Ground-state energy of the exciton-phonon system in a magnetic field

Upper bounds for the ground-state energy of the exciton-phonon system in a magnetic field are calculated variationally using a wavefunction whose symmetry is suited both to low and high magnetic fields. The displacement amplitudes for the exciton-phonon interaction are those known from the free field case. The results compare satisfactorily with experimental data for TlCl and TlBr.     

The ADM Hamiltonian at the postlinear approximation

The ADM Hamiltonian for a many-particle system is calculated up to the postlinear approximation, i.e., to the approximation that both the equations of motion for the particles and the equations of motion for the gravitational field in case of no-incoming radiation correctly result up to the postlinear approximation. The relation of this Hamiltonian to the ADM Hamiltonian obtained by a post-Newtonian approximation scheme which was applied up to the first radiation-reaction and radiation levels is discussed. From here the standard formulas for the mechanical angular momentum and energy losses as well as the radiated energy and angular momentum are deduced. Background logarithmic and logarithmic radiative terms are shown to be not present at our approximation if the condition of no-incoming radiation is fulfilled.     

Spin compensation temperatures induced by longitudinal fields in a mixed spin-3/2 and spin-5/2 Ising ferrimagnet

I studied the ferrimagnetic Ising model with nearest neighbour interactions for a square lattice and simple cubic one, using mean field theory. The free energy of a mixed spin Ising ferrimagnetic model was calculated from a mean field approximation of the Hamiltonian. By minimizing the free energy, I obtained the equilibrium magnetizations and the compensation temperatures. Clear indications of the single-ion anisotropies on the compensation points of the mixed spin-3/2 and spin-5/2 ferrimagnetic lattices are found. Some interesting behaviors of these systems are obtained depending not only on the values of magnetic anisotropies for both sublattice sites but also on the lattice structure. The longitudinal magnetic fields dependence of the spin compensation temperature is the main focus of research. The possibility of many compensation temperatures is indicated.     

Selected formulas for the magnetic susceptibility of systems with 4f-ions

Basic formula for the magnetic susceptibility of systems with 4f-ions within the LS-coupling scheme is introduced. The high temperature behaviour of thermodynamic average values is considered and the result is used for a high temperature expansion of the magnetic susceptibility. The results in the whole temperature range are given for systems described by one-particle Hamiltonians and effective one-particle Hamiltonians are considered. Explicit formulas are given for the case of a crystal field Hamiltonian and Heisenberg interaction Hamiltonian including molecular field approximation.     

Microcanonical variational transition-state theory for reaction rates in dissipative systems

Upper bounds for the classical escape rate of a particle trapped in a metastable well and interacting with a dissipative medium are derived based on the periodic orbits of a reduced two-degree-of-freedom Hamiltonian involving the unstable normal mode and a collective bath mode. It is shown that even in what is usually thought of as the spatial diffusion limit the reactive flux can involve an energy diffusion term due to energy transfer from the dissipative media, in addition to the standard spatial diffusion term.     

A self-consistent mean field calculation of the phenomenological coefficients in a multicomponent alloy with high jump frequency ratios

We present an improvement of the self-consistent mean field (SCMF) approximation of the L _ij which extends its applications to alloys presenting high jump frequency ratios. The theory uses a vacancy–atom exchange model which depends on temperature and local composition through thermodynamic and kinetic parameters. Kinetic correlations due to the vacancy mechanism are represented by a time-dependent effective Hamiltonian. In the case of high jump frequency ratios it is shown that long return paths of the vacancy need to be considered, which is shown to be equivalent to introducing many-body long-range effective interactions. We compare this theory to existing formalisms and Monte Carlo simulations for systems both without and with atomic interactions.     

Universal localizing bounds for compact invariant sets of natural polynomial Hamiltonian systems

In this Letter we study the localization problem of compact invariant sets of natural Hamiltonian systems with a polynomial Hamiltonian. Our results are based on applying the first order extremum conditions. We compute universal localizing bounds for some domain containing all compact invariant sets of a Hamiltonian system by using one quadratic function of a simple form. These bounds depend on the value of the total energy of the system, degree and some coefficients of a potential and, in addition, some positive number got as a result of a solution of one maximization problem. Besides, under some quasihomogeneity condition(s) we generalize our construction of the localization set.     

Analytic Approximations for the Velocity of Field-Driven Ising Interfaces

We present analytic approximations for the field, temperature, and orientation dependences of the interface velocity in a two-dimensional kinetic Ising model in a nonzero field. The model, which has nonconserved order parameter, is useful for ferromagnets, ferroelectrics, and other systems undergoing order–disorder phase transformations driven by a bulk free-energy difference. The solid-on-solid (SOS) approximation for the microscopic surface structure is used to estimate mean spin-class populations, from which the mean interface velocity can be obtained for any specific single-spin-flip dynamic. This linear-response approximation remains accurate for higher temperatures than the single-step and polynuclear growth models, while it reduces to these in the appropriate low-temperature limits. The equilibrium SOS approximation is generalized by mean-field arguments to obtain field-dependent spin-class populations for moving interfaces, and thereby a nonlinear-response approximation for the velocity. The analytic results for the interface velocity and the spin-class populations are compared with Monte Carlo simulations. Excellent agreement is found in a wide range of field, temperature, and interface orientation.     

Second-order correction to the positronium ground-state energy in ionic crystals

Upper and lower bounds on the second-order correction to the positronium ground-state energy due to the influence of the crystalline field in an ionic crystal are obtained, and the corresponding formulas are derived. The approximation adopted in the numerical calculations is the model of a point-ion potential. It is shown that neglecting the contribution of states in the continuous energy spectrum of the electron—positron pair to the correction yields an unsatisfactory upper bound. V. I. Lenin Moscow State Pedagogical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 37–41, April, 1998.     

Collective spin excitations in 2D paramagnet with dipole interaction

The collective spin excitations in the unbounded 2D paramagnetic system with dipole interactions are studied. The model Hamiltonian includes Zeeman energy and dipole interaction energy, while the exchange vanishes. The system is placed into a constant uniform magnetic field which is orthogonal to the lattice plane. It provides the equilibrium state with spin ordering along the field direction, and the saturation is reached at zero temperature. We consider the deviations of spin magnetic moments from its equilibrium position along the external field. The Holstein-Primakoff representation is applied to spin operators in low-temperature approximation. When the interaction between the spin waves is negligible and only two-magnon terms are taken into account, the Hamiltonian diagonalisation is possible. We obtain the dispersion relation for spin waves in the square and hexagonal honeycomb lattice. Bose-Einstein statistics determine the average number of spin deviations, and total system magnetization. The lattice structure does not influence on magnetization at the long-wavelength limit. The dependencies of the relative magnetization and longitudinal susceptibility on temperature and external field intensity are found. The internal energy and specific heat of the Bose gas of spin waves are calculated. The collective spin excitations play a significant role in the properties of the paramagnetic system at low temperature and strong external magnetic field.     

Quantum correlations in rotating nuclei

Using the Hamiltonian that consists of the separable quadrupole + pairing forces and the cranking term, we analyze the correlations associated with shape, orientation, and particle-number fluctuations in rotating nuclei. Quantum fluctuations around mean field solutions are treated in the random phase approximation (RPA), with special emphasis on the restoration of rotational symmetry and particle number conservation. The mean field calculations have been made within the self-consistent cranking model. The effect of the RPA correlation energy for the moment of inertia is studied with the integral representation method proposed.     

Variational derivation of KdV-type models for surface water waves

Using the Hamiltonian formulation of surface waves, we approximate the kinetic energy and restrict the governing generalized action principle to a submanifold of uni-directional waves. Different from the usual method of using a series expansion in parameters related to wave height and wavelength, the variational methods retains the Hamiltonian structure (with consequent energy and momentum conservation) and makes it possible to derive equations for any dispersive approximation. Consequentially, the procedure is valid for waves above finite and above infinite depth, and for any approximation of dispersion, while quadratic terms in the wave height are modeled correctly. For finite depth this leads to higher-order KdV type of equations with terms of different spatial order. For waves above infinite depth, the pseudo-differential operators cannot be approximated by finite differential operators and all quadratic terms are of the same spatial order.     

An introduced effective-field theory study of spin-1 transverse Ising model with crystal field anisotropy in a longitudinal magnetic field

A spin-1 transverse Ising model with longitudinal crystal field in a longitudinal magnetic field is examined by introducing an effective field approximation (IEFT) which includes the correlations between different spins that emerge when expanding the identities. The effects of the crystal field as well as the transverse and longitudinal magnetic fields on the thermal and magnetic properties of the spin system are discussed in detail. The order parameters, Helmholtz free energy, entropy and specific heat curves are calculated numerically as functions of the temperature and Hamiltonian parameters. A number of interesting phenomena such as reentrant phenomena originating from the temperature, crystal field, transverse and longitudinal magnetic fields have been found.     

Theoretical investigations of the vapour-liquid equilibrium and dielectric properties of dipolar Yukawa fluids in an external field

In a low field approximation, using the dipolar Yukawa fluid model (in mean spherical approximation as a reference system) a consistent field-dependent free energy expression is proposed for the calculation of the vapour-liquid equilibrium of polar fluids in an applied electric field. A perturbation theory high field approximation expression of the free energy is also proposed to study the field-dependent properties of fluids. In the high field approximation, equations for the field-dependent polarization and for the nonlinear dielectric constant (or Piekara constant) are also predicted. It has been discussed that our approximations are appropriate to describe the vapour-liquid-like phase equilibria and the magnetization curves of magnetic fluids.     

Optimal truncation procedures in renormalization-group calculations

Renormalization or rescaling transformations generally produce more complicated interactions than are present in the initial Hamiltonian. After each rescaling it is necessary to truncate the Hamiltonian to make the next rescaling mathematically tractable. One is faced with the problem of choosing the coupling constants of the truncated Hamiltonian to obtain the best approximation. Following ideas of McMillan, we consider truncation procedures which give lower and upper bounds to the free energy. Conditions for optimal lower- and upper-bound truncations are derived. These optimal truncations are seen to yield exact results for the free energy in both the high- and low-temperature limits. Some of the problems inherent in all renormalization transformations that incorporate an optimal lower- or upper-bound truncation are discussed. Calculations for the twodimensional Ising model based on renormalization transformations which combine decimation and an optimal truncation are described. Even in the simplest approximation in which only nearest-neighbor interactions are retained the free energy is obtained to an accuracy of better than 1% for all temperatures if an optimal truncation rather than an ordinary truncation with no readjustment of the coupling constants is made. However, the simplest calculations involving optimal truncations are less successful in predicting derivatives of the free energy and critical exponents than the free energy itself.     

Variational tight-binding theory of excitons in compositionally modified semiconductor superlattices

We present results for the binding energy of an exciton formed when an electron–hole pair is photoexcited within a single, compositionally modified layer of a semiconductor superlattice, for example by adding a small percentage of In atoms to a single GaAs layer of a GaAs/AlGaAs system. Such a system could serve as the basis for spatially-selective photoexcitation, a process whereby a laser pulse would create electron–heavy-hole pairs exclusively in the modified layer. We first derive an effective one-dimensional (1D) Hamiltonian for an electron, by averaging the 3D electron–hole Hamiltonian using a one-parameter trial wavefunction, which is dependent on the in-plane relative coordinates, as well as a normalized Wannier orbital for a single hole. The exciton binding energy is then obtained by computing the lowest bound-state energy of the effective 1D electron Hamiltonian in the nearest-neighbor tight-binding approximation. As a demonstration of the effectiveness of our approach, we find that for periodic superlattices our results for the exciton binding energy are in very good agreement both with experiment and the results of other theoretical calculations.     

Note on phase space contraction and entropy production in thermostatted Hamiltonian systems

The phase space contraction and the entropy production rates of Hamiltonian systems in an external field, thermostatted to obtain a stationary state, are considered. While for stationary states with a constant kinetic energy the two rates are formally equal for all numbers of particles N, for stationary states with constant total (kinetic and potential) energy this only obtains for large N. However, in both cases a large number of particles is required to obtain equality with the entropy production rate of Irreversible Thermodynamics. Consequences of this for the positivity of the transport coefficients and for the Onsager relations are discussed. Numerical results are presented for the special case of the Lorentz gas. (c) 1998 American Institute of Physics.