The Stability of the Non-Equilibrium Steady States

We show that the non-equilibrium steady state (NESS) of the free lattice Fermion model far from equilibrium is macroscopically unstable. The problem is translated to that of the spectral analysis of the Liouville Operator. We use the method of positive commutators to investigate it. We construct a positive commutator on the lattice Fermion system, whose dispersion relation is (k)=cosk–.     

Level density fluctuations and characterization of chaos in the realistic model spectra for odd-odd nuclei

Statistical properties of the realistic energy spectra of the odd-odd nuclei¹⁰⁶Ag,¹⁹⁸Au,¹³⁴Cs,⁴⁰K and⁹⁴Rb, calculated within the Interacting Boson Fermion Fermion Model, are investigated by means of theΔ ₃ statistics and the Nearest Neighbor Spacing Distribution method. New probability distribution function, which describes well the calculated results and enables the characterization of chaos with a physically meaningfull parameter, is proposed. Level spacing fluctuations of the examined nuclei exhibit the transitional behavior between Poisson and GOE limits, revealing different degrees of chaoticity in their dynamics. Communicated by X. Campi     

Coexistence model of anisotropic electron hole pairing and unconventional superconductivity in Heavy Fermion compounds

Various Heavy Fermion compounds exhibit unconventional superconductivity together with another electronic instability like a spin density wave or possibly a more general type of anisotropic electron-hole pairing, e.g. a spin nematic state. The coexistence behaviour of these order parameters is studied within a simple weak coupling model. It is found that depeding on the symmetry of the order parameters coexistence or phase expulsion may occur. Whereas the former case is possibly realized for theU-based superconductors, CeCu₂Si₂ may be an example of the second case as observed and discussed in the context of elastic constant anomalies.     

Reduction Formula for Fermion Loops and Density Correlations of the 1D Fermi Gas

Fermion N-loops with an arbitrary number of density vertices N>d+1 in d spatial dimensions can be expressed as a linear combination of (d+1)-loops with coefficients that are rational functions of external momentum and energy variables. A theorem on symmetrized products then implies that divergences of single loops for low energy and small momenta cancel each other when loops with permuted external variables are summed. We apply these results to the one-dimensional Fermi gas, where an explicit formula for arbitrary N-loops can be derived. The symmetrized N-loop, which describes the dynamical N-point density correlations of the 1D Fermi gas, does not diverge for low energies and small momenta. We derive the precise scaling behavior of the symmetrized N-loop in various important infrared limits.     

Electromagnetic response of unconventional superconductors

The magnetic field penetration depth, surface resistance and far infrared reflectivity are calculated for two anisotropic order parameters having either points or lines of nodes in the energy gap. Resonant impurity scattering is taken into account for a wide range of scattering rates. Comparison with experimental results on heavy Fermion superconductors shows that the order parameter cannot be deduced unambiguously from the temperature dependence of the penetration depth. Fits to surface resistance measurements on UBe₁₃ are best in the Born approximation, rather than the unitarity limit. Experiments on high-T _c materials are largely inconclusive, offering little support for the applicability of BCS theory and providing no evidence against novel pairing interactions leading to unusual order parameters.     

A one-dimensionalN Fermion problem with factorizedS matrix

A one dimensionalN Fermion problem with attractive or repulsive function interaction is solved by Bethe's hypothesis. TheS matrix factorizes and is explicitly given.     

Quantum-Statistical Entropy of Six-Dimensional Spherically Symmetric Black Holes

Using the membrane model which is based on the brick-wall model, we calculated the free energy and entropy of six-dimensional spherically black holes. The result shows that both the entropy of Boson field (spin s = 0) and that of Fermion field (spin s = 1/2) are exactly proportional to the event horizon area. This is just the same as in the four dimensional case. Furthermore, the entropies of Bosons and Fermions have similar form. There is only a different coefficient between them.     

Correlation mediated superconductivity in a “HighT c ” model

We present a simple model to account for the High-T _c perovskite superconductors. The superconducting mechanism is purely electronic and comes from local Hubbard correlations. The model comprises a Hubbard model for the Copper sites with a single particle Oxygen band between the two Copper Hubbard bands. The electrons move only between nearest neighbour atoms which are of different types. Using two very different approximation schemes, one related to Slave-Boson mean field theory and the other based on an exact local Fermion transformation, we show the possibility of Copper-Oxygen or a mixture of Copper-Oxygen and Oxygen-Oxygen pairing. We believe that the most promising situation for superconductivity is with the Oxygen band over half-filled and closer in energy to the lower Hubbard band.     

Quantumq-white noise and aq-central limit theorem

We establish a connection between the Azéma martingales and certain quantum stochastic processes with increments satisfyingq-commutation relations. This leads to a theory ofq-white noise onq-*-bialgebras and to a generalization of the Fock space representation theorem for white noise on *-bialgebras. In particular, quantum Azéma noise,q-interpolations between Fermion and Boson quantum Brownian motion and unitary evolutions withq-independent multiplicative increments are studied. It follows from our results that the Azéma martingales and theq-interpolations are central limits of sums ofq-independent, identically distributed quantum random variables.     

Description of multi-band structures in154Gd and156Gd on symmetry considerations

The observed similarities of the yrast band level energies of several pairs of lighter rare-earth even-even nuclei are indicative of a particle-hole type symmetry for nuclei withA =164±a. This feature is sought to be described in terms of the representations of theSU(7) group in the interacting Fermion picture.SU(3) reduction of this group leads to the prediction of characteristic multi-band structures in these nuclei. Detailed comparison of the single-parameter predictions of this scheme with the available experimental informations on the level schemes for the nuclei¹⁵⁴Gd and¹⁵⁶Gd reveals striking agreement between the theory and the experiments. The results are discussed in comparison with the predictions of the simple Interacting Boson Model.     

Level density fluctuations and characterization of chaos in the realistic model spectra for odd-odd nuclei

Statistical properties of the realistic energy spectra of the odd-odd nuclei ¹⁰⁶Ag, ¹⁹⁸Au, ¹³⁴Cs, ⁴⁰K and ⁹⁴Rb, calculated within the Interacting Boson Fermion Fermion Model, are investigated by means of the Δ₃ statistics and the Nearest Neighbor Spacing Distribution method. New probability distribution function, which describes well the calculated results and enables the characterization of chaos with a physically meaningfull parameter, is proposed. Level spacing fluctuations of the examined nuclei exhibit the transitional behavior between Poisson and GOE limits, revealing different degrees of chaoticity in their dynamics.     

Fermion condensation and non Fermi liquid behavior in a model with long range forces

The phenomenon of the so called Fermion condensation, a phase transition analogous to Bose condensation but for Fermions, postulated in the past to occur in systems with strong momentum dependent forces, is reanalyzed in a model with infinite range interactions. The strongly non Fermi Liquid behavior of this system is demonstrated analytically at T = 0 and at T ≠ 0 in the superconducting and normal phases. The validity of the quasiparticle picture is investigated and seen to hold true for temperatures less than the characteristic temperature T _f of the Fermion condensation.     

The spectrum of the transfer matrix in theC*-algebra of the Ising model at high temperatures

We investigate the state on the Fermion algebra which gives rise to the thermodynamic limit of the Gibbs ensemble in the two-dimensional Ising model on a half lattice with nearest neighbour interaction. It is shown that the operatorP ^– in the GNS space, which performs the essential functions of the renormalized transfer matrix, has a quasi-particle structure.     

Exotic (E6) particles in e+e− annihilation

Fermion mixing is analyzed in (E₆) extensions of the standard model. Cross sections and signatures for the production in present and future e⁺e⁻ colliders are discussed in detail.     

RPA in wavefunction representation

The RPA is formulated in subspaces of coordinate-like and momentum-like 1 ph operators. This allows to embed a large class of approximative schemes into a generalized RPA treatment. We give a detailed formulation in terms of wavefunctions in coordinate space which is ideally suited to practical programming. In particular, we work out the reduction to spherical tensors in the case of spherical symmetry which is most often the starting point in finite Fermion systems.     

Exchange contribution to the surface energy of an arbitrary fermion system within the infinite barrier model

The surface energy of a many electron system within the infinite barrier model has produced a considerable amount of interest. These studies have provided solutions for the exchange and correlation (within the RPA) surface energies with which approximate treatments of more realistic surfaces have been compared. In this note we present the first generalization, within this model, of the exchange contribution to the surface energy for a general Fermion system of arbitrary interparticle interaction. Such results should be useful for testing approximate methods for a much wider range of Fermion systems.     

Superconductivity in the presence of fermion condensation

Fermion condensation (FC) is studied within the density functional theory. FC can fulfill the role of a boundary, separating the region of strongly interacting electron liquid from the region of strongly correlated electron liquid. Consideration of the superconductivity in the presence of FC shows that, under certain circumstances, at temperatures above T _c the superconductivity vanishes and the superconducting gap smoothly transforms into a pseudogap. The pseudogap occupies only a part of the Fermi surface, and one that shrinks with increasing temperature and vanishes at T=T*, and the single-particle excitations of the gapped area of the Fermi surface have a width γ ∼(T-T _c ). Pis’ma Zh. éksp. Teor. Fiz. 68, No. 6, 491–496 (25 September 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

FERMION COHERENT STATE AND QUARK CONFINEMENT

Two characteristics of the Fermion coherent state are given in this paper. One is the duality of the Fermion coherent state. The other is the indefiniteness of their eigenvalues. The SLAC bag model is also discussed by using the Fermion coherent state methodology. Our zesults agree with the SLAC bounded state iolutions, so that quark confinement can be phenomenally, illustrated.In addition, rje have found a gluon-ball solution and a non-bounded state solution, which are absent from the SLAC theory. Hence,the method of the Fermion coherent state is effective.