Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations

We study stochastic Hamilton-Jacobi-Bellman equations and the corresponding Hamiltonian systems driven by jump-type Lévy processes. The main objective of the present paper is to show existence, uniqueness and a (locally in time) diffeomorphism property of the solution: the solution trajectory of the system is a diffeomorphism as a function of the initial momentum. This result enables us to implement a stochastic version of the classical method of characteristics for the Hamilton-Jacobi equations. An –in itself interesting– auxiliary result are pointwise a.s. estimates for iterated stochastic integrals driven by a vector of not necessarily independent jump-type semimartingales

Finite size effects in the Gross-Neveu model with isospin chemical potential

The properties of the two-flavored Gross-Neveu model in the (1+1)-dimensional $R^1\times S^1$ spacetime with compactified space coordinate are investigated in the presence of the isospin chemical potential $\mu_I$. The consideration is performed in the limit $N_c\to\infty$, i.e. in the case with infinite number of colored quarks. It is shown that at $L=\infty$ ($L$ is the length of the circumference $S^1$) the pion condensation phase is realized for arbitrary small nonzero $\mu_I$. At finite values of $L$, the phase portraits of the model in terms of parameters $\nu\sim\mu_I$ and $\lambda\sim 1/L$ are obtained both for periodic and antiperiodic boundary conditions of the quark field. It turns out that in the plane $(\lambda,\nu)$ there is a strip $0\le\lambda<\lambda_c$ which lies as a whole inside the pion condensed phase. In this phase the pion condensation gap is an oscillating function vs both $\lambda$ (at fixed $\nu$) and $\nu$ (at fixed $\lambda$).Comment: 12 pages, 8 figures; one reference added; accepted for publication in PR

Studies of the Response of the Prototype CMS Hadron Calorimeter, Including Magnetic Field Effects, to Pion, Electron, and Muon Beams

We report on the response of a prototype CMS hadron calorimeter module to charged particle beams of pions, muons, and electrons with momenta up to 375 GeV/c. The data were taken at the H2 and H4 beamlines at CERN in 1995 and 1996. The prototype sampling calorimeter used copper absorber plates and scintillator tiles with wavelength shifting fibers for readout. The effects of a magnetic field of up to 3 Tesla on the response of the calorimeter to muons, electrons, and pions are presented, and the effects of an upstream lead tungstate crystal electromagnetic calorimeter on the linearity and energy resolution of the combined calorimetric system to hadrons are evaluated. The results are compared with Monte Carlo simulations and are used to optimize the choice of total absorber depth, sampling frequency, and longitudinal readout segmentation.Comment: 89 pages, 41 figures, to be published in NIM, corresponding author: P de Barbaro, [email protected]

Pion condensation of quark matter in the static Einstein universe

In the framework of an extended Nambu--Jona-Lasinio model we are studying pion condensation in quark matter with an asymmetric isospin composition in a gravitational field of the static Einstein universe at finite temperature and chemical potential. This particular choice of the gravitational field configuration enables us to investigate phase transitions of the system with exact consideration of the role of this field in the formation of quark and pion condensates and to point out its influence on the phase portraits. We demonstrate the effect of oscillations of the thermodynamic quantities as functions of the curvature and also refer to a certain similarity between the behavior of these quantities as functions of curvature and finite temperature. Finally, the role of quantum fluctuations for spontaneous symmetry breaking in the case of a finite volume of the universe is shortly discussed.Comment: RevTex4; 15 pages, 10 figure

Transience and non-explosion of certain stochastic Newtonian systems

We give sufficient conditions for non-explosion and transience of the solution (xt,pt) (in dimensions >= 3) to a stochastic Newtonian system of the form { dxdt = ptdt dpt = -δV(xt)/δx dt - δc(xt)/δx dξt where {ξt}t>=0 is a d-dimensional Lévy process, dξt is an Itô differential and c ∈ C2(Rd,Rd), V ∈ C2(Rd,R) such that V >= 0

Boundary-value problems for Hamiltonian systems and absolute minimizers in calculus of variations

We apply the method of Hamilton shooting to obtain the well-posedness of boundary value problems for certain Hamiltonian systems and some estimates for their solutions. The examples of Hamiltonian functions covered by the method include elliptic polynomials and exponentially growing functions. As a consequence we prove global existence, smoothness and almost everywhere uniqueness of absolute minimizers in the corresponding problem of calculus of variations and hence construct the global field of extremals

A high-resolution detector based on liquid-core scintillating fibres with readout via an electron-bombarded charge-coupled device

This paper is a presentation of results from tests in a 5 GeV/c hadron beam of detectors based on liquid-core scintillating fibres, each fibre consisting of a glass capillary filled with organic liquid scintillator. Fibre readout was performed via an Electron-Bombarded Charge-Coupled Device (EBCCD) image tube, a novel instrument that combines the functions of a high-gain, gated image intensifier and a Charge-Coupled Device. Using 1-methylnaphthalene doped with 3 g/l of R45 as liquid scintillator, the attenuation lengths obtained for light propagation over distances greater than 16 cm were 1.5 m in fibres of 20 mu m core and 1.0 m in fibres of 16 mu m core. For particles that crossed the fibres of 20 mu m core at distances of similar to 1.8 cm and similar to 95 cm from the fibres' readout ends, the recorded hit densities were 5.3 mm(-1) and 2.5 mm(-1) respectively. Using 1-methylnaphthalene doped with 3.6 g/l of R39 as liquid scintillator and fibres of 75 mu m core, the hit density obtained for particles that crossed the fibres at a distance of similar to 1.8 cm from their readout ends was 8.5 mm(-1). With a specially designed bundle of tapered fibres, having core diameters that smoothly increase from 16 mu m to 75 mu m, a spatial precision of 6 mu m was measured