464,425 research outputs found
Dymanics of Generalized Coherent States
We show that generalized coherent states follow Schr\"{o}dinger dynamics in
time-dependent potentials. The normalized wave-packets follow a classical
evolution without spreading; in turn, the Schr\"{o}dinger potential depends on
the state through the classical trajectory. This feedback mechanism with
continuous dynamical re-adjustement allows the packets to remain coherent
indefinetely.Comment: 8 pages, plain latex, no figure
Pressure anisotropy generation in a magnetized plasma configuration with a shear flow velocity
The nonlinear evolution of the Kelvin Helmholtz instability in a magnetized
plasma with a perpendicular flow close to, or in, the supermagnetosonic regime
can produce a significant parallel-to-perpendicular pressure anisotropy. This
anisotropy, localized inside the flow shear region, can make the configuration
unstable either to the mirror or to the firehose instability and, in general,
can affect the development of the KHI. The interface between the solar wind and
the Earth's magnetospheric plasma at the magnetospheric equatorial flanks
provides a relevant setting for the development of this complex nonlinear
dynamics.Comment: 11 pages, 7 figures, submitted to Plasma Phys. Control. Fusio
Diffusion Processes and Coherent States
It is shown that stochastic processes of diffusion type possess, in all
generality, a structure of uncertainty relations and of coherent and squeezed
states. This fact is used to obtain, via Nelson stochastic formulation of
quantum mechanics, the harmonic-oscillator coherent and squeezed states. The
method allows to derive new minimum uncertainty states in time-dependent
oscillator potentials and for the Caldirola-Kanai model of quantum damped
oscillator.Comment: 11 pages, plain LaTe
Scarred eigenstates for quantum cat maps of minimal periods
In this paper we construct a sequence of eigenfunctions of the ``quantum
Arnold's cat map'' that, in the semiclassical limit, show a strong scarring
phenomenon on the periodic orbits of the dynamics. More precisely, those states
have a semiclassical limit measure that is the sum of 1/2 the normalized
Lebesgue measure on the torus plus 1/2 the normalized Dirac measure
concentrated on any a priori given periodic orbit of the dynamics. It is known
(the Schnirelman theorem) that ``most'' sequences of eigenfunctions
equidistribute on the torus. The sequences we construct therefore provide an
example of an exception to this general rule. Our method of construction and
proof exploits the existence of special values of Planck's constant for which
the quantum period of the map is relatively ``short'', and a sharp control on
the evolution of coherent states up to this time scale. We also provide a
pointwise description of these states in phase space, which uncovers their
``hyperbolic'' structure in the vicinity of the fixed points and yields more
precise localization estimates.Comment: LaTeX, 49 pages, includes 10 figures. I added section 6.6. To be
published in Commun. Math. Phy
Exponential mixing and log h time scales in quantized hyperbolic maps on the torus
We study the behaviour, in the simultaneous limits \hbar going to 0, t going
to \infty, of the Husimi and Wigner distributions of initial coherent states
and position eigenstates, evolved under the quantized hyperbolic toral
automorphisms and the quantized baker map. We show how the exponential mixing
of the underlying dynamics manifests itself in those quantities on time scales
logarithmic in \hbar. The phase space distributions of the coherent states,
evolved under either of those dynamics, are shown to equidistribute on the
torus in the limit \hbar going to 0, for times t between |\log\hbar|/(2\gamma)
and |\log|\hbar|/\gamma, where \gamma is the Lyapounov exponent of the
classical system. For times shorter than |\log\hbar|/(2\gamma), they remain
concentrated on the classical trajectory of the center of the coherent state.
The behaviour of the phase space distributions of evolved position eigenstates,
on the other hand, is not the same for the quantized automorphisms as for the
baker map. In the first case, they equidistribute provided t goes to \infty as
\hbar goes to 0, and as long as t is shorter than |\log\hbar|/\gamma. In the
second case, they remain localized on the evolved initial position at all such
times
The role of magnetic field for quiescence-outburst models in CVs
In this paper we present the elementary assumptions of our research on the
role of the magnetic field in modelling the quiescence-outbursts cycle in
Cataclysmic Variables (CVs). The behaviour of the magnetic field is crucial not
only to integrate the disk instability model (Osaki 1974), but also to
determine the cause and effect nexus among parameters affecting the behavior of
complex systems. On the ground of our interpretation of the results emerging
from the literature, we suggest that in models describing DNe outbursts, such
as the disk instability model, the secondary instability model (Bath 1973) and
the thermonuclear runaway model (Mitrofanov 1978), the role of the magnetic
field is at least twofold. On the one hand, it activates a specific dynamic
pathway for the accreting matter by channelling it. On the other hand, it could
be indirectly responsible for switching a particular outburst modality. In
order to represent these two roles of the magnetic field, we need to integrate
the disk instability model by looking at the global behaviour of the system
under analysis. Stochastic resonance in dynamo models, we believe, is a
suitable candidate for accomplishing this task. We shall present the MHD model
including this mechanism elsewhere.Comment: 5 pages, 2 figures, CTU Proceedings, Acta Polytechnica (accepted
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