Two-dimensional monomer-dimer systems are computationally intractable

The classic problem of counting monomer-dimer arrangements on a two-dimensional lattice is analyzed using techniques from theoretical computer science. Under a certain assumption, made precise in the text, it can be shown that the general problem is computationally intractable. This negative result contrasts with the special case of a system with monomer density zero, for which efficient solutions have been known for some time. A second, much easier result, obtained under the same assumption, is that the partition function of a three-dimensional Ising system is computationally intractable. Again, the negative result contrasts with known efficient techniques for evaluating the partition function of a two-dimensional system.     

Adsorption-desorption kinetics of the monomer-dimer mixture

The kinetics of the monomer-dimer mixtures is formulated in the framework of the kinetic lattice gas model. The so-called local evolution rules are used to derive the hierarchy of coupled differential equations for coverage and other correlators, when processes like adsorption, desorption and diffusion are included. The hierarchy of equation is truncated by using mean-field (m,n) closures. Equilibrium properties are analyzed. In particular, adsorption isotherms as a function of the nearest neighbor lateral interaction are presented. The irreversible kinetics are also considered. Temperature-programmed-desorption (TPD) with readsorption is of special interest and this experiment is simulated under different conditions giving different spectra. In these spectra, the influence of adsorbate mobility is analyzed in two dimensions by Monte Carlo simulations.     

Approximating the number of monomer-dimer coverings of a lattice

We study the problem of counting the number of coverings of ad-dimensional rectangular lattice by a specified number of monomers and dimers. This problem arises in several models in statistical physics, and has been widely studied. A classical technique due to Fisher, Kasteleyn, and Temperley solves the problem exactly in two dimensions when the number of monomers is zero (the dimer covering problem), but is not applicable in higher dimensions or in the presence of monomers. This paper presents the first provably polynomial-time approximation algorithms for computing the number of coverings with any specified number of monomers ind-dimensional rectangular lattices with periodic boundaries, for any fixed dimensiond, and in two-dimensional lattices with fixed boundaries. The algorithms are based on Monte Carlo simulation of a suitable Markov chain, and, in constrast to most Monte Carlo algorithms in statistical physics, have rigorously derived performance guarantees that do not rely on any assumptions. The method generalizes to counting coverings of any finite vertex-transitive graph, a class which includes most natural finite lattices with periodic boundary conditions.     

Theory of open systems I

A new method of treating open systems is presented. The normal treatment using the generalized master equation with the projection of Argyres and Kelley is meaningful only if the state of the reservoir never deviates appreciably from the reference state which appears in the projection. Otherwise, one must make at least a partial resummation of the perturbative expansion of the kernel of the generalized master equation. The present method avoids the introduction of a projection operator and allows us to overcome such resummation difficulties. It is based on an integrodifferential equation for the statistical operator of the composite system, which naturally provides a hierarchy of equations involving the statistical operator ?(t) of the open system and suitable quantities describing higher and higher order bath-system correlations. Treating the deviations of the bath from its initial equilibrium or stationary state as expansion parameters, one gets an approximation scheme, each step of which gives a closed system of equations for ?(t) and a suitable set of correlation quantities.Eliminating such quantities one obtains a closed linear integrodifferential equation for ?(t). The zeroth approximation in the deviations coincides with the Born approximation of the generalized master equation which uses the projection of Argyres and Kelley.On the other hand, even the first approximation is equivalent to the resummation of infinite contribution of the Born series of such a generalised master equation. When it is suitable, the concentration of the bath can also be used as an expansion parameter to handle the hierarchy.     

Theory of diffusion in premelting systems

Summary The diffusion in premelting films and surfaces is described by the Fokker-Planck equation with a periodic potential whose amplitude depends on the temperature and vanishes at the bulk melting temperature. The self-part of the dynamic structure factor is calculated and the results are compared with neutron scattering data from CH₄ premelting films adsorbed on MgO and with atom scattering data from the (110) surface of Pb. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

Theory of coherent luminescence of inverted systems

A study of a system of N two-level molecules excited by a series of resonant laser pulses is made. Upon inversion such a system may give rise to coherent photon avalanches. If the system is irradiated with a subsequent pulse one should observe “light echoes” whose intensity is proportional to the square of the density of dipole moments of the system.     

Theory of hopping transfer in disordered systems

The problem of hopping conduction in a system with randomly distributed impurity centers at low temperatures has been considered in terms of the linearized balance equation. The Gochanour-Andersen-Fayer diagram technique has been used to obtain a self-consistent expression for the configuration-averaged Green’s function, which describes the charge transfer in a disordered system with inclusion of Fermi correlations. In the framework of the developed formalism, a relationship has been derived for hopping conductivity as a function of the temperature with a power law of the density of states. The results obtained agree well with the percolation approach and, in the static limit, lead to the Mott’s law.     

Theory of tunnel ionization in complex systems

A quasianalytical theory of tunnel ionization is developed that is applicable to general complex systems, such as large molecules. Our analysis reveals strong deviations from conventional tunnel ionization theories, dependent upon the system's geometry, angular momentum, and polarizability. A comparison of our theory with recent C(60) ionization experiments yields reasonable agreement.     

Theory of hyperfine interactions in lithiumlike systems

The valence, exchange core polarization and correlation contributions to the magnetic hyperfine constants in the ground states of the lithiumlike ions Be⁺, B²⁺, C³⁺, N⁴⁺, O⁵⁺, F⁶⁺, Ne⁷⁺ and Bi⁸⁰⁺ are investigated using relativistic many-body perturbation theory. Radiative corrections have also been studied. Comparison is made with available experimental data and the trends in the various contributions are analyzed.     

Theory of cluster systems in plasma-like media

The conditions of existence of stable formations of charged particles (clusters) moving in a plasma-like medium are discussed in this paper. The interaction of clusters is considered in the framework of a one-dimensional model. It is shown that the stability of a cluster depends strongly on the number of particles that form part of it. When two clusters moving with respect to each other interact, they break up if the relative velocity is fairly low. Fast-moving clusters hardly interact with each other.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 83–87, May, 1987.     

Theory of superionic conduction in hydrogen-bonded systems

Among superionic conduction phenomena in various ionic materials, the conduction phenomenon associated with the motion of protons in hydrogen-bonded systems has aroused considerable interests with regard to a problem of whether the proton motion should be treated quantum mechanically or classically. In this paper we first describe a quantum mechanical mechanism of proton-induced ionic conduction in the superionic phase in zero-dimensional hydrogen-bonded M₃H(XO₄)₂[M = K, Rb, Cs, X = S,Se] materials, by giving a brief review on the theory developed by Ito and Kamimura. Then we discuss the characteristic difference between quantum mechanical and clasiical mechanisms in the case of proton-induced superionic condcuction, in paticular, by comparing characteristic time scales in quantum mechanical and classical diffusions in hydrogen-bonded systems. Finally a prediction is made on an anomalous behavior of terahertz spectra for Rb₃H(SeO₄)₂.     

Theory of negative magnetoresistance in three-dimensional systems

Theory of negative magnetoresistance in two-dimensional systems due to delocalization of electrons by magnetic field by Hikami, Larkin, and Nagoaka is extended to the case of three-dimension. The increase in conductivity by magnetic field is independent of the direction of the current relative to that of the magnetic field, and is proportional to $\text{H}{}^2\text{τ}{}_{\mathrm{?}}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$, τ_? being energy relaxation time of electrons, when the magnetic field H is small. If τ_? is large enough at low temperature and H is not too small, it is independent of the parameter characterizing the system, and is of the form $\text{0.918?H mho cm}{}^{\mathrm{?1}}$ (H in kOe).     

Theory of diffusive decomposition of supersaturated multicomponent systems

A closed system of equations, which describes the evolution of supersaturated multicomponent solutions, is obtained. A general solution of these equations is determined in the late stage of decomposition, which is determined by nonlinear diffusive interaction of macrodefects.The algebraic equations, which determine the coexistent phases, are obtained.The size of distribution function for particles is determined for each phase. The boundaries of the coexistent phases are defined.     

Theory of spin diffusion in liquid-phase polymer systems

A general theory of spin diffusion in condensed media is constructed by the method of Zwanzig-Mori projection operators using the superpositional approximation to decouple the many-particle correlation functions. The spin diffusion coefficient is expressed in the form D _sp=D _tr+D _f , where D _tr is the contribution associated with translational displacements of the molecules and D _f is the contribution caused by intermolecular flip-flop processes. The expression for D _tr differs from the well-known Kubo-Green formula for the self-diffusion coefficient D _sd in that the integrand contains an additional factor P _f (t), which is the probability of the molecular spins not participating in intermolecular flip-flop transitions over the time t. A microscopic expression is obtained for D _f in the form of a time integral of the intermolecular dipole-dipole dynamic correlation functions. For liquid-phase polymer system with fairly high molecular mass the condition D _sp≫D _sd is satisfied. Zh. éksp. Teor. Fiz. 114, 538–554 (August 1998)