32,715 research outputs found
Corrigendum to "Knot Floer homology detects fibred knots"
We correct a mistake on the citation of JSJ theory in \cite{Ni}. Some
arguments in \cite{Ni} are also slightly modified accordingly.Comment: 3 page
The definability criterions for convex projective polyhedral reflection groups
Following Vinberg, we find the criterions for a subgroup generated by
reflections \Gamma \subset \SL^{\pm}(n+1,\mathbb{R}) and its finite-index
subgroups to be definable over where is an integrally
closed Noetherian ring in the field . We apply the criterions for
groups generated by reflections that act cocompactly on irreducible properly
convex open subdomains of the -dimensional projective sphere. This gives a
method for constructing injective group homomorphisms from such Coxeter groups
to \SL^{\pm}(n+1,\mathbb{Z}). Finally we provide some examples of
\SL^{\pm}(n+1,\mathbb{Z})-representations of such Coxeter groups. In
particular, we consider simplicial reflection groups that are isomorphic to
hyperbolic simplicial groups and classify all the conjugacy classes of the
reflection subgroups in \SL^{\pm}(n+1,\mathbb{R}) that are definable over
. These were known by Goldman, Benoist, and so on previously.Comment: 31 pages, 8 figure
Initial Time Singularities in Non-Equilibrium Evolution of Condensates and Their Resolution in the Linearized Approximation
The real time non-equilibrium evolution of condensates in field theory
requires an initial value problem specifying an initial quantum state or
density matrix. Arbitrary specifications of the initial quantum state (pure or
mixed) results in initial time singularities which are not removed by the usual
renormalization counterterms. We study the initial time singularities in the
linearized equation of motion for the scalar condensate in a renormalizable
Yukawa theory in 3+1 dimensions. In this renormalizable theory the initial time
singularities are enhanced. We present a consistent method for removing these
initial time singularities by specifying initial states where the distribution
of high energy quanta is determined by the initial conditions and the
interaction effects. This is done through a Bogoliubov transformation which is
consistently obtained in a perturbative expansion.The usual renormalization
counterterms and the proper choice of the Bogoliubov coefficients lead to a
singularity free evolution equation. We establish the relationship between the
evolution equations in the linearized approximation and linear response theory.
It is found that only a very specific form of the external source for linear
response leads to a real time evolution equation which is singularity free. We
focus on the evolution of spatially inhomogeneous scalar condensates by
implementing the initial state preparation via a Bogoliubov transformation up
to one-loop. As a concrete application, the evolution equation for an
inhomogenous condensate is solved analytically and the results are carefully
analyzed. Symmetry breaking by initial quantum states is discussed.Comment: LaTex, 26 pages, 2 .ps figure
Diamagnetism and flux creep in bilayer exciton superfluids
We discuss the diamagnetism induced in an isolated quantum Hall bilayer with
total filling factor one by an in-plane magnetic field. This is a signature of
counterflow superfluidity in these systems. We calculate magnetically induced
currents in the presence of pinned vortices nucleated by charge disorder, and
predict a history-dependent diamagnetism that could persist on laboratory
timescales. For current samples we find that the maximum in-plane moment is
small, but with stronger tunneling the moments would be measurable using torque
magnetometry. Such experiments would allow the persistent currents of a
counterflow superfluid to be observed in an electrically isolated bilayer.Comment: 8 pages, 2 figures. v2: updated to accepted version, extended
presentatio
Resumming the large-N approximation for time evolving quantum systems
In this paper we discuss two methods of resumming the leading and next to
leading order in 1/N diagrams for the quartic O(N) model. These two approaches
have the property that they preserve both boundedness and positivity for
expectation values of operators in our numerical simulations. These
approximations can be understood either in terms of a truncation to the
infinitely coupled Schwinger-Dyson hierarchy of equations, or by choosing a
particular two-particle irreducible vacuum energy graph in the effective action
of the Cornwall-Jackiw-Tomboulis formalism. We confine our discussion to the
case of quantum mechanics where the Lagrangian is . The
key to these approximations is to treat both the propagator and the
propagator on similar footing which leads to a theory whose graphs have the
same topology as QED with the propagator playing the role of the photon.
The bare vertex approximation is obtained by replacing the exact vertex
function by the bare one in the exact Schwinger-Dyson equations for the one and
two point functions. The second approximation, which we call the dynamic Debye
screening approximation, makes the further approximation of replacing the exact
propagator by its value at leading order in the 1/N expansion. These two
approximations are compared with exact numerical simulations for the quantum
roll problem. The bare vertex approximation captures the physics at large and
modest better than the dynamic Debye screening approximation.Comment: 30 pages, 12 figures. The color version of a few figures are
separately liste
From fields to a super-cluster: the role of the environment at z=0.84 with HiZELS
At z=0, clusters are primarily populated by red, elliptical and massive
galaxies, while blue, spiral and lower-mass galaxies are common in low-density
environments. Understanding how and when these differences were established is
of absolute importance for our understanding of galaxy formation and evolution,
but results at high-z remain contradictory. By taking advantage of the widest
and deepest H-alpha narrow-band survey at z=0.84 over the COSMOS and UKIDSS UDS
fields, probing a wide range of densities (from poor fields to rich groups and
clusters, including a confirmed super-cluster with a striking filamentary
structure), we show that the fraction of star-forming galaxies falls
continuously from ~40% in fields to approaching 0% in rich groups/clusters. We
also find that the median SFR increases with environmental density, at least up
to group densities - but only for low and medium mass galaxies, and thus such
enhancement is mass-dependent at z~1. The environment also plays a role in
setting the faint-end slope (alpha) of the H-alpha luminosity function. Our
findings provide a sharper view on galaxy formation and evolution and reconcile
previously contradictory results at z~1: stellar mass is the primary predictor
of star formation activity, but the environment also plays a major role.Comment: 5 pages, 4 figures, to appear in the proceedings of JENAM 2010 S2:
`Environment and the Formation of Galaxies: 30 years later', ASSP, Springe
Particle Production and Effective Thermalization in Inhomogeneous Mean Field Theory
As a toy model for dynamics in nonequilibrium quantum field theory we
consider the abelian Higgs model in 1+1 dimensions with fermions. In the
approximate dynamical equations, inhomogeneous classical (mean) Bose fields are
coupled to quantized fermion fields, which are treated with a mode function
expansion. The effective equations of motion imply e.g. Coulomb scattering, due
to the inhomogeneous gauge field. The equations are solved numerically. We
define time dependent fermion particle numbers with the help of the single-time
Wigner function and study particle production starting from inhomogeneous
initial conditions. The particle numbers are compared with the Fermi-Dirac
distribution parametrized by a time dependent temperature and chemical
potential. We find that the fermions approximately thermalize locally in time.Comment: 16 pages + 6 eps figures, some clarifications and two references
added, typos corrected; to appear in Phys.Rev.
Equilibrium and nonequilibrium properties associated with the chiral phase transition at finite density in the Gross-Neveu Model
We study the dynamics of the chiral phase transition at finite density in the
Gross-Neveu (GN) model in the leading order in large-N approximation. The phase
structure of the GN model in this approximation has the property that there is
a tricritical point at a fixed temperature and chemical potential separating
regions where the chiral transition is first order from that where it is second
order. We consider evolutions starting in local thermal and chemical
equilibrium in the massless unbroken phase for conditions pertaining to
traversing a first or second order phase transition. We assume boost invariant
kinematics and determine the evolution of the order parameter , the
energy density and pressure as well as the effective temperature, chemical
potential and interpolating number densities as a function of the proper time
. We find that before the phase transition, the system behaves as if it
were an ideal fluid in local thermal equilibrium with equation of state
. After the phase transition, the system quickly reaches its true
broken symmetry vacuum value for the fermion mass and for the energy density.
The single particle distribution functions for Fermions and anti-Fermions go
far out of equilibrium as soon as the plasma traverses the chiral phase
transition. We have also determined the spatial dependence of the "pion"
Green's function as a function of the proper time.Comment: 39 pages, 23 figure
Non-Equilibrium Large N Yukawa Dynamics: marching through the Landau pole
The non-equilibrium dynamics of a Yukawa theory with N fermions coupled to a
scalar field is studied in the large N limit with the goal of comparing the
dynamics predicted from the renormalization group improved effective potential
to that obtained including the fermionic backreaction. The effective potential
is of the Coleman-Weinberg type. Its renormalization group improvement is
unbounded from below and features a Landau pole. When viewed self-consistently,
the initial time singularity does not arise. The different regimes of the
dynamics of the fully renormalized theory are studied both analytically and
numerically. Despite the existence of a Landau pole in the model, the dynamics
of the mean field is smooth as it passes the location of the pole. This is a
consequence of a remarkable cancellation between the effective potential and
the dynamical chiral condensate. The asymptotic evolution is effectively
described by a quartic upright effective potential. In all regimes, profuse
particle production results in the formation of a dense fermionic plasma with
occupation numbers nearly saturated up to a scale of the order of the mean
field. This can be interpreted as a chemical potential. We discuss the
implications of these results for cosmological preheating.Comment: 36 pages, 14 figures, LaTeX, submitted to Physical Review
Chaos in Time Dependent Variational Approximations to Quantum Dynamics
Dynamical chaos has recently been shown to exist in the Gaussian
approximation in quantum mechanics and in the self-consistent mean field
approach to studying the dynamics of quantum fields. In this study, we first
show that any variational approximation to the dynamics of a quantum system
based on the Dirac action principle leads to a classical Hamiltonian dynamics
for the variational parameters. Since this Hamiltonian is generically nonlinear
and nonintegrable, the dynamics thus generated can be chaotic, in distinction
to the exact quantum evolution. We then restrict attention to a system of two
biquadratically coupled quantum oscillators and study two variational schemes,
the leading order large N (four canonical variables) and Hartree (six canonical
variables) approximations. The chaos seen in the approximate dynamics is an
artifact of the approximations: this is demonstrated by the fact that its onset
occurs on the same characteristic time scale as the breakdown of the
approximations when compared to numerical solutions of the time-dependent
Schrodinger equation.Comment: 10 pages (12 figures), RevTeX (plus macro), uses epsf, minor typos
correcte
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