52 research outputs found
Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering for systems with broken time reversal invariance
Assuming the validity of random matrices for describing the statistics of a
closed chaotic quantum system, we study analytically some statistical
properties of the S-matrix characterizing scattering in its open counterpart.
In the first part of the paper we attempt to expose systematically ideas
underlying the so-called stochastic (Heidelberg) approach to chaotic quantum
scattering. Then we concentrate on systems with broken time-reversal invariance
coupled to continua via M open channels. By using the supersymmetry method we
derive:
(i) an explicit expression for the density of S-matrix poles (resonances) in
the complex energy plane
(ii) an explicit expression for the parametric correlation function of
densities of eigenphases of the S-matrix.
We use it to find the distribution of derivatives of these eigenphases with
respect to the energy ("partial delay times" ) as well as with respect to an
arbitrary external parameter.Comment: 51 pages, RevTEX , three figures are available on request. To be
published in the special issue of the Journal of Mathematical Physic
Femtoscopy of Pb-Pb and pp collisions at the LHC with the ALICE experiment
We report on the results of femtoscopic analysis of Pb-Pb collisions at
sqrt(s_NN)=2.76 TeV and pp collisions at sqrt(s)=0.9, 2.76 and 7 TeV with
identical pions and kaons. Detailed femtoscopy studies in heavy-ion collisions
at SPS and RHIC have shown that emission region sizes ("HBT radii") decrease
with increasing pair transverse momentum k_T, which is understood as a
manifestation of the collective behavior of matter. The trend was predicted to
persist at the LHC. The data from Pb-Pb collisions confirm the existence of a
flowing medium and provide strict constraints on the dynamical models. Similar
analysis is carried out for pp collisions for pions and kaons and qualitative
similarities to heavy-ion data are seen, especially in collisions producing
large number of particles. The observed trends give insight into the soft
particle production mechanism in pp collisions. 3D radii were also found to
universally scale with event multiplicity in heavy-ion collisions. We extend
the range of multiplicities both upwards with the Pb-Pb data and downwards with
the pp data to test the scaling in new areas. In particular the high
multiplicity pp collisions reach particle densities comparable to the ones
measured in peripheral Cu-Cu and Au-Au collisions at RHIC. This allows for the
first time to directly compare freeze-out sizes for systems with very different
initial states.Comment: 8 pages, 5 figures, Proceedings of the Quark Matter 2011 plenary tal
Quantum mechanical time-delay matrix in chaotic scattering
We calculate the probability distribution of the matrix Q = -i \hbar S^{-1}
dS/dE for a chaotic system with scattering matrix S at energy E. The
eigenvalues \tau_j of Q are the so-called proper delay times, introduced by E.
P. Wigner and F. T. Smith to describe the time-dependence of a scattering
process. The distribution of the inverse delay times turns out to be given by
the Laguerre ensemble from random-matrix theory.Comment: 4 pages, RevTeX; to appear in Phys. Rev. Let
A sensitive test for models of Bose-Einstein correlations
Accurate and sensitive measurements of higher order cumulants open up new
approaches to pion interferometry. It is now possible to test whether a given
theoretical prediction can consistently match cumulants of both second and
third order. Our consistency test utilizes a new technique combining
theoretically predicted functions with experimentally determined weights in a
quasi-Monte Carlo approach. Testing a general quantum statistics-based
framework of Bose-Einstein correlations with this technique, we find that
predictions for third order cumulants differ significantly from UA1 data. This
discrepancy may point the way to more detailed dynamical information.Comment: 5 pages, 2 figures, revte
Lambda-proton correlations in relativistic heavy ion collisions
The prospect of using lambda-proton correlations to extract source sizes in
relativistic heavy ion collisions is investigated. It is found that the strong
interaction induces a large peak in the correlation function that provides more
sensitive source size measurements than two-proton correlations under some
circumstances. The prospect of using lambda-proton correlations to measure the
time lag between lambda and proton emissions is also studied.Comment: 4 pages, 3 figure, revtex style. Two short paragraphs are added at
referees' recommendations. Phys. Rev. Lett. in pres
Density Matrix Kinetic Equation Describing a Passage of Fast Atomic Systems Through Matter
The quantum-mechanical consideration of a passage of fast dimesoatoms through
matter is given. A set of quantum-kinetic equations for the density matrix
elements describing their internal state evolution is derived. It is shown that
probabilistic description of internal dynamics of hydrogen-like atoms is
impossible even at sufficiently low energies because of the ``accidental''
degeneracy of their energy levels.Comment: 12 pages, LATEX, submitted to J. Phys.
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