We study analogues of $mathcal{F}$-saturation games, first introduced by Furedi, Reimer and Seress in 1991, and named as such by West. We examine analogous games on directed graphs, and show tight results on the walk-avoiding game. We also examine an
intermediate game played on undirected graphs, such that there exists an orientation avoiding a given family of directed graphs, and show bounds on the score. This last game is shown to be equivalent to a recent game studied by Hefetz, Krivelevich, Naor and Stojakovic, and we give new bounds for bias
We formulate computationally efficient classical stochastic measurement trajectories for a multimode quantum system under continuous observation. Specifically, we consider the nonlinear dynamics of an atomic Bose-Einstein condensate contained within
an optical cavity subject to continuous monitoring of the light leaking out of the cavity. The classical trajectories encode within a classical phase-space representation a continuous quantum measurement process conditioned on a given detection record. We derive a Fokker-Planck equation for the quasi-probability distribution of the combined condensate-cavity system. We unravel the dynamics into stochastic classical trajectories that are conditioned on the quantum measurement process of the continuously monitored system, and that these trajectories faithfully represent measurement records of individual experimental runs. Since the dynamics of a continuously measured observable in a many-atom system can be closely approximated by classical dynamics, the method provides a numerically efficient and accurate approach to calculate the measurement record of a large multimode quantum system. Numerical simulations of the continuously monitored dynamics of a large atom cloud reveal considerably fluctuating phase profiles between different measurement trajectories, while ensemble averages exhibit local spatially varying phase decoherence. Individual measurement trajectories lead to spatial pattern formation and optomechanical motion that solely result from the measurement backaction. The backaction of the continuous quantum measurement process, conditioned on the detection record of the photons, spontaneously breaks the symmetry of the spatial profile of the condensate and can be tailored to selectively excite collective modes.
We study F-saturation games, first introduced by Furedi, Reimer and Seress in 1991, and named as such by West. The main question is to determine the length of the game whilst avoiding various classes of graph, playing on a large complete graph. We sh
ow lower bounds on the length of path-avoiding games, and more precise results for short paths. We show sharp results for the tree avoiding game and the star avoiding game.
Cavity optomechanics offers powerful methods for controlling optical fields and mechanical motion. A number of proposals have predicted that this control can be extended considerably in devices where multiple cavity modes couple to each other via the
motion of a single mechanical oscillator. Here we study the dynamical properties of such a multimode optomechanical device, in which the coupling between cavity modes results from mechanically-induced avoided crossings in the cavitys spectrum. Near the avoided crossings we find that the optical spring shows distinct features that arise from the interaction between cavity modes. Precisely at an avoided crossing, we show that the particular form of the optical spring provides a classical analog of a quantum-nondemolition measurement of the intracavity photon number. The mechanical oscillators Brownian motion, an important source of noise in these measurements, is minimized by operating the device at cryogenic temperature (500 mK).
We theoretically analyze the Bragg spectroscopic interferometer of two spatially separated atomic Bose-Einstein condensates that was experimentally realized by Saba et al. [Science 2005 v307 p1945] by continuously monitoring the relative phase evolut
ion. Even though the atoms in the light-stimulated Bragg scattering interact with intense coherent laser beams, we show that the phase is created by quantum measurement-induced back-action on the homodyne photo-current of the lasers, opening possibilities for quantum-enhanced interferometric schemes. We identify two regimes of phase evolution: a running phase regime which was observed in the experiment of Saba et al., that is sensitive to an energy offset and suitable for an interferometer, and a trapped phase regime, that can be insensitive to applied forces and detrimental to interferometric applications.
X-ray observations of many clusters of galaxies reveal the presence of edges in surface brightness and temperature, known as cold fronts. In relaxed clusters with cool cores, these edges have been interpreted as evidence for the sloshing of the core
gas in the clusters gravitational potential. The smoothness of these edges has been interpreted as evidence for the stabilizing effect of magnetic fields draped around the front surfaces. To check this hypothesis, we perform high-resolution magnetohydrodynamics simulations of magnetized gas sloshing in galaxy clusters initiated by encounters with subclusters. We go beyond previous works on the simulation of cold fronts in a magnetized intracluster medium by simulating their formation in realistic, idealized mergers with high resolution ({Delta}x ~ 2 kpc). Our simulations sample a parameter space of plausible initial magnetic field strengths and field configurations. In the simulations, we observe strong velocity shears associated with the cold fronts amplifying the magnetic field along the cold front surfaces, increasing the magnetic field strength in these layers by up to an order of magnitude, and boosting the magnetic pressure up to near-equipartition with thermal pressure in some cases. In these layers, the magnetic field becomes strong enough to stabilize the cold fronts against Kelvin-Helmholtz instabilities, resulting in sharp, smooth fronts as those seen in observations of real clusters. These magnetic fields also result in strong suppression of mixing of high and low-entropy gas in the cluster, seen in our simulations of mergers in the absence of a magnetic field. As a result, the heating of the core due to sloshing is very modest and is unable to stave off a cooling catastrophe.
(abridged) The ICM has been suggested to be buoyantly unstable in the presence of magnetic field and anisotropic thermal conduction. We perform first cosmological simulations of galaxy cluster formation that simultaneously include magnetic fields, ra
diative cooling and anisotropic thermal conduction. In isolated and idealized cluster models, the magnetothermal instability (MTI) tends to reorient the magnetic fields radially. Using cosmological simulations of the Santa Barbara cluster we detect radial bias in the velocity and magnetic fields. Such radial bias is consistent with either the inhomogeneous radial gas flows due to substructures or residual MTI-driven field rearangements that are expected even in the presence of turbulence. Although disentangling the two scenarios is challenging, we do not detect excess bias in the runs that include anisotropic thermal conduction. The anisotropy effect is potentially detectable via radio polarization measurements with LOFAR and SKA and future X-ray spectroscopic studies with the IXO. We demonstrate that radiative cooling boosts the amplification of the magnetic field by about two orders of magnitude beyond what is expected in the non-radiative cases. At z=0 the field is amplified by a factor of about 10^6 compared to the uniform magnetic field evolved due to the universal expansion alone. Interestingly, the runs that include both radiative cooling and anisotropic thermal conduction exhibit stronger magnetic field amplification than purely radiative runs at the off-center locations. In these runs, shallow temperature gradients away from the cluster center make the ICM neutrally buoyant. The ICM is more easily mixed in these regions and the winding up of the frozen-in magnetic field is more efficient resulting in stronger magnetic field amplification.
Epitaxial thin films of hexagonal ErMnO3 fabricated on Pt(111)/Al2O3(0001) and YSZ(111) substrates exhibited both ferroelectric character and magnetic ordering at low temperatures. As the temperature was reduced, the ErMnO3 films first showed antifer
romagnetism. At lower temperatures, the films deposited at lower oxygen partial pressures exhibited spin glass behavior. This re-entrant spin glass behavior was attributed to competition between an antiferromagnetic interaction in the hexagonal geometry and a ferromagnetic interaction caused by a change in Mn valence induced by excess electrons from the oxygen vacancies.
