One electron atoms in both a squeezed vacuum and a magnetic field via path integral methods

In the present paper we study the dynamics of one-electron atoms in the presence of both a linearly polarized squeezed vacuum and a magnetic field along the polarization vector of the photonic field. We adopt the dipole approximation and approach the problem via path integral methods. After integrating over the light variables for certain initial and final squeezed vacuum states we treat the path integral over the spatial variables via Monte-Carlo methods. As an application we calculate the survival probability of the ground state of a one-electron atom for various values of the magnetic field. Received 30 November 2000 and Received in final form 15 February 2001     

Aging and non-linear glassy dynamics in a mean field model

The mean field approach of glassy dynamics successfully describes systems which are out-of-equilibrium in their low temperature phase. In some cases an aging behaviour is found, with no stationary regime ever reached. In the presence of dissipative forces however, the dynamics is indeed stationary, but still out-of-equilibrium, as inferred by a significant violation of the fluctuation dissipation theorem. The mean field dynamics of a particle in a random but short-range correlated environment, offers the opportunity of observing both the aging and driven stationary regimes. Using a geometrical approach previously introduced by the author, we study here the relation between these two situations, in the pure relaxational limit, i.e. the zero temperature case. In the stationary regime, the velocity (v)-force (F) characteristics is a power law v∼F ⁴, while the characteristic times scale like powers of v, in agreement with an early proposal by Horner. The cross-over between the aging, linear-response regime and the non-linear stationary regime is smooth, and we propose a parametrization of the correlation functions valid in both cases, by means of an “effective time”. We conclude that aging and non-linear response are dual manifestations of a single out-of-equilibrium state, which might be a generic situation. Received 7 May 2000 and Received in final form 22 August 2000     

Non perturbative calculations for three particles in a linear chain within the generalized Hubbard model

A real-space method has been introduced to study the pairing problem within the generalized Hubbard Hamiltonian. This method includes the bond-charge interaction term as an extension of the previously proposed mapping method [1] for the Hubbard model. The generalization of the method is based on mapping the correlated many-body problem onto an equivalent site- and bond-impurity tight-binding one in a higher dimensional space, where the problem can be solved exactly. In a one-dimensional lattice, we analyzed the three particle correlation by calculating the binding energy at the ground state, using different values of the bond-charge, the on-site (U) and the nearest-neighbor (V) interactions. A pairing asymmetry is found between electrons and holes for the generalized hopping amplitude, where the hole pairing is not always easier than the electron case. For some special values of the hopping parameters and for all kinds of interactions in the Hubbard Hamiltonian, an analytical solution is obtained. Received 21 January 2000 and Received in final form 18 July 2000     

The influence of the dynamics of ionic multiplets onto electronic transport properties of heavy-fermion systems: a semi-phenomenological approach

We present calculations of the electronic transport properties of heavy-fermion systems within a semi-phenomenological approach to the dynamical mean field theory. In this approach the dynamics of the Hund's rules 4f (5f )-ionic multiplet split in a crystalline environment is taken into account. Within the scope of this calculation we use the linear response theory to reproduce qualitative features of the temperature-dependent resistivity and hall conductivity, the magneto-resistivity and the thermoelectric power typical for heavy-fermion systems. The model calculations are directly compared with experimental results on CeCu ₂ Si ₂. Received 30 June 2000 and Received in final form 15 December 2000     

Scaling and infrared divergences in the replica field theory of the Ising spin glass

Replica field theory for the Ising spin glass in zero magnetic field is studied around the upper critical dimension d=6. A scaling theory of the spin glass phase, based on Parisi's ultrametrically organised order parameter, is proposed. We argue that this infinite step replica symmetry broken (RSB) phase is nonperturbative in the sense that amplitudes of scaling forms cannot be expanded in term of the coupling constant w². Infrared divergent integrals inevitably appear when we try to compute amplitudes perturbatively, nevertheless the -expansion of critical exponents seems to be well-behaved. The origin of these problems can be traced back to the unusual behaviour of the free propagator having two mass scales, the smaller one being proportional to the perturbation parameter w² and providing a natural infrared cutoff. Keeping the free propagator unexpanded makes it possible to avoid producing infrared divergent integrals. The role of Ward-identities and the problem of the lower critical dimension are also discussed. Received 23 December 1998 and Received in final form 23 March 1999     

Gauge and Lorentz covariant quark propagator in an arbitrary gluon field

The quark propagator in the presence of an arbitrary gluon field is calculated gauge and Lorentz covariantly order by order in terms of powers of the gluon field and its derivatives. The result is independent of the path connecting the ends of the propagator, and the leading order result coincides with the exact propagator in the trivial case of a vanishing gluon field. Received: 5 February 2003 / Published online: 23 May 2003     

Hydrogenic impurity ground state in quantum well: the envelope function revisited

We present a new variationnal method for calculating the ground state energy of an electron bound to an impurity located in a quantum well. This method relies on an envelope function which is determined exactly from a formal minimization procedure. The obtained energies are lower by as much as 10% than the ones found by the widely used free electron envelope function. Their large width limits are reached with exponentially small corrections as they should. We also find that, except for narrow wells, the shape of these exact envelope functions strongly depends on the impurity position, being consequently quite different from the usual free electron ones. In order to discuss the improvements brought by our new procedure in the most striking way, we have used a model semiconductor quantum well with infinite barrier height and simplified band structure. Extensions can be made to finite barrier and more realistic band structures, following the same technique. Received 11 December 2000     

Tunnelling process between a semiconductor or a metal and a polymer

The tunnelling lifetime of an electron lying in a p-type orbital localised at a given distance from a semiconductor or a metal is calculated by using Bardeen's method. It is then shown that even in the absence of broad bands, the hole injection process from semiconductors and metals into polymers should follow a Fowler-Nordheim dependence, provided that the current is not bulk-limited. In the semiconductor case, the current can be expressed by a fully analytical formula, and by an approximate one in the case of a metal. It is demonstrated that the effective Fowler-Nordheim barrier is not the mere difference between the metal work function or the semiconductor electron affinity and the HOMO level of the polymer, but a simple function of both levels. Received 6 April 2001 and Received in final form 29 May 2001     

Correlation functions for a Bose-Einstein condensate in the Bogoliubov approximation

In this article we introduce a differential equation for the first order correlation function G ⁽¹⁾ of a Bose-Einstein condensate at T = 0. The Bogoliubov approximation is used. Our approach points out directly the dependence on the physical parameters. Furthermore it suggests a numerical method to calculate G ⁽¹⁾ without solving an eigenvector problem. The G ⁽¹⁾ equation is generalized to the case of non zero temperature. Received 20 September 2000     

Many-body Green's function theory for the magnetic reorientation of thin ferromagnetic films

The field-induced reorientation of the magnetization of ferromagnetic films is treated within the framework of many-body Green's function theory by considering all components of the magnetization. We present a new method for the calculation of expectation values in terms of the eigenvalues and eigenvectors of the equations of motion matrix for the set of Green's functions. This formulation allows a straightforward extension of the monolayer case to thin films with many layers and for arbitrary spin and moreover provides a practicable procedure for numerical computation. The model Hamiltonian includes a Heisenberg term, an external magnetic field, a second-order uniaxial single-ion anisotropy, and the magnetic dipole-dipole coupling. We utilize the Tyablikov (RPA) decoupling for the exchange interaction terms and the Anderson-Callen decoupling for the anisotropy terms. The dipole coupling is treated in the mean-field approximation, a procedure which we demonstrate to be a sufficiently good approximation for realistic coupling strengths. We apply the new method to monolayers with spin and to multilayer systems with S=1. We compare some of our results to those where mean-field theory (MFT) is applied to all interactions, pointing out some significant differences. Received 19 June 2000 and Received in final form 2 August 2000     

Unconventional field and angle dependences of the Shubnikov-de Haas oscillations spectra in the quasi two-dimensional organic superconductor (BEDO-TTF) 2ReO 4H 2O

We report on the inter-layer oscillatory conductance of the two-dimensional organic superconductor (BEDO-TTF)₂ReO₄H₂O measured in static and pulsed magnetic fields of up to 15 and 52 T, respectively. In agreement with previous in-plane studies, two Shubnikov-de Haas oscillation series linked to the two electron and the hole orbits are observed. The influence of the magnitude and orientation of the magnetic field with respect to the conducting plane is studied in the framework of the conventional two- and three-dimensional Lifshits-Kosevich (LK) model. Deviations of the data from this model are observed in low fields strongly tilted with respect to the normal to the conducting plane. In this latter case, the observed behaviour is consistent with an unexplained lowering of the cyclotron effective mass. At high magnetic field, the oscillatory data could have been compatible with the occurrence of a magnetic breakdown orbit built from the hole and electron orbits. However, the increase of the cyclotron effective mass, linked to the electron orbits, as the magnetic field increases above ∼12 T is consistent with a field-induced phase transition. In the lower field range, where the conventional LK model holds, the analysis of the angle dependence of the oscillations amplitude suggests significant renormalisation of the effective Landé factor. Received 22 August 2000 and Received in final form 20 December 2000     

Fermion gases in magnetic fields: a semiclassical treatment

The study of quantum degenerate gases has received much interest in these last years essentially thanks to the extremely important experimental results of the achievement of Bose-Einstein condensation of atoms and, very recently, of almost complete degeneracy of atomic fermion gases. Here we want to present the results of a semi-analytical method for the study of an interacting degenerate fermion gas based on semiclassical kinetic theory; special care has been devoted to the study of a rotating electron gas, in a cylindrically symmetrical configuration, radially confined by a uniform magnetic field. The model will lead to a particular Thomas-Fermi equation which is generalized to take into account finite temperature and average velocity of the gas, and which is further developed to consider the effects of external fields. Received 10 March 2000     

On the evaluation of the specific heat and general off-diagonal n-point correlation functions within the loop algorithm

We present an efficient way to compute diagonal and off-diagonal n-point correlation functions for quantum spin-systems within the loop algorithm. We show that the general rules for the evaluation of these correlation functions take an especially simple form within the framework of directed loops. These rules state that contributing loops have to close coherently. As an application we evaluate the specific heat for the case of spin chains and ladders. Recieved 10 January 2000 and Received in final form 9 February 2000     

The thermal Green functions in nonextensive quantum statistical mechanics

The thermal Green functions of the quantum-mechanical harmonic oscillator are constructed within the framework of nonextensive statistical mechanics with normalized q -expectation values. For the Tsallis index q greater than unity, these functions are found to be expressed analytically in terms of the Hurwitz zeta function. It is found that influence of the nonextensivity on the time-ordered thermal propagator is relevant only at the “on-shell” states. In particular, the finite-temperature contribution to the thermal propagator becomes enhanced for the strong nonextensivity. Received 30 September 1998     

Effective potential of the O(N) linear sigma-model at finite temperature

We study the O(N) symmetric linear sigma-model at finite temperature as the low-energy effective models of quantum chromodynamics (QCD) using the Cornwall-Jackiw-Tomboulis (CJT) effective action for composite operators. It has so far been claimed that the Nambu-Goldstone theorem is not satisfied at finite temperature in this framework unless the large-N limit in the O(N) symmetry is taken. We show that this is not the case. The pion is always massless below the critical temperature, if one determines the propagator within the form such that the symmetry of the system is conserved, and defines the pion mass as the curvature of the effective potential. We use a regularization for the CJT effective potential in the Hartree approximation, which is analogous to the renormalization of auxiliary fields. A numerical study of the Schwinger-Dyson equation and the gap equation is carried out including the thermal and quantum loops. We point out a problem in the derivation of the sigma meson mass without quantum correction at finite temperature. A problem about the order of the phase transition in this approach is also discussed. Received: 21 June 2000 / Accepted: 13 September 2000     

Two-pion production processes, chiral symmetry and NN interaction in the medium

We study the two-pion propagator in the nuclear medium. This quantity appears in the ππ T-matrix and we show that it also enters the QCD scalar susceptibility. The medium effects on this propagator are due to the influence of the individual nucleon response to a scalar field through their pion clouds. This response is appreciably increased by the nuclear environment. It produces an important convergence effect between the scalar and pseudoscalar susceptibilities, reflecting the reshaping of the scalar strength observed in 2π production experiments. While a large modifications of the σ propagator follows, due to its coupling to two pion states, we show that the NN potential remains instead unaffected.     

Electron captures by positrons from hydrogenic ions in nonideal classical plasmas

In nonideal classical plasmas, the electron captures by positrons from hydrogenic ions are investigated. An effective pseudopotential model taking into account the plasma screening effects and collective effects is applied to describe the interaction potential in nonideal plasmas. The classical Bohr-Lindhard model has been applied to obtain the electron capture radius and electron capture probability. The modified hyperbolic trajectory method is applied to the motion of the projectile positron in order to visualize the electron capture probability as a function of the impact parameter, nonideal plasma parameter, projectile velocity, and plasma parameters. The results show that the electron capture probability in nonideal plasmas is always greater than that in ideal plasmas descried by the Debye-Hückel potential, i.e., the collective effect increases the electron capture probability. It is also found that the collective effect is decreased with increasing the projectile velocity. Received 21 January 2000 and Received in final form 27 April 2000