242 research outputs found
States of the Dirac equation in confining potentials
We study the Dirac equation in confining potentials with pure vector
coupling, proving the existence of metastable states with longer and longer
lifetimes as the non-relativistic limit is approached and eventually merging
with continuity into the Schr\"odinger bound states. We believe that the
existence of these states could be relevant in high energy model construction
and in understanding possible resonant scattering effects in systems like
Graphene. We present numerical results for the linear and the harmonic cases
and we show that the the density of the states of the continuous spectrum is
well described by a sum of Breit-Wigner lines. The width of the line with
lowest positive energy, as expected, reproduces very well the Schwinger pair
production rate for a linear potential: we thus suggest a different way of
obtaining informations on the pair production in unbounded, non uniform
electric fields, where very little is known.Comment: 4 page
Resonances in a spring-pendulum: algorithms for equivariant singularity theory
A spring-pendulum in resonance is a time-independent Hamiltonian model system for formal reduction to one degree of freedom, where some symmetry (reversibility) is maintained. The reduction is handled by equivariant singularity theory with a distinguished parameter, yielding an integrable approximation of the Poincaré map. This makes a concise description of certain bifurcations possible. The computation of reparametrizations from normal form to the actual system is performed by Gröbner basis techniques.
The Elliptic Billiard: Subtleties of Separability
Some of the subtleties of the integrability of the elliptic quantum billiard
are discussed. A well known classical constant of the motion has in the quantum
case an ill-defined commutator with the Hamiltonian. It is shown how this
problem can be solved. A geometric picture is given revealing why levels of a
separable system cross. It is shown that the repulsions found by Ayant and
Arvieu are computational effects and that the method used by Traiber et al. is
related to the present picture which explains the crossings they find. An
asymptotic formula for the energy-levels is derived and it is found that the
statistical quantities of the spectrum P(s) and \Delta(L) have the form
expected for an integrable system.Comment: 10 pages, LaTeX, 3 Figures (postscript). Submitted to European
Journal of Physic
Intrathecal Morphine for Laparoscopic Segmental Colonic Resection as Part of an Enhanced Recovery Protocol: A Randomized Controlled Trial
Background and Objectives: Management of postoperative pain after laparoscopic segmental colonic resections remains controversial. We compared 2 methods of analgesia within an Enhanced Recovery After Surgery (ERAS) program. The goal of the study was to investigate whether admin
New Results for Diffusion in Lorentz Lattice Gas Cellular Automata
New calculations to over ten million time steps have revealed a more complex
diffusive behavior than previously reported, of a point particle on a square
and triangular lattice randomly occupied by mirror or rotator scatterers. For
the square lattice fully occupied by mirrors where extended closed particle
orbits occur, anomalous diffusion was still found. However, for a not fully
occupied lattice the super diffusion, first noticed by Owczarek and Prellberg
for a particular concentration, obtains for all concentrations. For the square
lattice occupied by rotators and the triangular lattice occupied by mirrors or
rotators, an absence of diffusion (trapping) was found for all concentrations,
except on critical lines, where anomalous diffusion (extended closed orbits)
occurs and hyperscaling holds for all closed orbits with {\em universal}
exponents and . Only one point on these critical lines can be related to a
corresponding percolation problem. The questions arise therefore whether the
other critical points can be mapped onto a new percolation-like problem, and of
the dynamical significance of hyperscaling.Comment: 52 pages, including 18 figures on the last 22 pages, email:
[email protected]
An Intersecting Loop Model as a Solvable Super Spin Chain
In this paper we investigate an integrable loop model and its connection with
a supersymmetric spin chain. The Bethe Ansatz solution allows us to study some
properties of the ground state. When the loop fugacity lies in the physical
regime, we conjecture that the central charge is for integer .
Low-lying excitations are examined, supporting a superdiffusive behavior for
. We argue that these systems are interesting examples of integrable
lattice models realizing conformal field theories.Comment: latex file, 7 page
Excited Charmed Mesons: Observations, Analyses and Puzzles
We review the status of recently observed positive parity charmed resonances,
both in the non-strange and in the strange sector. We describe the experimental
findings, the main theoretical analyses and the open problems deserving further
investigations.Comment: LaTeX, 25 pages, 5 figures. Invited revie
Metastable states in glassy systems
Truly stable metastable states are an artifact of the mean-field
approximation or the zero temperature limit. If such appealing concepts in
glass theory as configurational entropy are to have a meaning beyond these
approximations, one needs to cast them in a form involving states with finite
lifetimes.
Starting from elementary examples and using results of Gaveau and Schulman,
we propose a simple expression for the configurational entropy and revisit the
question of taking flat averages over metastable states. The construction is
applicable to finite dimensional systems, and we explicitly show that for
simple mean-field glass models it recovers, justifies and generalises the known
results. The calculation emphasises the appearance of new dynamical order
parameters.Comment: 4 fig., 20 pages, revtex; added references and minor change
Thermodynamic formalism for systems with Markov dynamics
The thermodynamic formalism allows one to access the chaotic properties of
equilibrium and out-of-equilibrium systems, by deriving those from a dynamical
partition function. The definition that has been given for this partition
function within the framework of discrete time Markov chains was not suitable
for continuous time Markov dynamics. Here we propose another interpretation of
the definition that allows us to apply the thermodynamic formalism to
continuous time.
We also generalize the formalism --a dynamical Gibbs ensemble construction--
to a whole family of observables and their associated large deviation
functions. This allows us to make the connection between the thermodynamic
formalism and the observable involved in the much-studied fluctuation theorem.
We illustrate our approach on various physical systems: random walks,
exclusion processes, an Ising model and the contact process. In the latter
cases, we identify a signature of the occurrence of dynamical phase
transitions. We show that this signature can already be unravelled using the
simplest dynamical ensemble one could define, based on the number of
configuration changes a system has undergone over an asymptotically large time
window.Comment: 64 pages, LaTeX; version accepted for publication in Journal of
Statistical Physic
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