Rigorous Derivation of the Gross-Pitaevskii Equation

The time dependent Gross-Pitaevskii equation describes the dynamics of initially trapped Bose-Einstein condensates. We present a rigorous proof of this fact starting from a many-body bosonic Schroedinger equation with a short scale repulsive interaction in the dilute limit. Our proof shows the persistence of an explicit short scale correlation structure in the condensate.Comment: 4 pages, 1 figur

Zooming in on local level statistics by supersymmetric extension of free probability

We consider unitary ensembles of Hermitian NxN matrices H with a confining potential NV where V is analytic and uniformly convex. From work by Zinn-Justin, Collins, and Guionnet and Maida it is known that the large-N limit of the characteristic function for a finite-rank Fourier variable K is determined by the Voiculescu R-transform, a key object in free probability theory. Going beyond these results, we argue that the same holds true when the finite-rank operator K has the form that is required by the Wegner-Efetov supersymmetry method of integration over commuting and anti-commuting variables. This insight leads to a potent new technique for the study of local statistics, e.g., level correlations. We illustrate the new technique by demonstrating universality in a random matrix model of stochastic scattering.Comment: 38 pages, 3 figures, published version, minor changes in Section

Ionization of Atoms by Intense Laser Pulses

The process of ionization of a hydrogen atom by a short infrared laser pulse is studied in the regime of very large pulse intensity, in the dipole approximation. Let $A$ denote the integral of the electric field of the pulse over time at the location of the atomic nucleus. It is shown that, in the limit where $|A| \to \infty$, the ionization probability approaches unity and the electron is ejected into a cone opening in the direction of $-A$ and of arbitrarily small opening angle. Asymptotics of various physical quantities in $|A|^{-1}$ is studied carefully. Our results are in qualitative agreement with experimental data reported in \cite{1,2}.Comment: 27 pages, 1 figure

Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime

While Hartree\u2013Fock theory is well established as a fundamental approximation for interacting fermions, it has been unclear how to describe corrections to it due to many-body correlations. In this paper we start from the Hartree\u2013Fock state given by plane waves and introduce collective particle\u2013hole pair excitations. These pairs can be approximately described by a bosonic quadratic Hamiltonian. We use Bogoliubov theory to construct a trial state yielding a rigorous Gell-Mann\u2013Brueckner\u2013type upper bound to the ground state energy. Our result justifies the random-phase approximation in the mean-field scaling regime, for repulsive, regular interaction potentials

A Study of Inclusive Double-Pomeron-Exchange in p pbar -> p X pbar at root s = 630 GeV

We report measurements of the inclusive reaction, p pbar -> p X pbar, in events where either or both the beam-like final-state baryons were detected in Roman-pot spectrometers and the central system was detected in the UA2 calorimeter. A Double-Pomeron-Exchange (DPE) analysis of these data and single diffractive data from the same experiment demonstrates that, for central masses of a few GeV, the extracted Pomeron-Pomeron total cross section exhibits an enhancement which exceeds factorization expectations by an order-of-magnitude. This may be a signature for glueball production. The enhancement is shown to be independent of uncertainties connected with possible non-universality of the Pomeron flux factor. Based on our analysis, we present DPE cross section predictions, for unit (1 mb) Pomeron-Pomeron total cross section, at the Tevatron, LHC and the 920 GeV fixed-target experiment, HERA-B.Comment: 52 pages, 27 Encapsulated Postscript figures, 3 Tables, LaTex, Revised version as it will appear in European Physics Journal

Cross Section Measurements of Hard Diffraction at the SPS-Collider

The UA8 experiment previously reported the observation of jets in diffractive events containing leading protons (``hard diffraction''), which was interpreted as evidence for the partonic structure of an exchanged Reggeon, believed to be the Pomeron . In the present Letter, we report the final UA8 hard-diffractive (jet) cross section results and their interpretation. After corrections, the fraction of single diffractive events with mass from 118 to 189 GeV that have two scattered partons, each with Et_jet > 8 GeV, is in the range 0.002 to 0.003 (depending on x_p). We determine the product, fK, of the fraction by which the Pomeron's momentum sum rule is violated and the normalization constant of the Pomeron-Flux-Factor of the proton. For a pure gluonic- or a pure qqbar-Pomeron , respectively: fK = 0.30 +- 0.05 +- 0.09) and (0.56 +- 0.09 +- 0.17) GeV^-2.Comment: 20 pages, 5 Encapsulated Postscript figures, LaTex, Final Version, Physics Letters B (in Pess 1998

Pseudorapidity Distribution of Charged Particles in PbarP Collisions at root(s)= 630GeV

Using a silicon vertex detector, we measure the charged particle pseudorapidity distribution over the range 1.5 to 5.5 using data collected from PbarP collisions at root s = 630 GeV. With a data sample of 3 million events, we deduce a result with an overall normalization uncertainty of 5%, and typical bin to bin errors of a few percent. We compare our result to the measurement of UA5, and the distribution generated by the Lund Monte Carlo with default settings. This is only the second measurement at this level of precision, and only the second measurement for pseudorapidity greater than 3.Comment: 9 pages, 5 figures, LaTeX format. For ps file see http://hep1.physics.wayne.edu/harr/harr.html Submitted to Physics Letters

A new gamma*-p / pbar-p factorization test in diffraction, valid below Q^2 about 6 GeV^2

One of the key experimental issues in high energy hadron physics is the extent to which data from the diffractive interaction mechanism may be described by a factorized formula which is the product of a universal term describing the probability of finding a Pomeron in a proton (loosely referred to as the "Pomeron flux-factor") and a term decribing the Pomeron's interaction with the other incident proton. In the present paper, after demonstrating that existing data on diffractive gamma*-p and pbar-p interactions show that the Pomeron flux-factor is not universal, we present the results of a new test of factorization in these interactions which does not rely on universality of the flux-factor. The test is satisfied to within ~20% for 1 < Q^2 ~ 6 GeV^2 and beta < 0.2 in the gamma*-p interactions, suggesting that the resons for non-universality of the flux-factor have a limited effect on the factorization itself. However, a clear breakdown of this test is observed at larger Q^2. Kharzeev and Levin suggest that this can be attributed to the onset of QCD evolution effects in the Pomeron's structure. The breakdown occurs in a Q^2 region which agrees with their estimates of a small Pomeron size.Comment: 20 pages, 7 Encapsulated Postscript figures, LaTex, submitted to European Phisical Journal

On Blowup for time-dependent generalized Hartree-Fock equations

We prove finite-time blowup for spherically symmetric and negative energy solutions of Hartree-Fock and Hartree-Fock-Bogoliubov type equations, which describe the evolution of attractive fermionic systems (e. g. white dwarfs). Our main results are twofold: First, we extend the recent blowup result of [Hainzl and Schlein, Comm. Math. Phys. \textbf{287} (2009), 705--714] to Hartree-Fock equations with infinite rank solutions and a general class of Newtonian type interactions. Second, we show the existence of finite-time blowup for spherically symmetric solutions of a Hartree-Fock-Bogoliubov model, where an angular momentum cutoff is introduced. We also explain the key difficulties encountered in the full Hartree-Fock-Bogoliubov theory.Comment: 24 page