2,862 research outputs found
Hierarchy of boundary driven phase transitions in multi-species particle systems
Interacting systems with driven particle species on a open chain or
chains which are coupled at the ends to boundary reservoirs with fixed particle
densities are considered. We classify discontinuous and continuous phase
transitions which are driven by adiabatic change of boundary conditions. We
build minimal paths along which any given boundary driven phase transition
(BDPT) is observed and reveal kinetic mechanisms governing these transitions.
Combining minimal paths, we can drive the system from a stationary state with
all positive characteristic speeds to a state with all negative characteristic
speeds, by means of adiabatic changes of the boundary conditions. We show that
along such composite paths one generically encounters discontinuous and
continuous BDPTs with taking values depending on
the path. As model examples we consider solvable exclusion processes with
product measure states and particle species and a non-solvable
two-way traffic model. Our findings are confirmed by numerical integration of
hydrodynamic limit equations and by Monte Carlo simulations. Results extend
straightforwardly to a wide class of driven diffusive systems with several
conserved particle species.Comment: 12 pages, 11 figure
Application of approximation theory by nonlinear manifolds in Sturm-Liouville inverse problems
We give here some negative results in Sturm-Liouville inverse theory, meaning
that we cannot approach any of the potentials with integrable derivatives
on by an -parametric analytic family better than order
of .
Next, we prove an estimation of the eigenvalues and characteristic values of
a Sturm-Liouville operator and some properties of the solution of a certain
integral equation. This allows us to deduce from [Henkin-Novikova] some
positive results about the best reconstruction formula by giving an almost
optimal formula of order of .Comment: 40 page
The existence of a real pole-free solution of the fourth order analogue of the Painleve I equation
We establish the existence of a real solution y(x,T) with no poles on the
real line of the following fourth order analogue of the Painleve I equation,
x=Ty-({1/6}y^3+{1/24}(y_x^2+2yy_{xx})+{1/240}y_{xxxx}). This proves the
existence part of a conjecture posed by Dubrovin. We obtain our result by
proving the solvability of an associated Riemann-Hilbert problem through the
approach of a vanishing lemma. In addition, by applying the Deift/Zhou
steepest-descent method to this Riemann-Hilbert problem, we obtain the
asymptotics for y(x,T) as x\to\pm\infty.Comment: 27 pages, 5 figure
First-order symmetric-hyperbolic Einstein equations with arbitrary fixed gauge
We find a one-parameter family of variables which recast the 3+1 Einstein
equations into first-order symmetric-hyperbolic form for any fixed choice of
gauge. Hyperbolicity considerations lead us to a redefinition of the lapse in
terms of an arbitrary factor times a power of the determinant of the 3-metric;
under certain assumptions, the exponent can be chosen arbitrarily, but
positive, with no implication of gauge-fixing.Comment: 5 pages; Latex with Revtex v3.0 macro package and style; to appear in
Phys. Rev. Let
From St\"{a}ckel systems to integrable hierarchies of PDE's: Benenti class of separation relations
We propose a general scheme of constructing of soliton hierarchies from
finite dimensional St\"{a}ckel systems and related separation relations. In
particular, we concentrate on the simplest class of separation relations,
called Benenti class, i.e. certain St\"{a}ckel systems with quadratic in
momenta integrals of motion.Comment: 24 page
``Good Propagation'' Constraints on Dual Invariant Actions in Electrodynamics and on Massless Fields
We present some consequences of non-anomalous propagation requirements on
various massless fields. Among the models of nonlinear electrodynamics we show
that only Maxwell and Born-Infeld also obey duality invariance. Separately we
show that, for actions depending only on the F_\mn^2 invariant, the permitted
models have . We also characterize acceptable
vector-scalar systems. Finally we find that wide classes of gravity models
share with Einstein the null nature of their characteristic surfaces.Comment: 11 pages, LaTeX, no figure
How to detect level crossings without looking at the spectrum
We remind the reader that it is possible to tell if two or more eigenvalues
of a matrix are equal, without calculating the eigenvalues. We then use this
property to detect (avoided) crossings in the spectra of quantum Hamiltonians
representable by matrices. This approach provides a pedagogical introduction to
(avoided) crossings, is capable of handling realistic Hamiltonians
analytically, and offers a way to visualize crossings which is sometimes
superior to that provided by the spectrum. We illustrate the method using the
Breit-Rabi Hamiltonian to describe the hyperfine-Zeeman structure of the ground
state hydrogen atom in a uniform magnetic field.Comment: Accepted for publication in the American Journal of Physic
Calculating the Fine Structure of a Fabry-Perot Resonator using Spheroidal Wave Functions
A new set of vector solutions to Maxwell's equations based on solutions to
the wave equation in spheroidal coordinates allows laser beams to be described
beyond the paraxial approximation. Using these solutions allows us to calculate
the complete first-order corrections in the short-wavelength limit to
eigenmodes and eigenfrequencies in a Fabry-Perot resonator with perfectly
conducting mirrors. Experimentally relevant effects are predicted. Modes which
are degenerate according to the paraxial approximation are split according to
their total angular momentum. This includes a splitting due to coupling between
orbital angular momentum and spin angular momentum
Time evolution and squeezing of the field amplitude in cavity QED
We present the conditional time evolution of the electromagnetic field
produced by a cavity QED system in the strongly coupled regime. We obtain the
conditional evolution through a wave-particle correlation function that
measures the time evolution of the field after the detection of a photon. A
connection exists between this correlation function and the spectrum of
squeezing which permits the study of squeezed states in the time domain. We
calculate the spectrum of squeezing from the master equation for the reduced
density matrix using both the quantum regression theorem and quantum
trajectories. Our calculations not only show that spontaneous emission degrades
the squeezing signal, but they also point to the dynamical processes that cause
this degradation.Comment: 12 pages. Submitted to JOSA
Measurement Theory in Lax-Phillips Formalism
It is shown that the application of Lax-Phillips scattering theory to quantum
mechanics provides a natural framework for the realization of the ideas of the
Many-Hilbert-Space theory of Machida and Namiki to describe the development of
decoherence in the process of measurement. We show that if the quantum
mechanical evolution is pointwise in time, then decoherence occurs only if the
Hamiltonian is time-dependent. If the evolution is not pointwise in time (as in
Liouville space), then the decoherence may occur even for closed systems. These
conclusions apply as well to the general problem of mixing of states.Comment: 14 pages, IASSNS-HEP 93/6
- âŠ