Thermo field dynamics of quantum spin systems

Thermo field dynamics of quantum spin systems is formulated, which gives a new variational principle at finite temperatures. The KMS relation is reformulated as identities among thermal vacuum states. Path integral formulations of the thermal vacuum state are given, which yield a new thermo field Monte Carlo method. Thermo field dynamics of finite-spin systems are studied in detail as simple examples of the present method. Pertubational expansion methods of the thermal state and time-dependent state are also given.     

Approximation and Reconstruction of the Electrostatic Field in Wire–Plate Precipitators by a Low-Order Model

The numerical computation of the ionic space charge and electric field produced by corona discharge in a wire–plate electrostatic precipitator (ESP) is considered. The electrostatic problem is defined by a reduced set of the Maxwell equations. Since self-consistent conditions at the wire and at the plate cannot be specified a priori, a time-consuming iterative numerical procedure is required. The efficiency of all numerical solvers of the reduced Maxwell equations depends in particular on the accuracy of the initial guess solution. The objectives of this work are two: first, we propose a semianalytical technique based on the Karhunen–Loève (KL) decomposition of the current density field J, which can significantly improve the performance of a numerical solver; second, we devise a procedure to reconstruct the complete electric field from a given J. The approximate solution of the current density field is based on the derivation of an analytical approximation , which, added to a linear combination of few KL basis functions, constitutes an accurate approximation of J. In the first place, this result is useful for optimization procedures of the current density field, which involve the computation of many different configurations. Second, we show that from the current density field we can obtain an accurate estimate for the complete electrostatic field which can be used to speed up the convergence of the iterative procedure of standard numerical solvers.     

CO adsorption on the Cu(1 1 1) surface: A density functional study

The adsorption of CO on the Cu(1 1 1) surface has been studied with ab initio density functional theory. The adsorbate-metal system was analyzed with the local density approximation, the gradient corrected functional of Perdew and Wang and the B3LYP hybrid functional, for comparison. A slab model was used for the pattern at a coverage of 1/3. The local density approximation and the gradient corrected functional give the fcc site as the favorable adsorption site. In contrast, the B3LYP functional results in the preference of the top site, in agreement with the experiment. These results confirm the suggested explanation for the failure of standard functionals, based on the position of the highest occupied and lowest unoccupied molecular orbital. The results of total energy calculations are presented, together with projected densities of states and Mulliken populations. In addition, the basis set superposition error is discussed for CO/Cu(1 1 1) and for CO/Pt(1 1 1).     

Response function of the second kind in many-body systems

We analyze a new type of response function which portrays the properties of a system perturbed by an external field in terms of the perturbed two-point correlations of density fluctuations rather than in terms of perturbed averages of physical quantities. This response function of the second kind satisfies both fluctuation-dissipation-like theorems, relating it to three-point equilibrium functions, and hierarchical relationship linking it to conventional quadratic (rather than linear) response functions. In the equal-time limit, when the two density fluctuations are observed at the same time, the response function of the second kind is intimately connected to the two-particle correlation function of kinetic theory. This linkage opens an avenue for developing novel approximation techniques for correlated many-body systems.     

Truncation of QCD with four-quark interaction

We examine conditions for models with fourquark interaction and a finite cutoff to be a reasonable approximation to the QCD at low energies. The flavourdependent part of QCD vacuum energy is identified with an effective potential for quark model. The independence on the cutoff and the scale anomaly of QCD is exploited in the quark sector to establish the scaling law for QCD-motivated effective coupling constants. On the contrary the insensitivity of effective potential in respect to intrinsic field dilatations leads to a selection rule for parameters of quark models to make a truncation of QCD.     

Microcanonical density functionals for critical systems: An exact one-dimensional example

Free-energy functionals suitable for describing realistic, nonuniform systems near criticality are discussed with emphasis on the advantages of a local formalism. It is proposed to investigatemicro canonical functionals in which both the usual order-parameter (or magnetization) density m(r)and the local energy density (r), which has independent critical fluctuations, are employed. This approach is tested by an exact calculation of the microcanonical functional [{m}, {}] in the continuum limit for a one-dimensional Ising model. Remarkably, the microcanonical functional is found to be local irrespective of the proximity to the critical point (located at zero temperature and zero field). Furthermore, its form relates closely to the scaling postulate advanced earlier by de Gennes and Fisher and displays features of conformal covariance.     

External Fields, Density Functionals, and the Gibbs Inequality

By combining the upper and lower bounds to the free energy as given by the Gibbs inequality for two systems with the same intermolecular interactions but with external fields differing from each other only in a finite region of space , we show that the corresponding equilibrium densities must also differ from each other somewhere in . We note that the basic equations of density functional theory arise naturally from a simple rearrangement and reinterpretation of the terms in the upper bound Gibbs inequality for such systems and briefly discuss some of the complications that occur when the intermolecular interactions of the two systems also differ.     

The adiabatic approximation for quantum spin systems with a spectral gap

Summary We estimate the accuracy of the adiabatic approximation in predicting the time evolution of local observables for an XY quantum magnet with a slowly variable external magnetic field. The system evolves according to the natural Hamiltonian dynamics and the spectral gap produced by the magnetic field is assumed to be large with respect to the term inducing quantum fluctutions. The proof is based on a finite order truncation of a time dependent cluster expansion in inverse powers of the time scale . In the analytic case, we show that the accuracy of this truncated expansion is of order for any >1. If the time dependent perturbation is suddenly switched on at time zero and switched off at time , the accuracy of the adiabatic approximation is proven to be of orderO( ^–1.     

Quantization as analysis in partial differential varieties

Replacing positive-energy considerations by considerations of invariance under theS-operator, and applying Paneitz' extension of the stability theory of the school of M. G. Krein, a long-sought canonical positive symplectic complex structure in the stable phase space of infinite-dimensional classical field-theoretic systems can be mathematically determined. This almost-Kählerization of the phase space then yields a (positive-definite) infinite-dimensional Riemannian structure that serves to specify formally, and convergently in finite-mode approximation, the physical vacuum measure for functional integrals involved in the associated quantized field. The method applies to a general class of nonlinear wave equations including that of Yang-Mills.Invited talk at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–21, 1981.     

Self-energy-functional approach: Analytical results and the Mott-Hubbard transition

The self-energy-functional approach proposed recently is applied to the single-band Hubbard model at half-filling to study the Mott-Hubbard metal-insulator transition within the most simple but non-trivial approximation. This leads to a mean-field approach which is interesting conceptually: Trial self-energies from a two-site single-impurity Anderson model are used to evaluate an exact and general variational principle. While this restriction of the domain of the functional represents a strong approximation, the approach is still thermodynamically consistent by construction and represents a conceptual improvement of the linearized DMFT which has been suggested previously as a handy approach to study the critical regime close to the transition. It turns out that the two-site approximation is able to reproduce the complete (zero and finite-temperature) phase diagram for the Mott transition. For the critical point at T = 0, the entire calculation can be done analytically. This calculation elucidates different general aspects of the self-energy-functional theory. Furthermore, it is shown how to deal with a number of technical difficulties which appear when the self-energy functional is evaluated in practice.Received: 3 November 2003, Published online: 23 December 2003PACS: 71.10.-w Theories and models of many-electron systems - 71.15.-m Methods of electronic structure calculations - 71.30. + h Metal-insulator transitions and other electronic transitions     

Hybridisation and crystal field in YbPd2Si2

Experimental data in the hybridized compound YbPd₂Si₂ is compared with the results obtained with a recently proposed hybridisation model, based on the large-degeneracy expansion approximation, which takes into account the crystal field splittings of the rare earth ion energy levels. With a unique set of parameters, satisfactory agreement is simultaneously obtained for the thermal variation of the electronic specific heat, of the magnetic susceptibility and of the electric field gradient at the Yb site, as well as for the field variation of the low temperature magnetisation.     

Time and temperature in semi-classical gravity

It is shown how in the functional integral approach, time arises as a natural parametrization for the way matter adiabatically follows gravitational configurations where the latter are treated in the semi-classical approximation. In the presence of horizons this time becomes complex and if the motion is periodic behind the horizon such functional integrals become partition functions. So the functional integral approach naturally associates the very concept of time and horizon thermal radiation.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Weak-noise in nondissipative periodic systems

A class of stochastic differential equations is considered which describe dynamical systems without systematic relaxation terms but subjected to external noise. A stationary distribution is derived in the weak-noise limit and criteria are given in how far this yields an approximation for finite noise stationary distributions. Concerning time dependent behaviour it is shown how reduced statistical information may be drawn from period broadening. As example the harmonic oscillator and a richer non-linear model are discussed.     

Equation of state and symmetry energy within the stability valley

We apply the direct variational method to derive the equation of state for finite nuclei within the stability valley. The extended Thomas-Fermi approximation for the energy functional with Skyrme forces is used. Applying the leptodermous expansion for the profile nucleon densities, we have studied the neutron coat and the isospin symmetry energy for neutron-rich nuclei. Using the equation of state for the pressure, we derive the region of spinodal instability of finite nuclei and its dependence on the mass number, the asymmetry parameter and the Skyrme force parameters. We suggest the procedure of derivation of the isospin symmetry energy from the analysis of the isospin shift of the chemical potential = - beyond the beta-stability line. We show that both the structure of the neutron coat and the position of the drip line depend significantly on the Skyrme force parameters.     

Complete solution of the XXZ-model on finite rings

The thermodynamical properties of the XXZ-model are studied by means of a complete diagonalization of the XXZ-Hamiltonian on rings withN=4,6...16 sites. Based on a finite size analysis we are able to extract the universal term in the free energy as it is predicted by conformal invariance. We also study the finite site scaling properties of the density of states in a properly chosen scaling variable for the excitation energies. The thermal averages of the modulus of the momentum and of the reflection parity appear to be independent of the temperature in the thermodynamical limit.     

Correlations in Ising ferromagnets. III

An inequality relating binary correlation functions for an Ising model with purely ferromagnetic interactions is derived by elementary arguments and used to show that such a ferromagnet cannot exhibit a spontaneous magnetization at temperatures above the mean-field approximation to the Curie or critical point. (As a consequence, the corresponding lattice gas cannot undergo a first order phase transition in density (condensation) above this temperature.) The mean-field susceptibility in zero magnetic field at high temperatures is shown to be an upper bound for the exact result.Research supported in part by the National Science Foundation. Alfred P. Sloan research fellow.     

Thermal fluctuations and ac response of weakly pinned charge density waves

The Fukuyama-Lee theory for the ac response () of weakly pinned charge density waves is extended to include thermal fluctuations. The equation of motion for the local phase includes an extrinsic damping and a distinction is made between static and dynamic parameters in it. It is split into static, thermally fluctuating and response contributions to the phase, respectively. The static problem is treated using a result from Feigel'man's theory which provides a revised value for the weak pinning constant. The impurity averaging of the response equation is performed using the simplifying statistical properties of the stochastic pinning force following Bleher's recent work. The main emphasis is on the treatment of the thermal fluctuations via a thermal field _th. The non-linear Langevin equation for _th is linearized and further simplified by an RPA type approximation which eliminates the impurity fluctuations from _th. The resulting equation is solved exactly. It is shown that the correlation function of the thermal field decays initially with a short time constant. This allows to treat the thermal fluctuations on an equal footing with the impurity fluctuations in the self-consistent Born approximation. The main contribution of the thermal fluctuations results in powers of a thermal factor exp(- _th ² /2) to the first and second order self energies of the phason Green's function. Numerical results due to these modifications are given for (,T). It is found that the absorption peak in Re () broadens and shifts to lower frequencies when the temperature is raised. The corresponding treatment for three spatial dimensional is indicated. The thermal factor is evaluated for this case and differences to Maki's result are noted. The questions of analyticity and conductivity sum rule are also dealt with.Dedicated to Professor Helmut Reik on the occasion of his 60th birthday     

The weak second law of thermodynamics for classical gas in rectangular box

We prove, using the methods of probability theory, that the density of particles in closed classical systems consisting of a finite numberN of non-interacting point particles constrained to move in a rectangular box of the volumeV will approach a uniform density as t , if the initial states of the systems were created by random attribution of positions and velocities to particles. The time evolution of the systems is assumed to be entirely determined by the initial state: the particle dynamics contains no element of randomness. It is shown that if the number of particlesN (V remaining constant), the systems behave thermodynamically, i.e. they do not show any fluctuations of relative density of particles. The proved behaviour serves as the first step in a new approach to mathematically rigorous derivation of the second law of thermodynamics from the classical mechanics which makes no use of thermodynamic limit.     

Structural and electronic properties of matlockite MFX (MSr, Ba, Pb; XCl, Br, I) compounds

First-principles calculations have been used to study the structural and electronic properties of technologically important matlockite compounds MFX (MBa, Sr, Pb; XCl, Br, I) using a full potential linearized augmented plane-wave method within density functional theory. We used the local density approximation and the generalized gradient approximation, as well as the Engel-Vosko's GGA formalism to find the band gap and the partial density of states at equilibrium volume. We also optimized internal parameters by relaxing the atomic positions in the force directions. The calculated total energy allowed us to investigate several structural properties in particular the equilibrium lattice constants a and c, c/a ratio, bulk modulus, pressure derivative of the bulk modulus, cohesive energy, interatomic distances, interlayer distances along c axis and the angles between different atomic bonds. We calculated the valence charge density at the equilibrium volume for BaFCl and PbFCl and concluded that the bonding nature in these compounds is mainly ionic. Results are discussed and compared with experimental and other theoretical data.