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Register a new userSymmetry Reduction and Semiclassical Analysis of Axially Symmetric Systems
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We derive a semiclassical trace formula for a symmetry reduced part of the spectrum in axially symmetric systems. The classical orbits that contribute are closed in (rho,z,p_rho,p_z) and have p_phi = mhbar where m is the azimuthal quantum number. For m > 0, these orbits vary with energy and almost never lie on periodic trajectories in the full phase space in contrast to the case of discrete symmetries. The transition from m=0 to m > 0 is however not dramatic as our numerical results indicate, suggesting that contributing orbits occur in topologically equivalent families within which p_phi varies smoothly.
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We introduce a systematic and direct procedure to generate hairy rotating black holes by deforming a spherically symmetric seed solution. We develop our analysis in the context of the gravitational decoupling approach, without resorting to the Newman-Janis algorithm. As examples of possible applications, we investigate how the Kerr black hole solution is modified by a surrounding fluid with conserved energy-momentum tensor. We find non-trivial extensions of the Kerr and Kerr-Newman black holes with primary hair. We prove that a rotating and charged black hole can have the same horizon as Kerrs, Schwarzschilds or Reissner-Nordstroms, thus showing possible observational effects of matter around black holes.
Classical open systems with balanced gain and loss, i.e. parity-time ($mathcal{PT}$) symmetric systems, have attracted tremendous attention over the past decade. Their exotic properties arise from exceptional point (EP) degeneracies of non-Hermitian Hamiltonians that govern their dynamics. In recent years, increasingly sophisticated models of $mathcal{PT}$-symmetric systems with time-periodic (Floquet) driving, time-periodic gain and loss, and time-delayed coupling have been investigated, and such systems have been realized across numerous platforms comprising optics, acoustics, mechanical oscillators, optomechanics, and electrical circuits. Here, we introduce a $mathcal{PT}$-symmetric (balanced gain and loss) system with memory, and investigate its dynamics analytically and numerically. Our model consists of two coupled $LC$ oscillators with positive and negative resistance, respectively. We introduce memory by replacing either the resistor with a memristor, or the coupling inductor with a meminductor, and investigate the circuit energy dynamics as characterized by $mathcal{PT}$-symmetric or $mathcal{PT}$-symmetry broken phases. Due to the resulting nonlinearity, we find that energy dynamics depend on the sign and strength of initial voltages and currents, as well as the distribution of initial circuit energy across its different components. Surprisingly, at strong inputs, the system exhibits self-organized Floquet dynamics, including $mathcal{PT}$-symmetry broken phase at vanishingly small dissipation strength. Our results indicate that $mathcal{PT}$-symmetric systems with memory show a rich landscape.
Extensive early observations proved that the ejecta of supernova 1987A (SN 1987A) are aspherical. Fifteen years after the supernova explosion, the Hubble Space Telescope has resolved the rapidly expanding ejecta. The late-time images and spectroscopy provide a geometrical picture that is consistent with early observations and suggests a highly structured, axially symmetric geometry. We present here a new synthesis of the old and new data. We show that the Bochum event, presumably a clump of $^{56}$Ni, and the late-time image, the locus of excitation by $^{44}$Ti, are most naturally accounted for by sharing a common position angle of about 14degree, the same as the mystery spot and early speckle data on the ejecta, and that they are both oriented along the axis of the inner circumstellar ring at 45degree to the plane of the sky. We also demonstrate that the polarization represents a prolate geometry with the same position angle and axis as the early speckle data and the late-time image and hence that the geometry has been fixed in time and throughout the ejecta. The Bochum event and the Doppler kinematics of the [Ca II]/[O II] emission in spatially resolved HST spectra of the ejecta can be consistently integrated into this geometry. The radioactive clump is deduced to fall approximately along the axis of the inner circumstellar ring and therefore to be redshifted in the North whereas the [Ca II]/[O II] 7300 AA emission is redshifted in the South. We present a jet-induced model for the explosion and argue that such a model can account for many of the observed asymmetries. In the jet models, the oxygen and calcium are not expected to be distributed along the jet, but primarily in an expanding torus that shares the plane and northern blue shift of the inner circumstellar ring.
Regular generalizations of spherically and axially symmetric metrics and their properties are considered. Newton gravity law generalizations are reduced for null geodesic.
We consider integrable Hamiltonian systems in three degrees of freedom near an elliptic equilibrium in 1:1:-2 resonance. The integrability originates from averaging along the periodic motion of the quadratic part and an imposed rotational symmetry about the vertical axis. Introducing a detuning parameter we find a rich bifurcation diagram, containing three parabolas of Hamiltonian Hopf bifurcations that join at the origin. We describe the monodromy of the resulting ramified 3-torus bundle as variation of the detuning parameter lets the system pass through 1:1:-2 resonance.
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