Characterizing the behaviour of strongly coupled quantum systems out of equilibrium is a cardinal challenge for both theory and experiment. With diverse applications ranging from the dynamics of the ...quark-gluon plasma to transport in novel states of quantum matter, establishing universal results and organizing principles out of equilibrium is crucial. We present a universal description of energy transport between quantum critical heat baths in arbitrary dimension. The current-carrying non-equilibrium steady state (NESS) is a Lorentz-boosted thermal state. In the context of gauge/gravity duality this reveals an intimate correspondence between far-from-equilibrium transport and black hole uniqueness theorems. We provide analytical expressions for the energy current and the generating function of energy current fluctuations, together with predictions for experiment.
The problem of the existence and uniqueness of solutions of boundary value problems (BVPs) for a nonlinear fractional differential equation of order 2<α ≤ 3 is studied. The BVP is transformed into an ...integral equation and discussed by means of a fixed point problem for an integral operator. Conditions for the existence and uniqueness of a fixed point for the integral operator are derived via b‐comparison functions on complete b‐metric spaces. In addition, estimates for the convergence of the Picard iteration sequence are given. An estimate for the Green's function related with the problem is provided and employed in the proof of the existence and uniqueness theorem for the solution of the given problem. Illustrative examples are presented to support the theoretical results.
The black hole uniqueness and the no-hair theorems imply that the quasinormal spectrum of any astrophysical black hole is determined solely by its mass and spin. The countably infinite number of ...quasinormal modes of a Kerr black hole are thus related to each other, and any deviations from these relations provide a strong hint for physics beyond the general theory of relativity. To test the no-hair theorem using ringdown signals, it is necessary to detect at least two quasinormal modes. In particular, one can detect the fundamental mode along with a subdominant overtone or with another angular mode, depending on the mass ratio and the spins of the progenitor binary. Also in the light of the recent discovery of GW190412, studying how the mass ratio affects the prospect of black hole spectroscopy using overtones or angular modes is pertinent, and this is the major focus of our study. First, we provide ready-to-use fits for the amplitudes and phases of both the angular modes and overtones as a function of mass ratio q ∈ 0 , 10 . Using these fits, we estimate the minimum signal-to-noise ratio for detectability, resolvability, and measurability of subdominant modes/tones. We find that performing black hole spectroscopy with angular modes is preferable when the binary mass ratio is larger than q ≈ 1.2 (provided that the source is not located at a particularly disfavored inclination angle). For nonspinning, equal-mass binary black holes, the overtones seem to be the only viable option to perform a spectroscopy test of the no-hair theorem. However, this would require a large ringdown signal-to-noise ratio ( ≈ 100 for a 5% accuracy test with two overtones) and the inclusion of more than one overtone to reduce modeling errors, making black hole spectroscopy with overtones impractical in the near future.
Abstract
For amenable discrete groupoids
$\mathcal {G}$
and row-finite directed graphs
E
, let
$(\mathcal {G},E)$
be a self-similar groupoid and let
$C^*(\mathcal {G}, E)$
be the associated
$C^*$
...-algebra. We introduce a weaker faithfulness condition than those in the existing literature that still guarantees that
$C^*(\mathcal {G})$
embeds in
$C^*(\mathcal {G}, E)$
. Under this faithfulness condition, we prove a gauge-invariant uniqueness theorem.
The analysis of the validity of Birkhoff's theorem about the uniqueness of the spherically symmetric solution of the gravitational field equations is extended to the framework of the Poincaré gauge ...gravity theory. The class of models with the most general Lagrangians of the Yang-Mills type constructed from all possible quadratic invariants of the curvature and the torsion is considered, including both parity-even and parity-odd sectors. We find the families of models in which the weak and strong versions of the generalized Birkhoff theorem are valid, by making use of the double duality technique.
In this paper, the Pfaff equations with continuous coefficients are considered. Analogs of Peano’s existence theorem and Kamke’s theorem on the uniqueness of the solution to the Cauchy problem are ...established, and a method for approximate solution of the Cauchy problem for the Pfaff equation is proposed.
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