Constants of motion of the four-particle Calogero model

We present the explicit expressions of the complete set of constants of motion of four-particle Calogero model with excluded center of mass, i.e. of the A ₃ rational Calogero model. Then we find the constants of motion of its spherical part, defining two-dimensional 12-center spherical oscillator, with the force centers located at the vertexes of cuboctahedron.     

Hubbard model,conserved quantities,and computer algebra

The constants of motion of the half-filled four-point Hubbard model with cyclic boundary conditions are given in Wannier and Bloch representation. The total number operator and total spin operator are conserved and spin-reversal symmetry exists. In Wannier representation we have additionally the C_4v symmetry and in Bloch representation we have the total momentum operator which is conserved. The anticommutation relations for Fermi operators with spin are implemented using computer algebra. Using computer algebra, all the constants of motion are given. The one-dimensional Hubbard model admits a Lax representation. From the Lax pair we find a new constant of motion.     

Standard model with partial gauge invariance

We study cosmological solutions in the effective heterotic string theory with ????-correction terms in the string frame. It is pointed out that the effective theory has an ambiguity via field redefinition and we analyze generalized effective theories due to this ambiguity. We restrict our analysis to the effective theories which give equations of motion of second order in the derivatives, just as ??Galileon?? field theory. This class of effective actions contains two free coupling constants. We find de Sitter solutions as well as the power-law expanding universes in our four-dimensional Einstein frame. The accelerated expanding universes are always attractors in the present dynamical system.     

Integrable model for interacting electrons in metallic grains.

We find an integrable generalization of the BCS model with nonuniform Coulomb and pairing interaction. The Hamiltonian is integrable by construction since it is a functional of commuting operators; these operators, which therefore are constants of motion of the model, contain the anisotropic Gaudin Hamiltonians. The exact solution is obtained diagonalizing them by means of Bethe ansatz. Uniform pairing and Coulomb interaction are obtained as the "isotropic limit" of the Gaudin Hamiltonians. We discuss possible applications of this model to a single grain and to a system of few interacting grains.     

Complete integrability of geodesic motion in general higher-dimensional rotating black-hole spacetimes

We explicitly exhibit n-1=[D/2]-1 constants of motion for geodesics in the general D-dimensional Kerr-NUT-AdS rotating black hole spacetime, arising from contractions of even powers of the 2-form obtained by contracting the geodesic velocity with the dual of the contraction of the velocity with the (D-2)-dimensional Killing-Yano tensor. These constants of motion are functionally independent of each other and of the D-n+1 constants of motion that arise from the metric and the D-n=[(D+1)/2] Killing vectors, making a total of D independent constants of motion in all dimensions D. The Poisson brackets of all pairs of these D constants are zero, so geodesic motion in these spacetimes is completely integrable.     

Symmetries and Motions in NUT-Taub Spinning Space

We review the geodesic motion of pseudo-classical spinning particles in curved space. We describe the generalized Killing equations for spinning spaces and express the constants of motion. We apply the formalism to solve for the motion of a pseudo-classical Dirac fermion in NUT-Taub spinning space and analyze the motion on a cone and on a plane.     

Spinning Particles in Curved Spacetime

We briefly discuss the relevant equations for the motion of spinning particles in curved spacetime. We describe the generalized Killing equations for spinning spaces and derive the constants of motion. We apply the formalism to solve for the motion of a pseudoclassical spinning particle in Schwarzschild–de Sitter spacetime.     

Orbital and epicyclic motion of charged test particles around non-rotating Einstein-Æther black holes

The study of charged test particle dynamics in the combined black hole gravitational field and magnetic field around it could provide important theoretical insight into astrophysical processes around such compact object. We have explored the orbital and epicyclic motion of charged test particles in the background of non-rotating Einstein-Æther black holes in the presence of external uniform magnetic field. We numerically integrate the equations of motion and analyze the trajectories of the charged test particles. We examined the stability of circular orbits using effective potential technique and study the characteristics of innermost stable circular orbits. We analyze the key features of quasi-harmonic oscillations of charged test particles nearby the stable circular orbits in an equatorial plane of the black hole, and investigate the radial profiles of the frequencies of latitudinal as well as radial harmonic oscillations in dependence on the strength of magnetic field, mass of the black hole and dimensionless coupling constants of the theory. We demonstrate that the magnetic field and dimensionless parameters of the theory have strong influence on charged particle motion around Einstein-Æther black holes.     

Integration of the continuous Heisenberg spin chain through the inverse scattering method

The inverse scattering method is applied to the Heisenberg chain. We give the general scheme of the solution of the equations of motion. We describe the process of solitons scattering and show the existence of an infinite series of constants of motion.     

Propagation of a femtosecond pulse in a microresonator visualized in time

A noninvasive pulse-tracking technique has been exploited to observe the time-resolved motion of an ultrashort light pulse within an integrated optical microresonator. We follow a pulse as it completes several round trips in the resonator, directly mapping the resonator modes in space and time. Our time-dependent and phase-sensitive measurement provides direct access to the angular group and phase velocity of the modes in the resonator. From the measurement the coupling constants between the access waveguides and the resonator are retrieved while at the same time the loss mechanisms throughout the structure are directly visualized.     

Rolling as a “continuing collision”

We show that two basic mechanical processes, the collision of particles and rolling motion of a sphere on a plane, are intimately related. According to our recent findings, the restitution coefficient for colliding spherical particles , which characterizes the energy loss upon collision, is directly related to the rolling friction coefficient for a viscous sphere on a hard plane. We quantify both coefficients in terms of material constants which allows to determine either of them provided the other is known. This relation between the coefficients may give rise to a novel experimental technique to determine alternatively the coefficient of restitution or the coefficient of rolling friction. Received 5 May 1999     

Rotational levels of double-minimum potentials: The linear BAB molecule with unequal bond lengths

The rotational constants and energy levels for the linear BAB system are studied under the assumption of unequal AB bond lengths. The quantum mechanical Hamiltonians is derived according to a formalism which allows for a large-amplitude antisymmetric stretching motion. A numberical integration technique is used to obtain solutions of the one-dimensional Schroedinger equation corresponding to a zeroth-order approximation of the Hamiltonian. The behavior of the resulting rotational constants for various heights of the barrier in the double-minimum potential is discussed.     

Spinning Particles in NUT–Reissner–Nordstrom Space–Time

We study the geodesic motion of pseudo-classical spinning particles in the NUT–Reissner–Nordstrom space–time. We investigate the generalized Killing equations for spinning space and derive the constants of the motion in terms of the solutions of these equations. We give an analysis of the motion on a cone and on a plane.     

Spinning Particles in Reissner-Nordström-de Sitter Spacetime

We study the geodesic motion of pseudo-classical spinning particles in the Reissner-Nordström-de Sitter spacetime. We investigate the generalized Killing equations for spinning space and derive the constants of motion in terms of the solutions of these equations. We discuss bound state orbits in a plane.     

Constants of motion in NMR spectroscopy

We present a general method for constructing a subset of the constants of motion in terms of products of spin operators. These operators are then used to give insight into the multi-spin orders comprising the quasi-equilibrium state formed under a Jeener-Broekaert sequence in small, dipolar-coupled, spin systems. We further show that constants of motion that represent single-quantum coherences are present due to the symmetry of the dipolar Hamiltonian under 180 degrees spin rotations, and that such coherences contribute a DC component to the FID which vanishes in the absence of the flip-flop terms and is only present for spin clusters with an odd number of spins.     

Analytic form of the simplest limit cycle in the Lorenz model

A method to obtain the analytic form of limit cycles is presented from a viewpoint of constants of motion in dissipative systems. The method is applied to the Lorenz equation in the high-Rayleigh-number limit. The analytic form of the simplest limit cycle is obtained, which is in a good agreement with the result of computer simulation.     

New model of kaon regeneration

It is shown that in the standard model of K_S~0 regeneration a system of non-coupled equations of motion is used instead of the coupled ones. A model alternative to the standard one is proposed. A calculation performed by means of the diagram technique agrees with that based on exact solution of the equations of motion.     

Geodesic Motions in Euclidean Taub-NUT Spinning Spaces

We investigate the geodesic motions of pseudo-classical spin- \frac12\frac{1}{2} point particles in the Euclidean Taub-NUT space. We derive the constants of motion from the solutions of the generalized Killing equations for spinning spaces and exploiting those the motion of pseudo-classical Dirac fermions are analyzed on a cone and plane.     

On the chiral hubbard model and the chiral Kondo lattice model

The integrability of the one-dimensional chiral Hubbard model is discussed in the limit of strong interaction,U=. The system is shown to be integrable in the sense of the existence of an infinite number of constants of motion. The system is related to a chiral Kondo lattice model at strong interactionJ=+.