The slicing dependence of non-spherically symmetric quasi-local horizons in Vaidya Spacetimes

It is well known that quasi-local black hole horizons depend on the choice of a time coordinate in a spacetime. This has implications for notions such as the surface of the black hole and also on quasi-local physical quantities such as horizon measures of mass and angular momentum. In this paper, we compare different horizons on non-spherically symmetric slicings of Vaidya spacetimes. The spacetimes we investigate include both accreting and evaporating black holes. For some simple choices of the Vaidya mass function function corresponding to collapse of a hollow shell, we compare the area for the numerically found axisymmetric trapping horizons with the area of the spherically symmetric trapping horizon and event horizon. We find that as expected, both the location and area are dependent on the choice of foliation. However, the area variation is not large, of order $0.035\%$ for a slowly evolving horizon with $\dot{m}=0.02$. We also calculate analytically the difference in area between the spherically symmetric quasi-local horizon and event horizon for a slowly accreting black hole. We find that the difference can be many orders of magnitude larger than the Planck area for sufficiently large black holes.Comment: 10 pages, 5 figures, corrected minor typo

Development and Flight of a Robust Optical-Inertial Navigation System Using Low-Cost Sensors

This research develops and tests a precision navigation algorithm fusing optical and inertial measurements of unknown objects at unknown locations. It provides an alternative to the Global Positioning System (GPS) as a precision navigation source, enabling passive and low-cost navigation in situations where GPS is denied/unavailable. This paper describes two new contributions. First, a rigorous study of the fundamental nature of optical/inertial navigation is accomplished by examining the observability grammian of the underlying measurement equations. This analysis yields a set of design principles guiding the development of optical/inertial navigation algorithms. The second contribution of this research is the development and flight test of an optical-inertial navigation system using low-cost and passive sensors (including an inexpensive commercial-grade inertial sensor, which is unsuitable for navigation by itself). This prototype system was built and flight tested at the U.S. Air Force Test Pilot School. The algorithm that was implemented leveraged the design principles described above, and used images from a single camera. It was shown (and explained by the observability analysis) that the system gained significant performance by aiding it with a barometric altimeter and magnetic compass, and by using a digital terrain database (DTED). The (still) low-cost and passive system demonstrated performance comparable to high quality navigation-grade inertial navigation systems, which cost an order of magnitude more than this optical-inertial prototype. The resultant performance of the system tested provides a robust and practical navigation solution for Air Force aircraft

On Upper Bounds for Toroidal Mosaic Numbers

In this paper, we work to construct mosaic representations of knots on the torus, rather than in the plane. This consists of a particular choice of the ambient group, as well as different definitions of contiguous and suitably connected. We present conditions under which mosaic numbers might decrease by this projection, and present a tool to measure this reduction. We show that the order of edge identification in construction of the torus sometimes yields different resultant knots from a given mosaic when reversed. Additionally, in the Appendix we give the catalog of all 2 by 2 torus mosaics.Comment: 10 pages, 111 figure

Tower of quantum scars in a partially many-body localized system

Isolated quantum many-body systems are often well-described by the eigenstate thermalization hypothesis. There are, however, mechanisms that cause different behavior: many-body localization and quantum many-body scars. Here, we show how one can find disordered Hamiltonians hosting a tower of scars by adapting a known method for finding parent Hamiltonians. Using this method, we construct a spin-1/2 model which is both partially localized and contains scars. We demonstrate that the model is partially localized by studying numerically the level spacing statistics and bipartite entanglement entropy. As disorder is introduced, the adjacent gap ratio transitions from the Gaussian orthogonal ensemble to the Poisson distribution and the entropy shifts from volume-law to area-law scaling. We investigate the properties of scars in a partially localized background and compare with a thermal background. At strong disorder, states initialized inside or outside the scar subspace display different dynamical behavior but have similar entanglement entropy and Schmidt gap. We demonstrate that localization stabilizes scar revivals of initial states with support both inside and outside the scar subspace. Finally, we show how strong disorder introduces additional approximate towers of eigenstates.Comment: 18 pages, 12 figures, v2: accepted versio

Stability of an electroweak string with a fermion condensate

A solution of the standard electroweak theory with a single lepton family is constructed, consisting of a cosmic string and a fermion condensate within its core. The stability of this system to small perturbations is examined, and it is found that stability is not enhanced relative to the bare electroweak string. The presence of quark zero modes is shown to violate the existence criteria for embedded defects.Comment: 13 pages, preprint DAMTP 94-9, SWAT/2

Area laws in quantum systems: mutual information and correlations

The holographic principle states that on a fundamental level the information content of a region should depend on its surface area rather than on its volume. This counterintuitive idea which has its roots in the nonextensive nature of black-hole entropy serves as a guiding principle in the search for the fundamental laws of Planck-scale physics. In this paper we show that a similar phenomenon emerges from the established laws of classical and quantum physics: the information contained in part of a system in thermal equilibrium obeys an area law. While the maximal information per unit area depends classically only on the number of microscopic degrees of freedom, it may diverge as the inverse temperature in quantum systems. A rigorous relation between area laws and correlations is established and their explicit behavior is revealed for a large class of quantum many-body states beyond equilibrium systems.Comment: 5 pages, 2 figures, published version with appendi

Efficient qubit detection using alkali earth metal ions and a double STIRAP process

We present a scheme for robust and efficient projection measurement of a qubit consisting of the two magnetic sublevels in the electronic ground state of alkali earth metal ions. The scheme is based on two stimulated Raman adiabatic passages (STIRAP) involving four partially coherent laser fields. We show how the efficiency depends on experimentally relevant parameters: Rabi frequencies, pulse widths, laser linewidths, one- and two-photon detunings, residual laser power, laser polarization and ion motion.Comment: 14 pages, 15 figure

Approximate Hofstadter- and Kapit-Mueller-like parent Hamiltonians for Laughlin states on fractals

Recently, it was shown that fractional quantum Hall states can be defined on fractal lattices. Proposed exact parent Hamiltonians for these states are nonlocal and contain three-site terms. In this work, we look for simpler, approximate parent Hamiltonians for bosonic Laughlin states at half filling, which contain only onsite potentials and two-site hopping with the interaction generated implicitly by hardcore constraints (as in the Hofstadter and Kapit-Mueller models on periodic lattices). We use an ``inverse method'' to determine such Hamiltonians on finite-generation Sierpi\'{n}ski carpet and triangle lattices. The ground states of some of the resulting models display relatively high overlap with the model states if up to third neighbor hopping terms are considered, and by increasing the maximum hopping distance one can achieve nearly perfect overlaps. When the number of particles is reduced and additional potentials are introduced to trap quasiholes, the overlap with a model quasihole wavefunction is also high in some cases, especially for the nonlocal Hamiltonians. We also study how the small system size affects the braiding properties for the model quasihole wavefunctions and perform analogous computations for Hamiltonian models.Comment: Version accepted in Phys. Rev. A. See the Ancillary Files for the Supplementary Materia