Lie symmetry and Mei symmetry of a rotational relativistic system in phase space

The Lie symmetry and the Mei symmetry of a rotational relativistic system in phase space are studied. The definition, criterion and conserved quantity of the Lie symmetry and the Mei symmetry of a rotational relativistic system in phase space are given. The relation between the Lie symmetry and the Mei symmetry is found. An example is given to illustrate the application of the result.     

A schematic model for collective states including non-locality effects: (I). Isoscalar quadrupole and rotational modes

Schematic forces including non-locality terms are derived in a self-consistent way in the framework of the time-dependent Hartree-Fock formalism. The usual dispersion relation of the vibrating potential model is generalized to include current effects. The model is explicitly solved for the isoscalar quadrupole and rotational modes and the role of the effective mass is pointed out.     

A modified fermi model for wave-particle interactions in plasmas

Wave-particle interactions in plasmas are investigated through a nonlinear map that describes elastic collisions between an ensemble of particles and two barriers. The amplitude of the barriers, proportional to the energy of the wave, can increase or decrease due to the sequence of stochastic collisions. After an initial exponential decrease, the nonlinear strong trapping regime is characterized by low-frequency oscillations of the amplitude of the barriers around a certain saturation value. This is a transitory phenomenon stemming from the dynamical approach towards equilibrium in the wave-particle conservative system.     

Theory of symmetry for a rotational relativistic Birkhoff system

The theory of symmetry for a rotational relativistic Birkhoff system is studied. In terms of the invariance of the rotational relativistic Pfaff－Birkhoff－D'Alembert principle under infinitesimal transformations, the Noether symmetries and conserved quantities of a rotational relativistic Birkhoff system are given. In terms of the invariance of rotational relativistic Birkhoff equations under infinitesimal transformations, the Lie symmetries and conserved quantities of the rotational relativistic Birkhoff system are given.     

Functional approach to nuclear field theory: A schematic model with pairing and particle-hole forces

Path integral techniques in collective variables are applied to a schematic model with monopole pairing and particle-hole forces. The single-particle and collective excitation modes of the system for various kinds of phase transitions are discussed. We formulate a modified perturbation theory (loop expansion) from which, finally, nuclear field theory (NFT) is obtained. The NFT Lagrangian is strictly derived. The graphical rules of the NFT expansion come out automatically.     

A schematic model for the investigation of nuclear reactions

An extension of the schematic model of Lipkin, Glick and Meshkov to include reaction modes with one particle in the continuum is introduced. The model set up is amenable to the investigation of various approximations necessary in realistic shell model in the continuum calculations. The first application centering on the use of truncated bound state shell-model spaces is given.     

Renormalization for collective motion within a truncated space of the spherical shell model. I. Intrinsic frame in a schematic model

Using schematic Hamiltonians in the ²⁰Ne example, the series of perturbation terms for effective interactions and operators in a truncated space of a spherical shell model is found that, when summed, yields the results for intrinsic moments and energy of the unrestricted deformed Hartree-Fock state. Black-box and random phase approximation diagrams are shown to be important as is another (little used and to be called IBG) diagram and the ladder diagrams. A black-dot vertex renormalization is introduced corresponding to consistent renormalization of every transformation within the model space. The black-dot corresponds exactly to the self consistency of deformed Hartree-Fock.     

Negative parity rotational bands in28Si: A cluster model approach

Describing the expanding fireballs in a relativistic gas dynamical approach the formation of deuterons is calculated under consideration of inmedium corrections. The theoretical results are in good agreement with experimental data.     

Heisenberg ferromagnet with Dzyaloshinsky-Moriya interactions: A real space renormalization group approach

We study the anisotropic Heisenberg ferromagnet with anti-symmetric Dzyaloshinsky-Moriya (DM) interactions for arbitrary dimensions. We use a real space renormalization group approach of the Migdal-Kadanoff type in order to obtain the phase diagrams and critical exponents. The effect of the Dzyaloshinsky-Moriya term in the global phase diagram is worked out in detail. Our results suggest that in all dimensions the effect of the DM interaction is to renormalize the parameters of the anisotropic exchange Hamiltonian. Finally we discuss the modification of hyperscaling associated with the zero temperature Heisenberg-like fixed point.     

A new method for the thermomodynamics of the BCS model

Using large deviations in combination with the Berezin-Lieb inequalities, we analyse the phase-transition in the BCS model with non-constant energies and interactions.     

A sum rule for the rotational band of a molecule with C3V symmetry

A sum rule is derived for the integrated intensity of the rotational band of a symmetric top molecule with C_3V symmetry, simply by direct summation over all the rotational transitions.     

Self-consistent selection of a superconducting representation for the BCS model

Taking the BCS Hamiltonian written in second-quantized form, a modified form of Umezawa's self-consistent field theory method is applied, and a unitarily nonequivalent representation is selected in which the Hamiltonian obviously describes a superconducting system. This result is not at all obvious, since the original Hamiltonian is completely symmetric, and there is no reason a priori for expecting it to describe an asymmetric superconducting configuration. All higher order terms are accounted for, and in doing so, one finds the existence of the energy-gap condition for Cooper pairs. The representation is picked out without using the adiabatic theorem or pair approximation, as is typically done in the self-consistent method for superconductivity.     

Axial anomaly and chiral symmetry breaking in Schwinger model: A canonical approach

We use a recently introduced canonical surface formalism, to study the problem of chiral symmetry breaking in the Schwinger model. We perfect the parallel between QCD₄ and QED₂ in this respect.     

Stationary solutions for a modified Peyrard-Bishop DNA model with up to third-neighbor interactions

We investigate a DNA model that takes into account stacking interactions with neighbors up to three bases away. The model is a generalization of the well-known Peyrard-Bishop (PB) model and is motivated by studies that suggest that nearest-neighbor models for base-pair interaction in a DNA chain might not be enough to capture the mechanism and dynamics of DNA base-pair opening. We study stationary solutions of the modified model and investigate their stability. A comparison with the PB model reveals that under a wide range of parameter values the main characteristics of the original model --such as the hyperbolicity of the equilibrium at the origin-- are preserved, but new types of stationary solutions emerge.     

An equation of motion method for deriving microscopic effective interactions in a correlated model space

Starting from a diagrammatic analysis of the equation of motion method, we derive an effective interaction theory for a correlated model space where the basis vectors correspond physically to the addition of valence particles and/or holes to the true ground state of the core nucleus. The resulting effective interaction $\text{V}$ is valence linked and connected, energy independent, and contains folded diagrams. In addition, it gives directly model eigenvectors with amplitudes that correspond to spectroscopic factors. With terms having the same number of folds grouped together, the general structure of $\text{V}$ is very simple. This is very useful in the application of the present theory to actual microscopic nuclear structure calculations. The treatment of core projection insertions is discussed in some detail. A proof of the cancellation of the disconnected diagrams is given. When folded diagrams are summed up using a partial summation method, the present effective interaction theory is shown to be consistent with the usual Green function theory for many-body problems.     

A schematic model discussion of the conductor to insulator transition for particle motion in a random potential

A schematic model for the dynamics of a particle moving in a random environment is discussed where the latter is assumed to cause normal scattering and also scattering with time inversion symmetry breaking. The second mechanism changes the exponent unity to one half for the vanishing of the conductivity near the percolation threshold. It alters also the exponent of the critical conductivity spectrum from 1/2 to 1/3. The dynamics near the transition including all cross over phenomena to the usual effective medium theory results are described by a two parameter scaling law.Dedicated to Professor W. Brenig on the occasion of his 60th birthday     

Coevolutionary motion and swarming in a niche space model of ecological species interactions

Organisms are involved in coevolutionary relationships with their competitors, predators, preys and parasites. In this context, we present a simple model for the co-evolution of species in a common niche space, where the fitness of each species is defined via the network of interactions with all other species. In our model, the sign and type of the pairwise interactions (being either beneficial, harmful or neutral) is given by a pre-determined community matrix, while the interaction strength depends on the niche-overlap, i.e. the pairwise distances between species in niche space. The evolutionary process drives the species toward the places with the higher local fitness along the fitness gradient. This gives rise to a dynamic fitness landscape, since the evolutionary motion of a single species can change the landscape of the others (known as the Red Queen Principle). In the simplest case of only two-species we observe either a convergence/divergence equilibrium or a coevolutionary arms race. For a larger number of species our analysis concentrates on an antisymmetric interaction matrix, where we observe a large range of dynamic behaviour, from oscillations, quasiperiodic to chaotic dynamics. In dependence of the value of a first integral of motion we observe either quasiperiodic motion around a central region in niche space or unbounded movement, characterised by chaotic scattering of species pairs. Finally, in a linear food-chain we observe complex swarming behaviour in which the swarm moves as a whole only if the chain consists of an even number of species. Our results could be an important contribution to evolutionary niche theory.