Quantum Fidelity Decay of Quasi-Integrable Systems

We show, via numerical simulations, that the fidelity decay behavior of quasi-integrable systems is strongly dependent on the location of the initial coherent state with respect to the underlying classical phase space. In parallel to classical fidelity, the quantum fidelity generally exhibits Gaussian decay when the perturbation affects the frequency of periodic phase space orbits and power-law decay when the perturbation changes the shape of the orbits. For both behaviors the decay rate also depends on initial state location. The spectrum of the initial states in the eigenbasis of the system reflects the different fidelity decay behaviors. In addition, states with initial Gaussian decay exhibit a stage of exponential decay for strong perturbations. This elicits a surprising phenomenon: a strong perturbation can induce a higher fidelity than a weak perturbation of the same type.Comment: 11 pages, 11 figures, to be published Phys. Rev.

Lead telluride bonding and segmentation study Semiannual phase report, Aug. 1, 1967 - Jan. 31, 1968

Constitutional studies of SnTe and Si-Ge metal systems, segmented Si-Ge-PdTe thermocouple efficiencies, and pore migration in PbSnTe thermoelement

Lead telluride bonding and segmentation study Interim report, 1 Nov. 1966 - 31 Jul. 1967

Lead telluride bonding and segmentation studies including couple design, test devices, and life testin

Filtering bases and cohomology of nilpotent subalgebras of the Witt algebra and the algebra of loops in sl 2

We study the cohomology with trivial coefficients of the Lie algebras L k, k ≥ 1, of polynomial vector fields with zero k-jet on the circle and the cohomology of similar subalgebras ℒk of the algebra of polynomial loops with values in sl 2 The main result is a construction of special bases in the exterior complexes of these algebras. Using this construction, we obtain the following results. We calculate the cohomology of L k and ℒL. We obtain formulas in terms of Schur polynomials for cycles representing the homology of these algebras. We introduce "stable” filtrations of the exterior complexes of L k and ℒk, thus generalizing Goncharova's notion of stable cycles for L k, and give a polynomial description of these filtrations. We find the spectral resolutions of the Laplace operators for L 1 and ℒ

Fidelity Decay as an Efficient Indicator of Quantum Chaos

Recent work has connected the type of fidelity decay in perturbed quantum models to the presence of chaos in the associated classical models. We demonstrate that a system's rate of fidelity decay under repeated perturbations may be measured efficiently on a quantum information processor, and analyze the conditions under which this indicator is a reliable probe of quantum chaos and related statistical properties of the unperturbed system. The type and rate of the decay are not dependent on the eigenvalue statistics of the unperturbed system, but depend on the system's eigenvector statistics in the eigenbasis of the perturbation operator. For random eigenvector statistics the decay is exponential with a rate fixed precisely by the variance of the perturbation's energy spectrum. Hence, even classically regular models can exhibit an exponential fidelity decay under generic quantum perturbations. These results clarify which perturbations can distinguish classically regular and chaotic quantum systems.Comment: 4 pages, 3 figures, LaTeX; published version (revised introduction and discussion

Template-based Gravitational-Wave Echoes Search Using Bayesian Model Selection

The ringdown of the gravitational-wave signal from a merger of two black holes has been suggested as a probe of the structure of the remnant compact object, which may be more exotic than a black hole. It has been pointed out that there will be a train of echoes in the late-time ringdown stage for different types of exotic compact objects. In this paper, we present a template-based search methodology using Bayesian statistics to search for echoes of gravitational waves. Evidence for the presence or absence of echoes in gravitational-wave events can be established by performing Bayesian model selection. The Occam factor in Bayesian model selection will automatically penalize the more complicated model that echoes are present in gravitational-wave strain data because of its higher degree of freedom to fit the data. We find that the search methodology was able to identify gravitational-wave echoes with Abedi et al.'s echoes waveform model about 82.3% of the time in simulated Gaussian noise in the Advanced LIGO and Virgo network and about 61.1% of the time in real noise in the first observing run of Advanced LIGO with $\geq 5\sigma$ significance. Analyses using this method are performed on the data of Advanced LIGO's first observing run, and we find no statistical significant evidence for the detection of gravitational-wave echoes. In particular, we find $<1\sigma$ combined evidence of the three events in Advanced LIGO's first observing run. The analysis technique developed in this paper is independent of the waveform model used, and can be used with different parametrized echoes waveform models to provide more realistic evidence of the existence of echoes from exotic compact objects.Comment: 16 pages, 6 figure