Consequence Of Conservation Laws Research Articles

Black Hole Images as Tests of General Relativity: Effects of Plasma Physics

The horizon-scale images of black holes obtained with the Event Horizon Telescope have provided new probes of their metrics and tests of general relativity. The images are characterized by a bright, near-circular ring from the gravitationally lensed emission from the hot plasma and a deep central depression cast by the black hole. The metric tests rely on the fact that the bright ring closely traces the boundary of the black hole shadow with a small displacement that has been quantified using simulations. In this paper we develop a self-consistent covariant analytic model of the accretion flow that spans a broad range of plasma conditions and black hole properties to explore the general validity of this result. We show that, for any physical model of the accretion flow, the ring always encompasses the outline of the shadow and is not displaced by it by more than half the ring width. This result is a consequence of conservation laws and basic thermodynamic considerations and does not depend on the microphysics of the plasma or the details of the numerical simulations. We also present a quantitative measurement of the bias between the bright ring and the shadow radius based on the analytical models.

Entanglement entropy in particle decay

The decay of a parent particle into two or more daughter particles results in an entangled quantum state as a consequence of conservation laws in the decay process. Recent experiments at Belle and BaBar take advantage of quantum entanglement and the correlations in the time evolution of the product particles to study CP and T violations. If one (or more) of the product particles are not observed, their degrees of freedom are traced out of the pure state density matrix resulting from the decay, leading to a mixed state density matrix and an entanglement entropy. This entropy is a measure of the loss of information present in the original quantum correlations of the entangled state. We use the Wigner-Weisskopf method to construct an approximation to this state that evolves in time in a {\em manifestly unitary} way. We then obtain the entanglement entropy from the reduced density matrix of one of the daughter particles obtained by tracing out the unobserved states, and follow its time evolution. We find that it grows over a time scale determined by the lifetime of the parent particle to a maximum, which when the width of the parent particle is narrow, describes the phase space distribution of maximally entangled Bell-like states. The method is generalized to the case in which the parent particle is described by a wave packet localized in space. Possible experimental avenues to measure the entanglement entropy in the decay of mesons at rest are discussed.

Dynamics of a passive tracer in a velocity field of four identical point vortices

The dynamics of a passive tracer in the velocity field of four identical point vortices, moving under the influence of their self-induced advection, is investigated. Of interest is the change in mixing and transport properties of the tracer for the three different classes of vortex motion: periodic, quasi-periodic and chaotic. As a consequence of conservation laws, the vortex motion is confined to a finite region of phase space; therefore, the tracer phase space can be partitioned into an inner and an outer region. We find that in the case of quasi-periodic vortex motion the tracer phase space exhibits a well-defined barrier to transport between the central chaotic region and the outer region, where the trajectories are regular. In the case of chaotic vortex motion the barrier becomes permeable. The particle dynamics goes through an intermittent behaviour, where forays into the central region alternate with trapping in outer annular orbits. In the far field, an estimate of diffusion rates is made through a multipole expansion of the tracer velocity field. We make use of a specific stochastic model for the tracer velocity field which predicts no diffusion for the case of quasi-periodic vortex motion and, for the case of chaotic vortex motion, a diffusion rate that goes to zero at large distances from the vortex cluster.

Avalanches, hydrodynamics, and discharge events in models of sandpiles.

Motivated by recent studies of Bak, Tang, and Wiesenfeld [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)], we study self-organized criticality in models of ``running'' sandpiles. Our analysis reveals rich temporal structures in the flow of sand: at very short time scales, the flow is dominated by single avalanches. These avalanches overlap at intermediate time scales; their interactions lead to 1/f noise in the flow. We show that scaling in this region is a consequence of conservation laws and is exhibited in many examples of driven-diffusion equations for transport. At very long time scales, the sandpiles exhibit system-wide discharge events. These events also obey scaling and are found to be anticorrelated. We derive the ${\mathit{f}}^{1/2}$ mean-field power spectrum for these events and show that a threshold instability of the model, coupled with some stochasticity, is the underlying origin of the long-time anticorrelation.

Restricted Friedel sum rules and Korringa relations as consequences of conservation laws

In a general model for impurities in a metallic host it is shown that separate Friedel sum rules hold for the total excess charge, spin and orbital momentum associated with the impurity. These relations are consequences of the conservation laws for charge, spin and orbital magnetic momentum, respectively. Furthermore, the Korringa relations are the exact consequences of the Ward identities, which are, in turn, consequences of some conservation laws in the Anderson model. Thus the Korringa relations are not valid for any of crystalline splitting, spin-orbit interaction and direct electron-electron interaction in the conduction band.

Atom-field correlation, conservation laws and the phase transition of the laser

The Fokker-Planck equation of a single-mode laser is solved by a novel method, which shows that the correlation between photon-number and atomic inversion is a consequence of conservation laws. Thus the behaviour of the atomic system at the phase transition threshold of the laser is intimately connected with the characteristic change of the photon statistics.