The uniformly driven kink in the damped φ4-chain

The motion and the linear modes of a uniformly driven kink (domain wall) in the damped ⁴-chain are examined in classical continuum approximation. The model-specific component of the Büttiker-Thomas formula (yielding the velocity-field characteristic of a kink driven between two different domains of a multistable system) is calculated explicitly. Similarly to the free ⁴-kink, the driven ⁴-kink is linearly stable. We find, however, that the (single) bound state of the free kink can only survive in the driven and damped system below a critical strengthF _c of the driving field, where (i.e. forF<F _c<F _max) it is splitted off in two localized relaxation modes. The only localized modes present in the whole existence domainF<F _max of the driven kink are (1) the zero frequency translation mode and (2) the inertia mode, which is a universal smooth relaxation mode of the driven kinks in all the linearly damped multistable systems. Further key words: Landauer formula (mobility), nerve impulses, Schlögl model, Rosen-Morse potential.Work supported by the Swiss National Science Foundation     

Ground state of spin liquids,hole-hole attraction and high-T csuperconductivity

We develop a notion of high-T _csuperconductivity, which considers that phenomenon as a general property of close to half-filled bands of strongly correlated electrons confined to low-dimensional orbital lattices. Based on Andersons suggestion [1] we initially investigate the Cud electron system of the undoped mother substances of the high-T _c superconductors in the framework of the spin 1/2 Heisenberg model. We derive a new representation of the corresponding Hamiltonian in terms of triplet quasi-particles. The triplet representation leads to simple physical pictures for the spin liquid state and to a hierarchy of nearly exact variational wave functions for the ground state of the linear chain. These wave functions are employed as vacuum states for doping with holes. Holes are shown to form a conduction band embedded in the Hubbard-Mott insulating phase of strongly correlated electrons. The chemical binding forces among these localized electrons entail a strong attractive pair potential acting between the mobile defects. The generality of the hole-hole attraction and its independence of a strict localization of the electrons in the Hubbard-Mott phase is demonstrated by nearly exact solutions of the Hubbard and Pariser-Parr-Pople models of small regular electron chains at various degrees of electron correlation. It is suggested that this exchange-driven attraction leads to an instability of the free hole gas towards Cooper pair formation.     

Gap and out-gap breathers in a binary modulated discrete nonlinear Schrödinger model

We consider a modulated discrete nonlinear Schrödinger (DNLS) model with alternating on-site potential, having a linear spectrum with two branches separated by a forbidden gap. Nonlinear localized time-periodic solutions with frequencies in the gap and near the gap -- discrete gap and out-gap breathers (DGBs and DOGBs) -- are investigated. Their linear stability is studied varying the system parameters from the continuous to the anti-continuous limit, and different types of oscillatory and real instabilities are revealed. It is shown, that generally DGBs in infinite modulated DNLS chains with hard (soft) nonlinearity do not possess any oscillatory instabilities for breather frequencies in the lower (upper) half of the gap. Regimes of exchange of stability between symmetric and antisymmetric DGBs are observed, where an increased breather mobility is expected. The transformation from DGBs to DOGBs when the breather frequency enters the linear spectrum is studied, and the general bifurcation picture for DOGBs with tails of different wave numbers is described. Close to the anti-continuous limit, the localized linear eigenmodes and their corresponding eigenfrequencies are calculated analytically for several gap/out-gap breather configurations, yielding explicit proof of their linear stability or instability close to this limit.Received: 31 October 2003, Published online: 17 February 2004PACS: 63.20.Pw Localized modes - 63.20.Ry Anharmonic lattice modes - 42.65.Wi Nonlinear waveguides     

Effects of the coulomb interaction on the 2D localized modes of soliton in the photoexcited polyacetylene

We have studied the effects of electron-electron interaction on the 2D localized modes of a soliton using the two-dimensional model that includes the bond-bending term and pinning effects in the photoexcited samples. The result shows that seven localized modes always exist, but the frequencies slightly move for different parameter and their localization are strengthened.     

Theoretical analysis of acoustic-optic frequency shifter by dual mode fiber

The frequency shifting between two modes in an optical fiber resulting from acoustic wave propagation has been studied theoretically. Our theoretical results confirm the earlier experimental work. The polarization effect introduced by acoustic waves has been examined as well. The analysis shows that the polarization characteristic and symmetry property of the modes are not preserved in the coupling process of acoustic-optic frequency shifting for arbitrary ratio of the fiber cladding radius to the acoustic wavelengthd/ _a, in contrast to stable mechanical microbending, and that for the givend/ _a = 0.397, the polarized light signal at frequency ₂, shifted from that at frequency ₁, is quasi-linearly polarized for any acoustic-optic interaction length. However, the polarization effect can be neglected when the fiber cladding radius is much smaller than the acoustic wavelength.     

Network-theoretical model of the gyrotron oscillator part II: Empty cavity oscillation modes

A network-theoretical model of the gyrotron has been elaborated which is both conspicious and rigorous. The electromagnetic field in the presence of the electron beam, to be determined in a self-consistent calculation, might be regarded as an abstract vector in infinite-dimensionalHilbert space. In the first part of this paper, a method was described to determine the oscillation modes of empty gyrotron cavities. Once these oscillation modes are known, their fields can be used as the coordinate system for the representation of this vector. In this representation,Maxwell's equations reduce to a system of ordinary differential equations — the so-called resonator equations, describing the linear dependence of the field amplitudes on the excitation coefficients. They are readily solved in the frequency domain. The solution can be represented as a parallel resonance circuit, if the mode amplitudes are identified with equivalent voltages, and the exciation coefficients with equivalent currents.The nonlinear dependence of the excitation coefficients on the mode amplitudes, on the other hand, is then identified with the device (or electron beam) admittance. The latter is determined numerically, for a number of points in the amplitude-frequency plane, and subsequently represented in the frequency domain. In order to efficiently compute the device admittance, the coordinates are transformed into the electron beam frame, and afterwards an averaging method is applied. The interaction of these admittances determines the behaviour of the gyrotron.     

Coherent and incoherent exciton motion in a linear chain: Solution of the Haken-Strobl-model

The model of Haken and Strobl describing the coupled coherent and incoherent exciton motion in molecular crystals is solved for a linear chain with next-nearest-neighbour interaction. The well-known solutions of the two limiting cases are recovered. Our solution consists of two parts: one describing damped oscillations and the other describing pure damping. Introducing a new quantityA, called degree of incoherence, we may show that the relative size of the two parts of the solution depends onA in a well defined manner. Our solution can be immediately applied to the calculation of correlation functions for the following experiments: diffusion, optical absorption and emission, NMR and ESR.Part of a PhD thesis, Universität Stuttgart (1974).     

Reversible dynamics and the macroscopic rate law for a solvable Kolmogorov system: The three bakers' reaction

We investigate a piecewise linear (area-preserving) mapT describing two coupled baker transformations on two squares, with coupling parameter 0c1. The resulting dynamical system is Kolmogorov for anyc0. For rational values ofc, we construct a generating partition on whichT induces a Markov chain. This Markov structure is used to discuss the decay of correlation functions: exponential decay is found for a class of functions related to the partition. Explicit results are given forc=2^–n. The macroscopic analog of our model is a leaking process between two (badly) stirred containers: according to the Markov analysis, the corresponding progress variable decays exponentially, but the rate coefficients characterizing this decay are not those determined from the one-way flux across the cell boundary. The validity of the macroscopic rate law is discussed.     

Parametric excitation of spherical modes in ferromagnetic spheres by perpendicular and parallel pumping

The fine structures of the threshold of subsidiary absorption and parallel pumping, observed on highly polished YIG spheres in 1975 by W. Jantz et al., are discussed with a model which uses instead of plane spin-waves the true modes regarding the shape of the sphere. These spherical modes are magnetostatic modes taking additionally the exchange interaction into account. At the closely spaced resonances of the fine structure of parallel pumping single spherical modes with angular-momentum quantum numberm=0 are excited, whereas at the resonances of subsidiary absorption pairs of spherical modes with big angular-momentum quantum numbers (|m|1000) satisfying the selection rulem+m=1 are excited. The analysis of the fine structure of subsidiary absorption shows that in regimes where the plane wave approximation predicts the excitation of spin-waves with formalk0, modes withk1.5·10⁵ cm^–1 have the lowest threshold. This discrepancy is discussed with the effect of surface pit scattering, which increases the threshold of modes withk < 2/_pit, where _pit is a typical size of the surface pits. Consequently modes withk22/_pit instead ofk0 have the lowest threshold.     

Electron quasi-confined-optical-phonon interactions in wurtzite GaN/AlN quantum wells

The equation of motion for the p-polarization field in a wurtzite GaN/AlN multilayer heterostructure is solved for the quasi-confined-optical-phonon modes based on the dielectric-continuum model and Loudons uniaxial crystal model. The polarization eigenvector, the dispersion relation of the quasi-confined-optical-phonon modes and the electron-quasi-confined-phonon interaction Fröhlich-like Hamiltonian are derived. The analytical formulas can be directly applied to single/multiple quantum wells (QWs) and superlattices. The electron-quasi-confined-phonon coupling functions are investigated for a given AlN/GaN/AlN single QW with full account of the strains of the QW structures and the anisotropy effect of wurtzite crystals. We find that there are two kinds of quasi-confined-optical-phonon modes in the GaN/AlN QWs: the GaN-layer quasi-confined-optical-phonon modes and the AlN-layer quasi-confined-optical-phonon modes. There are infinite quasi-confined-optical-phonon branches, labelled by a quantum number n (n=1,2,...), with definite symmetry with respect to the center of the AlN/GaN/AlN single QW for a given phonon wave number q. The dispersions of the quasi-confined-optical-phonon modes with smaller n are more obvious than the ones with larger n. Moreover, the modes with smaller n are much more important for their electron-quasi-confined-phonon interactions than those with larger n. In most cases, it is enough to consider the modes with n 8 for the electron-quasi-confined-phonon interactions in a single GaN/AlN QW. The higher frequency modes are more significant than the lower ones. The long-wavelength quasi-confined-optical-phonon modes are much more important for the electron-quasi-confined-phonon interactions. The GaN-layer quasi-confined-optical-phonon energies and their electron-quasi-confined-phonon interaction strength are markedly increased due to the strains of the QW structures. The influence of the strains on the the AlN-layer electron-quasi-confined-phonon interactions can be ignored.     

Thermodynamics of a dense self-avoiding walk with contact interactions

A lattice model is used to study the properties of an infinite self-avoiding linear polymer chain that occupies a fraction, 01, of sites on ad-dimensional hypercubic lattice. The model introduces an (attractive or repulsive) interaction energy between nonbonded monomers that are nearest neighbors on the lattice. The lattice cluster theory enables us to derive a double series expansion in and d^–1 for the chain free energy per segment while retaining the full dependence. Thermodynamic quantities, such as the entropy, energy, and mean number of contacts per segment, are evaluated, and their dependences on, , andd are discussed. The results are in good accordance with known limiting cases.     

Groundstate properties of a generalized VBS-model

We study a generalized q-deformed VBS-model. This is a spin-1 quantum antiferromagnet with nearest neighbour interaction on a linear chain. The exact grounstate is determined in the form of a matrix-product of individual site-contributions. All relevant groundstate properties are calculated. The groundstate is unique, it has a finite gap to the excitations, and correlations decay exponentially. Thus the model has all the properties described by Haldane to be generic for certain quantum antiferromagnets with integral spin.Work performed within the research program of the Sonderforschungsbereich 341, Köln-Aachen-Jülich     

Green's functions for body-centred cubic lattices

The presented paper contains the tables of Green's functions for bcc lattices for outband frequencies 1·0/ _m 1·6. The central-force model is used, the interaction with 8 nearest and 6 next-nearest neighbours is considered and the number of different Green's functions is fairly decreased by symmetry. Numerical difficulties arising by computing Green's functions are discussed. The derivation of symmetry relations for a dynamical matrix is generalized for the matrix of Green's functions.     

Arnold resonances and quantum states

The dynamics of one electron interacting with a linear chain of heavy atoms bears a strong similarity with the propagation of a classical wave in a periodic non linear medium. Arnold resonances of the dynamical system play a central role. Some of the quantum states associated with these resonances are delocalized and contribute to phenomena such as Peierls dimerization while other ones are localized and are similar to the gap solitons of the classical wave theory, we call them Braggons. Complex Braggons containing several electrons inside the same localized profile are also described.     

Equations in Dual Variables for Whittaker Functions

It is known that the Whittaker functions w(q) associated with the group GL(N) are eigenfunctions of the Hamiltonians of the open Toda chain, hence satisfy a set of differential equations in the Toda variables q _i . Using the expression of the q _i for the closed Toda chain in terms of Sklyanin variables _i , and the known relations between the open and the closed Toda chains, we show that Whittaker functions also satisfy a set of new difference equations in _i .     

Detailed Examination of Transport Coefficients in Cubic-Plus-Quartic Oscillator Chains

We examine the thermal conductivity and bulk viscosity of a one-dimensional (1D) chain of particles with cubic-plus-quartic interparticle potentials and no on-site potentials. This system is equivalent to the FPU-α β system in a subset of its parameter space. We identify three distinct frequency regimes which we call the hydrodynamic regime, the perturbative regime and the collisionless regime. In the lowest frequency regime (the hydrodynamic regime) heat is transported ballistically by long wavelength sound modes. The model that we use to describe this behaviour predicts that as ω→0 the frequency dependent bulk viscosity, , and the frequency dependent thermal conductivity, , should diverge with the same power law dependence on ω. Thus, we can define the bulk Prandtl number, , where m is the particle mass and k _B is Boltzmann’s constant. This dimensionless ratio should approach a constant value as ω→0. We use mode-coupling theory to predict the ω→0 limit of Pr _ζ . Values of Pr _ζ obtained from simulations are in agreement with these predictions over a wide range of system parameters. In the middle frequency regime, which we call the perturbative regime, heat is transported by sound modes which are damped by four-phonon processes. This regime is characterized by an intermediate-frequency plateau in the value of . We find that the value of in this plateau region is proportional to T ⁻² where T is the temperature; this is in agreement with the expected result of a four-phonon Boltzmann-Peierls equation calculation. The Boltzmann-Peierls approach fails, however, to give a nonvanishing bulk viscosity for all FPU-α β chains. We call the highest frequency regime the collisionless regime since at these frequencies the observing times are much shorter than the characteristic relaxation times of phonons.     

The Generalized Master equation approach to the phonon-assisted hopping

The Generalized Master Equation (GME) approach to the phonon-assisted hopping via localized single-particle states interacting with harmonic phonon continuum is presented. Starting from the Nakajima-Zwanzig form of the GME, the memory functions governing the electron kinetics are evaluated. It is proved that any direct expansion (in powers of the electron-phonon coupling constantg and overlap parameter of localized orbitalsW) of the exponentialexp {–i(1–D) L} (whereL andD are the Liouville and projection superoperators) entering the memory functions is of little use due to the presence of undamped (constant in time) terms (or terms g ²/( + i) singular at + i 0 after taking the Fourier transform). In the memory functions, however, these singular terms are verified to cancel each other at least to the fourth power ofgW. This result enables to justify the usual rate equation for the site occupation probabilities f_m in absence of an external field in the lowest order ingW. Problems with phonon-less contributions to the memory functions (W ² g ⁴) are discussed. The theory applies to the electron (exciton) transport in e.g. disordered semiconductors as well as the hopping via non-degenerated molecular orbitals in finite molecules as long as the heat bath may be approximated by a continuum harmonic phonon field.     

Wave propagation in strongly coupled classical plasmas in an external magnetic field

When a small perturbation is applied to the plasma dispersion, a small shift of frequency due to correlation occurs. This is justified even for strong coupling, since the effect is proportional tok ² (k is the wave vector) and it is sufficient to consider thek 0 limit. Then by solving the dispersion relations for, the shift of frequency due to correlation, at different angles of propagation, we obtain all information needed. The plasma modes in which we are primarily interested are the whistler and the extraordinary modes. In this work the STLS (Singwi, Tosi, Land, and Sjolander) approximation scheme is used. It is seen that the correlational effects enter only through terms of orderk ⁶ for the whistler mode and terms of orderk ² for the nonresonant situation of the extraordinary mode.     

Plasmon and magneto-plasmon excitations in double heterostructures

The plasmon and magneto-plasmon spectra are analyzed for an electron system which consists of two parallel two-dimensional electron layers which are separated from each other by a certain distance2d. Our approach allows to consider these electron liquids to be on different levelsE ₁ andE ₂ and to regard an arbitrary tunneling probabilityt between them. The Coulomb interaction is treated by means of a random-phase approximation. The resulting modes reflect typical features of the system: there are different plasmon branches connected with either the total or the reduced charge density and a further collective mode consisting of electron transitions from one to another electron layer. The influence of a static external magnetic fieldB applied perpendicularly to the electron layers leads to characteristic combinations of the plasmon modes (forB=0) with the cyclotron frequency _c .     

Proving the linear theory of gradiental electrooptical deflectors

The passage of a light ray through an anisotropic medium with a refractivity gradient is analyzed here, on the basis of the Fermi principle, and the results are applied to an electrooptical deflector crystal. Two modes of deflector operation are considered, corresponding to different polarizations of a light ray relative to the plane in which it deflects. It is shown that, when the refractive index varies only little (n/n 1), the linear theory describes very accurately both modes.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 22–25, September, 1974.