8,485 research outputs found
A semiclassical theory of quantum noise in open chaotic systems
We consider the quantum evolution of classically chaotic systems in contact
with surroundings. Based on -scaling of an equation for time evolution
of the Wigner's quasi-probability distribution function in presence of
dissipation and thermal diffusion we derive a semiclassical equation for
quantum fluctuations. This identifies an early regime of evolution dominated by
fluctuations in the curvature of the potential due to classical chaos and
dissipation. A stochastic treatment of this classical fluctuations leads us to
a Fokker-Planck equation which is reminiscent of Kramers' equation for
thermally activated processes. This reveals an interplay of three aspects of
evolution of quantum noise in weakly dissipative open systems; the reversible
Liouville flow, the irreversible chaotic diffusion which is characteristic of
the system itself, and irreversible dissipation induced by the external
reservoir. It has been demonstrated that in the dissipation-free case a
competition between Liouville flow in the contracting direction of phase space
and chaotic diffusion sets a critical width in the Wigner function for quantum
fluctuations. We also show how the initial quantum noise gets amplified by
classical chaos and ultimately equilibrated under the influence of dissipation.
We establish that there exists a critical limit to the expansion of phase
space. The limit is determined by chaotic diffusion and dissipation. Making use
of appropriate quantum-classical correspondence we verify the semiclassical
analysis by the fully quantum simulation in a chaotic quartic oscillator.Comment: Plain Latex, 27 pages, 6 ps figure, To appear in Physica
Anomalous structural and mechanical properties of solids confined in quasi one dimensional strips
We show using computer simulations and mean field theory that a system of
particles in two dimensions, when confined laterally by a pair of parallel hard
walls within a quasi one dimensional channel, possesses several anomalous
structural and mechanical properties not observed in the bulk. Depending on the
density and the distance between the walls , the system shows
structural characteristics analogous to a weakly modulated liquid, a strongly
modulated smectic, a triangular solid or a buckled phase. At fixed , a
change in leads to many reentrant discontinuous transitions involving
changes in the number of layers parallel to the confining walls depending
crucially on the commensurability of inter-layer spacing with . The solid
shows resistance to elongation but not to shear. When strained beyond the
elastic limit it fails undergoing plastic deformation but surprisingly, as the
strain is reversed, the material recovers completely and returns to its
original undeformed state. We obtain the phase diagram from mean field theory
and finite size simulations and discuss the effect of fluctuations.Comment: 14 pages, 13 figures; revised version, accepted in J. Chem. Phy
Transverse energy distributions and production in Pb+Pb collisions
We have analyzed the latest NA50 data on transverse energy distributions and
suppression in Pb+Pb collisions. The transverse energy distribution
was analysed in the geometric model of AA collisions. In the geometric model,
fluctuations in the number of NN collisions at fixed impact parameter are taken
into account. Analysis suggests that in Pb+Pb collisions, individual NN
collisions produces less , than in other AA collisions. The nucleons are
more transparent in Pb+Pb collisions. The transverse energy dependence of the
suppression was obtained following the model of Blaizot et al, where
charmonium suppression is assumed to be 100% effective above a threshold
density. With fluctuations in number of NN collisions taken into account, good
fit to the data is obtained, with a single parameter, the threshold density.Comment: Revised version with better E_T fit. 4 pages, 2 figure
Nuclear absorption of Charmoniums in pA and AA collisions
We have analysed the latest NA50 data on production in pA and AA
collisions. The production is assumed to be a two step process, (i)
formation of pairs, perturbatively calculable, and (ii) formation of
from the pair, a non-perturbative process, which is conviniently
parametrized. In a nuclear medium, as the pair passes through the
nuclear medium, it gain relative square momentum and some of the pairs can gain
enough square momentum to cross the threshold for open charm meson, leading to
suppression in nuclear medium. Few parameters of the model were fixed from the
latest high statistics NA50 pA and NA38 SU total cross sectional data.
The model then reproduces the centrality dependence of over Drell-Yan
ration in 200 GeV/c S+U and 158 GeV/c Pb+Pb collisions. We also discuss the
centrality dependence of suppression at RHIC energy.Comment: 4 pages including 3 figures, Revised version, to be published in
Phys.Rev.
A model for projectile fragmentation
A model for projectile fragmentation is developed whose origin can be traced
back to the Bevalac era. The model positions itself between the
phenomenological EPAX parametrization and transport models like "Heavy Ion
Phase Space Exploration" (HIPSE) model and antisymmetrised molecular dynamics
(AMD) model. A very simple impact parameter dependence of input temperature is
incorporated in the model which helps to analyze the more peripheral
collisions. The model is applied to calculate the charge, isotopic
distributions, average number of intermediate mass fragments and the average
size of largest cluster at different Z_{bound} of different projectile
fragmentation reactions at different energies.Comment: Talk given by Gargi Chaudhuri at the 11th International Conference on
Nucleus-Nucleus Collisions (NN2012), San Antonio, Texas, USA, May 27-June 1,
2012. 10 pages, 7 figure
Differentially Private Model Selection with Penalized and Constrained Likelihood
In statistical disclosure control, the goal of data analysis is twofold: The
released information must provide accurate and useful statistics about the
underlying population of interest, while minimizing the potential for an
individual record to be identified. In recent years, the notion of differential
privacy has received much attention in theoretical computer science, machine
learning, and statistics. It provides a rigorous and strong notion of
protection for individuals' sensitive information. A fundamental question is
how to incorporate differential privacy into traditional statistical inference
procedures. In this paper we study model selection in multivariate linear
regression under the constraint of differential privacy. We show that model
selection procedures based on penalized least squares or likelihood can be made
differentially private by a combination of regularization and randomization,
and propose two algorithms to do so. We show that our private procedures are
consistent under essentially the same conditions as the corresponding
non-private procedures. We also find that under differential privacy, the
procedure becomes more sensitive to the tuning parameters. We illustrate and
evaluate our method using simulation studies and two real data examples
suppression in Pb+Pb collisions and broadening
We have analysed the NA50 data, on the centrality dependence of
broadening of 's, in Pb+Pb collisions, at the CERN-SPS. The data were
analysed in a QCD based model, where 's are suppressed in 'nuclear'
medium. Without any free parameter, the model could explain the NA50
broadening data. The data were also analysed in a QGP based threshold model,
where suppression is 100% above a critical density. The QGP based
model could not explain the NA50 broadening data. We have also predicted
the centrality dependence of suppression and broadening at RHIC
energy. Both the models, the QGP based threshold model and the QCD based
nuclear absorption model, predict broadening very close to each other.Comment: The paper was completely revised. The conclusion is also changed. 5
pages, 4 figure
Improvements to model of projectile fragmentation
In a recent paper [Phys. Rev. C 044612 (2011)] we proposed a model for
calculating cross-sections of various reaction products which arise from
disintegration of projectile like fragment resulting from heavy ion collisions
at intermediate or higher energy. The model has three parts: (1) abrasion, (2)
disintegration of the hot abraded projectile like fragment (PLF) into nucleons
and primary composites using a model of equilibrium statistical mechanics and
(3) possible evaporation of hot primary composites. It was assumed that the PLF
resulting from abrasion has one temperature T. Data suggested that while just
one value of T seemed adequate for most cross-sections calculations, it failed
when dealing with very peripheral collisions. We have now introduced a variable
T=T(b) where b is the impact parameter of the collision. We argue there are
data which not only show that T must be a function of b but, in addition, also
point to an approximate value of T for a given b. We propose a very simple
formula: T(b)=D_0+D_1(A_s(b)/A_0) where A_s(b) is the mass of the abraded PLF
and A_0 is the mass of the projectile; D_0 and D_1 are constants. Using this
model we compute cross-sections for several collisions and compare with data.Comment: 27 pages, 16 figure
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