135,865 research outputs found
Stable Direct Adaptive Control of Linear Infinite-dimensional Systems Using a Command Generator Tracker Approach
A command generator tracker approach to model following contol of linear distributed parameter systems (DPS) whose dynamics are described on infinite dimensional Hilbert spaces is presented. This method generates finite dimensional controllers capable of exponentially stable tracking of the reference trajectories when certain ideal trajectories are known to exist for the open loop DPS; we present conditions for the existence of these ideal trajectories. An adaptive version of this type of controller is also presented and shown to achieve (in some cases, asymptotically) stable finite dimensional control of the infinite dimensional DPS
Coherent States and Modified de Broglie-Bohm Complex Quantum Trajectories
This paper examines the nature of classical correspondence in the case of
coherent states at the level of quantum trajectories. We first show that for a
harmonic oscillator, the coherent state complex quantum trajectories and the
complex classical trajectories are identical to each other. This congruence in
the complex plane, not restricted to high quantum numbers alone, illustrates
that the harmonic oscillator in a coherent state executes classical motion. The
quantum trajectories are those conceived in a modified de Broglie-Bohm scheme
and we note that identical classical and quantum trajectories for coherent
states are obtained only in the present approach. The study is extended to
Gazeau-Klauder and SUSY quantum mechanics-based coherent states of a particle
in an infinite potential well and that in a symmetric Poschl-Teller (PT)
potential by solving for the trajectories numerically. For the coherent state
of the infinite potential well, almost identical classical and quantum
trajectories are obtained whereas for the PT potential, though classical
trajectories are not regained, a periodic motion results as t --> \infty.Comment: More example
Anyon trajectories and the systematics of the three-anyon spectrum
We develop the concept of trajectories in anyon spectra, i.e., the continuous
dependence of energy levels on the kinetic angular momentum. It provides a more
economical and unified description, since each trajectory contains an infinite
number of points corresponding to the same statistics. For a system of
non-interacting anyons in a harmonic potential, each trajectory consists of two
infinite straight line segments, in general connected by a nonlinear piece. We
give the systematics of the three-anyon trajectories. The trajectories in
general cross each other at the bosonic/fermionic points. We use the
(semi-empirical) rule that all such crossings are true crossings, i.e.\ the
order of the trajectories with respect to energy is opposite to the left and to
the right of a crossing.Comment: 15 pages LaTeX + 1 attached uuencoded gzipped file with 7 figure
Langevin Trajectories between Fixed Concentrations
We consider the trajectories of particles diffusing between two infinite
baths of fixed concentrations connected by a channel, e.g. a protein channel of
a biological membrane. The steady state influx and efflux of Langevin
trajectories at the boundaries of a finite volume containing the channel and
parts of the two baths is replicated by termination of outgoing trajectories
and injection according to a residual phase space density. We present a
simulation scheme that maintains averaged fixed concentrations without creating
spurious boundary layers, consistent with the assumed physics
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