22,785 research outputs found
Experimental studies of vortex flows
This final report describes research work on vortex flows done during a four-year period beginning in March 1984 and funded by NASA Grant NCC2-294 from the Fluid Dynamics Research Branch of NASA Ames Research Center. After a brief introduction of the main topics addressed by the completed research, the accomplishments are summarized in chronological order
Random Matrices with Correlated Elements: A Model for Disorder with Interactions
The complicated interactions in presence of disorder lead to a correlated
randomization of states. The Hamiltonian as a result behaves like a
multi-parametric random matrix with correlated elements. We show that the
eigenvalue correlations of these matrices can be described by the single
parametric Brownian ensembles. The analogy helps us to reveal many important
features of the level-statistics in interacting systems e.g. a critical point
behavior different from that of non-interacting systems, the possibility of
extended states even in one dimension and a universal formulation of level
correlations.Comment: 19 Pages, No Figures, Major Changes to Explain the Mathematical
Detail
Why the Universe Started from a Low Entropy State
We show that the inclusion of backreaction of massive long wavelengths
imposes dynamical constraints on the allowed phase space of initial conditions
for inflation, which results in a superselection rule for the initial
conditions. Only high energy inflation is stable against collapse due to the
gravitational instability of massive perturbations. We present arguments to the
effect that the initial conditions problem {\it cannot} be meaningfully
addressed by thermostatistics as far as the gravitational degrees of freedom
are concerned. Rather, the choice of the initial conditions for the universe in
the phase space and the emergence of an arrow of time have to be treated as a
dynamic selection.Comment: 12 pages, 2 figs. Final version; agrees with accepted version in
Phys. Rev.
Energy correlations for a random matrix model of disordered bosons
Linearizing the Heisenberg equations of motion around the ground state of an
interacting quantum many-body system, one gets a time-evolution generator in
the positive cone of a real symplectic Lie algebra. The presence of disorder in
the physical system determines a probability measure with support on this cone.
The present paper analyzes a discrete family of such measures of exponential
type, and does so in an attempt to capture, by a simple random matrix model,
some generic statistical features of the characteristic frequencies of
disordered bosonic quasi-particle systems. The level correlation functions of
the said measures are shown to be those of a determinantal process, and the
kernel of the process is expressed as a sum of bi-orthogonal polynomials. While
the correlations in the bulk scaling limit are in accord with sine-kernel or
GUE universality, at the low-frequency end of the spectrum an unusual type of
scaling behavior is found.Comment: 20 pages, 3 figures, references adde
A 3-component laser-Doppler velocimeter data acquisition and reduction system
A laser doppler velocimeter capable of measuring all three components of velocity simultaneously in low-speed flows is described. All the mean velocities, Reynolds stresses, and higher-order products can be evaluated. The approach followed is to split one of the two colors used in a 2-D system, thus creating a third set of beams which is then focused in the flow from an off-axis direction. The third velocity component is computed from the known geometry of the system. The laser optical hardware and the data acquisition electronics are described in detail. In addition, full operating procedures and listings of the software (written in BASIC and ASSEMBLY languages) are also included. Some typical measurements obtained with this system in a vortex/mixing layer interaction are presented and compared directly to those obtained with a cross-wire system
Jacobi Crossover Ensembles of Random Matrices and Statistics of Transmission Eigenvalues
We study the transition in conductance properties of chaotic mesoscopic
cavities as time-reversal symmetry is broken. We consider the Brownian motion
model for transmission eigenvalues for both types of transitions, viz.,
orthogonal-unitary and symplectic-unitary crossovers depending on the presence
or absence of spin-rotation symmetry of the electron. In both cases the
crossover is governed by a Brownian motion parameter {\tau}, which measures the
extent of time-reversal symmetry breaking. It is shown that the results
obtained correspond to the Jacobi crossover ensembles of random matrices. We
derive the level density and the correlation functions of higher orders for the
transmission eigenvalues. We also obtain the exact expressions for the average
conductance, average shot-noise power and variance of conductance, as functions
of {\tau}, for arbitrary number of modes (channels) in the two leads connected
to the cavity. Moreover, we give the asymptotic result for the variance of
shot-noise power for both the crossovers, the exact results being too long. In
the {\tau} \rightarrow 0 and {\tau} \rightarrow \infty limits the known results
for the orthogonal (or symplectic) and unitary ensembles are reproduced. In the
weak time-reversal symmetry breaking regime our results are shown to be in
agreement with the semiclassical predictions.Comment: 24 pages, 5 figure
Quantum Charge Transport and Conformational Dynamics of Macromolecules
We study the dynamics of quantum excitations inside macromolecules which can
undergo conformational transitions. In the first part of the paper, we use the
path integral formalism to rigorously derive a set of coupled equations of
motion which simultaneously describe the molecular and quantum transport
dynamics, and obey the fluctuation/dissipation relationship. We also introduce
an algorithm which yields the most probable molecular and quantum transport
pathways in rare, thermally-activated reactions. In the second part of the
paper, we apply this formalism to simulate the propagation of a charge during
the collapse of a polymer from an initial stretched conformation to a final
globular state. We find that the charge dynamics is quenched when the chain
reaches a molten globule state. Using random matrix theory we show that this
transition is due to an increase of quantum localization driven by dynamical
disorder.Comment: 11 pages, 2 figure
Subnormalized states and trace-nonincreasing maps
We investigate the set of completely positive, trace-nonincreasing linear
maps acting on the set M_N of mixed quantum states of size N. Extremal point of
this set of maps are characterized and its volume with respect to the
Hilbert-Schmidt (Euclidean) measure is computed explicitly for an arbitrary N.
The spectra of partially reduced rescaled dynamical matrices associated with
trace-nonincreasing completely positive maps belong to the N-cube inscribed in
the set of subnormalized states of size N. As a by-product we derive the
measure in M_N induced by partial trace of mixed quantum states distributed
uniformly with respect to HS-measure in .Comment: LaTeX, 21 pages, 4 Encapsuled PostScript figures, 1 tabl
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