Showing papers in "European Physical Journal B in 1984"
TL;DR: In this article, the dynamics of diffusively coupled strange attractors are studied and the stability of this state depends on the relation between the Lyapunov exponent and the coupling constant, and statistical properties are determined for weakly inhomogeneous disturbances near a stable homogeneous regime.
Abstract: This paper deals with the dynamics of diffusively coupled strange attractors. Such interaction tends to equalize their instantaneous states and, for large coupling constant, results in a homogeneous state that is chaotic in time. The stability of this state depends on the relation between the Lyapunov exponent and the coupling constant. Statistical properties are determined for weakly inhomogeneous disturbances near a stable homogeneous regime. The inhomogeneous state beyond the stability threshold is treated by using the mean-field approximation. We show that both cases of soft (supercritical) and hard (subcritical) excitation of the inhomogeneous state may occur.
250 citations
TL;DR: In this article, the renormalization group equations, including both localization effects and Coulomb correlations, are derived, and the spin density correlation function reveals that the system exhibits a tendency for spin density rearrangement.
Abstract: Interacting electrons, diffusing in a two-dimensional (2d) disordered system, are studied. The renormalization group equations, including both localization effects and Coulomb correlations, are derived. We encounter a qualitatively new situation: the constants describing electron interaction diverge as a result of the renormalization when a certain scale is achieved, whereas the resistence proves to be finite. Calculation of the spin density correlation function reveals that the system exhibits a tendency for spin density rearrangement.
209 citations
TL;DR: In this article, a phenomenological stochastic model of the process of thermal and quantal fluctuations of a damped harmonic oscillator is presented, and the divergence of the momentum dispersion associated with the Markovian limit is removed by a Drude regularization.
Abstract: A phenomenological stochastic modelling of the process of thermal and quantal fluctuations of a damped harmonic oscillator is presented. The divergence of the momentum dispersion associated with the Markovian limit is removed by a Drude regularization. The variances of position and momentum are evaluated in closed form at arbitrary temperature and for arbitrary damping. Properties of real and imaginary time correlation functions are discussed, and a spectral decomposition of the equilibrium density matrix is given.
197 citations
TL;DR: In this paper, an attempt is made to explain the occurrence of superconductivity in Kondo lattice systems with special reference to CeCu2Si2 with the Fermi liquid approach.
Abstract: An attempt is made to explain the occurrence of superconductivity in Kondo lattice systems with special reference to CeCu2Si2. Starting point is the Fermi liquid approach. It is generalized from a Kondo impurity to the Kondo lattice by means of the Korringa-Kohn-Rostocker method. From it a hybridization model is derived and discussed in detail. Two electron-phonon mechanisms are investigated which appear in Kondo lattices. One results from the additional phase shifts caused by the Kondo ions while the other is responsible for the so-called Kondo volume collapse. It is shown that the latter is sufficiently strong in order to explain why CeCu2Si2 is a superconductor while LaCu2Si2 is not. An estimate for the superconducting transition temperatureT
c produces the right order of magnitude.
177 citations
TL;DR: In this paper, a stochastic formulation of the stability of nonequilibrium states is discussed, including the effect of both the macroscopic evolution and of the fluctuations, and an entropy balance equation is derived.
Abstract: A stochastic formulation of the stability of, nonequilibrium states is discussed. An entropy balance equation, including the effect of both the macroscopic evolution and of the fluctuations is derived. In the linear region of thermodynamics Prigogine's minimum entropy production, theorem is extended to include the effect of fluctuations. The latter are shown to reinforce the return of the system to its steady state distribution.
145 citations
TL;DR: In this article, a one-dimensional bistable flow driven by additive, exponentially correlated Gaussian noise is considered and the small relaxation time Fokker-Planck approximations, widely used in the recent literature, are derived and possible shortcomings of those approximation schemes are discussed.
Abstract: A one-dimensional bistable flow driven by additive, exponentially correlated Gaussian noise is considered. The small relaxation time Fokker-Planck approximations, widely used in the recent literature, are derived and possible shortcomings of those approximation schemes are discussed. In particular, it is pointed out that higher order non-Fokker-Planck type contributions are generally of the same order as the Fokker-Planck terms. In principle, those contributions cannot be neglected if the global behavior of the probability solutions is to be described accurately. The result for the activation rate (Arrhenius factor), as evaluated from the approximative Fokker-Planck schemes, does not coincide in leading order in the correlation time τ of the noise with a computer simulation of the rate at low noise level. This result indicates that the wings of the stationary probability\(\bar p(x)\) are in leading order in τ not recovered correctly from the approximative Fokker-Planck schemes. Some implications of our study for adiabatic elimination procedures are also discussed.
142 citations
TL;DR: In this article, the relation between classical and quantum mechanical integrability is investigated for a boson mode coupled to a two-level system, and different semi-classical approximations of this system are obtained by factorization of expectation values of the two-state variable and the boson.
Abstract: The relation between classical and quantum mechanical integrability is investigated for a boson mode coupled to a two-level system. Different semi-classical approximations of this system are considered which are obtained by (i) factorization of expectation values of the two-state variable and the boson, (ii) making a WKB-type approximation, (iii) replacing the boson by a classical field of constant amplitude and fixed frequency and (iv) putting the boson into a self-consistent coherent state. The results vary considerably and include cases of non-integrable and integrable classical dynamics. Quantum mechanically the system is found to satisfy a criterion of quantum mechanical integrability, which we formulate, but the separated Hamiltonian of the boson alone does not have a well-defined classical limit. Numerical results for the energy spectrum and expectation values are obtained, which show a high degree of regularity but also display overlapping avoided crossings usually associated with non-integrable Hamiltonians. The exact dynamics of the occupation probabilities of the two levels is also analysed numerically. The dependence of quantum mechanical recurrence effects (in quantum optics known as revivals) on coupling strength, frequency detuning and initial conditions is studied. The revivals are found to disappear in the case of strong coupling. The Fourier spectra of the dynamical expectation values are also calculated
136 citations
TL;DR: In this article, a mathematical model for a nonlinear equation of motion for correlation functions is considered which describes the essential features of the self consistent current relaxation theory for a system experiencing some interaction with a static random field in addition to some quadratic self interaction.
Abstract: A mathematical model for a nonlinear equation of motion for correlation functions is considered which describes the essential features of the self consistent current relaxation theory for a system experiencing some interaction with a static random field in addition to some quadratic self interaction. It is shown that the plane spanned by the two coupling parameters is separated into a region of ergodic motion and another region where the motion is nonergodic. At the separation line of the two phases all correlation functions can be discussed in terms of scaling laws. The critical exponents vary along the separation line continuously and they can be evaluated explicitely. The separation line consists of two pieces. Transitions across the first piece are characterized by a polarization catastrophy, by a vanishing of the transport coefficient and by a diverging low frequency spectrum ruled by one critical frequency scale. Transitions across the second piece do not exhibit a polarization divergence but show also a power law decrease to zero of the transport coefficient. The low frequency spectrum is the sum of two diverging parts. Each part is described by a scaling law, but the scaling frequencies and the scaling functions are quite different.
122 citations
TL;DR: The exact solution of the Kondo model forn-flavours of electrons with the spin 1/2 scattered by the S-spin impurity is presented in this article. But it is not shown that atn>2S the effective exchange coupling approaches a finite fixed point as the energy scale decreases.
Abstract: The exact solution of the Kondo model forn-flavours of electrons with the spin 1/2 scattered by theS-spin impurity is presented. Forn=2S=5 the model describes manganese impurities dissolved in a metal. It is shown that atn>2S the effective exchange coupling approaches a finite fixed point as the energy scale decreases. It means that atn>2S the Gell-Mann-Low function turns to zero in this point and the scaling behaviour of physical quantities is observed. The scaling behaviour, first obtained in the 1D quantum field theory, can be analyzed on the basis of the exact solution. In the casen≦2S the effective coupling becomes infinitely strong at low energies.
111 citations
TL;DR: In this article, the zero temperature limit of the self-consistent perturbation theory of a degenerate Anderson impurityin a metal is partially solved with analytical methods, and the energy scales relevant to the system are made explicit and closed expressions are derived for the local level propagator around the Fermi energy and for the dynamical susceptibility.
Abstract: The zero temperature limit of the self-consistent perturbation theory of a degenerate Anderson impurityin a metal is partially solved with analytical methods. In particular, the energy scales relevant to the system are made explicit and closed expressions are derived for the local level propagator around the Fermi energy and for the dynamical susceptibility. Results are compared with what is known from Fermi liquid theory. The argument that the theory is valid for large degeneracy is disturbed by certain pathologies.
106 citations
TL;DR: In this article, the mean field equations of the simple cubic or tetragonal ANNNI model are studied on finite lattices and structure combination branching processes are found which allow to considerably refine previous mean field calculations on the model.
Abstract: The mean field equations of the simple cubic or tetragonal ANNNI model are studied on finite lattices. Structure combination branching processes are found which allow us to considerably refine previous mean field calculations on the model.
TL;DR: In this article, the vibration spectra of α and β-phase PdH(D)x have been measured by neutron inelastic scattering and it was shown that the potentials for hydrogen and deuterium are very similar and strongly anharmonic.
Abstract: The vibration spectra of α and β-phase PdH(D)x have been measured by neutron inelastic scattering. From a detailed analysis of the spectra, we conclude that the potentials for hydrogen and deuterium are very similar and strongly anharmonic. The results show definitively that anharmonicity is the principal contribution to the anomalous isotope dependence of the superconducting transition temperature in PdH(D).
TL;DR: In this article, low frequency elastic properties of dielectric, normal conducting and superconducting metallic glasses at audio-frequencies (f≃1 kHz) and temperatures down to 10 mK were investigated.
Abstract: We have measured the low frequency elastic properties of dielectric, normal conducting and superconducting metallic glasses at audio-frequencies (f≃1 kHz) and temperatures down to 10 mK. Our results are discussed in the framework of the tunneling model of glasses. The major assumption of the tunneling model regarding the tunneling states with long relaxation time has been verified, but discrepancies to high frequency measurements have been found. In addition, our experiments on superconducting metallic glasses seem to indicate that the present treatment of the electron-tunneling state interaction is not sufficient.
Abstract: Etude des proprietes dynamiques des systemes a valence fluctuante au zero absolu. Des resultats numeriques extensifs sont rapportes pour les densites d'etats 4f et la susceptibilite magnetique. Ces resultats correspondent a la fois aux problemes de la valence intermediaire et de valence entiere de systemes a impurete cerium
TL;DR: In this paper, the tunnelling and torsional motions of methyl groups in lithium acetate dihydrate (CH3COOLi·2H2O) have been studied in detail by incoherent inelastic neutron scattering.
Abstract: The tunnelling and torsional motions of methyl groups in lithium acetate dihydrate (CH3COOLi·2H2O) have been studied in detail by incoherent inelastic neutron scattering. The results are interpreted by a model of pairs of methyl groups performing a coupled tunnelling motion. The strength of the coupling term is estimated to be about twice as strong as the threefold hindering barrier for the single particle motion.
TL;DR: In this paper, the elastic constants of CeB6 were determined by ultrasonic and Brillouin scattering measurements, and all elastic constants were found to be positive, especially c12.
Abstract: Elastic constants of CeB6 were redetermined by ultrasonic and Brillouin scattering measurements. We found all elastic constants to be positive, especiallyc12. The temperature and magnetic field dependence of the elastic modesc44 and (c11-c12)/2 is explained on the basis of the newly proposed crystalline-electric-field level scheme for CeB6 with theΓ7 level 545 K above theΓ8 ground state. The deduced quadrupolar coupling constants give an antiferroquadrupolar ordering temperature of 3.3 K in agreement with experiment.
TL;DR: In this paper, a one-dimensional dynamic Ginzburg-Landau theory of the martensitic phase transition in shape-memory alloys is established, and nonlinear equations of motion yield solitary wave solutions of kink and of soliton type.
Abstract: A one-dimensional dynamic Ginzburg-Landau theory of the martensitic phase transition in shape-memory alloys is established. The nonlinear equations of motion yield solitary wave solutions of kink and of soliton type. The kink solutions which cannot move without external force represent single domain walls either between austenite and martensite or between two martensite variants. The soliton solutions correspond to a matrix of austenite or of martensite containing a moving sheet of the other phase. The velocity of the solitons depends on their amplitude. In the static case they reduce to the critical nucleus. The energy of each type of solitary waves is calculated.
TL;DR: In this paper, specific heat and dielectric constants of Metmyoglobin at low temperatures were measured and found to be similar to those of amorphous dielectrics, which provides evidence for the existence of two level systems in the protein.
Abstract: Specific heat and dielectric constant of Metmyoglobin crystals at low temperatures are measured and found to be similar to those of amorphous dielectrics. This provides evidence for the existence of two level systems in the protein. Possibility of many conformational substates and the frozen in disorder in the protein is proposed as the origin of these excitations.
TL;DR: In this article, single-hump 1−d maps are investigated which generate ergodic process on an interval mapped everywhere two-to-one onto itself, and it is shown that such maps are related by smooth transformations to each other.
Abstract: Single-hump 1−d maps are investigated which generate ergodic process on an interval mapped everywhere two-to-one onto itself. Introducing a new transformation transverse to conjugation it is shown that such maps are related by smooth transformations to each other. It is found that each of the families consisting of conjugate maps contains a map everywhere expanding and producing ergodic iterations according to the uniform probability density. The general framework is used to construct maps together with their probability density functions. Quantities characterizing the dynamics are calculated and their parameter dependence while maintaining the fully developed chaotic state is studied. Furthermore, universal maps exhibiting fully developed chaos are considered.
TL;DR: In this article, the transverse auto-correlation functions of the spin at the modified bond were considered at T = 0 and their asymptotic time dependence was determined, and the results were applied to other one-and two-dimensional problems.
Abstract: We study the isotropic spin one-half XY-chain with one arbitrarily modified coupling. The transverse auto-correlation functions of the spin at the modified bond are considered atT=0 and their asymptotic time dependence is determined. The results are applied to other one- and two-dimensional problems.
TL;DR: In this article, the authors calculate the time dependent wave function and energy spectrum resulting from the passage of a monoenergetic (plane wave) neutron beam through a chopper consisting of a slit with time dependent width.
Abstract: We calculate the time dependent wave function and energy spectrum resulting from the passage of a monoenergetic (plane wave) neutron beam through a chopper consisting of a slit with time dependent width. Experimental possibilities of observing the predicted effects are discussed. A new type of inelastic scattering spectrometer involving the use of frame overlap in a time of flight instrument is proposed.
TL;DR: In this paper, the authors give a theoretical explanation of the T 1.3 dependence of the holewidth, which is based on the strain field coupling between impurity molecules and two-level tunneling states leading to a kind of "spectral diffusion" of the optical excitation energy.
Abstract: Recently photochemical holeburning experiments have been carried out in organic glasses down to 0.4 K. Here we give a theoretical explanation of theT1.3-dependence of the holewidth. It is based on the strain field coupling between impurity molecules and two-level tunneling states leading to a kind of “spectral diffusion” of the optical excitation energy.
TL;DR: In this paper, the authors studied the cross-section for x-ray scattering under conditions of total reflection on surfaces of semi-infinite systems undergoing a continuous phase transition in the bulk.
Abstract: We study the cross-section for x-ray scattering under conditions of total reflection on surfaces of semi-infinite systems undergoing a continuous phase transition in the bulk. Because of their finite penetration, totally reflected x-rays probe the local surface order parameter and its critical fluctuations. The angular and temperature dependence of the scattered intensity gives experimental access to several critical surface exponents.
TL;DR: In this article, the critical behavior of the hamiltonian model was analyzed and the critical behaviour of the model was found to be identical to the spherical model and the model ind = r+1 dimensions.
Abstract: The spherical model ind=r+1 dimensions is treated using the hamiltonian formulation. The critical behaviour of the model is obtained and is found to be identical to the spherical model.
TL;DR: In this article, a general formula for the decay rate at finite temperatures is obtained by a method which is based on the framework recently described by Caldeira and Leggett, where the form of the potential enters only through the frequency of small oscillations about the metastable minimum and the "length" of the zero temperature bounce trajectory.
Abstract: The quantum decay of a metastable system which interacts with an environment at temperatureT is considered. A general formula for the decay rate at finite temperatures is obtained by a method which is based on the framework recently described by Caldeira and Leggett. The thermal enhancement of the tunnelling rate at low temperatures is discussed for arbitrary metastable potentials, and it is found that the exponent of the rate obeys a power law in a dissipative system. The power law exponent is shown to be a characteristic feature of the dissipative mechanism. Finally, a universally valid formula for the thermal enhancement factor is given, where the form of the potential enters only through the frequency of small oscillations about the metastable minimum and the “length” of the zero temperature bounce trajectory.
TL;DR: In this article, a renormalized perturbation theory for the Anderson lattice model with phonons was proposed to take into account the coupling mediated by breathing of rare earth ions and the effect of strong local Coulomb correlations on these ions.
Abstract: The phenomenon of Heavy Fermion Superconductivity in Kondo lattice systems is investigated via renormalized perturbation theory for the Anderson lattice model with inclusion of phonons. It is demonstrated how the conventional theory of superconductivity can be modified to take into account the coupling mediated by breathing of Rare Earth ions and the effect of strong local Coulomb correlations on these ions. The results give support to a recent theory of Razafimandimby, Fulde and Keller, which is based on an intermediate Fermi liquid picture.
TL;DR: In this article, the effect of heatbaths is taken into account by means of damping terms and fluctuating forces, and the resulting semiclassical equations are solved for the stationary state.
Abstract: We start from the microscopic Hamiltonian formulated by means of creation and annihilation operators for the field modes, and creation and annihilation operators for the electrons. The virtual transitions via the intermediate atomic level are eliminated by second order perturbation theory so that an effective Hamiltonian results which describes two-photon creation or annihilation. In the next step Heisenberg equations of motion are derived for the field amplitudes, the atomic dipole moments, and the inversion. The effect of heatbaths is taken into account by means of damping terms and fluctuating forces. In the present paper these equations are averaged over the fluctuating forces and the resulting semiclassical equations are solved for the stationary state. We treat the degenerate and nondegenerate case including detuning and atomic levels with homogeneous and inhomogeneous broadening. The field modes may be either running or standing waves. A detailed discussion of the laser condition is given.
TL;DR: In this paper, the temperature dependence of the exchange splitting of Ni in the temperature range 0.5≦T/Tc≦0.94 was investigated and it was shown that transverse and longitudinal spin fluctuations are responsible for the broadening of the spin-resoived energy distribution curves.
Abstract: Using spin-polarized photoemission with high energy- and angle resolution (ΔE=100 meV, ΔΘ=±3°) we have investigated the temperature dependence of the exchange splitting of Ni in the temperature range 0.5≦T/T
c≦0.94. At room temperature we findΔ
ex=0.18 eV for the exchange splitting of theS
4 band at theX point of the Brillouin zone. With increasing temperature the total (spin-averaged) energy distribution shows a narrowing and merges into one peak. The spin-resolved energy distribution curves approach each other and are strongly broadened. A discussion of the data within current theories of itinerant electron magnetism is given. The spectra indicate that neither the pure Stoner model nor the prediction of local band theory, assuming a temperature independent exchange splitting are justified for Ni. We conclude that the exchange splitting decreases with increasing temperature and that transverse as well as longitudinal spin fluctuations are responsible for the broadening of the spin-resoived energy distribution curves.
TL;DR: In this paper, a non-linear partial differential equation describing the temperature field is used to calculate the evolving convection patterns in different geometries, e.g. of rolls or hexagons.
Abstract: Using a recently derived non-linear partial differential equation describing the temperature field we have performed computer calculations on the evolving convection patterns in different geometries. In this way we calculate the generation of various patterns e.g. of rolls or hexagons.