3,339 research outputs found
On the instability of classical dynamics in theories with higher derivatives
The development of instability in the dynamics of theories with higher
derivatives is traced in detail in the framework of the Pais-Uhlenbeck fourth
oder oscillator. For this aim the external friction force is introduced in the
model and the relevant solutions to equations of motion are investigated. As a
result, the physical implication of the energy unboundness from below in
theories under consideration is revealed.Comment: 9 pages, no figures and no tables, revtex4; a few misprints are
correcte
Relative entropy as a measure of inhomogeneity in general relativity
We introduce the notion of relative volume entropy for two spacetimes with
preferred compact spacelike foliations. This is accomplished by applying the
notion of Kullback-Leibler divergence to the volume elements induced on
spacelike slices. The resulting quantity gives a lower bound on the number of
bits which are necessary to describe one metric given the other. For
illustration, we study some examples, in particular gravitational waves, and
conclude that the relative volume entropy is a suitable device for quantitative
comparison of the inhomogeneity of two spacetimes.Comment: 15 pages, 7 figure
Spectral singularities in PT-symmetric periodic finite-gap systems
The origin of spectral singularities in finite-gap singly periodic
PT-symmetric quantum systems is investigated. We show that they emerge from a
limit of band-edge states in a doubly periodic finite gap system when the
imaginary period tends to infinity. In this limit, the energy gaps are
contracted and disappear, every pair of band states of the same periodicity at
the edges of a gap coalesces and transforms into a singlet state in the
continuum. As a result, these spectral singularities turn out to be analogous
to those in the non-periodic systems, where they appear as zero-width
resonances. Under the change of topology from a non-compact into a compact one,
spectral singularities in the class of periodic systems we study are
transformed into exceptional points. The specific degeneration related to the
presence of finite number of spectral singularities and exceptional points is
shown to be coherently reflected by a hidden, bosonized nonlinear
supersymmetry.Comment: 16 pages, 3 figures; a difference between spectral singularities and
exceptional points specified, the version to appear in PR
How to fix a broken symmetry: Quantum dynamics of symmetry restoration in a ferromagnetic Bose-Einstein condensate
We discuss the dynamics of a quantum phase transition in a spin-1
Bose-Einstein condensate when it is driven from the magnetized
broken-symmetry phase to the unmagnetized ``symmetric'' polar phase. We
determine where the condensate goes out of equilibrium as it approaches the
critical point, and compute the condensate magnetization at the critical point.
This is done within a quantum Kibble-Zurek scheme traditionally employed in the
context of symmetry-breaking quantum phase transitions. Then we study the
influence of the nonequilibrium dynamics near a critical point on the
condensate magnetization. In particular, when the quench stops at the critical
point, nonlinear oscillations of magnetization occur. They are characterized by
a period and an amplitude that are inversely proportional. If we keep driving
the condensate far away from the critical point through the unmagnetized
``symmetric'' polar phase, the amplitude of magnetization oscillations slowly
decreases reaching a non-zero asymptotic value. That process is described by
the equation that can be mapped onto the classical mechanical problem of a
particle moving under the influence of harmonic and ``anti-friction'' forces
whose interplay leads to surprisingly simple fixed-amplitude oscillations. We
obtain several scaling results relating the condensate magnetization to the
quench rate, and verify numerically all analytical predictions.Comment: 15 pages, 11 figures, final version accepted in NJP (slight changes
with respect to the former submission
Critical dynamics of decoherence
We study decoherence induced by a dynamic environment undergoing a quantum
phase transition. Environment's susceptibility to perturbations - and,
consequently, efficiency of decoherence - is amplified near a critical point.
Over and above this near-critical susceptibility increase, we show that
decoherence is dramatically enhanced by non-equilibrium critical dynamics of
the environment. We derive a simple expression relating decoherence to the
universal critical exponents exhibiting deep connections with the theory of
topological defect creation in non-equilibrium phase transitions.Comment: 8 pages; version accepted in PR
Scattering map for two black holes
We study the motion of light in the gravitational field of two Schwarzschild
black holes, making the approximation that they are far apart, so that the
motion of light rays in the neighborhood of one black hole can be considered to
be the result of the action of each black hole separately. Using this
approximation, the dynamics is reduced to a 2-dimensional map, which we study
both numerically and analytically. The map is found to be chaotic, with a
fractal basin boundary separating the possible outcomes of the orbits (escape
or falling into one of the black holes). In the limit of large separation
distances, the basin boundary becomes a self-similar Cantor set, and we find
that the box-counting dimension decays slowly with the separation distance,
following a logarithmic decay law.Comment: 20 pages, 5 figures, uses REVTE
Edgeworth Expansion of the Largest Eigenvalue Distribution Function of GUE Revisited
We derive expansions of the resolvent
Rn(x;y;t)=(Qn(x;t)Pn(y;t)-Qn(y;t)Pn(x;t))/(x-y) of the Hermite kernel Kn at the
edge of the spectrum of the finite n Gaussian Unitary Ensemble (GUEn) and the
finite n expansion of Qn(x;t) and Pn(x;t). Using these large n expansions, we
give another proof of the derivation of an Edgeworth type theorem for the
largest eigenvalue distribution function of GUEn. We conclude with a brief
discussion on the derivation of the probability distribution function of the
corresponding largest eigenvalue in the Gaussian Orthogonal Ensemble (GOEn) and
Gaussian Symplectic Ensembles (GSEn)
Whittaker-Hill equation and semifinite-gap Schroedinger operators
A periodic one-dimensional Schroedinger operator is called semifinite-gap if
every second gap in its spectrum is eventually closed. We construct explicit
examples of semifinite-gap Schroedinger operators in trigonometric functions by
applying Darboux transformations to the Whittaker-Hill equation. We give a
criterion of the regularity of the corresponding potentials and investigate the
spectral properties of the new operators.Comment: Revised versio
Discontinuous Molecular Dynamics for Semi-Flexible and Rigid Bodies
A general framework for performing event-driven simulations of systems with
semi-flexible or rigid bodies interacting under impulsive torques and forces is
outlined. Two different approaches are presented. In the first, the dynamics
and interaction rules are derived from Lagrangian mechanics in the presence of
constraints. This approach is most suitable when the body is composed of
relatively few point masses or is semi-flexible. In the second method, the
equations of rigid bodies are used to derive explicit analytical expressions
for the free evolution of arbitrary rigid molecules and to construct a simple
scheme for computing interaction rules. Efficient algorithms for the search for
the times of interaction events are designed in this context, and the handling
of missed interaction events is discussed.Comment: 16 pages, double column revte
Lagrangian analysis of alignment dynamics for isentropic compressible magnetohydrodynamics
After a review of the isentropic compressible magnetohydrodynamics (ICMHD)
equations, a quaternionic framework for studying the alignment dynamics of a
general fluid flow is explained and applied to the ICMHD equations.Comment: 12 pages, 2 figures, submitted to a Focus Issue of New Journal of
Physics on "Magnetohydrodynamics and the Dynamo Problem" J-F Pinton, A
Pouquet, E Dormy and S Cowley, editor
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