Continuous canonical transformation for the double exchange model

The method of continuous canonical transformation is applied to the double exchange model with a purpose to eliminate the interaction term responsible for non conservation of magnon number. Set of differential equations for the effective Hamiltonian parameters is derived. Within the lowest order (approximate) solution we reproduce results of the standard (single step) canonical transformation. Results of the selfconsistent numerical treatment are compared with the other known studies for this model.     

Temperature and angular momentum dependence of the quadrupole deformation in sd-shell

Temperature and angular momentum dependence of the quadrupole deformation is studied in the middle of the sd-shell for ²⁸Si and ²⁷Si isotopes using the spherical shell model approach. The shell model calculations have been performed using the standard universal sd-shell (USD) interaction and the canonical partition function constructed from the calculated eigensolutions. It is shown that the extracted average quadrupole moments show a transitional behaviour as a function of temperature and the infered transitional temperature is shown to vary with angular momentum. The quadrupole deformation of the individual eigenstate is also analysed.     

The thermodynamic model for nuclear multifragmentation

A great many observables seen in intermediate energy heavy ion collisions can be explained on the basis of statistical equilibrium. Calculations based on statistical equilibrium can be implemented in microcanonical ensemble (energy and number of particles in the system are kept fixed), canonical ensemble (temperature and number of particles are kept fixed) or grand canonical ensemble (fixed temperature and a variable number of particles but with an assigned average). This paper deals with calculations with canonical ensembles. A recursive relation developed recently allows calculations with arbitrary precision for many nuclear problems. Calculations are done to study the nature of phase transition in intermediate energy heavy ion collision, to study the caloric curves for nuclei and to explore the possibility of negative specific heat because of the finiteness of nuclear systems. The model can also be used for detailed calculations of other observables not connected with phase transitions, such as populations of selected isotopes in a heavy ion collision.The model also serves a pedagogical purpose. For the problems at hand, both the canonical and grand canonical solutions are obtainable with arbitrary accuracy hence we can compare the values of observables obtained from the canonical calculations with those from the grand canonical. Sometimes, very interesting discrepancies are found.To illustrate the predictive power of the model, calculated observables are compared with data from the central collisions of Sn isotopes.     

Nuclear multifragmentation: Basic concepts

We present a brief overview of nuclear multifragmentation reaction. Basic formalism of canonical thermodynamical model based on equilibrium statistical mechanics is described. This model is used to calculate basic observables of nuclear multifragmentation like mass distribution, fragment multiplicity, isotopic distribution and isoscaling. Extension of canonical thermodynamical model to a projectile fragmentation model is outlined. Application of the projectile fragmentation model for calculating average number of intermediate mass fragments and the average size of the largest cluster at different Z _bound, differential charge distribution and cross-section of neutron-rich nuclei of different projectile fragmentation reactions at different energies are described. Application of nuclear multifragmentation reaction in basic research as well as in other domains is outlined.     

Elastic interaction and the phase transition in coherent metal-hydrogen systems

We study the statistical mechanics of hydrogen dissolved in metals. The underlying model is based on the assumption that the dominant attractive interaction between the protons in the metal is of an elastic nature.

In the first part of the paper we review some general properties of the elastic interaction. We then discuss the importance of boundary conditions for the form of the elastic interaction, which turns out to be of the Curie-Weiss type with macroscopic range.

In the second part we investigate the a-a' (‘gas-liquid’) phase transition in the hydrogen lattice fluid. The long-range part of the elastic interaction is treated in mean field approximation. In the canonical ensemble as opposed to the grand canonical ensemble one finds no co-existing phases near the critical point. Instead there is a continuous transition which changes into a first-order transition at tricritical points. In the temperature-density region which normally corresponds to the two-phase co-existence region the hydrogen density is inhomogeneous and varies on a macroscopic scale.

The peculiar nature of the a-a' phase transition is due to the long-range character of the elastic interaction, which ultimately results from the requirement of coherency of the host crystal. We argue that coherent metal-hydrogen systems offer examples of real systems where the classical theory of phase transitions applies.     

哈密顿正则方程在生物膜与胶体粒子相互作用研究中的应用

介绍经典分析力学中的哈密顿正则方程在生物膜与胶体粒子相互作用研究中的一个具体应用.由Helfrich理论模型得到体系的哈密顿,用正则方程给出一组常微分方程,并用打靶法对其进行求解得到体系的稳定构型随膜参数变化的规律.     

Reynolds stress models applied to canonical shock-turbulence interaction

Shock waves in high-speed flows can drastically alter the nature of Reynolds stresses in a turbulent flow. We study the canonical interaction of homogeneous isotropic turbulence passing through a normal shock, where the shock wave generates significant anisotropy of Reynolds stresses. Existing Reynolds stress models are applied to this canonical problem to predict the amplification of the stream-wise and transverse normal Reynolds stresses across the shock wave. In particular, the efficacy of the different models for the rapid pressure–strain correlation is evaluated by comparing the results with available direct numerical simulation (DNS) data. The model predictions are found to be grossly inaccurate, especially at high-Mach numbers. We propose physics-based improvement to the Reynolds stress-transport equation in the form of shock-unsteadiness effect and enstrophy amplification for turbulent dissipation rate . The resulting model is found to capture the essential physics of Reynolds stress amplification, and match DNS data for a range of Mach numbers. Numerical error encountered at shock waves are also analysed and the model equations are cast in conservative form to obtain physically consistent results with successive grid refinement. Finally, the proposed model for canonical shock-turbulence interaction is generalised to multi-dimensional flows with shock of arbitrary orientation.     

Tripartite entanglement dynamics for an atom interacting with nonlinear couplers

In this communication we introduce a new model which represents the interaction between an atom and two fields injected simultaneously within a cavity including the nonlinear couplers. By using the canonical transformation the model can be regarded as a generalization of several well-known models. We calculate and discuss entanglement between the tripartite system of one atom and the two cavity modes. For a short interaction time, similarities between the behavior based on our solution compared with the other simulation based on a numerical linear algebra solution of the original Hamiltonian with truncated Fock bases for each mode, is shown. For a specific value of the Kerr-like medium defined in this letter, we find that the entanglement, as measured by concurrence, may terminate abruptly in a finite time.     

Long-range correlations and ensemble inequivalence in a generalized ABC model

A generalization of the ABC model, a one-dimensional model of a driven system of three particle species with local dynamics, is introduced, in which the model evolves under either (i) density-conserving or (ii) nonconserving dynamics. For equal average densities of the three species, both dynamical models are demonstrated to exhibit detailed balance with respect to a Hamiltonian with long-range interactions. The model is found to exhibit two distinct phase diagrams, corresponding to the canonical (density-conserving) and grand canonical (density nonconserving) ensembles, as expected in long-range interacting systems. The implications of this result to nonequilibrium steady states, such as those of the ABC model with unequal average densities, are briefly discussed.     

Theory of resonant tunneling through quantum dots in the presence of electron-phonon interaction

Structures where the electrons of a two-dimensional electron gas are confined to disconnected regions can be fabricated by the use of appropriate gate geometries. The transport between these electrostatically defined quantum dots takes place by tunneling. Using the tunneling Hamiltonian approach we present a theoretical model of the system including electron-phonon interaction. The relevant coupling constants are determined from realistic wave functions for the expected confinement potentials. The phonon part of the Hamiltonian is diagonalized using a canonical transformation. Starting from the determination of the transmission matrix for the interacting system we calculate the current-voltage characteristics for different temperatures and phonon coupling strengths.     

Magnetic moment of a two-dimensional degenerate electron gas in mesoscopic samples

The orbital magnetism of two-dimensional electrons in mesoscopic samples is studied in models where the interaction between electrons is neglected. Various geometries are considered as there are disc, plaquette, bracelet with hard wall confinement and also a confinement with a parabolic potential. We calculate the average magnetic moment which means an average with respect to size fluctuations and de Haas-van Alphen oscillations which arise in the case of a sharp Fermi cutoff. We see three distinct ranges in the magnetic field: (i) small field region where perturbation theory applies; (ii) moderate fields where edge currents play a prominent role; and (iii) the high field range with a Landau type susceptibility. In a quasiclassical picture, the electronic orbits are not qualitatively changed by a magnetic field in (i); skipping orbits are important in (ii); and in (iii), the cyclotron radius is smaller than the sample size. As a rule, we find an enhancement of the magnetic response which increases with k_FL, that is, with sample size divided by the Fermi wave length. Also, we have found out that the quasiclassical approximation fails in the calculation of the magnetic properties; on the other hand, we have seen no essential differences between the canonical ensemble (fixed particle number) and the grand canonical ensemble (chemical potential given). In the case of plaquettes, in particular for samples in the form of squares, we have found agreement with experimental results by Lévy, Reich, Pfeiffer and West.     

Quantum Field Formalism for the Electromagnetic Interaction of Composite Particles in a Nonrelativistic Gauge Model

A classical nonrelativistic U(1) × U(1) gauge field model for the electromagnetic interaction of composite particles is proposed and the quantum formalism is constructed. This gauge model containing a Chern–Simons U(1) field and the electromagnetic U(1) field can be coupled to both a bosonic or a fermionic matter field. We explicitly consider the second case, a composite fermion system in the presence of an electromagnetic field, and we carry out the canonical quantization by the Dirac method. The path integral approach is developed and the Feynman rules are established. A simplified model is considered. As an alternative path integral method, the BRST formalism for this gauge model is also treated.     

Dynamics of amplitude and phase mode and infrared absorption of linear conductors

The dynamics of the Amplitude and Phase mode in the incommensurate case is reduced to the dynamics of a diatomic molecule. Using this Hamiltonian, σ(ω) is given as a canonical average for a Penn model with fluctuating gap.     

Canonical dressing in the multimode two-quantum Jaynes-Cummings model

Based upon the hidden Lie SU(1,1) symmetry, we have constructed the unitary decoupling transformation which diagonalizes the multimode two-quantum Jaynes-Cummings model and provides us with an extremely convenient basis to gain a deeper understanding of the dressing processes present in the matter-field interaction. This canonical transformation approach is very simple and can be easily extended to other generalized Jaynes-Cummings models. Received: 5 July 1997 / Revised: 3 November 1997 / Accepted: 14 November 1997     

Covariance Structure Behind Breaking of Ensemble Equivalence in Random Graphs

For a random graph subject to a topological constraint, the microcanonical ensemble requires the constraint to be met by every realisation of the graph (‘hard constraint’), while the canonical ensemble requires the constraint to be met only on average (‘soft constraint’). It is known that breaking of ensemble equivalence may occur when the size of the graph tends to infinity, signalled by a non-zero specific relative entropy of the two ensembles. In this paper we analyse a formula for the relative entropy of generic discrete random structures recently put forward by Squartini and Garlaschelli. We consider the case of a random graph with a given degree sequence (configuration model), and show that in the dense regime this formula correctly predicts that the specific relative entropy is determined by the scaling of the determinant of the matrix of canonical covariances of the constraints. The formula also correctly predicts that an extra correction term is required in the sparse regime and in the ultra-dense regime. We further show that the different expressions correspond to the degrees in the canonical ensemble being asymptotically Gaussian in the dense regime and asymptotically Poisson in the sparse regime (the latter confirms what we found in earlier work), and the dual degrees in the canonical ensemble being asymptotically Poisson in the ultra-dense regime. In general, we show that the degrees follow a multivariate version of the Poisson–Binomial distribution in the canonical ensemble.     

Inverse Monte Carlo study on effective interaction potential of Ag--Rh alloy from pair correlation functions

This paper presents an inverse Monte Carlo method to reconstruct pair interaction potential from pair correlation function. This approach adopts an iterative algorithm on interaction potential to fit known pair correlation function by compelling deviations of canonical average to meet with Hamiltonian parameters on a basis of statistical mechanism. The effective interaction potential between particles in liquid Ag--Rh alloys has been calculated with the inverse Monte Carlo method. It demonstrates an effective and simple way to obtain the effective potential of complex melt systems.     

Canonising the Hartle-Hawking proposal

The canonical formulation of the Hartle-Hawking proposal is discussed in a class of spatially homogeneous minisuperspace model. Relying on arguments of consistency with the classical variational principle, we find a set of canonical variables in which the Hartle-Hawking boundary condition is obtained by fixing in the path integral the final values of the canonical coordinates but the initial values of the canonical momenta. A canonical measure of this kind offers a natural starting point for skeletonising the minisuperspace Hartle-Hawking path integral.     

Entropy and variance squeezing of two coupled modes interacting with a two-level atom: Frequency converter type

A modified Jaynes-Cummings model which consists of a two-level atom interacting with two modes of the electromagnetic field is introduced. More precisely we have considered a Hamiltonian model that includes two types of interaction: One is the field-field (frequency converter type) and the other is the atom-field interaction. By invoking a canonical transformation an exact solution of the wave function in the Schrödinger picture is obtained. The result presented in this context is used to discuss the atomic inversion as well as the entropy squeezing and variance squeezing phenomena. We have shown that the existence of the second field coupling parameter reduces the amount of squeezing in all quadratures, while the effect of the detuning parameter would lead to the superstructure phenomenon which becomes more pronounced upon increasing the mean photon numbers, in the states which are taken to be converter states.