315 research outputs found

### Ergodic Properties of Infinite Harmonic Crystals: an Analytic Approach

We give through pseudodifferential operator calculus a proof that the quantum
dynamics of a class of infinite harmonic crystals becomes ergodic and mixing
with respect to the quantum Gibbs measure if the classical infinite dynamics is
respectively ergodic and mixing with respect to the classical infinite Gibbs
measure. The classical ergodicity and mixing properties are recovered as
$\hbar\to 0$, and the infinitely many particles limits of the quantum Gibbs
averages are proved to be the averages over a classical infinite Gibbs measure
of the symbols generating the quantum observables under Weyl quantization.Comment: 30 pages, plain LaTe

### Energy Landscape Statistics of the Random Orthogonal Model

The Random Orthogonal Model (ROM) of Marinari-Parisi-Ritort [MPR1,MPR2] is a
model of statistical mechanics where the couplings among the spins are defined
by a matrix chosen randomly within the orthogonal ensemble. It reproduces the
most relevant properties of the Parisi solution of the Sherrington-Kirckpatrick
model. Here we compute the energy distribution, and work out an extimate for
the two-point correlation function. Moreover, we show exponential increase of
the number of metastable states also for non zero magnetic field.Comment: 23 pages, 6 figures, submitted to J. Phys.

### Quantal Overlapping Resonance Criterion in the Pullen Edmonds Model

In order to highlight the onset of chaos in the Pullen-Edmonds model a
quantal analog of the resonance overlap criterion has been examined. A quite
good agreement between analytical and numerical results is obtained.Comment: 12 pages, LATEX, 2 figures available upon request to the Authors,
submitted to Mod. Phys. Lett.

### Statistics of energy levels and zero temperature dynamics for deterministic spin models with glassy behaviour

We consider the zero-temperature dynamics for the infinite-range, non
translation invariant one-dimensional spin model introduced by Marinari, Parisi
and Ritort to generate glassy behaviour out of a deterministic interaction. It
is shown that there can be a large number of metatastable (i.e., one-flip
stable) states with very small overlap with the ground state but very close in
energy to it, and that their total number increases exponentially with the size
of the system.Comment: 25 pages, 8 figure

### Thermodynamical Limit for Correlated Gaussian Random Energy Models

Let \{E_{\s}(N)\}_{\s\in\Sigma_N} be a family of $|\Sigma_N|=2^N$ centered
unit Gaussian random variables defined by the covariance matrix $C_N$ of
elements \displaystyle c_N(\s,\tau):=\av{E_{\s}(N)E_{\tau}(N)}, and H_N(\s)
= - \sqrt{N} E_{\s}(N) the corresponding random Hamiltonian. Then the quenched
thermodynamical limit exists if, for every decomposition $N=N_1+N_2$, and all
pairs (\s,\t)\in \Sigma_N\times \Sigma_N: c_N(\s,\tau)\leq \frac{N_1}{N}
c_{N_1}(\pi_1(\s),\pi_1(\tau))+ \frac{N_2}{N} c_{N_2}(\pi_2(\s),\pi_2(\tau))
where \pi_k(\s), k=1,2 are the projections of \s\in\Sigma_N into
$\Sigma_{N_k}$. The condition is explicitly verified for the
Sherrington-Kirckpatrick, the even $p$-spin, the Derrida REM and the
Derrida-Gardner GREM models.Comment: 15 pages, few remarks and two references added. To appear in Commun.
Math. Phy

### Distributional Borel Summability for Vacuum Polarization by an External Electric Field

It is proved that the divergent perturbation expansion for the vacuum
polarization by an external constant electric field in the pair production
sector is Borel summable in the distributional sense.Comment: 14 page

### Perturbation theory of PT-symmetric Hamiltonians

In the framework of perturbation theory the reality of the perturbed
eigenvalues of a class of \PTsymmetric Hamiltonians is proved using stability
techniques. We apply this method to \PTsymmetric unperturbed Hamiltonians
perturbed by \PTsymmetric additional interactions

### Mean-Field- and Classical Limit of Many-Body Schr\"odinger Dynamics for Bosons

We present a new proof of the convergence of the N-particle Schroedinger
dynamics for bosons towards the dynamics generated by the Hartree equation in
the mean-field limit. For a restricted class of two-body interactions, we
obtain convergence estimates uniform in the Planck constant , up to an
exponentially small remainder. For h=0, the classical dynamics in the
mean-field limit is given by the Vlasov equation.Comment: Latex 2e, 18 page

### A Novel Mechanism of H^0 Di-baryon Production in Proton-Proton Interactions from Parton Based Gribov-Regge Theory

A novel mechanism of H^0 and strangelet production in hadronic interactions
within the Gribov-Regge approach is presented. In contrast to traditional
distillation approaches, here the production of multiple (strange) quark bags
does not require large baryon densities or a QGP. The production cross section
increases with center of mass energy. Rapidity and transverse momentum
distributions of the H^0 are predicted for pp collisions at E_lab = 160 AGeV
(SPS) and \sqrt s = 200 AGeV (RHIC). The predicted total H^0 multiplicities are
of order of the Omega-baryon yield and can be accessed by the NA49 and the STAR
experiments.Comment: 4 page

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