68,932 research outputs found
Quasi-exactly solvable symmetrized quartic and sextic polynomial oscillators
The symmetrized quartic polynomial oscillator is shown to admit an sl(2,)
algebraization. Some simple quasi-exactly solvable (QES) solutions are
exhibited. A new symmetrized sextic polynomial oscillator is introduced and
proved to be QES by explicitly deriving some exact, closed-form solutions by
resorting to the functional Bethe ansatz method. Such polynomial oscillators
include two categories of QES potentials: the first one containing the
well-known analytic sextic potentials as a subset, and the second one of novel
potentials with no counterpart in such a class.Comment: 14 pages, 4 figures; published version; main changes are in
introduction, conclusion, and reference
Aharonov-Bohm ring with fluctuating flux
We consider a non-interacting system of electrons on a clean one-channel
Aharonov-Bohm ring which is threaded by a fluctuating magnetic flux. The flux
derives from a Caldeira-Leggett bath of harmonic oscillators. We address the
influence of the bath on the following properties: one- and two-particle
Green's functions, dephasing, persistent current and visibility of the
Aharonov-Bohm effect in cotunneling transport through the ring. For the bath
spectra considered here (including Nyquist noise of an external coil), we find
no dephasing in the linear transport regime at zero temperature.
PACS numbers: 73.23.-b, 73.23.Hk, 73.23.Ra, 03.65.YzComment: 17 pages, 8 figures. To be published in PRB. New version contains
minor corrections and additional discussion suggested by referee. A simple
introduction to the basics of dephasing can be found at
http://iff.physik.unibas.ch/~florian/dephasing/dephasing.htm
Trajectories for the Wave Function of the Universe from a Simple Detector Model
Inspired by Mott's (1929) analysis of particle tracks in a cloud chamber, we
consider a simple model for quantum cosmology which includes, in the total
Hamiltonian, model detectors registering whether or not the system, at any
stage in its entire history, passes through a series of regions in
configuration space. We thus derive a variety of well-defined formulas for the
probabilities for trajectories associated with the solutions to the
Wheeler-DeWitt equation. The probability distribution is peaked about classical
trajectories in configuration space. The ``measured'' wave functions still
satisfy the Wheeler-DeWitt equation, except for small corrections due to the
disturbance of the measuring device. With modified boundary conditions, the
measurement amplitudes essentially agree with an earlier result of Hartle
derived on rather different grounds. In the special case where the system is a
collection of harmonic oscillators, the interpretation of the results is aided
by the introduction of ``timeless'' coherent states -- eigenstates of the
Hamiltonian which are concentrated about entire classical trajectories.Comment: 37 pages, plain Tex. Second draft. Substantial revision
Plasticity and learning in a network of coupled phase oscillators
A generalized Kuramoto model of coupled phase oscillators with slowly varying
coupling matrix is studied. The dynamics of the coupling coefficients is driven
by the phase difference of pairs of oscillators in such a way that the coupling
strengthens for synchronized oscillators and weakens for non-synchronized
pairs. The system possesses a family of stable solutions corresponding to
synchronized clusters of different sizes. A particular cluster can be formed by
applying external driving at a given frequency to a group of oscillators. Once
established, the synchronized state is robust against noise and small
variations in natural frequencies. The phase differences between oscillators
within the synchronized cluster can be used for information storage and
retrieval.Comment: 10 page
Collective Phase Chaos in the Dynamics of Interacting Oscillator Ensembles
We study chaotic behavior of order parameters in two coupled ensembles of
self-sustained oscillators. Coupling within each of these ensembles is switched
on and off alternately, while the mutual interaction between these two
subsystems is arranged through quadratic nonlinear coupling. We show
numerically that in the course of alternating Kuramoto transitions to synchrony
and back to asynchrony, the exchange of excitations between two subpopulations
proceeds in such a way that their collective phases are governed by an
expanding circle map similar to the Bernoulli map. We perform the Lyapunov
analysis of the dynamics and discuss finite-size effects.Comment: 19 page
Time Delay Effects on Coupled Limit Cycle Oscillators at Hopf Bifurcation
We present a detailed study of the effect of time delay on the collective
dynamics of coupled limit cycle oscillators at Hopf bifurcation. For a simple
model consisting of just two oscillators with a time delayed coupling, the
bifurcation diagram obtained by numerical and analytical solutions shows
significant changes in the stability boundaries of the amplitude death, phase
locked and incoherent regions. A novel result is the occurrence of amplitude
death even in the absence of a frequency mismatch between the two oscillators.
Similar results are obtained for an array of N oscillators with a delayed mean
field coupling and the regions of such amplitude death in the parameter space
of the coupling strength and time delay are quantified. Some general analytic
results for the N tending to infinity (thermodynamic) limit are also obtained
and the implications of the time delay effects for physical applications are
discussed.Comment: 20 aps formatted revtex pages (including 13 PS figures); Minor
changes over the previous version; To be published in Physica
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