Magnetic-field-induced valence transition in rare-earth systems

The magnetic-field-induced valence transition in rare-earth systems has been investigated using the periodic Anderson model supplemented by the Falicov-Kimball term. This model has been solved by first decoupling the Falicov-Kimball term as proposed by Khomskii and Koharjan and then taking the limit of infinite intra-site Coulomb repulsion. The valence transition both in the absence and in the presence of magnetic field as a function of temperature is studied. It has been found that the system makes transition from non-magnetic to magnetic state when the magnetic field increases beyond a critical value H _c. The phase boundary defined in terms of reduced field H _c(T)/H _c(0) and reduced temperature T/T _v (T _v being the valence transition temperature in the absence of field) is almost independent of the position of the localized level. The results are in qualitative agreement with experimental observations in Yb- and Eu-compounds.     

Head-on and head-off collisions of discrete breathers in two-dimensional anharmonic crystal lattices

The ground-state phase diagram of the extended Falicov-Kimball model with f-f electron hopping is studied numerically in the one-dimensional case. To identify the nature of ground states three complementary numerical methods are used, and namely, (i) the small-cluster exact-diagonalization method, (ii) the density-matrix-renormalization-group method (DMRG) and (iii) an approximate, but very accurate, numerical method based on the reduction of the Hilbert space. It is found that the physics of the Falicov-Kimball model found for the zero value of the f-electron hopping integral t _f (including the existence of the devil’s staircase structure) persists also at finite values of t _f . The critical values of t ^c _f below which the physics of the Falicov-Kimball model dominates are calculated numerically and it is shown that they depend very strongly on the f-electron concentration n _f and only very weakly on the Coulomb interaction. In particular, we have found that for strong Coulomb interactions the value of t ^c _f rapidly increases from t ^c _f ~ 0.003 found for n _f = 1 / 4 up to relatively large t ^c _f ~ 0.4 found for n _f near the half-filled band case n _f = 1 / 2. In addition, the complete picture of valence transitions is presented for non-zero t _f and strong Coulomb interactions.     

Exact superconducting ground states of the extended Anderson model

We obtain exact ground states of an extended periodic Anderson model (EPAM) with non-local hybridization and Coulomb repulsion between f and c electrons (Falicov-Kimball term) in one dimension. We show that for a range of parameter values these ground states exhibit composite hole pairing and superconductivity that originate from purely electronic interactions.     

On the absence of purely electronic phase transition in extended Falicov-Kimball model

The Falicov-Kimball model extended by the hybridization between the localized and band electrons is considered in the approximation valid for the narrow band. The limit of infinite Coulomb repulsion G is considered. In spite of the fact that the approximation involved favour the abrupt change of the occupation number of ?-states we have not found any discontinuous solution. This suggests that the first order phase transition in SmS can not be considered as being or purely electronic nature.     

Some exact results for the spin-1/2 Falicov-Kimball model in the strong coupling limit

The spin-1/2 Falicov-Kimball model for electronically driven valence and metal-insulator transitions is studied analytically using strong-coupling perturbation theory. It is shown that in the limit of the infinite interaction strength between localized and itinerant electrons the Falicov-Kimball model undergoes two types of discontinuous valence transitions: the insulator-metal transitions from an integer-valence ground state (n _f = 1) into an inhomogeneous intermediate-valence ground state (0 < n _f < 1) and the insulator-metal transitions from n _f = 1 to n _f = 0. In addition, we discuss the role of the electron-phonon interaction on the mechanism of valence transitions and we present possible extensions of the exact one dimensional results to higher dimensions.     

Magnetic susceptibility of mixed valence compounds

Magnetic susceptibility of mixed-valence compounds has been calculated as a function of pressure using Falicov-Kimball model wherein thef-s hybridisation has been taken into account. This model can very well explain the continuous as well as discontinuous transitions from ground states of integral to intermediate valence. Our results for magnetic susceptibility are in qualitative agreement with recent experimental results on some mixed-valence compounds.     

Phase Diagram of the Two-dimensional t–t′ Falicov-Kimball Model

The ground-state phase diagram of the two-dimensional Falicov-Kimball model with nearest-neighbour and next-nearest-neighbour hoppings has been studied in the perturbative regime where hoppings are small compared with the on-site Coulomb interaction. The phase diagram at fourth-order exhibits a richer structure than the one of the ordinary Falicov-Kimball model. PACS numbers: 71.10.Fd, 71.21.+a, 75.10.Hk, 75.30.Kz     

On the first order valence transition in SmS

The valence transition in SmS is investigated on the basis of a model which incorporates the Falicov-Kimball (F-K) interaction, f-d hybridization and electron-phonon interaction. We find that the transition is of first order even in the absence of electron-phonon interaction if the F-K interaction is sufficiently strong. Electron-phonon interaction makes the first order transition possible for a weaker F-K interaction. The effect is further enhanced if phonon-induced f-f and f-d coupling are simultaneously present. All calculations are done for finite temperature and the temperature dependence of the transition is found to be in agreement with the phase diagram of SmS.     

Hybridization effect on the Falicov-Kimball model

The extended Falicov-Kimball model which includes the hybridization effect between the localized electron state and the conduction band is treated within the Hartree-Fock approximation at T=0 K. The occupation number n_e of the conduction band is calculated as a function of the localized level. The both discontinuous and continuous changes of n_e appear in a certain region of parameters. This result may correspond to the experimental facts of samarium-monochalcogenides under pressure.     

An extended Lipkin-type model with residual proton-neutron interaction

The Lipkin-Meshkov-Glick (LMG) model is extended to explicitly take into account the proton and neutron degrees of freedom. The proton and neutron Hamiltonians are taken to be of the LMG form, and, in addition, a residual proton-neutron interaction is include. Exact solutions in an SU(2) ⊗ SU(2) basis as well as the RPA solutions for the energy spectrum of the model Hamiltonian are obtained. The spectrum of the exact solutions is degenerate in the limit of no proton-neutron residual interaction, but this degeneracy is totally removed when this type of residual interaction is turned on. The spectrum obtained with RPA is compressed or expanded, as compared to the LMG model with the same total number of nucleons (N), depending of the relative magnitudes of the like- and unlike-particle residual interactions. Furthermore, the behavior of the first collective excited state is studied as function of the interaction parameters of the model using the exact and RPA methods. At a given N, it was found that the RPA result is closer to the exact one when the like- and unlike-particle residual interactions are both taken into account in the model Hamiltonian, as compared to the case when residual interaction of only one type (e.g. either like- or unlike-particle type) is involved.     

Ground-state properties of the Falicov-Kimball model in one and two dimensions

A new numerical method is used to study the ground-state properties of the spinless Falicov-Kimball model in one and two dimensions. The resultant solutions are used to examine the phase diagram of the model as well as possibilities for valence and metal-insulator transitions. In one dimension a comprehensive phase diagram of the model is presented. On the base of this phase diagram, the complete picture of valence and metal-insulator transitions is discussed. In two dimensions the structure of ground-state configurations is described for intermediate interactions between f and d electrons. In this region the phase separation and metal-insulator transitions are found at low f-electron concentrations. It is shown that valence transitions exhibit a staircase structure. Received 20 October 2000     

Prospects for high-energy P−P beams: Study of hadronic jets and possible intermediate bosons

Predictions for large p_T hadronic jets in high-energy proton-antiproton collisions, produced by strong interactions alone or through intermediate boson production and decay, and strong interactions, are calculated and compared. Two alternative models are considered for the strong interactions between partons: the phenomenological model of quark-scattering and lowest order QCD. In the last case, gluons are also taken into account as partons, with different choices of the gluon distribution inside the proton. The differential cross-sections for two-jet productions are given in the more interesting regions of the phase-space, as well as the predictions for the mean charge of the jets. Possible signatures for the detection of the W are stressed. In particular, W's could show up only for jets with p_T near its maximum value. Our conclusions are mostly independent of the weak interaction model: the Weinberg-Salam one is considered for definiteness but alternative models are also discussed. The mean charge of the hadronic jets arising from either the weak or the strong interactions could be a rather distinctive tool in the search for the W. However, if gluons are present, their interactions could preponderate in the jet production mechanism and obstruct the search for intermediate bosons in the hadronic channels.     

Scale-Free Static and Dynamical Correlations in Melts of Monodisperse and Flory-Distributed Homopolymers

It has been assumed until very recently that all long-range correlations are screened in three-dimensional melts of linear homopolymers on distances beyond the correlation length ?? characterizing the decay of the density fluctuations. Summarizing simulation results obtained by means of a variant of the bond-fluctuation model with finite monomer excluded volume interactions and topology violating local and global Monte Carlo moves, we show that due to an interplay of the chain connectivity and the incompressibility constraint, both static and dynamical correlations arise on distances r???. These correlations are scale-free and, surprisingly, do not depend explicitly on the compressibility of the solution. Both monodisperse and (essentially) Flory-distributed equilibrium polymers are considered.     

The properties of 116in excited states

Gamma and conversion electron spectra from the ¹¹⁵In(n, γ)¹¹⁶In reaction in the energy range 20–700 keV and 20–850 keV respectively have been measured with bent crystal and magnetic spectrometers. Gamma-gamma coincidences in the energy range 50–500 keV have been investigated with Ge(Li)-Ge(Li) arrangement. Proton spectra from the 12 MeV deuteron-induced (d, p) reaction taken at the University of Pittsburgh Tandem Van de Graaf accelerator were reanalysed. The ¹¹⁶In level scheme consisting of 56 levels in the energy range 0–1.4 MeV has been constructed. Parity is determined for all the levels introduced. Unique spin values are assigned to 37 levels. The information obtained was used to place limits to the J-values for the rest of the levels. The main components of the wave function are established for 23 levels, considered to be components of p-n multiplets in which the proton hole and odd neutron are in in one of the Z = 28 → 50 and N = 50 → 82 shell states, respectively. Energy splittings of p-n configurations by residual interactions taken as a combination of short range Wigner and singlet forces have been calculated. It is noted that many excited states cannot be described in the framework of two-quasiparticle configurations.     

Stripe phases in the two-dimensional Falicov-Kimball model

The observation of charge stripe order in the doped nickelate and cuprate materials has motivated much theoretical effort to understand the underlying mechanism of the stripe phase. Numerical studies of the Hubbard model show two possibilities: (i) stripe order arises from a tendency toward phase separation and its competition with the long-range Coulomb interaction or (ii) stripe order inherently arises as a compromise between itinerancy and magnetic interactions. Here we determine the restricted phase diagram of the two-dimensional Falicov-Kimball model and see that it displays rich behavior illustrating both possibilities in different regions.     

Correlations of particle orientation in monolayer films

Two-dimensional and three-dimensional models of an extended layer that consists of orientation-ally ordered particles are used to describe the ordering in monolayer films. In both models, when the distance between particles of the layer increases, the correlation function decreases to zero (for the parameter of adhesion to the substrate a = 0) or remains constant (for a ≠ 0, i.e., when the energy of interaction between the particles and the substrate is taken into account). In the latter case, this means that the layers have a long-range orientation order. The proposed models of an extended monolayer can be used to interpret data obtained by the light scattering and molecular dynamics methods for Langmuir-Blodgett films with the adhesion parameter a = 0.05 and the particle-particle interaction parameter b = 0.6 in the three-dimensional model or b = 1 in the two-dimensional model. The smaller value of b in the three-dimensional layer model can be explained by a stronger effect of cooperation of particle-particle interactions as compared to the two-dimensional layer model.     

Dynamical Aspects of Mean Field Plane Rotators and the Kuramoto Model

The Kuramoto model has been introduced in order to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc. We look at the Kuramoto model with white noise forces: in mathematical terms it is a set of N oscillators, each driven by an independent Brownian motion with a constant drift, that is each oscillator has its own frequency, which, in general, changes from one oscillator to another (these frequencies are usually taken to be random and they may be viewed as a quenched disorder). The interactions between oscillators are of long range type (mean field). We review some results on the Kuramoto model from a statistical mechanics standpoint: we give in particular necessary and sufficient conditions for reversibility and we point out a formal analogy, in the N→∞ limit, with local mean field models with conservative dynamics (an analogy that is exploited to identify in particular a Lyapunov functional in the reversible set-up). We then focus on the reversible Kuramoto model with sinusoidal interactions in the N→∞ limit and analyze the stability of the non-trivial stationary profiles arising when the interaction parameter K is larger than its critical value K _c . We provide an analysis of the linear operator describing the time evolution in a neighborhood of the synchronized profile: we exhibit a Hilbert space in which this operator has a self-adjoint extension and we establish, as our main result, a spectral gap inequality for every K>K _c .     

Monte Carlo event generator MCMHA for high energy hadron-nucleus collisions and intranuclear cascade interactions

The Monte Carlo event generator for high energy hadron-nucleus (h-A) collisions has been developed, which is based on the multi-chain model. The concept of formation zone and the cascade interactions of secondary particles are properly taken account into this Monte Carlo code. Comparing the results of this code with experimental data, the importance of intranuclear cascade interactions becomes very clear.     

Higher orders in residual two-electron interaction

Precise methods of calculations of many-electron atoms are under intensive development. In such calculations, higher orders of the perturbation theory in regard to residual interaction of electrons should be taken into account. In this study, a model of an atom with two electrons in its core and two valence electrons is considered. In terms of this model, expansion with respect to residual interaction is analyzed for two initial approximations based on the potentials V ⁽²⁾ and V ⁽⁴⁾. It turns out that the higher order corrections are nearly the same in both cases. At the same time, the potential V ⁽²⁾ has a number of advantages.     

The role of hybridization on valence transitions in the spinless Falicov-Kimball model

The spinless Falicov-Kimball model with hybridization is studied in one dimension using small-cluster exact-diagonalization calculations. The resultant exact solutions are used to examine the f-state occupation n ^f as a function of f-level energy E _f, hybridization V and d-f interaction U. In addition, the phase diagram based on the finite-size scaling analysis of the single particle excitation energy is discussed both for the symmetric (E _f = 0) and unsymmetric (E _f ≠ 0) case. A number of remarkable results are found. (i) The f-electron occupation number as a function of E _f changes continuously, confirming renormalization-group results. No discontinuous transitions are observed at finite V. (ii) In the symmetric case the insulating state persists as the ground state for all nonzero V. (iii) Outside the symmetric point the hybridization stabilizes the metallic state for lower V and the insulating state for higher V. (iv) The metal-insulator transition takes place at V = V _c > 0. The values of the critical hybridization strength V _c are of order 10^?2.