Locality and topology in the molecular Aharonov-Bohm effect

It is shown that the molecular Aharonov-Bohm effect is neither nonlocal nor topological in the sense of the standard magnetic Aharonov-Bohm effect. It is further argued that there is a close relationship between the molecular Aharonov-Bohm effect and the Aharonov-Casher effect for an electrically neutral spin$-{1/2}$ particle encircling a line of charge.Comment: 3 pages, no figure

Coupling SPH and thermochemical models of planets: Methodology and example of a Mars-sized body

Giant impacts have been suggested to explain various characteristics of terrestrial planets and their moons. However, so far in most models only the immediate effects of the collisions have been considered, while the long-term interior evolution of the impacted planets was not studied. Here we present a new approach, combining 3-D shock physics collision calculations with 3-D thermochemical interior evolution models. We apply the combined methods to a demonstration example of a giant impact on a Mars-sized body, using typical collisional parameters from previous studies. While the material parameters (equation of state, rheology model) used in the impact simulations can have some effect on the long-term evolution, we find that the impact angle is the most crucial parameter for the resulting spatial distribution of the newly formed crust. The results indicate that a dichotomous crustal pattern can form after a head-on collision, while this is not the case when considering a more likely grazing collision. Our results underline that end-to-end 3-D calculations of the entire process are required to study in the future the effects of large-scale impacts on the evolution of planetary interiors.Comment: 29 pages, 10 figures, accepted for publication in Icaru

Correlated two-photon emission by transitions of Dirac-Volkov states in intense laser fields: QED predictions

In an intense laser field, an electron may decay by emitting a pair of photons. The two photons emitted during the process, which can be interpreted as a laser-dressed double Compton scattering, remain entangled in a quantifiable way: namely, the so-called concurrence of the photon polarizations gives a gauge-invariant measure of the correlation of the hard gamma rays. We calculate the differential rate and concurrence for a backscattering setup of the electron and photon beam, employing Volkov states and propagators for the electron lines, thus accounting nonperturbatively for the electron-laser interaction. The nonperturbative results are shown to differ significantly compared to those obtained from the usual double Compton scattering.Comment: 32 pages, 12 figure

Searching for degeneracies of real Hamiltonians using homotopy classification of loops in SO(nn)

Topological tests to detect degeneracies of Hamiltonians have been put forward in the past. Here, we address the applicability of a recently proposed test [Phys. Rev. Lett. {\bf 92}, 060406 (2004)] for degeneracies of real Hamiltonian matrices. This test relies on the existence of nontrivial loops in the space of eigenbases SO$(n)$. We develop necessary means to determine the homotopy class of a given loop in this space. Furthermore, in cases where the dimension of the relevant Hilbert space is large the application of the original test may not be immediate. To remedy this deficiency, we put forward a condition for when the test is applicable to a subspace of Hilbert space. Finally, we demonstrate that applying the methodology of [Phys. Rev. Lett. {\bf 92}, 060406 (2004)] to the complex Hamiltonian case does not provide any new information.Comment: Minor changes, journal reference adde

Sufficient Conditions for Fast Switching Synchronization in Time Varying Network Topologies

In previous work, empirical evidence indicated that a time-varying network could propagate sufficient information to allow synchronization of the sometimes coupled oscillators, despite an instantaneously disconnected topology. We prove here that if the network of oscillators synchronizes for the static time-average of the topology, then the network will synchronize with the time-varying topology if the time-average is achieved sufficiently fast. Fast switching, fast on the time-scale of the coupled oscillators, overcomes the descychnronizing decoherence suggested by disconnected instantaneous networks. This result agrees in spirit with that of where empirical evidence suggested that a moving averaged graph Laplacian could be used in the master-stability function analysis. A new fast switching stability criterion here-in gives sufficiency of a fast-switching network leading to synchronization. Although this sufficient condition appears to be very conservative, it provides new insights about the requirements for synchronization when the network topology is time-varying. In particular, it can be shown that networks of oscillators can synchronize even if at every point in time the frozen-time network topology is insufficiently connected to achieve synchronization.Comment: Submitted to SIAD

Canonical Timing and Spectral Behavior of LMC X-3 in the Low/Hard State

We present results from three observations with the Rossi X-ray Timing Explorer (RXTE) of LMC X-3, obtained while the source was in an extended 'low/hard' state. The data reveal a hard X-ray spectrum which is well fit by a pure power law with photon index Gamma=1.69+/-0.02, with a source luminosity at 50 kpc of 5-16x10^{36}erg/s (2--10 keV). Strong broad-band (0.01-100 Hz) time variability is also observed, with fractional rms amplitude 40+/-4%, plus a quasi-periodic oscillation (QPO) peak at 0.46+/-0.02 Hz with rms amplitude \~14%. This is the first reported observation in which the full canonical low/hard state behavior (pure hard power law spectrum combined with strong broad-band noise and QPO) for LMC X-3 is seen. We reanalyze several archival RXTE observations of LMC X-3 and derive consistent spectral and timing parameters, and determine the overall luminosity variation between high/soft and low/hard states. The timing and spectral properties of LMC X-3 during the recurrent low/hard states are quantitatively similar to that typically seen in the Galactic black hole candidates.Comment: 5 pages, 3 figures, accepted for ApJ Letter

Action and Hamiltonian for eternal black holes

We present the Hamiltonian, quasilocal energy, and angular momentum for a spacetime region spatially bounded by two timelike surfaces. The results are applied to the particular case of a spacetime representing an eternal black hole. It is shown that in the case when the boundaries are located in two different wedges of the Kruskal diagram, the Hamiltonian is of the form $H = H_+ - H_-$, where $H_+$ and $H_-$ are the Hamiltonian functions for the right and left wedges respectively. The application of the obtained results to the thermofield dynamics description of quantum effects in black holes is briefly discussed.Comment: 24 pages, Revtex, 5 figures (available upon request

Border Collision Route to Quasiperiodicity: Numerical Investigation and Experimental Confirmation

Numerical studies of higher-dimensional piecewise-smooth systems have recently shown how a torus can arise from a periodic cycle through a special type of border-collision bifurcation. The present article investigates this new route to quasiperiodicity in the two-dimensional piecewise-linear normal form map. We have obtained the chart of the dynamical modes for this map and showed that border-collision bifurcations can lead to the birth of a stable closed invariant curve associated with quasiperiodic or periodic dynamics. In the parameter regions leading to the existence of an invariant closed curve, there may be transitions between an ergodic torus and a resonance torus, but the mechanism of creation for the resonance tongues is distinctly different from that observed in smooth maps. The transition from a stable focus point to a resonance torus may lead directly to a new focus of higher periodicity, e.g., a period-5 focus. This article also contains a discussion of torus destruction via a homoclinic bifurcation in the piecewise-linear normal map. Using a dc-dc converter with two-level control as an example, we report the first experimental verification of the direct transition to quasiperiodicity through a border-collision bifurcation

S(k) for Haldane Gap Antiferromagnets: Large-scale Numerical Results vs. Field Theory and Experiment

The structure function, S(k), for the s=1, Haldane gap antiferromagnetic chain, is measured accurately using the recent density matrix renormalization group method, with chain-length 100. Excellent agreement with the nonlinear $\sigma$ model prediction is obtained, both at $k\approx \pi$ where a single magnon process dominates and at $k\approx 0$ where a two magnon process dominates. We repeat our calculation with crystal field anisotropy chosen to model NENP, obtaining good agreement with both field theory predictions and recent experiments. Correlation lengths, gaps and velocities are determined for both polarizations.Comment: 11 pages, 3 postscript figures included, REVTEX 3.0, UBCTP-93-02