avellaneda and Majda [1990 {\it Commun. Math. Phys.}
{\bf 131} 381] within the context of passive scalar advection. This model can
describe a rich class of physical situations. It is shown that, depending on
the values of parameters that define self-interaction of the order parameter
and the relation between the exponent and the space dimension , the
system exhibits various types of large-scale scaling behaviour, associated with
different infrared attractive fixed points of the renormalization-group
equations. In addition to known asymptotic regimes (critical dynamics of the
Potts model and passively advected field without self-interaction), existence
of a new, non-equilibrium and strongly anisotropic, type of critical behaviour
(universality class) is established, and the corresponding critical dimensions
are calculated to the leading order of the double expansion in and
(one-loop approximation). The scaling appears strongly
anisotropic in the sense that the critical dimensions related to the directions
parallel and perpendicular to the flow are essentially different.Comment: 21 page, LaTeX source, 7 eps figures. arXiv admin note: substantial
text overlap with arXiv:cond-mat/060701
On Locality, Holography and Unfolding
We study the functional class and locality problems in the context of
higher-spin theories and Vasiliev's equations. A locality criterion that is
sufficient to make higher-spin theories well-defined as field theories on
Anti-de-Sitter space is proposed. This criterion identifies admissible
pseudo-local field redefinitions which preserve AdS/CFT correlation functions
as we check in the 3d example. Implications of this analysis for known
higher-spin theories are discussed. We also check that the cubic coupling
coefficients previously fixed in 3d at the action level give the correct CFT
correlation functions upon computing the corresponding Witten diagrams.Comment: 36 pages, LaTex. References added, typos corrected. Final version to
appear in JHE
Critical behavior at superconductor-insulator phase transitions near one dimension
I argue that the system of interacting bosons at zero temperature and in
random external potential possesses a simple critical point which describes the
proliferation of disorder-induced topological defects in the superfluid ground
state, and which is located at weak disorder close to and above one dimension.
This makes it possible to address the critical behavior at the superfluid-Bose
glass transition in dirty boson systems by expanding around the lower critical
dimension d=1. Within the formulated renormalization procedure near d=1 the
dynamical critical exponent is obtained exactly and the correlation length
exponent is calculated as a Laurent series in the parameter \sqrt{\epsilon},
with \epsilon=d-1: z=d, \nu=1/\sqrt{3\epsilon} for the short range, and z=1,
\nu=\sqrt{2/3\epsilon}, for the long-range Coulomb interaction between bosons.
The identified critical point should be stable against the residual
perturbations in the effective action for the superfluid, at least in
dimensions 1\leq d \leq 2, for both short-range and Coulomb interactions. For
the superfluid-Mott insulator transition in the system in a periodic potential
and at a commensurate density of bosons I find \nu=(1/2\sqrt{\epsilon})+
1/4+O(\sqrt{\epsilon}), which yields a result reasonably close to the known XY
critical exponent in d=2+1. The critical behavior of the superfluid density,
phonon velocity and the compressibility in the system with the short-range
interactions is discussed.Comment: 23 pages, 1 Postscript figure, LaTe
Ensemble dependence of Critical Casimir Forces in Films with Dirichlet Boundary Conditions
In a recent study [Phys. Rev. E \textbf{94}, 022103 (2016)] it has been shown
that, for a fluid film subject to critical adsorption, the resulting critical
Casimir force (CCF) may significantly depend on the thermodynamic ensemble.
Here, we extend that study by considering fluid films within the so-called
ordinary surface universality class. We focus on mean-field theory, within
which the OP profile satisfies Dirichlet boundary conditions and produces a
nontrivial CCF in the presence of external bulk fields or, respectively, a
nonzero total order parameter within the film. Our analytical results are
supported by Monte Carlo simulations of the three-dimensional Ising model. We
show that, in the canonical ensemble, i.e., when fixing the so-called total
mass within the film, the CCF is typically repulsive instead of attractive as
in the grand canonical ensemble. Based on the Landau-Ginzburg free energy, we
furthermore obtain analytic expressions for the order parameter profiles and
analyze the relation between the total mass in the film and the external bulk
field.Comment: 22 pages, 15 figures. Version 2: minor corrections; added Journal
referenc
Influence of Non-Markovian Dynamics in Thermal-Equilibrium Uncertainty-Relations
Contrary to the conventional wisdom that deviations from standard
thermodynamics originate from the strong coupling to the bath, it is shown that
in quantum mechanics, these deviations originate from the uncertainty principle
and are supported by the non-Markovian character of the dynamics. Specifically,
it is shown that the lower bound of the dispersion of the total energy of the
system, imposed by the uncertainty principle, is dominated by the bath power
spectrum and therefore, quantum mechanics inhibits the system
thermal-equilibrium-state from being described by the canonical Boltzmann's
distribution. We show that for a wide class of systems, systems interacting via
central forces with pairwise-self-interacting environments, this general
observation is in sharp contrast to the classical case, for which the thermal
equilibrium distribution, irrespective of the interaction strength, is
\emph{exactly} characterized by the canonical Boltzmann distribution and
therefore, no dependence on the bath power spectrum is present. We define an
\emph{effective coupling} to the environment that depends on all energy scales
in the system and reservoir interaction. Sample computations in regimes
predicted by this effective coupling are demonstrated. For example, for the
case of strong effective coupling, deviations from standard thermodynamics are
present and, for the case of weak effective coupling, quantum features such as
stationary entanglement are possible at high temperatures.Comment: 9 pages, 3 figure
Gravity as an emergent phenomenon: a GFT perspective
While the idea of gravity as an emergent phenomenon is an intriguing one,
little is known about concrete implementations that could lead to viable
phenomenology, most of the obstructions being related to the intrinsic
difficulties of formulating genuinely pregeometric theories. In this paper we
present a preliminary discussion of the impact of critical behavior of certain
microscopic models for gravity, based on group field theories, on the dynamics
of the macroscopic regime. The continuum limit is examined in light of some
scaling assumption, and the relevant consequences for low energy effective
theories are discussed, the role of universality, the corrections to scaling,
the emergence of gravitational theories and the nature of their thermodynamical
behavior.Comment: 1+26 page
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