Vlasov equation and collisionless hydrodynamics adapted to curved spacetime

The modification of the Vlasov equation, in its standard form describing a charged particle distribution in the six-dimensional phase space, is derived explicitly within a formal Hamiltonian approach for arbitrarily curved spacetime. The equation accounts simultaneously for the Lorentz force and the effects of general relativity, with the latter appearing as the gravity force and an additional force due to the extrinsic curvature of spatial hypersurfaces. For an arbitrary spatial metric, the equations of collisionless hydrodynamics are also obtained in the usual three-vector form

State-space distribution and dynamical flow for closed and open quantum systems

We present a general formalism for studying the effects of dynamical heterogeneity in open quantum systems. We develop this formalism in the state space of density operators, on which ensembles of quantum states can be conveniently represented by probability distributions. We describe how this representation reduces ambiguity in the definition of quantum ensembles by providing the ability to explicitly separate classical and quantum sources of probabilistic uncertainty. We then derive explicit equations of motion for state space distributions of both open and closed quantum systems and demonstrate that resulting dynamics take a fluid mechanical form analogous to a classical probability fluid on Hamiltonian phase space, thus enabling a straightforward quantum generalization of Liouville's theorem. We illustrate the utility of our formalism by analyzing the dynamics of an open two-level system using the state-space formalism that are shown to be consistent with the derived analytical results

Adiabatic nonlinear waves with trapped particles: II. Wave dispersion

A general nonlinear dispersion relation is derived in a nondifferential form for an adiabatic sinusoidal Langmuir wave in collisionless plasma, allowing for an arbitrary distribution of trapped electrons. The linear dielectric function is generalized, and the nonlinear kinetic frequency shift $\omega_{\rm NL}$ is found analytically as a function of the wave amplitude $a$. Smooth distributions yield $\omega_{\rm NL} \propto \sqrt{a}$, as usual. However, beam-like distributions of trapped electrons result in different power laws, or even a logarithmic nonlinearity, which are derived as asymptotic limits of the same dispersion relation. Such beams are formed whenever the phase velocity changes, because the trapped distribution is in autoresonance and thus evolves differently from the passing distribution. Hence, even adiabatic $\omega_{\rm NL}(a)$ is generally nonlocal.Comment: submitted together with Papers I and II

Spectroscopic Searches for Evolutionary Orbital Period Changes in WR+OB Binaries: the Case of WR 127 (Hen 3-1772)

We aim at searching for secular evolution of the orbital period in the short-period binary system WR 127 (WN3b+O9.5V, $P = 9.555^d$). We performed new low-resolution spectroscopic observations of WR 127 on 2.5-m CMO SAI telescope to construct the radial velocity curves of the components suggesting the component masses $M_\mathrm{WR}\sin^3(i) = 11.8\pm1.4$ $M_{\odot}$, $M_\mathrm{O}\sin^3(i)=17.2\pm1.4$ $M_{\odot}$. The comparison with archival radial velocity curves enabled us to calculate the $(O-C)$ plot with accuracy sufficient to search for the orbital period change in WR 127. We report on the reliable detection of a secular increase in the orbital period of WR 127 at a rate of \dot{P} = 0.83\pm0.14~\mbox{s~yr}^{-1} corresponding to the dynamical mass-loss rate from the WR star $\dot{M}_\mathrm{WR} = (2.6\pm0.5)\times 10^{-5}$ $M_{\odot}$ yr$^{-1}$. The mass-loss rate from WR stars in three WR+OB binaries (WR 127, CX Cep and V444 Cyg) as inferred from spectroscopic and photometric measurements suggests a preliminary empirical correlation between the WR star mass and the dynamical mass-loss rate $\dot M_\mathrm{WR}\sim M_\mathrm{WR}^{1.8}$. This relation is important for the understanding of the evolution of massive close binaries with WR stars -- precursors of gravitational-wave binary merging events with neutron stars and black holes.Comment: 5 pages, 5 figures. Accepted for publication in Astronomy & Astrophysics Letters on March 4, 202