Multiparticle Interference, GHZ Entanglement, and Full Counting Statistics

We investigate the quantum transport in a generalized N-particle Hanbury Brown--Twiss setup enclosing magnetic flux, and demonstrate that the Nth-order cumulant of current cross correlations exhibits Aharonov-Bohm oscillations, while there is no such oscillation in all the lower-order cumulants. The multiparticle interference results from the orbital Greenberger-Horne-Zeilinger entanglement of N indistinguishable particles. For sufficiently strong Aharonov-Bohm oscillations the generalized Bell inequalities may be violated, proving the N-particle quantum nonlocality.Comment: 4 pages, 1 figure, published versio

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

Breaking of ergodicity and long relaxation times in systems with long-range interactions

The thermodynamic and dynamical properties of an Ising model with both short range and long range, mean field like, interactions are studied within the microcanonical ensemble. It is found that the relaxation time of thermodynamically unstable states diverges logarithmically with system size. This is in contrast with the case of short range interactions where this time is finite. Moreover, at sufficiently low energies, gaps in the magnetization interval may develop to which no microscopic configuration corresponds. As a result, in local microcanonical dynamics the system cannot move across the gap, leading to breaking of ergodicity even in finite systems. These are general features of systems with long range interactions and are expected to be valid even when the interaction is slowly decaying with distance.Comment: 4 pages, 5 figure

Thermodynamics of self-gravitating systems

Self-gravitating systems are expected to reach a statistical equilibrium state either through collisional relaxation or violent collisionless relaxation. However, a maximum entropy state does not always exist and the system may undergo a ``gravothermal catastrophe'': it can achieve ever increasing values of entropy by developing a dense and hot ``core'' surrounded by a low density ``halo''. In this paper, we study the phase transition between ``equilibrium'' states and ``collapsed'' states with the aid of a simple relaxation equation [Chavanis, Sommeria and Robert, Astrophys. J. 471, 385 (1996)] constructed so as to increase entropy with an optimal rate while conserving mass and energy. With this numerical algorithm, we can cover the whole bifurcation diagram in parameter space and check, by an independent method, the stability limits of Katz [Mon. Not. R. astr. Soc. 183, 765 (1978)] and Padmanabhan [Astrophys. J. Supp. 71, 651 (1989)]. When no equilibrium state exists, our relaxation equation develops a self-similar collapse leading to a finite time singularity.Comment: 54 pages. 25 figures. Submitted to Phys. Rev.

Spectrum of cosmic rays, produced in supernova remnants

Nonlinear kinetic theory of cosmic ray (CR) acceleration in supernova remnants is employed to calculate CR spectra. The magnetic field in SNRs is assumed to be significantly amplified by the efficiently accelerating nuclear CR component. It is shown that the calculated CR spectra agree in a satisfactory way with the existing measurements up to the energy $10^{17}$ eV. The power law spectrum of protons extends up to the energy $3\times 10^{15}$ eV with a subsequent exponential cutoff. It gives a natural explanation for the observed knee in the Galactic CR spectrum. The maximum energy of the accelerated nuclei is proportional to their charge number $Z$. Therefore the break in the Galactic CR spectrum is the result of the contribution of progressively heavier species in the overall CR spectrum so that at $10^{17}$ eV the CR spectrum is dominated by iron group nuclei. It is shown that this component plus a suitably chosen extragalactic CR component can give a consistent description for the entire Galactic CR spectrum.Comment: 4 pages with emulateapj, 3 figures, accepted for publication in the Astrophysical Journal Letter

Irreducible actions and compressible modules

Any finite set of linear operators on an algebra $A$ yields an operator algebra $B$ and a module structure on A, whose endomorphism ring is isomorphic to a subring $A^B$ of certain invariant elements of $A$. We show that if $A$ is a critically compressible left $B$-module, then the dimension of its self-injective hull $A$ over the ring of fractions of $A^B$ is bounded by the uniform dimension of $A$ and the number of linear operators generating $B$. This extends a known result on irreducible Hopf actions and applies in particular to weak Hopf action. Furthermore we prove necessary and sufficient conditions for an algebra A to be critically compressible in the case of group actions, group gradings and Lie actions

X 1908+075: An X-ray Binary with a 4.4 day Period

X 1908+075 is an optically unidentified and highly absorbed X-ray source that appears in early surveys such as Uhuru, OSO-7, Ariel V, HEAO-1, and the EXOSAT Galactic Plane Survey. These surveys measured a source intensity in the range of 2-12 mCrab at 2-10 keV, and the position was localized to ~ 0.5 degrees. We use the Rossi X-ray Timing Explorer (RXTE) All Sky Monitor (ASM) to confirm our expectation that a particular Einstein IPC detection (1E 1908.4+0730) provides the correct position for X 1908+075. The analysis of the coded mask shadows from the ASM for the position of 1E 1908.4+0730 yields a persistent intensity ~ 8 mCrab (1.5-12 keV) over a 3 year interval beginning in 1996 February. Furthermore, we detect a period of 4.400 +- 0.001 days with a false alarm probability < 1.0e-7 . The folded light curve is roughly sinusoidal, with an amplitude that is 22 % of the mean flux. The X-ray period may be attributed to the scattering and absorption of X-rays through a stellar wind combined with the orbital motion in a binary system. We suggest that X 1908+075 is an X-ray binary with a high mass companion star.Comment: 6 pages, two-column,"emulateapj" style, submitted to Ap

Interfering Doorway States and Giant Resonances. II: Transition Strengths

The mixing of the doorway components of a giant resonance (GR) due to the interaction via common decay channels influences significantly the distribution of the multipole strength and the energy spectrum of the decay products of the GR. The concept of the partial widths of a GR becomes ambiguous when the mixing is strong. In this case, the partial widths determined in terms of the $K$- and $S$-matrices must be distinguished. The photoemission turns out to be most sensitive to the overlapping of the doorway states. At high excitation energies, the interference between the doorway states leads to a restructuring towards lower energies and apparent quenching of the dipole strength.Comment: 17 pages, LaTeX, 5 figures as JPEG, to appear in PRC (July 1997

Time-dependent magnetohydrodynamic self-similar extragalactic jets

Extragalactic jets are visualized as dynamic erruptive events modelled by time-dependent magnetohydrodynamic (MHD) equations. The jet structure comes through the temporally self-similar solutions in two-dimensional axisymmetric spherical geometry. The two-dimensional magnetic field is solved in the finite plasma pressure regime, or finite $\beta$ regime, and it is described by an equation where plasma pressure plays the role of an eigenvalue. This allows a structure of magnetic lobes in space, among which the polar axis lobe is strongly peaked in intensity and collimated in angular spread comparing to the others. For this reason, the polar lobe overwhelmes the other lobes, and a jet structure arises in the polar direction naturally. Furthermore, within each magnetic lobe in space, there are small secondary regions with closed two-dimensional field lines embedded along this primary lobe. In these embedded magnetic toroids, plasma pressure and mass density are much higher accordingly. These are termed as secondary plasmoids. The magnetic field lines in these secondary plasmoids circle in alternating sequence such that adjacent plasmoids have opposite field lines. In particular, along the polar primary lobe, such periodic plasmoid structure happens to be compatible with radio observations where islands of high radio intensities are mapped

Sensitivity of CPT Tests with Neutral Mesons

The sensitivity of experiments with neutral mesons to possible indirect CPT violation is examined. It is shown that experiments conventionally regarded as equivalent can have CPT reaches differing by orders of magnitude within the framework of a minimal CPT- and Lorentz-violating extension of the standard model.Comment: 4 pages REVTeX, published in Physical Review Letter