J. M. C. Malbouisson

Thermal quantum field theory - Algebraic aspects and applications

General Principles: Elements of Thermodynamics Elements of Statistical Mechanics Partition Function and Path Integral Interacting Fields Thermal Field Theory: Thermofield Dynamics (TFD) Thermal Oscillators: Bosons and Fermions Representation of the Thermo-Poincare Group Free Fields at Finite Temperature Thermal Interacting Fields Scattering Processes and Reaction Rates via TFD Applications to Quantum Optics: Thermal Quantum States of Field Mode Non-classical Properties of Thermal States Bipartite Systems and Thermal States Measure of Non-classicality and Temperature SU(2) and SU(1,1) States Thermal Confined Fields: About Confinement and Thermal Theories Casimir Effect for the Electromagnetic Field in Box Casimir Effect for Fermions Superconducting Transition Temperature in Films, Wires and Grains Critical Behavior of Type II Superconducting Films in a Magnetic Field First-Order Phase Transition in Superconducting Films Compactified GrossA-Neveu Model at T=0 Compactified GrossA-Neveu Model at Finite Temperature Applications to Open Systems: TFD, Wigner Functions and Kinetic Theory Schrodinger Approach, TFD and Nonequilibrium Systems Dressed State Approach to the Thermalization Processes.

The geometrical basis of the eyelid contour

Purpose To derive a two-dimensional, frontal-view model of eyelid contour. Methods Observational study. Palpebral fissure images of 110 normal subjects were acquired with a charge-coupled device camera and processed with National Institutes of Health Image software on a Macintosh computer. Monocular frontal-view images of the palpebral fissures were recorded and second-degree polynomial functions were fitted to both upper and lower eyelid contours for two areas: the whole eyelid margin (ciliated and inner canthal portions) and the ciliated portion alone. In addition, frontal and lateral palpebral fissure images were obtained. From the frontal view, the upper and lower ciliated contours were fitted with quadratic functions. From the lateral view, the upper and lower lateral angles, formed by the upper and lower eyelid margins and the axial axis, were measured. Results Exclusion of the inner canthal portion of the eyelid contour led to a much better quadratic fit for the contours. The sine (sin) of the upper lateral angle was strongly correlated with the parameter A of the quadratic function fitted to the upper eyelid (the parameter A determines the curvature of the function around its extremum point). For the lower eyelid, this correlation was not significant. Conclusions The parabolic shape of the upper ciliated contour seen in two-dimensional images can be justified geometrically in a simple way, allowing a precise quantification of its shape. The same was not true for the lower eyelid. The parabolic shape of the upper eyelid can be demonstrated, using the Taylor series, to be a close approximation of the arc of a circle.

Quantum fields in toroidal topology

Abstract The standard representation of c ∗ -algebra is used to describe fields in compactified space–time dimensions characterized by topologies of the type Γ D d = ( S 1 ) d × M D − d . The modular operator is generalized to introduce representations of isometry groups. The Poincare symmetry is analyzed and then we construct the modular representation by using linear transformations in the field modes, similar to the Bogoliubov transformation. This provides a mechanism for compactification of the Minkowski space–time, which follows as a generalization of the Fourier integral representation of the propagator at finite temperature. An important result is that the 2×2 representation of the real-time formalism is not needed. The end result on calculating observables is described as a condensate in the ground state. We initially analyze the free Klein–Gordon and Dirac fields, and then formulate non-abelian gauge theories in Γ D d . Using the S -matrix, the decay of particles is calculated in order to show the effect of the compactification.

Finite-size effects on the chiral phase diagram of four-fermion models in four dimensions

Abstract We study the size dependence of the dynamical symmetry breaking in the four-dimensional Nambu–Jona-Lasinio model. We show that the presence of boundaries reduces the chiral breaking region, and this effect is strengthened for a larger number of compactified dimensions. A critical value for the length of the compactified dimensions exists, below which the dynamical symmetry breaking is not possible. Considering finite temperature and chemical potential, the chiral phase structure for the system with compactified dimensions is obtained. A gradual decreasing of the chiral breaking region with increasing of chemical potential is found. Also, at fixed chemical potential, the decreasing of the size of the system changes the order of the chiral phase transition.

Boundary behaviour of the four-point function in the 3-dimensional Gross–Neveu model

We consider the N-components 3-dimensional massive Gross–Neveu model compactified in one spatial direction, the system being constrained to a slab of thickness L. We derive a closed formula for the renormalized L-dependent four-point function at vanishing external momenta in the large-N limit (the effective coupling constant), using bag-model boundary conditions. For values of the fixed coupling constant in absence of boundaries λ⩾λc≃19.16, we obtain small-distance asymptotic freedom (for L→0) and a singularity for a length L(c) such that 2.07m−1<L(c)≲2.82m−1, m being the fermionic mass. Taking for m an average of the masses of the quarks composing the proton, we obtain a “confining” length L(c)p which is comparable with an estimated proton diameter.

Finite-size effects on the phase diagram of difermion condensates in two-dimensional four-fermion interaction models

We investigate finite-size effects on the phase structure of chiral and difermion condensates at finite temperature and density in the framework of the two-dimensional large-N Nambu-Jona-Lasinio model. We take into account size-dependent effects by making use of zeta-function and compactification methods. The thermodynamic potential and the gap equations for the chiral and difermion condensed phases are then derived in the mean-field approximation. Size-dependent critical lines separating the different phases are obtained considering antiperiodic boundary conditions for the spatial coordinate.

Phase structure of difermion condensates in the Nambu–Jona-Lasinio model: The size-dependent properties

We investigate finite-size effects on the phase structure of difermion condensates at finite temperature and density in the framework of the two-dimensional large-N limit Nambu–Jona-Lasinio model. We take into account size-dependent effects on the system by making use of zeta-function and compactification methods. The thermodynamic potential and the gap equation for the difermion condensed phase are then derived in the mean-field approximation. Size-dependent critical lines separating trivial and non-trivial difermion condensed phases are obtained imposing either periodic or anti-periodic boundary conditions on the spatial coordinate.

Phase transition in the 3D massive Gross-Neveu model

We consider the 3-dimensional massive Gross-Neveu model at finite temperature as an effective theory for strong interactions. Using the Matsubara imaginary-time formalism, we derive a closed form for the renormalized T-dependent four-point function. This gives a singularity, suggesting a phase transition. Considering the free energy we obtain the T-dependent mass, which goes to zero for some temperature. These results lead us to the conclusion that there is a second-order phase transition.

Generation of the reciprocal-binomial state for optical fields

Abstract We compare the efficiencies of two interesting schemes to generate truncated states of the light field in running modes, namely the “quantum scissors” and the “beam-splitter array” schemes. The latter is applied to create the reciprocal-binomial state as a travelling wave, required to implement recent experimental proposals of phase-distribution determination and of quantum lithography.

Controlled hole burning in the photon-number distribution of field states in a cavity

Abstract A feasible experimental scheme to generate states of a field mode in a high-Q cavity possessing holes in their photon-number distributions at controlled positions is proposed. Such kind of states may be of interest to optical data storage and communications with a possible readout system consisting of an atomic deflection setup.