28,331 research outputs found
Negative moments of characteristic polynomials of random GOE matrices and singularity-dominated strong fluctuations
We calculate the negative integer moments of the (regularized) characteristic
polynomials of N x N random matrices taken from the Gaussian Orthogonal
Ensemble (GOE) in the limit as . The results agree nontrivially
with a recent conjecture of Berry & Keating motivated by techniques developed
in the theory of singularity-dominated strong fluctuations. This is the first
example where nontrivial predictions obtained using these techniques have been
proved.Comment: 13 page
On the Scale-Invariant Distribution of the Diffusion Coefficient for Classical Particles Diffusing in Disordered Media.-
The scaling form of the whole distribution P(D) of the random diffusion
coefficient D(x) in a model of classically diffusing particles is investigated.
The renormalization group approach above the lower critical dimension d=0 is
applied to the distribution P(D) using the n-replica approach. In the annealed
approximation (n=1), the inverse gaussian distribution is found to be the
stable one under rescaling. This identification is made based on symmetry
arguments and subtle relations between this model and that of fluc- tuating
interfaces studied by Wallace and Zia. The renormalization-group flow for the
ratios between consecutive cumulants shows a regime of pure diffusion for small
disorder, in which P(D) goes to delta(D-), and a regime of strong disorder
where the cumulants grow infinitely large and the diffusion process is ill
defined. The boundary between these two regimes is associated with an unstable
fixed-point and a subdiffusive behavior: =Ct**(1-d/2). For the quenched
case (n goes to 0) we find that unphysical operators are generated raisng
doubts on the renormalizability of this model. Implications to other random
systems near their lower critical dimension are discussed.Comment: 21 pages, 1 fig. (not included) Use LaTex twic
Achievable efficiencies for probabilistically cloning the states
We present an example of quantum computational tasks whose performance is
enhanced if we distribute quantum information using quantum cloning.
Furthermore we give achievable efficiencies for probabilistic cloning the
quantum states used in implemented tasks for which cloning provides some
enhancement in performance.Comment: 9 pages, 8 figure
A novel haptic model and environment for maxillofacial surgical operation planning and manipulation
This paper presents a practical method and a new haptic model to support manipulations of bones and their segments during the planning of a surgical operation in a virtual environment using a haptic interface. To perform an effective dental surgery it is important to have all the operation related information of the patient available beforehand in order to plan the operation and avoid any complications. A haptic interface with a virtual and accurate patient model to support the planning of bone cuts is therefore critical, useful and necessary for the surgeons. The system proposed uses DICOM images taken from a digital tomography scanner and creates a mesh model of the filtered skull, from which the jaw bone can be isolated for further use. A novel solution for cutting the bones has been developed and it uses the haptic tool to determine and define the bone-cutting plane in the bone, and this new approach creates three new meshes of the original model. Using this approach the computational power is optimized and a real time feedback can be achieved during all bone manipulations. During the movement of the mesh cutting, a novel friction profile is predefined in the haptical system to simulate the force feedback feel of different densities in the bone
Acceleration of small astrophysical grains due to charge fluctuations
We discuss a novel mechanism of dust acceleration which may dominate for
particles smaller than m. The acceleration is caused by their
direct electrostatic interactions arising from fluctuations of grain charges.
The energy source for the acceleration are the irreversible plasma processes
occurring on the grain surfaces. We show that this mechanism of
charge-fluctuation-induced acceleration likely affects the rate of grain
coagulation and shattering of the population of small grains.Comment: 8 pages, 2 figures, revised version, submitted to Astrophysical
Journa
Freezing Transition, Characteristic Polynomials of Random Matrices, and the Riemann Zeta-Function
We argue that the freezing transition scenario, previously explored in the
statistical mechanics of 1/f-noise random energy models, also determines the
value distribution of the maximum of the modulus of the characteristic
polynomials of large N x N random unitary (CUE) matrices. We postulate that our
results extend to the extreme values taken by the Riemann zeta-function zeta(s)
over sections of the critical line s=1/2+it of constant length and present the
results of numerical computations in support. Our main purpose is to draw
attention to possible connections between the statistical mechanics of random
energy landscapes, random matrix theory, and the theory of the Riemann zeta
function.Comment: published version with a few misprints corrected and references adde
Equation of state of charged colloidal suspensions and its dependence on the thermodynamic route
The thermodynamic properties of highly charged colloidal suspensions in
contact with a salt reservoir are investigated in the framework of the
Renormalized Jellium Model (RJM). It is found that the equation of state is
very sensitive to the particular thermodynamic route used to obtain it.
Specifically, the osmotic pressure calculated within the RJM using the contact
value theorem can be very different from the pressure calculated using the
Kirkwood-Buff fluctuation relations. On the other hand, Monte Carlo (MC)
simulations show that both the effective pair potentials and the correlation
functions are accurately predicted by the RJM. It is suggested that the lack of
self-consistency in the thermodynamics of the RJM is a result of neglected
electrostatic correlations between the counterions and coions
On the mean density of complex eigenvalues for an ensemble of random matrices with prescribed singular values
Given any fixed positive semi-definite diagonal matrix
we derive the explicit formula for the density of complex eigenvalues for
random matrices of the form } where the random unitary
matrices are distributed on the group according to the Haar
measure.Comment: 10 pages, 1 figur
Photodissociation in Quantum Chaotic Systems: Random Matrix Theory of Cross-Section Fluctuations
Using the random matrix description of open quantum chaotic systems we
calculate in closed form the universal autocorrelation function and the
probability distribution of the total photodissociation cross section in the
regime of quantum chaos.Comment: 4 pages+1 eps figur
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