On the integrability of the Calogero-Moser system in an external quartic potential and other many-body systems

The complete integrability of the Calogero-Moser system in an external quartic potential is proved and the Bäcklund transformation for this system is found. The admissible, within the isospectral deformation method, external potentials for other many-body systems are discussed.     

A trihamiltonian extension of the Toda lattice

A new Poisson structure is defined on a subspace of the Kupershmidt algebra, isomorphic to the space H$\mathfrak{H}$ of n×n$n\times n$ Hermitian matrices. The new Poisson structure is of Lie–Poisson type with respect to the standard Lie bracket of H$\mathfrak{H}$. This Poisson structure (together with two already known ones, obtained through a r$r$-matrix technique) allows to construct an extension of the periodic Toda lattice with n$n$ particles that fits in a trihamiltonian recurrence scheme. Some explicit examples of the construction and of the first integrals found in this way are given.     

Construction of exact dynamical invariants of two-dimensional classical system

A general method is used for the construction of second constant of motion of fourth order in momenta using the complex coordinates (z, _z ^- ). A fourth-order potential equation is obtained whose solutions directly provide a large class of integrable systems. The potential equation is tested with an interesting example which admits second constants of motion.     

The Non-Compact Quantum Dilogarithm and the Baxter Equations

A review of the recent formulation of the quantum discrete Liouville model in the strongly coupled regime (corresponding to the Virasoro central charge 1相似文献   

The Exact Solution of the Eigenvalue Problem for the Parametric Down Conversion Process in the Kerr Medium

The eigenproblem for a class of Hamiltonians of the parametric down conversion process in the Kerr medium is solved. Some physical characteristics of the system are calculated.     

Equations in Dual Variables for Whittaker Functions

It is known that the Whittaker functions w(q) associated with the group GL(N) are eigenfunctions of the Hamiltonians of the open Toda chain, hence satisfy a set of differential equations in the Toda variables q _i . Using the expression of the q _i for the closed Toda chain in terms of Sklyanin variables _i , and the known relations between the open and the closed Toda chains, we show that Whittaker functions also satisfy a set of new difference equations in _i .     

Exact propagator for an electron in a quadratic saddle-point potential and a magnetic field

We study the propagator for an electron moving in a two-dimensional (2D) quadratic saddle-point potential,in the presence of a perpendicular uniform magnetic field. A closed-form expression for the propagator is derived using the Feynmann path integrals.     

Integral Representation for the Eigenfunctions of a Quantum Periodic Toda Chain

An integral representation for the eigenfunctions of a quantum periodic Toda chain is constructed for the N-particle case. The multiple integral is calculated using the Cauchy residue formula. This gives the representation which reproduces the particular results obtained by Gutzwiller for the N=2,3 and 4-particle chain. Our method of solving the problem combines the ideas of Gutzwiller and the R-matrix approach of Sklyanin with the classical results in the theory of Whittaker functions. In particular, we calculate Sklyanin's invariant scalar product from the Plancherel formula for the Whittaker functions derived by Semenov-Tian-Shansky thus obtaining a natural interpretation of the Sklyanin measure in terms of the Harish-Chandra function.     

Exact surface energy and elementary excitations of the XXX spin-1/2 chain with arbitrary non-diagonal boundary fields

We study the physical properties of the XXX spin-1/2 chain with arbitrary non-diagonal boundary fields. By using a combination of numerical analysis and analytical method, we obtain the surface energy and elementary excitations of the model. It shows that the contributions of the two boundary fields to the surface energy are additive. We also find that there exists a kind of excitations related to the boundary string.     

On the exact solutions of nonlinear diffusion-reaction equations with quadratic and cubic nonlinearities

Attempts have been made to look for the soliton content in the solutions of the recently studied nonlinear diffusion-reaction equations [R S Kaushal, J. Phys. 38, 3897 (2005)] involving quadratic or cubic nonlinearities in addition to the convective flux term which renders the system nonconservative and the corresponding Hamiltonian non-Hermitian.     

On the solvability of the Calogero-Moser system in some external potentials and of other related hamiltonian systems

Explicit solutions for the Calogero-Moser system in a large class of external potentials including also some quartic oscillators are derived. The method applied extends to many other nonnatural hamiltonians related with the Calogero-Moser system.     

The Laughlin liquid in an external potential

We study natural perturbations of the Laughlin state arising from the effects of trapping and disorder. These are N-particle wave functions that have the form of a product of Laughlin states and analytic functions of the N variables. We derive an upper bound to the ground state energy in a confining external potential, matching exactly a recently derived lower bound in the large N limit. Irrespective of the shape of the confining potential, this sharp upper bound can be achieved through a modification of the Laughlin function by suitably arranged quasi-holes.     

Determining NMR flow propagator moments in porous rocks without the influence of relaxation

Flow propagators, used for the study of advective motion of brine solution in porous carbonate and sandstone rocks, have been obtained without the influence of Nuclear Magnetic Resonance (NMR) relaxation times, T₁ and T₂. These spin relaxation mechanisms normally result in a loss of signal that varies depending on the displacement ζ of the flowing spins, thereby preventing the acquisition of quantitative propagator data. The full relaxation behaviour of the system under flow needs to be characterised to enable the implementation of a true quantitative measurement. Two-dimensional NMR correlations of ζ − T₂ and T₁ − T₂ are used in combination to provide the flow propagators without relaxation weighting. T₁ − ζ correlations cannot be used due to the loss of T₁ information during the displacement observation time Δ. Here the moments of the propagators are extracted by statistical analysis of the full propagator shape. The measured displacements (first moments) are seen to correlate with the expected mean displacements for long observation times Δ. The higher order moments of the propagators determined by this method indicate those obtained previously using a correction were overestimated.     

On the dynamics of a particle on a cone

A detailed study of the classical and quantum mechanics of a free particle on a double cone and a particle bound to its tip by a harmonic oscillator potential is presented.     

Chaos in the hydrogen atom interacting with external fields

In this review we discuss the chaotic dynamics (both classical and quantal aspects) of a simple atomic system, namely hydrogen atom interacting with time independent and time dependent external fields. These include: i) static electric field, ii) static magnetic field, iii) combined electric and magnetic fields, in parallel and perpendicular configuration, iv) instantaneous and generalized van der Waals field, v) mass anisotropy and vi) linearly and circularly polarized microwave fields.     

Density of states of the binary alloy in the coherent potential approximation

The density of states of an electron in a binary alloy in the tight binding model is calculated in the single site coherent potential approximation (CPA) as a function of the concentration and the site energy difference. The fluctuations in the site energies due to the random environment is taken into account approximately by giving width to the site energy probability distribution function, which is normally a sum of two delta functions with proper weight factor.     

Entanglement evolution of a two-qubit system with decay beyond the rotating-wave approximation

The entanglement property of two identical atoms, initially entangled in Bell states, coupled to a single-mode cavity is considered. Based on the reduced non-perturbative quantum master equation method, the entanglement evolution of the two atoms with decay is investigated beyond the conventional rotating-wave approximation. We show that the counter-rotating wave terms, usually neglected, have a great influence on the disentanglement behaviour of the system. The phenomena of entanglement sudden death and entanglement sudden birth will occur. In addition, we show that the entanglement can be strengthened by introducing the dipole--dipole interaction of the two atoms.     

A GMSA calculation of the radial distribution functions of molten RbCl

Summary The generalized mean spherical approximation (GMSA) for a fluid of charged hard spheres of equal diameters is used for calculating the radial distribution functions of molten RbCl. The results are compared to neutron diffraction data and a good overall agreement is found between the experimental and the theoreticalg _ij (r). Further application of this same approach to the case of ionic melts with ionic species of different diameters is discussed. Work supported in part by Comitato Regionale Ricerche Nucleari and Struttura della Materia (CRRNSM), Sicily, Italy.     

Mean-field kinetic theory of a classical electron gas in a periodic potential. I. Formal solution of the Vlasov equation

We study the static and dynamic behavior of a classical electron gas in the periodic potential created by an ionic lattice. Using the well-known Vlasov approximation, we derive a mean-field kinetic equation for the density-response function of the electrons. This equation is formally solved in terms of the trajectories of one electron in the mean-field equilibrium potential which determines the local electronic density. The mean-field expressions of the static and dynamic structure factors are then obtained through the fluctuation-dissipation theorem. These expressions are used to show that within the mean-field approximation the system is a conductor at all temperatures and for all dimensions.