Multiscale model of deformed polycrystals. Hall-Petch problem

The paper puts forward a multiscale model of deformed polycrystals according to which the basis for self-consistent deformation of grains is rotational wave flows of planar structural transformations at their boundaries. Computer-aided engineering of grain boundaries reveals two types of rotational wave flows defined by the misorientation angle of adjacent grains. Grain boundary flows of the first type develop at low-angle boundaries and feature low curvature. These flows generate dislocations in the grain bulk and the Hall-Petch equation for them has the form σ=σ₀+kd^?1/2. Grain boundary flows of the second type develop at high-angle boundaries and feature high curvature. These flows generate curvature bands in near-boundary zones and inject them into the grain bulk, resulting in fragmentation of grains and breakdown of translation invariance. For such self-consistency of grains in a polycrystal, the Hall-Petch equation has the form σ=σ₀+kd^?1. Experimental data in support of the proposed multiscale model are presented.     

Differential calculus and gauge transformations on a deformed space

We consider a formalism by which gauge theories can be constructed on noncommutative space time structures. The coordinates are supposed to form an algebra, restricted by certain requirements that allow us to realise the algebra in terms of star products. In this formulation it is useful to define derivatives and to extend the algebra of coordinates by these derivatives. The elements of this extended algebra are deformed differential operators. We then show that there is a morphism between these deformed differential operators and the usual higher order differential operators acting on functions of commuting coordinates. In this way we obtain deformed gauge transformations and a deformed version of the algebra of diffeomorphisms. The deformation of these algebras can be clearly seen in the category of Hopf algebras. The comultiplication will be twisted. These twisted algebras can be realised on noncommutative spaces and allow the construction of deformed gauge theories and deformed gravity theory. Dedicated to the 60th birthday of Prof. Obregon.     

Twisted classical phase space

We consider relativistic phase space constructed by the twist procedure from the translation sector of the standard, nondeformed Poincaré algebra. Using the concept of cross product algebra we derive two kinds of phase space with noncommuting configuration space. The generalized uncertainty relations are formulated.     

Chiral-invariant phase space model

The masses of the SU(3)×SU(6) hadrons are calculated in the chiral-invariant phase space (CHIPS) model as a sum of the mean energies of the quarks at a constant temperature T _c with the color-magnetic splitting and the color-electric shift. The masses of hadrons are parametrized by four constants: T _c, m_s, E _CE and A _CM. With the same number of parameters the CHIPS model fits the masses of hadrons better than the classic bag model. The small mass of the d-quark ( m _d = 2.7MeV) is used to prove that the isotopic shifts of hadrons can be explained by the mass difference between the d- and u-quarks. The dibaryon mass is estimated in CHIPS to be 200MeV higher than in the bag model. The prediction for the mass of the α^* cluster is about the same in both models. It is close to 4 ^. m _Δ. Received: 12 December 2001 / Accepted: 23 May 2002     

Path integration in phase space

We develop a method for defining and performing path integrals in phase space. This work generalizes to phase space the method formulated in recent years for path integration in configuration space. We give the relationship between the Wiener measure and the Liouville measure.Dedicated to Achille Papapetrou on the occasion of his retirement.This paper was written while the author was Visiting Professor in the Departments of Physics and Mathematics at the University of Texas.     

Protonium decay and phase space

Nucleon-antinucleon at rest presents a variety of channels, where wide mesons often interfere, as shown by the analysis of protonium decay into three pions by the Asterix and Crystal Barrel experiments. A statistical model for emission of the narrow mesonsπ, η, η′ ω, K, ¯K is presented to account for the general profile of the reaction. It is an alternative to a model based on two-doorway state dominance proposed earlier. It allows direct prediction with phenomenological channels, but deals only with branching ratios, not with the detailed structure of the final states. The initial state interactions do not influence the bulk of predictions, although they matter for two-particle branching ratios, which are small. The model is in reasonable agreement with present experimental data and is offered as a standard for comparison with forthcoming results. Some obvious deviations claim for a dynamical explanation.     

Noncommutative geometry of phase space

A version of noncommutative geometry is proposed which is based on phase-space rather than position space. The momenta encode the information contained in the algebra of forms by a map which is the noncommutative extension of the duality between the tangent bundle and the cotangent bundle.     

Quantum friction in phase space

In this paper we shall study the problem of quantum friction in the Wigner representation. For quadratic Hamiltonians the Wigner equation coincides with the classical Liouville equation although there are distribution functions which depend on the Planck constant. For these distributions the product of the standard deviations of p and q is greater or equal to $\text{,NU>?}\text{2}$ so that the uncertainty principle of Heisenberg holds.     

Solving the two-center nuclear shell-model problem with arbitrarily oriented deformed potentials

A general new technique to solve the two-center problem with arbitrarily oriented deformed realistic potentials is demonstrated, which is based on the powerful potential separable expansion method. As an example, molecular single-particle spectra for (12)C+(12)C-->(24)Mg are calculated using deformed Woods-Saxon potentials. These clearly show that nonaxial symmetric configurations play a crucial role in molecular resonances observed in reaction processes for this system at low energy.     

Admissible states in quantum phase space

We address the question of which phase space functionals might represent a quantum state. We derive necessary and sufficient conditions for both pure and mixed phase space quantum states. From the pure state quantum condition we obtain a formula for the momentum correlations of arbitrary order and derive explicit expressions for the wave functions in terms of time-dependent and independent Wigner functions. We show that the pure state quantum condition is preserved by the Moyal (but not by the classical Liouville) time evolution and is consistent with a generic stargenvalue equation. As a by-product Baker's converse construction is generalized both to an arbitrary stargenvalue equation, associated to a generic phase space symbol, as well as to the time-dependent case. These results are properly extended to the mixed state quantum condition, which is proved to imply the Heisenberg uncertainty relations. Globally, this formalism yields the complete characterization of the kinematical structure of Wigner quantum mechanics. The previous results are then succinctly generalized for various quasi-distributions. Finally, the formalism is illustrated through the simple examples of the harmonic oscillator and the free Gaussian wave packet. As a by-product, we obtain in the former example an integral representation of the Hermite polynomials.     

Scalar field cosmology in phase space

Using dynamical systems methods, we describe the evolution of a minimally coupled scalar field and a Friedmann-Lemaître-Robertson-Walker universe in the context of general relativity, which is relevant for inflation and late-time quintessence eras. Focussing on the spatially flat case, we examine the geometrical structure of the phase space, locate the equilibrium points of the system (de Sitter spaces with a constant scalar field), study their stability through both a third-order perturbation analysis and Lyapunov functions, and discuss the late-time asymptotics. As we do not specify the scalar field’s origin or its potential, the results are independent of the high-energy model.     

Klein-Gordon oscillators in noncommutative phase space

We study the Klein-Gordon oscillators in non-commutative (NC) phase space.We find that the Klein-Gordon oscillators in NC space and NC phase-space have a similar behaviour to the dynamics of a particle in commutative space moving in a uniform magnetic field.By solving the Klein-Gordon equation in NC phase space,we obtain the energy levels of the Klein-Gordon oscillators,where the additional terms related to the space-space and momentum-momentum non-commutativity are given explicitly.     

Chaotic systems in complex phase space

This paper examines numerically the complex classical trajectories of the kicked rotor and the double pendulum. Both of these systems exhibit a transition to chaos, and this feature is studied in complex phase space. Additionally, it is shown that the short-time and long-time behaviours of these two PT-symmetric dynamical models in complex phase space exhibit strong qualitative similarities.     

Turbulence-induced laser-beam distortions in phase space

A consecutive analysis of spatial-temporal disturbances of a laser beam propagating through a turbulent media was carried out. Evolutionary equations for the intensity distributions were obtained for a channel with different types of regular and stochastic spatial dispersion. The relative simplicity and physical validity of the integral relationships allows one to build them in the control algorithm for jam-protection of open-space operating channels.