14,301 research outputs found
Tolman mass, generalized surface gravity, and entropy bounds
In any static spacetime the quasi-local Tolman mass contained within a volume
can be reduced to a Gauss-like surface integral involving the flux of a
suitably defined generalized surface gravity. By introducing some basic
thermodynamics and invoking the Unruh effect one can then develop elementary
bounds on the quasi-local entropy that are very similar in spirit to the
holographic bound, and closely related to entanglement entropy.Comment: V1: 4 pages. Uses revtex4-1; V2: Three references added; V3: Some
notational changes for clarity; introductory paragraph rewritten; no physics
changes. This version accepted for publication in Physical Review Letter
Gravitational vacuum polarization III: Energy conditions in the (1+1) Schwarzschild spacetime
Building on a pair of earlier papers, I investigate the various point-wise
and averaged energy conditions for the quantum stress-energy tensor
corresponding to a conformally-coupled massless scalar field in the in the
(1+1)-dimensional Schwarzschild spacetime. Because the stress-energy tensors
are analytically known, I can get exact results for the Hartle--Hawking,
Boulware, and Unruh vacua. This exactly solvable model serves as a useful
sanity check on my (3+1)-dimensional investigations wherein I had to resort to
a mixture of analytic approximations and numerical techniques. Key results in
(1+1) dimensions are: (1) NEC is satisfied outside the event horizon for the
Hartle--Hawking vacuum, and violated for the Boulware and Unruh vacua. (2) DEC
is violated everywhere in the spacetime (for any quantum state, not just the
standard vacuum states).Comment: 7 pages, ReV_Te
An analytical decomposition protocol for optimal implementation of two-qubit entangling gates
This paper addresses the question how to implement a desired two-qubit gate U
using a given tunable two-qubit entangling interaction H_int. We present a
general method which is based on the K_1 A K_2 decomposition of unitary
matrices in SU(4) to calculate analytically the smallest number of two-qubit
gates U_int [based on H_int] and single-qubit rotations, and the explicit
sequence of these operations that are required to implement U. We illustrate
our protocol by calculating the implementation of (1) the transformation from
standard basis to Bell basis, (2) the CNOT gate, and (3) the quantum Fourier
transform for two kinds of interaction - Heisenberg exchange interaction and
quantum inductive coupling - and discuss the relevance of our results for
solid-state qubits.Comment: 16 pages, published versio
Smelling out predators is innate in birds
The role of olfaction for predation risk assessment remains barely explored in birds, although predator chemical cues could be useful in predator detection under low visibility conditions for many bird species. We examine whether Great Tits Parus major are able to use the odour of mustelids to assess predation risk when selecting cavities for roosting. We analysed whether the response to predator chemical cues is innate and assessed whether the antipredatory response is associated with exploratory behaviour, a proxy for the personality of birds. In a choice experiment in aviaries, we offered naĂŻve adult Great Tits of known personality two nest-boxes, one control and one experimental. The experimental nest-box had the odour of a mustelid predator or a strong new odour without biological significance, the control nest-box contained no odour. When one of the cavities contained the odour of a predator, birds avoided the use of either of the two offered nest-boxes, whereas there was no avoidance of boxes when one of the nest-boxes contained a control odour. There was no relationship with exploratory behaviour. We show that the ability to use the chemical cues of predators is innate in birds, but individual differences in the response to predator chemical cues cannot be explained by the personality of the bird.
Geometric structure of the generic static traversable wormhole throat
Traversable wormholes have traditionally been viewed as intrinsically
topological entities in some multiply connected spacetime. Here, we show that
topology is too limited a tool to accurately characterize a generic traversable
wormhole: in general one needs geometric information to detect the presence of
a wormhole, or more precisely to locate the wormhole throat. For an arbitrary
static spacetime we shall define the wormhole throat in terms of a
2-dimensional constant-time hypersurface of minimal area. (Zero trace for the
extrinsic curvature plus a "flare-out" condition.) This enables us to severely
constrain the geometry of spacetime at the wormhole throat and to derive
generalized theorems regarding violations of the energy conditions-theorems
that do not involve geodesic averaging but nevertheless apply to situations
much more general than the spherically symmetric Morris-Thorne traversable
wormhole. [For example: the null energy condition (NEC), when suitably weighted
and integrated over the wormhole throat, must be violated.] The major technical
limitation of the current approach is that we work in a static spacetime-this
is already a quite rich and complicated system.Comment: 25 pages; plain LaTeX; uses epsf.sty (four encapsulated postscript
figures
Gravitational vacuum polarization IV: Energy conditions in the Unruh vacuum
Building on a series of earlier papers [gr-qc/9604007, gr-qc/9604008,
gr-qc/9604009], I investigate the various point-wise and averaged energy
conditions in the Unruh vacuum. I consider the quantum stress-energy tensor
corresponding to a conformally coupled massless scalar field, work in the
test-field limit, restrict attention to the Schwarzschild geometry, and invoke
a mixture of analytical and numerical techniques. I construct a semi-analytic
model for the stress-energy tensor that globally reproduces all known numerical
results to within 0.8%, and satisfies all known analytic features of the
stress-energy tensor. I show that in the Unruh vacuum (1) all standard
point-wise energy conditions are violated throughout the exterior region--all
the way from spatial infinity down to the event horizon, and (2) the averaged
null energy condition is violated on all outgoing radial null geodesics. In a
pair of appendices I indicate general strategy for constructing semi-analytic
models for the stress-energy tensor in the Hartle-Hawking and Boulware states,
and show that the Page approximation is in a certain sense the minimal ansatz
compatible with general properties of the stress-energy in the Hartle-Hawking
state.Comment: 40 pages; plain LaTeX; uses epsf.sty (ten encapsulated postscript
figures); two tables (table and tabular environments). Should successfully
compile under both LaTeX 209 and the 209 compatibility mode of LaTeX2
Tolman wormholes violate the strong energy condition
For an arbitrary Tolman wormhole, unconstrained by symmetry, we shall define
the bounce in terms of a three-dimensional edgeless achronal spacelike
hypersurface of minimal volume. (Zero trace for the extrinsic curvature plus a
"flare-out" condition.) This enables us to severely constrain the geometry of
spacetime at and near the bounce and to derive general theorems regarding
violations of the energy conditions--theorems that do not involve geodesic
averaging but nevertheless apply to situations much more general than the
highly symmetric FRW-based subclass of Tolman wormholes. [For example: even
under the mildest of hypotheses, the strong energy condition (SEC) must be
violated.] Alternatively, one can dispense with the minimal volume condition
and define a generic bounce entirely in terms of the motion of test particles
(future-pointing timelike geodesics), by looking at the expansion of their
timelike geodesic congruences. One re-confirms that the SEC must be violated at
or near the bounce. In contrast, it is easy to arrange for all the other
standard energy conditions to be satisfied.Comment: 8 pages, ReV-TeX 3.
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