Domain wall dynamics of the spin-$\frac{1}{2}$ Ising-like antiferromagnetic chain in presence of Dzyaloshinskii-Moriya interactions

We consider a one-dimensional Ising-like S = \frac12\frac{1}{2} Heisenberg antiferromagnetic Hamiltonian and study the dynamics of domain wall excitations in presence of both uniform and staggered Dzyaloshinskii-Moriya interactions. We obtain dispersion relations and dynamical spin correlation functions, S ^{x x} (q, ω) using the basis of domain wall pair states. It is shown that the line shapes of S ^{x x} (q, ω) are highly asymmetric over the whole Brillouin zone such that the spectral weights mainly concentrate in the low energy side. It is observed that presence of staggered Dzyaloshinskii-Moriya interaction explains the experimental results on the Ising-like antiferromagnetic compounds CsCoCl₃ and CsCoBr₃ very well.     

Motion of bound domain walls in a spin ladder

The elementary excitation spectrum of the spin- \frac12\frac{1}{2} antiferromagnetic (AFM) Heisenberg chain is described in terms of a pair of freely propagating spinons. In the case of the Ising-like Heisenberg Hamiltonian spinons can be interpreted as domain walls (DWs) separating degenerate ground states. In dimension d > 1, the issue of spinons as elementary excitations is still unsettled. In this paper, we study two spin- \frac12\frac{1}{2} AFM ladder models in which the individual chains are described by the Ising-like Heisenberg Hamiltonian. The rung exchange interactions are assumed to be pure Ising-type in one case and Ising-like Heisenberg in the other. Using the low-energy effective Hamiltonian approach in a perturbative formulation, we show that the spinons are coupled in bound pairs. In the first model, the bound pairs are delocalized due to a four-spin ring exchange term in the effective Hamiltonian. The appropriate dynamic structure factor is calculated and the associated lineshape is found to be almost symmetric in contrast to the 1d case. In the case of the second model, the bound pair of spinons lowers its kinetic energy by propagating between chains. The results obtained are consistent with recent theoretical studies and experimental observations on ladder-like materials.     

Dynamical Lie algebra method for highly excited vibrational state of asymmetric linear tetratomic molecules

The highly excited vibrational states of asymmetric linear tetratomic molecules are studied in the framework of Lie algebra. By using symmetric groupU ₁(4)U ₂(4)⊗U ₃(4), we construct the Hamiltonian that includes not only Casimir operators but also Majorana operators M₁₂, M₁₃ and M₂₃, which are useful for getting potential energy surface and force constants in Lie algebra method. By Lie algebra treatment, we obtain the eigenvalues of the Hamiltonian, and make the concrete calculation for molecule C₂HF.     

Quasiclassical Statistical Thermodynamics and New Padé Approximations for the Free Charges in Strongly-Coupled Plasma

HNC equations in combination with effective quasi-classical potentials are used to calculate correlation functions and the thermodynamic properties of the free charges in semi-classical non-degenerate quantum plasmas. The interactions of the free particles are taken into account via effective potentials obtained from the Slater sum method. Analytical formulae reproducing the known limits and the HNC-results are constructed. Finally quantum effects are included as corrections by using known analytical results. This method is used to develope new Padé approximations for the subsystem of the free charges in mass-symmetrical as well as for mass-unsymmetrical hydrogen-like plasmas. The most essential result of our investigations is, that in the classical limit the scaling properties correspond to the OCP, e.g. the thermodynamic functions follow for large coupling strength Γ a Berlin-Montroll-Rosenfeld asymptotics via a Γ + b Γ^v + c ln Γ + d. Including quantum effects, the coefficients depend on the temperature, e.g. the slope a(T) increases with decreasing T converging to the classical limit. The new formulae are compared with earlier variants.     

Binary ionic mixtures and a solvable model

The theory of solutions of McMillan and Mayer is applied to the jellium model of a binary ionic mixture: two species of charged particles, with charges e and Ze, immersed in a neutralizing background. The density ρ₂ of the particles of charge Ze is considered as small, and is used as an expansion parameter. The free energy, the pair distribution functions, the internal energy, and the pressure of the mixture are expressed as power series in ρ₂; the coefficients are integrals of correlation functions defined in the system at ρ₂=0 (the reference system). Explicit expressions are obtained in the two-dimensional case, at a special temperature, since in that case the reference system (the two-dimensional, one-component plasma) is a solvable model.     

Thermodynamic inequalities for molecular fluids

We consider the application of the classical Gibbs inequality for the Helmholtz free energy to a fluid whose potential energy depends on positions and orientations of the constituent molecules. Properties of the given fluid are related to the properties of a corresponding ‘reference’ fluid whose potential is the unweighted orientational average of the given potential. It is shown that Aˇ-A ₀, where A and A ₀ are the free energies respectively of the given and corresponding reference fluids, and that the high temperature limit of A - A ₀ may be either zero or negative infinite, depending on the nature of the potential. As consequences, it is shown that no general inequality exists relating the entropies of these systems, and that the internal energies U and U ₀ are plausibly expected to satisfy Uˇ-U ₀ at sufficiently high temperature. The case for a general inequality relating U and U ₀ is not decided.     

Group theoretical aspects ofU B(6) ⊗U F(20) symmetry limits of IBFM related to theU B(5) andO B(6) limits of IBM

TheU ^B(6)⊗U ^F(20) Bose-Fermi dynamical symmetry of interacting boson-fermion model arises when the odd nucleon occupies single particle orbits withj=1/2, 3/2, 5/2, and 7/2. The subgroup structures ofU ^B(6)⊗U ^F(20) related to theU ^B(5) andO ^B(6) limits of sdIBM (U ^B(6)) are analysed. Broadly speaking,U ^B(6)⊗U ^F(20) admitsU ^BF(5)⊗U _s ^F (4), Spin^BF(5)⊗U _k ^F (5) andU ^BF(5)⊗U _s ^F (2) limits withU ^B(5) core and Spin^BF(6),O ^BF(5)⊗U _s ^F (4), Spin^BF(6)⊗U _k ^F (5) andO ^BF(6)⊗U _s ^F (2) limits withO ^B(6) core respectively. For each of these seven symmetry limits, group chains, quantum numbers labelling the basis states, generators and Casimir operators for the various subgroups and energy formulas are given. Recoupling coefficients (reduced Wigner coefficients) for constructing wavefunctions of low-lying states are tabulated and these will allow (together with sdIBMU ^B(5) andO ^B(6) limit results) one to calculateB(E2)’s,B(M1)’s, one and two nucleon transfer strengths etc. in the seven symmetry limits. Experimental examples for theU ^B(6)⊗U ^F(20) symmetry limits are briefly discussed.     

Calculations of thermal conductivity of complex (dusty) plasmas using homogenous nonequilibrium molecular simulations

The heat conductivity of three-dimensional Yukawa dusty plasma liquids (YDPLs) has been investigated by employing a homogenous nonequilibrium molecular dynamics (HNEMD) technique at a low normalized force field strength (F*). The obtained results for plasma heat conductivity with suitable normalizations are measured over a wide range of various plasma states of the Coulomb coupling (Γ) and screening length (κ) in a canonical ensemble (NVT). The calculations for lattice correlations (Ψ) show that our YDPLs system remains in a nonideal strongly coupled regime for a complete range of Γ. It has been shown that the presented Yukawa system obeys a simple analytical temperature demonstration of λ₀ with a normalized Einstein frequency. The employed HNEMD algorithm is found to have a more efficient method than that of different earlier numerical methods and it gives more satisfactory results for lower to intermediate Γ with small system sizes at low F*. The obtained simulation results at nearly equilibrium F* (=?0.002) are in reasonable agreement with different earlier numerical results and with the present reference set of data showed deviations within less than ±15% for most of the present data points and generally underpredicted the λ₀ by 2–22%, depending on (Γ, κ).     

Stark ladders of resonances: Wannier ladders and perturbation theory

LetH _B be any fixed one-dimensional Bloch Hamiltonian with only the firstm gaps open andH _F=H_B+F_x be the corresponding Stark Hamiltonian. For any positiveF small enoughH _F has onlym ladders of sharp resonances given by the analytic translation method, the decoupled band approximation and the regular perturbation theroy. This way, the Wannier conjecture becomes a definite regular perturbation theory for the Stark ladders as eigenvalues of the translated Hamiltonian.     

On the phase transitions for the electronic excitations in semiconductors

A model Hamiltonian for a system of interacting electrons, holes and Wannier excitons is derived. This system of electronic excitations is assumed to be in a quasi-equilibrium state. With the aid of Bogolubov's variational principal the thermodynamic potential is calculated. Using the most general mean-field Hamiltonian as a trial Hamiltonian, a set of coupled integral equations is obtained for the self-energies. These equations are solved numerically for equal effective masses of the electrons and holes. Below a critical temperature ofk _B T _c0.65E _ex ^b whereE _ex ^b is the exciton binding energy, we find a first order phase transition from an exciton rich phase into a degenerate electron-hole phase. The mechanical and thermal stability of both phases is proven. Below a critical temperaturek _B T _c0.11E _ex ^b the exciton system becomes degenerate (Bose-Einstein condensation). A complete phase diagram of these three phases is given.This is a project of the Sonderforschungsbereich Frankfurt/Darmstadt, financed by special funds of the Deutsche Forschungsgemeinschaft     

Flow equations for the ionic Hubbard model

Taking the site-diagonal terms of the ionic Hubbard model (IHM) in one and two spatial dimensions, as H₀, we employ Continuous Unitary Transformations (CUT) to obtain a “classical” effective Hamiltonian in which hopping term has been renormalized to zero. For this Hamiltonian spin gap and charge gap are calculated at half-filling and subject to periodic boundary conditions. Our calculations indicate two transition points. In fixed Δ, as U increases from zero, there is a region in which both spin gap and charge gap are positive and identical; characteristic of band insulators. Upon further increasing U, first transition occurs at U=Uc₁, where spin and charge gaps both vanish and remain zero up to U=Uc₂. A gap-less state in charge and spin sectors characterizes a metal. For U>Uc₂ spin gap remains zero and charge gap becomes positive. This third region corresponds to a Mott insulator in which charge excitations are gaped, while spin excitations remain gap-less.     

p-Adic string compactified on a torus

U(1) ^xD model with the Villain action on ag-loop generalizationF _g of the Bruhat-Tits tree for thep-adic linear groupGL(2, _p ) is considered. All correlation functions and the statistical sum are calculated. We compute also the averages of these correlation functions forN vertices attached to the boundary ofF _g. When the compactification radius tends to infinity the averages provide theg-loopN-point amplitudes of the uncompactifiedp-adic string theory, in particular forg=0 the Freund-Olson amplitudes.     

Maximal atmospheric neutrino mixing in an <Emphasis Type="Italic">SU</Emphasis>(5) model

We show that maximal atmospheric and large solar neutrino mixing can be implemented in SU(5) gauge theories, by making use of the U(1) _F symmetry associated with a suitably defined family number F, together with a Z₂ symmetry which does not commute with F. U(1) _F is softly broken by the mass terms of the right-handed neutrino singlets, which are responsible for the seesaw mechanism; in additio n, U(1) _F is also spontaneously broken at the electroweak scale. In our scenario, lepton mixing stems exclusively from the right-handed-neutrino Majorana mass matrix, whereas the CKM matrix originates solely in the up-type-quark sector. We show that, despite the non-supersymmetric character of our model, unification of the gauge couplings can be achieved at a scale 10¹⁶ GeV < m _U < 10¹⁹ GeV; indeed, we have found a particula r solution to this problem which yields results almost identical to the ones of the minimal supersymmetric standard model. Received: 29 November 2002 / Published online: 3 March 2003 RID="a" ID="a" e-mail: walter.grimus@univie.ac.at RID="b" ID="b" e-mail: balio@cfif.ist.utl.pt     

Statistics of inter-particle distances and angles in plasmas

Accurate treatment of the plasma density effects requires a detailed knowledge of the spatial distribution of individual ions around a test ion. In the present work, rigorous expressions are derived for the main 2- and 3-particle spatial distribution functions involving the nearest neighbor (NN) and the next-nearest neighbor (NNN) ions. These expressions, valid for both ideal and nonideal plasmas, present the distributions as functionals of the potentials U _NN and U _NNN at the nearest and next-nearest ion locations. All of the distribution functions except one are derived and discussed in the present work for the first time ever. For utilization of our results in practical calculations, we suggest semi-empirical expressions for U _NN and U _NNN in the ion-ion coupling parameter range 0 ?Γ < 1. In order to test the accuracy of our expressions for U _NN and U _NNN we conduct Molecular Dynamics (MD) simulations. The simulations utilize the pure Coulomb particle-particle interaction potentials, regularized at close range to avoid classical Coulomb collapse, and are free from the assumptions made to find U _NN and U _NNN. Thus, the results of the MD simulations provide an independent test of our theoretical results. Excellent agreement has been found between the results of the theory and of the MD simulations. Finally, we outline the implications of the present findings on the problem of tunneling and charge exchange in dense plasmas. Received 27 October 2000 and Received in final form 30 January 2001     

U(1) Invariant $F(\tilde{R})$ Hořava–Lifshitz gravity

This paper is devoted to the study of various aspects of projectable F(R) Hořava–Lifshitz (HL) gravity. We show that some versions of F(R) HL gravity may have stable de Sitter solution and unstable flat-space solution. In this case, the problem of scalar graviton does not appear because flat space is not vacuum state. Generalizing the U(1) HL theory proposed in , we formulate U(1) extension of scalar theory and of F(R) Hořava–Lifshitz gravity. The Hamiltonian approach for such the theory is developed in full detail. It is demonstrated that its Hamiltonian structure is the same as for the non-relativistic covariant HL gravity. The spectrum analysis performed around the flat background indicates the consistency of the theory because it contains a graviton with only transverse polarization. Finally, we analyze the spatially flat FRW equations for U(1) invariant F(R) Hořava–Lifshitz gravity.     

Electron capture in the ion-cluster collision: effect of the electronic interaction

We investigate the electron capture occurring in the collision between an ion A⁺ and a cluster A_n (n = 5). The process has been modelled within the Hubbard Hamiltonian,which takes into account the intrasite U electron correlation. An exact procedure has been numerically applied which involves all the excited states to examine the time evolution of the system during the collision. We have applied the model to the sodium case. We have investigated the time evolution of the electron population during the collision on the projectile versus the kinetic energy of the projectile. It displays some oscillations which means that the electron exchanges between the ion and the cluster occurs alternatively in one direction and the other. We also vary U and examine its influence on the dynamics of the oscillation of the average population. Finally the cross section is derived versus the energy and U. Received 29 November 2000     

Duality relations for asymmetric exclusion processes

We derive duality relations for a class ofU _q [SU(2)]-symmetric stochastic processes, including among others the asymmetric exclusion process in one dimension. Like the known duality relations for symmetric hopping processes, these relations express certainm-point correlation functions inN-particle systems (Nm) in terms of sums of correlation functions of the same system but with onlym particles. For the totally asymmetric case we obtain exact expressions for some boundary density correlation functions. The dynamical exponent for these correlators isz=2, which is different from the dynamical exponent for bulk density correlations, which is known to bez=3/2.     

Lower and upper variational bounds in calculations of Coulomb and nuclear systems

All formulas that are necessary for deriving not only upper (E _U) but also lower (E _L) variational bounds on the energy of systems featuring a few nonrelativistic particles are obtained with trial functions in the form of expansions in multidimensional Gaussian functions or exponentials. For potentials that are used most widely, all matrix elements are expressed in terms of known functions, a circumstance that simplifies considerably relevant numerical calculations. This is so for systems featuring an arbitrary number of particles in the case of a Gaussian basis and for three-particle systems in the case of an exponential basis. Numerical results for E _U and E _L, which are characterized by record accuracies, are presented for some Coulomb and nuclear systems such as the He atom; the e ⁺ e ^? e ^?, ppμ^?, 3α, and 4α systems; and hypertritium (pnΛ). Lower bounds with exponential trial functions are obtained for the first time (the corresponding formulas are presented for the first time as well); for a Gaussian basis, lower bounds for Coulomb systems have not been known either. Given E _L and E _U, limits within which the exact value of energy, E ₀, lies can be indicated with confidence. Moreover, an analysis of the correlation between E _L and E _U with increasing number of terms in the expansion of the trial function makes it possible to improve the accuracy (at least by one order of magnitude) of the value E _∞ extrapolated to infinity. By considering specific examples, it is shown that the exponential basis is advantageous in relation to the Gaussian one.