Quasi-set theory for bosons and fermions: Quantum distributions

Abstruct Quasi-set theory provides a mathematical background for dealing with coll ections of indistinguishable elementary particles. In this paper, we show how to obtain the quantum statistics into the scope of quasi-set theory and we also discuss the Helium atom, which represents the simplest example where indistinguishability plays an important role. One of the advantages of our approach is that one of the most basic principles of quantum theory, namely, the Indistinguishability Postulate, does not need to be assumed even implicitely in the axiomatic basis of quantum mechanics.     

Quantum statistical mechanics of ideal gas obeying fractional exclusion statistics: a systematic study

The quantum statistical mechanics of an ideal gas with a general free-particle energy obeying fractional exclusion statistics are systematically investigated in arbitrary dimensions. The pressure relations, the relation between pressure and internal energy, the equation of state, as well as the thermodynamic properties are thoroughly discussed. Some novel results are obtained. Received: 23 January 1998 / Accepted: 17 March 1998     

Quantum mechanics as relativistic statistics. II: The case of two interacting particles

It is shown that non-relativistic quantum mechanics of two particles interacting with external electromagnetic field or between each other can be considered as statistics of two-dimensional surfaces. These surfaces represent the relativistical state of two indeterministic particles in the eight-dimensional space which is a tensor product of space-times for each of the two particles.     

Interacting quantum wires: A possible explanation for the 0.7 anomalous conductance

We investigate an effective one-dimensional conducting channel considering both the contact umklapp and the Coulomb electron-electron interaction. We show that, at low electronic density, the proximity to the Wigner crystal reproduces the anomaly in conductance at 0.7G₀. The crucial ingredient of our theory is the fact that the gate voltage acts as a bias controlling the intensity of the umklapp term. At large gate voltages, the umklapp vanishes and we obtain a conducting quantum wire with a perfect conductance. At low gate voltages, the Wigner crystal is pinned by the umklapp term, giving rise to an insulating behavior with vanishing conductance. This crossover pattern has a transition point which can be identified with the anomalous conductance around 0.7G₀. This picture is obtained within the framework of a renormalization group calculation. The conductance static regime is achieved by taking first the limit of finite length and then the limit of zero frequency.     

A model for the structure of point-like fermions: Qualitative features and physical description

A model for the structure of point-like fermions as tightly bound composite states is described. The model is based upon the premise that electromagnetism is the only fundamental interaction. The fundamental entity of the model is an object called the vorton. Vortons are semiclassical monopole configurations of electromagnetic charge and field, constructed to satisfy Maxwell's equations. Vortons carry topological charge and one unit each of two different kinds of angular momenta, and are placed in magnetically bound pair states having angular momentum l=1/2. The topological charge prevents the mutual annihilation of the vorton pair. The helicity eigenstates of the vortons' intrinsic angular momenta form the basis for a set of internal quantum numbers for the pair which distinguish the different (point-like) pair states. Sixteen fourcomponent spinor states, eight leptonic and eight hadronic, are obtained. Eleven of these are identified with the quantum numbers of the experimentally known particles: e, v_e, μ, v_μ, τ, v_τ; p, n, Λ, Λ_c, and b. Thus one new heavy lepton with its neutrino and three new quark states are predicted. Some possibilities for the extension of this model are discussed.     

Dynamic microscopic basis for IBM-2: A new approach

A dynamic approach, based on deformed Hartree-Fock solution of a nucleus, is suggested for obtaining correlated identical nucleon pair wave function for neutrons and protons. Expressions for single pair energies and two pair interaction matrix elements amongst the neutron and proton pairs in the microscopic fermion basis are presented. These matrix elements define the IBM-2 Hamiltonian through Marumori mapping. The entire procedure is illustrated by obtaining the IBM-2 spectra of²⁰Ne,⁴⁴Ti,⁶⁰Zn and⁹⁴Mo and comparing them with shell model (SM) and/or experimental results. The Yrast levels given by our calculations match well with those of the SM and the experimental results for all the four nuclei, while the non-Yrast levels do not barring the case of⁹⁴Mo. This is due to the loss of isospin symmetry for light nuclei in IBM-2. These results are discussed in detail.     

A microscopic model for the black hole: Black string phase transition

Computations in general relativity have revealed an interesting phase diagram for the black hole–black string phase transition, with three different black objects present for a range of mass values. We can add charges to this system by ‘boosting’ plus dualities; this makes only kinematic changes in the gravity computation but has the virtue of bringing the system into the near-extremal domain where a microscopic model can be conjectured. When the compactification radius is very large or very small then we get the microscopic models of (4+1$4+1$)-dimensional near-extremal holes and (3+1$3+1$)-dimensional near-extremal holes respectively (the latter is a uniform black string in 4+1$4+1$ dimensions). We propose a simple model that interpolates between these limits and reproduces most of the features of the phase diagram. These results should help us understand how ‘fractionation’ of branes works in general situations.     

The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines

In this paper a microscopic quantum mechanical model of computers as represented by Turing machines is constructed. It is shown that for each numberN and Turing machineQ there exists a HamiltonianH _N ^Q and a class of appropriate initial states such that if c is such an initial state, then _Q ^N (t)=exp(–1H _N ^Q t) _Q ^N (0) correctly describes at timest ₃,t ₆,,t _3N model states that correspond to the completion of the first, second, , Nth computation step ofQ. The model parameters can be adjusted so that for an arbitrary time interval aroundt ₃,t ₆,,t _3N, the machine part of _Q ^N (t) is stationary.     

Spacetime as a topological insulator: mechanism for the origin of the fermion generations

We suggest a mechanism whereby the three generations of quarks and leptons correspond to surface modes in a five-dimensional theory. These modes arise from a nonlinear fermion dispersion relation in the extra dimension, much in the same manner as fermion surface modes in a topological insulator or lattice implementation of domain wall fermions. We also show that the topological properties can persist in a deconstructed version of the model in four dimensions.     

About the non vanishing of boundary terms in correlation functions as origin of phase transitions. A microscopic proof of a Goldstone theorem in classical statistical mechanics

We give a general microscopic proof that the well known Goldstone theorem connected with spontaneous symmetry breaking in quantum statistical mechanics and quantum field theory has a counterpart in classical statistical mechanics. Our approach is mainly based on the replacement of commutators by Poisson brackets as infinitesimal generators of symmetries and on the Fourier transformed version of the so called Kubo-Martin-Schwinger property of equilibrium states. Especially we show that the phase transition is related to the non vanishing of certain boundary contributions in Poisson brackets which from the naive point of view should vanish.     

Charge density: A probe for the nuclear interaction in microscopic transport models

The transport properties of the ³⁶Ar +⁵⁸Ni system at measured with the INDRA array, are studied within the BNV kinetic equation. A general protocol of comparison between the N-body experimental fragment information and the one-body distribution function is developed using global variables, with a special focus on charge density. This procedure avoids any definition of sources and any use of an afterburner in the simulation. We shall discuss the feasibility of such an approach and the distortions induced by the finite detection efficiency and the completeness requirements of the data selection. The sensitivity of the different global observables to the macroscopic parameters of the effective nuclear interaction will be studied in detail.Received: 21 January 2003, Published online: 5 August 2003PACS: 25.70.-z Low and intermediate energy heavy-ion reactions - 24.10.-i Nuclear reaction models and methodsN. Le Neindre: Permanent address: Institut de Physique Nuclaire, IN2P3-CNRS, F-91406 Orsay cedex, France.     

Microdiffusion: A microscopic technique for study of the diffusion of quinoline in PVC powder

Observation of the diffusion of quinoline inside PVC grains by microscopy represents a very sensitive method of PVC powder differentiation. The kinetics of microdiffusion is measured as a function of time and temperature (exponential function) by the fraction of impregnated grains of the powder which varies, on a broad range, as a function of resin properties, which are mainly influenced by the conversion factor. Gaussologarithmic representation of the phenomenon gives a Galton's straight line, the slope of which is related, more or less, to the homogeneous character of microdiffusion in the powder. That aspect is described in relation to the problem of formation of “fish eyes.”