Equivalence of the degrees of freedom in a unified gravitational theory

A discussion of the nouniqueness of physical laws and their invariance groups is illustrated by the construction of a physical theory (presented earlier) in which the law of motion of structureless and spinning particles is unified in the geometry of the manifold of the de Sitter groupSO(3,2). The theory has the structure of a non-Abelian Kaluza-Klein theory with very special properties resulting from the topology and noncompactness of the groups. The physical interpretation of the field equation is discussed. The physical requirement of equivalence of the interaction of spinning and orbiting systems, generally unconsidered in related theories, is here taken into account by the structure of the theory. The possibility of deviations from predictions of general relativity exists. Generalizations of the theoretical structure to higher dimensional groups are outlined and open the possibility for observations.     

Chiral dynamics with quark degrees of freedom

The possibility to detect DCC fluctuations is discussed. It is shown that interactions with quark background and dissipative effects due to interactions in the chiral field may result in damping of fluctuations. Since the magnitude of fluctuations depends strongly on the initial state and speed of chiral phase transition an accurate evaluation of all modifying processes is required to predict the observability of DCCs.     

Lattice dynamics of LaMnO3: Coupling of the lattice and orbital degrees of freedom

The lattice dynamics of regular LaMnO₃ is calculated within a shell model with pairwise interionic interaction potentials and with a Jahn-Teller (JT) contribution included into the energy and dynamic matrix of the crystal. A correlation is made between Raman spectral lines and lattice vibrations. The positions of some lines in the Raman spectrum are found to depend heavily on the linear JT coupling constant V _e . The effect of the JT coupling on the phonon density of states of LaMnO₃ is investigated.     

Shadowing high-dimensional hamiltonian systems: the gravitational N-body problem

A shadow is an exact solution to a chaotic system of equations that remains close to a numerically computed solution for a long time. Using a variable-order, variable-time-step integrator, we numerically compute solutions to a gravitational N-body problem in which many particles move and interact in a fixed potential. We then search for shadows of these solutions with the longest possible duration. We find that in "softened" potentials, shadow durations are sufficiently long for significant evolution to occur. However, in unsoftened potentials, shadow durations are typically very short.     

Collectivity and single-particle degrees of freedom

Intruder rotational bands in ⁴⁵Sc and ⁴⁵Ti have been investigated up to the maximum aligned angular momentum by means of EUROBALL IV and the Recoil Filter Detector (RFD). The use of the RFD allowed for a reduction of the -line Doppler broadening and, moreover, for a determination of very short level lifetimes. In the studied nuclei, the estimated deformation shows a gradual disappearance of the collectivity at the highest available spins.Received: 19 November 2002, Revised: 14 March 2003, Published online: 2 March 2004PACS: 21.10.Tg Lifetimes - 21.60.Cs Shell model - 27.40. + z P. Bednarczyk: Present address: GSI, Darmstadt, GermanyM.B. Smith: Present address: TRIUMF, Vancouver, Canada     

Coupling between internal spin dynamics and external degrees of freedom in the presence of colored noise

We observe asymmetric transition rates between Zeeman levels (spin flips) of magnetically trapped atoms. The asymmetry strongly depends on the spectral shape of an applied noise. This effect follows from the interplay between the internal states of the atoms and their external degrees of freedom, where different trapped levels experience different potentials. Such insight may prove useful for controlling atomic states by the introduction of noise, as well as provide a better understanding of the effect of noise on the coherent operation of quantum systems.     

Space-time and degrees of freedom of the elementary particle

First, a general property of Lie groups is used in the case of the Poincaré group in order to define the one particle phase space. It is eight-dimensional in the general case and six-dimensional for a spinless or massless particle.Embedding the Poincaré group into the similitude group of space-time permits us to interpret the dilatation operator as a dynamical variable. The connection between the similitude group and field equations is discussed. Lurçat's ideas on a possible dynamical role of spin and mass-spin spectra of particles (Regge trajectories) are discussed under the point of view of the degrees of freedom.This work constitutes a completed version of a preprint entitled Classical Hamiltonian Formalism for Spin, Argonne, September, 1966.On leave from Université de Marseille, France. Work supported in part by the National Science Foundation.     

Superfrustration of charge degrees of freedom

We review recent results, obtained with P. Fendley, on frustration of quantum charges in lattice models for itinerant fermions with strong repulsive interactions. A judicious tuning of kinetic and interaction terms leads to models possessing supersymmetry. In such models frustration takes the form of what we call superfrustration: an extensive degeneracy of supersymmetric ground states. We present a gallery of examples of superfrustration on a variety of 2D lattices.     

On chaotic dynamics in "pseudobilliard" Hamiltonian systems with two degrees of freedom

A new class of Hamiltonian dynamical systems with two degrees of freedom is studied, for which the Hamiltonian function is a linear form with respect to moduli of both momenta. For different potentials such systems can be either completely integrable or behave just as normal nonintegrable Hamiltonian systems with two degrees of freedom: one observes many of the phenomena characteristic of the latter ones, such as a breakdown of invariant tori as soon as the integrability is violated; a formation of stochastic layers around destroyed separatrices; bifurcations of periodic orbits, etc. At the same time, the equations of motion are simply integrated on subsequent adjacent time intervals, as in billiard systems; i.e., all the trajectories can be calculated explicitly: Given an initial data, the state of the system is uniquely determined for any moment. This feature of systems in interest makes them very attractive models for a study of nonlinear phenomena in finite-dimensional Hamiltonian systems. A simple representative model of this class (a model with quadratic potential), whose dynamics is typical, is studied in detail. (c) 1997 American Institute of Physics.     

Superstrings with tensor degrees of freedom

We add antisymmetric tensor degrees of freedom to the usual superstring coordinates. We show that super and kappa symmetries are only achieved for the spacetime dimensionD=4. We also address problems related to the quantization of the model and discuss the influences of this extended spacetime in the usual quantum field theory.     

A method of reduction of Einstein's equations of evolution and a natural symplectic structure on the space of gravitational degrees of freedom

A program is outlined which addresses the problem of thereduction of Einstein's equations, namely, that of writing Einstein's vacuum equations in (3+1)-dimensions as anunconstrained dynamical system where the variables are thetrue degrees of freedom of the gravitational field. Our analysis is applicable for globally hyperbolic Ricci-flat spacetimes that admit constant mean curvature compact orientable spacelike Cauchy hypersurfaces M with degM=0 andM not diffeomorphic toF ₆, the underlying manifold of a certain compact orientable flat affine 3-manifold. We find that for these spacetimes, modulo the extended Poincaré conjecture and the use of local cross-sections rather than a global cross-section, (3+1)-reduction can be completed much as in the (2+1)-dimensional case. In both cases, one gets as the reduced phase space the cotangent bundleT ^* T _M of theTeichmüller space T _M of conformal structures onM, whereM is a given initial constant mean curvature compact orientable spacelike Cauchy hypersurface in a spacetime (V, g _V ), and one gets reduction of the full classical non-reduced Hamiltonian system with constraints to a reduced Hamiltonian system without constraints onT ^* T _M . For these reduced systems, the time parameter is the parameter of a family of monotonically increasing constant mean curvature compact orientable spacelike Cauchy hypersurfaces in a neighborhood of a given initial one. In the (2+1)-dimensional case, the Hamiltonian is the area functional of these hypersurfaces, and in the (3+1)-dimensional case, the Hamiltonian is the volume functional of these hypersurfaces.     

Nonclassical degrees of freedom in the Riemann Hamiltonian

The Hilbert-Pólya conjecture states that the imaginary parts of the zeros of the Riemann zeta function are eigenvalues of a quantum Hamiltonian. If so, conjectures by Katz and Sarnak put this Hamiltonian in the Altland-Zirnbauer universality class?C. This implies that the system must have a nonclassical two-valued degree of freedom. In such a system, the dominant primitive periodic orbits contribute to the density of states with a phase factor of -1. This resolves a previously mysterious sign problem with the oscillatory contributions to the density of the Riemann zeros.     

Third-order geometrical null symmetries of gravitational fields

The first-, the second-, and the third-order null Killing vectors in a gravitational field are explored separately. When an algebraically special Petrov-type free gravitational field isaligned with a source-free (nonnull/null) electromagnetic field, their common propagation vectorl ^a is shown to be a third-order null Killing vector field ( _{l l l} g _ab = 0, _{l l} g _ab 0). When the two fields arenot aligned, the necessary and sufficient conditions for the existence of a third-order null symmetry are obtained in Newman-Penrose formalism.