Quantum to classical transition in a system with a mixed classical dynamics

We study how decoherence rules the quantum-classical transition of the Kicked Harmonic Oscillator (KHO). When the amplitude of the kick is changed the system presents a classical dynamics that range from regular to a strong chaotic behavior. We show that for regular and mixed classical dynamics, and in the presence of noise, the distance between the classical and the quantum phase space distributions is proportional to a single parameter $\chi\equiv K\hbar_{\rm eff}^2/4D^{3/2}$ which relates the effective Planck constant $\hbar_{\rm eff}$, the kick amplitude $K$ and the diffusion constant $D$. This is valid when $\chi < 1$, a case that is always attainable in the semiclassical regime independently of the value of the strength of noise given by $D$. Our results extend a recent study performed in the chaotic regime.Comment: 10 pages, 7 figure

Exact Quantum Solutions of Extraordinary N-body Problems

The wave functions of Boson and Fermion gases are known even when the particles have harmonic interactions. Here we generalise these results by solving exactly the N-body Schrodinger equation for potentials V that can be any function of the sum of the squares of the distances of the particles from one another in 3 dimensions. For the harmonic case that function is linear in r^2. Explicit N-body solutions are given when U(r) = -2M \hbar^{-2} V(r) = \zeta r^{-1} - \zeta_2 r^{-2}. Here M is the sum of the masses and r^2 = 1/2 M^{-2} Sigma Sigma m_I m_J ({\bf x}_I - {\bf x}_J)^2. For general U(r) the solution is given in terms of the one or two body problem with potential U(r) in 3 dimensions. The degeneracies of the levels are derived for distinguishable particles, for Bosons of spin zero and for spin 1/2 Fermions. The latter involve significant combinatorial analysis which may have application to the shell model of atomic nuclei. For large N the Fermionic ground state gives the binding energy of a degenerate white dwarf star treated as a giant atom with an N-body wave function. The N-body forces involved in these extraordinary N-body problems are not the usual sums of two body interactions, but nor are forces between quarks or molecules. Bose-Einstein condensation of particles in 3 dimensions interacting via these strange potentials can be treated by this method.Comment: 24 pages, Latex. Accepted for publication in Proceedings of the Royal Societ

Forming Galaxies with MOND

Beginning with a simple model for the growth of structure, I consider the dissipationless evolution of a MOND-dominated region in an expanding Universe by means of a spherically symmetric N-body code. I demonstrate that the final virialized objects resemble elliptical galaxies with well-defined relationships between the mass, radius, and velocity dispersion. These calculations suggest that, in the context of MOND, massive elliptical galaxies may be formed early (z > 10) as a result of monolithic dissipationless collapse. Then I reconsider the classic argument that a galaxy of stars results from cooling and fragmentation of a gas cloud on a time scale shorter than that of dynamical collapse. Qualitatively, the results are similar to that of the traditional picture; moreover, the existence, in MOND, of a density-temperature relation for virialized, near isothermal objects as well as a mass-temperature relation implies that there is a definite limit to the mass of a gas cloud where this condition can be met-- an upper limit corresponding to that of presently observed massive galaxies.Comment: 9 pages, 9 figures, revised in response to comments of referee. Table added, extended discussion, accepted MNRA

Quantum Instantons and Quantum Chaos

Based on a closed form expression for the path integral of quantum transition amplitudes, we suggest rigorous definitions of both, quantum instantons and quantum chaos. As an example we compute the quantum instanton of the double well potential.Comment: Extended version with new figures. Text (LaTeX), 5 Figures (epsi files

Analytical solutions of the lattice Boltzmann BGK model

Analytical solutions of the two dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plain Poiseuille flow and the plain Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time $\tau$ and the lattice spacing. The analytic solutions are the exact representation of these two flows without any approximation.Comment: 10 pages, no postscript figure provide

New results on GP Com

We present high resolution optical and UV spectra of the 46 min orbital period, helium binary, GP Com. Our data contains simultaneous photometric correction which confirms the flaring behaviour observed in previous optical and UV data. In this system all lines show a triple peaked structure where the outer two peaks are associated with the accretion disc around the compact object. The main aim of this paper is to constrain the origin of the central peak, also called ``central spike''. We find that the central spike contributes to the flare spectra indicating that its origin is probably the compact object. We also detect that the central spike moves with orbital phase following an S-wave pattern. The radial velocity semiamplitude of the S-wave is ~10 km/s indicating that its origin is near the centre of mass of the system, which in this case lies very close to the white dwarf. Our resolution is higher than that of previous data which allows us to resolve structure in the central peak of the line. The central spike in three of the HeI lines shows another peak blueshifted with respect to the main peak. We propose that one of the peaks is a neutral helium forbidden transition excited in a high electron density region. This forbidden transition is associated with the permitted one (the stronger peak in two of the lines). The presence of a high electron density region again favours the white dwarf as their origin.Comment: 14 pages, 16 figures. Accepted for publication in A&

A Phase-Space Approach to Collisionless Stellar Systems Using a Particle Method

A particle method for reproducing the phase space of collisionless stellar systems is described. The key idea originates in Liouville's theorem which states that the distribution function (DF) at time t can be derived from tracing necessary orbits back to t=0. To make this procedure feasible, a self-consistent field (SCF) method for solving Poisson's equation is adopted to compute the orbits of arbitrary stars. As an example, for the violent relaxation of a uniform-density sphere, the phase-space evolution which the current method generates is compared to that obtained with a phase-space method for integrating the collisionless Boltzmann equation, on the assumption of spherical symmetry. Then, excellent agreement is found between the two methods if an optimal basis set for the SCF technique is chosen. Since this reproduction method requires only the functional form of initial DFs but needs no assumptions about symmetry of the system, the success in reproducing the phase-space evolution implies that there would be no need of directly solving the collisionless Boltzmann equation in order to access phase space even for systems without any special symmetries. The effects of basis sets used in SCF simulations on the reproduced phase space are also discussed.Comment: 16 pages w/4 embedded PS figures. Uses aaspp4.sty (AASLaTeX v4.0). To be published in ApJ, Oct. 1, 1997. This preprint is also available at http://www.sue.shiga-u.ac.jp/WWW/prof/hozumi/papers.htm

Two-dimensional maps at the edge of chaos: Numerical results for the Henon map

The mixing properties (or sensitivity to initial conditions) of two-dimensional Henon map have been explored numerically at the edge of chaos. Three independent methods, which have been developed and used so far for the one-dimensional maps, have been used to accomplish this task. These methods are (i)measure of the divergence of initially nearby orbits, (ii)analysis of the multifractal spectrum and (iii)computation of nonextensive entropy increase rates. The obtained results strongly agree with those of the one-dimensional cases and constitute the first verification of this scenario in two-dimensional maps. This obviously makes the idea of weak chaos even more robust.Comment: 4 pages, 3 figure

Infinite ergodic theory and Non-extensive entropies

We bring into account a series of result in the infinite ergodic theory that we believe that they are relevant to the theory of non-extensive entropie

The last integrable case of kozlov-Treshchev Birkhoff integrable potentials

We establish the integrability of the last open case in the Kozlov-Treshchev classification of Birkhoff integrable Hamiltonian systems. The technique used is a modification of the so called quadratic Lax pair for $D_n$ Toda lattice combined with a method used by M. Ranada in proving the integrability of the Sklyanin case.Comment: 13 page