Gravitational and axial anomalies for generalized Euclidean Taub-NUT metrics

The gravitational anomalies are investigated for generalized Euclidean Taub-NUT metrics which admit hidden symmetries analogous to the Runge-Lenz vector of the Kepler-type problem. In order to evaluate the axial anomalies, the index of the Dirac operator for these metrics with the APS boundary condition is computed. The role of the Killing-Yano tensors is discussed for these two types of quantum anomalies.Comment: 23 page

Supersonic Discrete Kink-Solitons and Sinusoidal Patterns with "Magic" wavenumber in Anharmonic Lattices

The sharp pulse method is applied to Fermi-Pasta-Ulam (FPU) and Lennard-Jones (LJ) anharmonic lattices. Numerical simulations reveal the presence of high energy strongly localized ``discrete'' kink-solitons (DK), which move with supersonic velocities that are proportional to kink amplitudes. For small amplitudes, the DK's of the FPU lattice reduce to the well-known ``continuous'' kink-soliton solutions of the modified Korteweg-de Vries equation. For high amplitudes, we obtain a consistent description of these DK's in terms of approximate solutions of the lattice equations that are obtained by restricting to a bounded support in space exact solutions with sinusoidal pattern characterized by the ``magic'' wavenumber $k=2\pi/3$. Relative displacement patterns, velocity versus amplitude, dispersion relation and exponential tails found in numerical simulations are shown to agree very well with analytical predictions, for both FPU and LJ lattices.Comment: Europhysics Letters (in print

Statistics of Impedance, Local Density of States, and Reflection in Quantum Chaotic Systems with Absorption

We are interested in finding the joint distribution function of the real and imaginary parts of the local Green function for a system with chaotic internal wave scattering and a uniform energy loss (absorption). For a microwave cavity attached to a single-mode antenna the same quantity has a meaning of the complex cavity impedance. Using the random matrix approach, we relate its statistics to that of the reflection coefficient and scattering phase and provide exact distributions for systems with beta=2 and beta=4 symmetry class. In the case of beta=1 we provide an interpolation formula which incorporates all known limiting cases and fits excellently available experimental data as well as diverse numeric tests.Comment: 4 pages, 1 figur

The decay of photoexcited quantum systems: a description within the statistical scattering model

The decay of photoexcited quantum systems (examples are photodissociation of molecules and autoionization of atoms) can be viewed as a half-collision process (an incoming photon excites the system which subsequently decays by dissociation or autoionization). For this reason, the standard statistical approach to quantum scattering, originally developed to describe nuclear compound reactions, is not directly applicable. Using an alternative approach, correlations and fluctuations of observables characterizing this process were first derived in [Fyodorov YV and Alhassid Y 1998 Phys. Rev. A 58, R3375]. Here we show how the results cited above, and more recent results incorporating direct decay processes, can be obtained from the standard statistical scattering approach by introducing one additional channel.Comment: 7 pages, 2 figure

Peierls Instabilities in Quasi-One-Dimensional Quantum Double-Well Chains

Peierls-type instabilities in quarter-filled ($\bar{n}=1/2$) and half-filled ($\bar{n}=1$) quantum double-well hydrogen-bonded chain are investigated analytically in the framework of two-stage orientational-tunnelling model with additional inclusion of the interactions of protons with two different optical phonon branches. It is shown that when the energy of proton-phonon coupling becomes large, the system undergoes a transition to a various types of insulator states. The influence of two different transport amplitudes on ground states properties is studied. The results are compared with the pressure effect experimental investigations in superprotonic systems and hydrogen halides at low temperatures.Comment: 7 pages, RevTeX, 9 eps figure

Electron-ion recombination of Si IV forming Si III: Storage-ring measurement and multiconfiguration Dirac-Fock calculations

The electron-ion recombination rate coefficient for Si IV forming Si III was measured at the heavy-ion storage-ring TSR. The experimental electron-ion collision energy range of 0-186 eV encompassed the 2p(6) nl n'l' dielectronic recombination (DR) resonances associated with 3s to nl core excitations, 2s 2p(6) 3s nl n'l' resonances associated with 2s to nl (n=3,4) core excitations, and 2p(5) 3s nl n'l' resonances associated with 2p to nl (n=3,...,infinity) core excitations. The experimental DR results are compared with theoretical calculations using the multiconfiguration Dirac-Fock (MCDF) method for DR via the 3s to 3p n'l' and 3s to 3d n'l' (both n'=3,...,6) and 2p(5) 3s 3l n'l' (n'=3,4) capture channels. Finally, the experimental and theoretical plasma DR rate coefficients for Si IV forming Si III are derived and compared with previously available results.Comment: 13 pages, 9 figures, 3 tables. Accepted for publication in Physical Review

Discrete kink dynamics in hydrogen-bonded chains I: The one-component model

We study topological solitary waves (kinks and antikinks) in a nonlinear one-dimensional Klein-Gordon chain with the on-site potential of a double-Morse type. This chain is used to describe the collective proton dynamics in quasi-one-dimensional networks of hydrogen bonds, where the on-site potential plays role of the proton potential in the hydrogen bond. The system supports a rich variety of stationary kink solutions with different symmetry properties. We study the stability and bifurcation structure of all these stationary kink states. An exactly solvable model with a piecewise ``parabola-constant'' approximation of the double-Morse potential is suggested and studied analytically. The dependence of the Peierls-Nabarro potential on the system parameters is studied. Discrete travelling-wave solutions of a narrow permanent profile are shown to exist, depending on the anharmonicity of the Morse potential and the cooperativity of the hydrogen bond (the coupling constant of the interaction between nearest-neighbor protons).Comment: 12 pages, 20 figure

A supersonic crowdion in mica: Ultradiscrete kinks with energy between 40^{40}K recoil and transmission sputtering

In this chapter we analyze in detail the behaviour and properties of the kinks found in an one dimensional model for the close packed rows of potassium ions in mica muscovite. The model includes realistic potentials obtained from the physics of the problem, ion bombardment experiments and molecular dynamics fitted to experiments. These kinks are supersonic and have an unique velocity and energy. They are ultradiscrete involving the translation of an interstitial ion, which is the reason they are called 'crowdions'. Their energy is below the most probable source of energy, the decay of the $^{40}$K isotope and above the energy needed to eject an atom from the mineral, a phenomenon that has been observed experimentallyComment: 28 pages, 15 figure

Quantum degeneracy in mesoscopic matter: Casimir effect and Bose-Einstein condensation

The ground-state phonon pressure is an analogue to the famous Casimir pressure of vacuum produced by zero-point photons. The acoustic Casimir forces are, however, many orders of magnitude weaker than the electromagnetic Casimir forces, as the typical speed of sound is 100 000 times smaller than the speed of light. Because of its weakness, zero-point acoustic Casimir pressure was never observed, although the pressure of artificially introduced sound noise on a narrow aperture has been reported. However, the magnitude of Casimir pressure increases as $1/L^3$ with the decrease of the sample size $L$, and reaches picoNewtons in the sub-micron scales. We demonstrate and measure the acoustic Casimir pressure induced by zero-point phonons in solid helium adsorbed on a carbon nanotube. We have also observed Casimir-like "pushing out" thermal phonons with the decreasing temperature or the length. We also show that all thermodynamic quantities are size-dependent, and therefore in the mesoscopic range $L\lesssim\hbar{c}/(k_BT)$ quadruple points are possible on the phase diagram where four different phases coexist. Due to the smallness of solid helium sample, temperature of Bose-Einstein condensation (BEC) of vacancies is relatively high, $10-100$ mK. This allowed us to experimentally discover the BEC in a system of zero-point vacancies, predicted more than 50 years ago