171 research outputs found
Rotation of a spheroid in a simple shear at small Reynolds number
We derive an effective equation of motion for the orientational dynamics of a
neutrally buoyant spheroid suspended in a simple shear flow, valid for
arbitrary particle aspect ratios and to linear order in the shear Reynolds
number. We show how inertial effects lift the degeneracy of the Jeffery orbits
and determine the stabilities of the log-rolling and tumbling orbits at
infinitesimal shear Reynolds numbers. For prolate spheroids we find stable
tumbling in the shear plane, log-rolling is unstable. For oblate particles, by
contrast, log-rolling is stable and tumbling is unstable provided that the
aspect ratio is larger than a critical value. When the aspect ratio is smaller
than this value tumbling turns stable, and an unstable limit cycle is born.Comment: 25 pages, 5 figure
Coagulation by Random Velocity Fields as a Kramers Problem
We analyse the motion of a system of particles suspended in a fluid which has
a random velocity field. There are coagulating and non-coagulating phases. We
show that the phase transition is related to a Kramers problem, and use this to
determine the phase diagram, as a function of the dimensionless inertia of the
particles, epsilon, and a measure of the relative intensities of potential and
solenoidal components of the velocity field, Gamma. We find that the phase line
is described by a function which is non-analytic at epsilon=0, and which is
related to escape over a barrier in the Kramers problem. We discuss the
physical realisations of this phase transition.Comment: 4 pages, 3 figure
Fingerprints of Random Flows?
We consider the patterns formed by small rod-like objects advected by a
random flow in two dimensions. An exact solution indicates that their direction
field is non-singular. However, we find from simulations that the direction
field of the rods does appear to exhibit singularities. First, ` scar lines'
emerge where the rods abruptly change direction by . Later, these scar
lines become so narrow that they ` heal over' and disappear, but their ends
remain as point singularities, which are of the same type as those seen in
fingerprints. We give a theoretical explanation for these observations.Comment: 21 pages, 11 figure
Collective versus single-particle effects in the optical spectra of finite electronic quantum systems
We study optical spectra of finite electronic quantum systems at frequencies
smaller than the plasma frequency using a quasi-classical approach. This
approach includes collective effects and enables us to analyze how the nature
of the (single-particle) electron dynamics influences the optical spectra in
finite electronic quantum systems. We derive an analytical expression for the
low-frequency absorption coefficient of electro-magnetic radiation in a finite
quantum system with ballistic electron dynamics and specular reflection at the
boundaries: a two-dimensional electron gas confined to a strip of width a (the
approach can be applied to systems of any shape and electron dynamics --
diffusive or ballistic, regular or irregular motion). By comparing with results
of numerical computations using the random-phase approximation we show that our
analytical approach provides a qualitative and quantitative understanding of
the optical spectrum.Comment: 4 pages, 3 figure
The role of inertia for the rotation of a nearly spherical particle in a general linear flow
We analyse the angular dynamics of a neutrally buoyant nearly spherical
particle immersed in a steady general linear flow. The hydrodynamic torque
acting on the particle is obtained by means of a reciprocal theorem, regular
perturbation theory exploiting the small eccentricity of the nearly spherical
particle, and assuming that inertial effects are small, but finite.Comment: 7 pages, 1 figur
The decay of photoexcited quantum systems: a description within the statistical scattering model
The decay of photoexcited quantum systems (examples are photodissociation of
molecules and autoionization of atoms) can be viewed as a half-collision
process (an incoming photon excites the system which subsequently decays by
dissociation or autoionization). For this reason, the standard statistical
approach to quantum scattering, originally developed to describe nuclear
compound reactions, is not directly applicable. Using an alternative approach,
correlations and fluctuations of observables characterizing this process were
first derived in [Fyodorov YV and Alhassid Y 1998 Phys. Rev. A 58, R3375]. Here
we show how the results cited above, and more recent results incorporating
direct decay processes, can be obtained from the standard statistical
scattering approach by introducing one additional channel.Comment: 7 pages, 2 figure
Random matrix description of decaying quantum systems
This contribution describes a statistical model for decaying quantum systems
(e.g. photo-dissociation or -ionization). It takes the interference between
direct and indirect decay processes explicitely into account. The resulting
expressions for the partial decay amplitudes and the corresponding cross
sections may be considered a many-channel many-resonance generalization of
Fano's original work on resonance lineshapes [Phys. Rev 124, 1866 (1961)].
A statistical (random matrix) model is then introduced. It allows to describe
chaotic scattering systems with tunable couplings to the decay channels. We
focus on the autocorrelation function of the total (photo) cross section, and
we find that it depends on the same combination of parameters, as the
Fano-parameter distribution. These combinations are statistical variants of the
one-channel Fano parameter. It is thus possible to study Fano interference
(i.e. the interference between direct and indirect decay paths) on the basis of
the autocorrelation function, and thereby in the regime of overlapping
resonances. It allows us, to study the Fano interference in the limit of
strongly overlapping resonances, where we find a persisting effect on the level
of the weak localization correction.Comment: 16 pages, 2 figure
Universal eigenvector statistics in a quantum scattering ensemble
We calculate eigenvector statistics in an ensemble of non-Hermitian matrices
describing open quantum systems [F. Haake et al., Z. Phys. B 88, 359 (1992)] in
the limit of large matrix size. We show that ensemble-averaged eigenvector
correlations corresponding to eigenvalues in the center of the support of the
density of states in the complex plane are described by an expression recently
derived for Ginibre's ensemble of random non-Hermitian matrices.Comment: 4 pages, 5 figure
Spectral Statistics in Chaotic Systems with Two Identical Connected Cells
Chaotic systems that decompose into two cells connected only by a narrow
channel exhibit characteristic deviations of their quantum spectral statistics
from the canonical random-matrix ensembles. The equilibration between the cells
introduces an additional classical time scale that is manifest also in the
spectral form factor. If the two cells are related by a spatial symmetry, the
spectrum shows doublets, reflected in the form factor as a positive peak around
the Heisenberg time. We combine a semiclassical analysis with an independent
random-matrix approach to the doublet splittings to obtain the form factor on
all time (energy) scales. Its only free parameter is the characteristic time of
exchange between the cells in units of the Heisenberg time.Comment: 37 pages, 15 figures, changed content, additional autho
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