Quantum Statistical Correlations Research Articles

Particle Interferometry from 40 MeV to 40 TeV

Recent developments are summarized in the theory of Bose-Einstein and Fermi-Dirac correlations, with emphasis on the necessity of a simultaneous analysis of particle spectra and quantum statistical correlations for a detailed reconstruction of the space-time picture of particle emission. This review is limited to the following topics: basics and formalism of quantum-statistical correlations; the core/halo picture for n-particle Bose-Einstein correlations; particle interferometry in e+e- collisions including the Andersson-Hofmann model; the invariant Buda-Lund particle interferometry; the Buda-Lund, the Bertsch-Pratt and Yano-Koonin-Podgoretskii parameterizations, the Buda-Lund hydro model and its applications to (π/K)+p and Pb+Pb collisions at CERN SPS, and to low-energy heavy-ion collisions; the binary-source formalism and the related oscillations in the two-particle Bose-Einstein and Fermi-Dirac correlation functions; the experimental signals of expanding rings of fire and shells of fire in particle and heavy-ion physics and their similarity to planetary nebulae in stellar astronomy.

Optical Linewidth of a Low Density Fermi-Dirac Gas

We study propagation of light in a Fermi-Dirac gas at zero temperature. We analytically obtain the leading density correction to the optical linewidth. This correction is a direct consequence of the quantum statistical correlations of atomic positions that modify the optical interactions between the atoms at small interatomic separations. The gas exhibits a dramatic line narrowing already at very low densities.

One-dimensional modeling of light propagation in dense and degenerate samples

We study propagation of low-intensity light in a medium within a one-dimensional (1D) model electrodynamics. It is shown that the coupled theory for light and matter fields may be solved, in principle exactly, by means of stochastic simulations that account for both collective linewidths and line shifts, and for quantum statistical position correlations of the atoms. Such simulations require that one synthesize atomic positions that have correlation functions appropriate for the given type of atomic sample. We demonstrate how one may simulate both a Bose-Einstein condensate (BEC) and a zero-temperature noninteracting Fermi-Dirac gas. Results of simulations of light propagation in such quantum degenerate gases are compared with analytical density expansions obtained by adapting the approach of Morice, Castin, and Dalibard [Phys. Rev. A 51, 3896 (1995)] to the 1D electrodynamics. A BEC exhibits an optical resonance that narrows and stays somewhat below the atomic resonance frequency as collective effects set in with increasing atom density. The first two terms in the analytical density expansion are in excellent agreement with numerical results for a condensate. While fermions display a similar narrowing and shift of the resonance with increasing density, already in the limit of very dilute gas the linewidth is only half of the resonance linewidth of an isolated atom. We attribute this to the regular spacing between the atoms, which is enforced by the Pauli exclusion principle. The analytical density expansion successfully predicts the narrowing, and also gives the next term in the density expansion of the optical response in semiquantitative agreement with numerical simulations.

Quantum statistical correlations and single-particle distributions for slowly expanding systems with temperature profile

Competition among particle evaporation, temperature gradient and flow is investigated in a phenomenological manner, based on a simultaneous analysis of quantum statistical correlations and momentum distributions for a non-relativistic, spherically symmetric, three-dimensionally expanding, finite source. The parameters of the model emission function are constrained by fits to neutron and proton momentum distributions and correlation functions in intermediate energy heavy-ion collisions. The temperature gradient is related to the momentum dependence of the radius parameters of the two-particle correlation function, as well as to the momentum-dependent temperature parameter of the single particle spectrum, while a long duration of particle evaporation is found to be responsible for the low relative momentum behavior of the two-particle correlations.

Resonant magnetopolaron effect in D- centers in quantum wells.

The resonant magneto-optical transitions in ${\mathit{D}}^{\mathrm{\ensuremath{-}}}$ centers in GaAs/${\mathrm{Ga}}_{\mathit{x}}$${\mathrm{Al}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum wells in a high magnetic field are studied using the confined and interface phonon model for the electron-phonon interaction. Excellent agreement with the experimental results is found. Enhanced polaron effects are found in ${\mathit{D}}^{\mathrm{\ensuremath{-}}}$ centers and the source of this enhancement is identified as being due to the quantum statistical correlations between electrons. We compare the results of our model with those of the three-dimensional Fr\"ohlich model and find that for well width beyond 200 \AA{} the two models give practically the same results.

Quantum statistical correlations for slowly expanding systems

Quantum statistical correlations and momentum distributions are calculated for a spherically symmetric, three-dimensionally expanding finite fireballs, for non-relativistic expansions applying plane-wave approximation. The new concepts of the geometrical temperature as well as the thermal radius are presented for the simplest case. The symmetry properties of the correlation function are shown to reflect the symmetry properties of the emission function.

Structure functions of the nucleon in a statistical model

Deep inelastic scattering is considered in a statistical model of the nucleon. This incorporates certain features which are absent in the standard parton model such as quantum statistical correlations which play a role in the propagation of particles when considering Feynman diagrams containing internal lines.The inclusion of theO(αs) corrections in our numerical calculations allows a good fit to the data forx≥0.25. The fit corresponds to values of temperature and chemical potential of approximatelyT=0.067 GeV and μ=0.133 GeV. The latter values of parameters, however, give rise, for allx, to a large value forR=σ L /σ T . Even when taking into account that all measurements ofR suffer from large experimental errors due to the weak dependence of the deep inelastic cross section for charged leptons onR, the size of the discrepancy remains unacceptable. This indicates a shortcoming of the statistical model in its present form to reproduce the structure function of the proton.

On surprises from Bose-Einstein correlations

Recent theoretical work has shown that there may be differences between π 0 π 0 and π ± π ± correlations and quantum statistical correlations between π + and π −. I discuss the physical origin of such effects and how they may come about in the framework of the string model.

Multiplicity fluctuations in finite rapidity windows. Intermittency or quantum statistical correlation?

It is shown that the experimentally observed dependence of moments of multiplicity distributions on the width of the rapidity window can be interpreted by simple quantum statistical properties of the emitting system(s) and does not necessarily imply evidence for intermittency.

On the possibility of a phase-space reconstruction of quantum statistics: A refutation of the Bell-Wigner locality argument

J. S. Bell's argument that only “nonlocal” hidden variable theories can reproduce the quantum statistical correlations of the singlet spin state in the case of two separated spin-1/2 particles is examined in terms of Wigner's formulation. It is shown that a similar argument applies to a single spin-1/2 particle, and that the exclusion of hidden variables depends on an obviously untenable assumption concerning conditional probabilities. The problem of completeness is discussed briefly, and the grounds for rejecting a phase-space reconstruction of the quantum statistics are clarified.

A Quantum Statistical Theory of Ferromagnetic Resonance with Parallel Pumping. II Correlation Function Treatment of Parametric Spin Wave Excitation and Nonlinear Interactions

AbstractBased on equations, symmetry and boundary conditions of quantum statistical correlation functions of renormalized spin wave excitations in a HEISENBERG ferromagnet including dipolar coupling, the parallel pumping effect under special considering the nonlinear three magnon interaction is discussed. An asymptotic approximation procedure enables us to interpret the fundamental equations in terms of the LANGEVIN theory of BROWNian motion and to find solutions by seperation ansatzes. For all cases of practical interest, the differences between the classical and the quantum statistical threshold condition can be neglected. The validity of SCHLÖMANN'S subthreshold χ″ formula is proved. Above the threshold, the steady state χ″ is larger than proposed by semiclassical theories because the strongly excited spin waves are influenced by a certain nonlinear fluctuating field; for YIG, a sufficient agreement between experimental and theoretical χ″ values and a qualitative explanation of the parameter dependence are found. Some non‐equilibrium correlation functions are given explicitly.