9,732 research outputs found
Spacelike hypersurfaces in standard static spacetimes
In this work we study spacelike hypersurfaces immersed in spatially open
standard static spacetimes with complete spacelike slices. Under appropriate
lower bounds on the Ricci curvature of the spacetime in directions tangent to
the slices, we prove that every complete CMC hypersurface having either bounded
hyperbolic angle or bounded height is maximal. Our conclusions follow from
general mean curvature estimates for spacelike hypersurfaces. In case where the
spacetime is a Lorentzian product with spatial factor of nonnegative Ricci
curvature and sectional curvatures bounded below, we also show that a complete
maximal hypersurface not intersecting a spacelike slice is itself a slice. This
result is obtained from a gradient estimate for parametric maximal
hypersurfaces.Comment: 50 page
Teleportation transfers only speakable quantum information
We show that a quantum clock cannot be teleported without prior
synchronization between sender and receiver: every protocol using a finite
amount of entanglement and an arbitrary number of rounds of classical
communication will necessarily introduce an error in the teleported state of
the clock. Nevertheless, we show that entanglement can be used to achieve
synchronization with precision higher than any classical correlation allows,
and we give the optimized strategy for this task. The same results hold also
for arbitrary continuous quantum reference frames, which encode general
unspeakable information,-information that cannot be encoded into a number, but
instead requires a specific physical support, like a clock or a gyroscope, to
be conveyed.Comment: 5 pages, no figures, published versio
Translationally invariant conservation laws of local Lindblad equations
We study the conditions under which one can conserve local translationally
invariant operators by local translationally invariant Lindblad equations in
one-dimensional rings of spin-1/2 particles. We prove that for any 1-local
operator (e.g., particle density) there exist Lindblad dissipators that
conserve that operator, while on the other hand we prove that among 2-local
operators (e.g., energy density) only trivial ones of the Ising type can be
conserved, while all the other cannot be conserved, neither locally nor
globally, by any 2- or 3-local translationally invariant Lindblad equation. Our
statements hold for rings of any finite length larger than some minimal length
determined by the locality of Lindblad equation. These results show in
particular that conservation of energy density in interacting systems is
fundamentally more difficult than conservation of 1-local quantities.Comment: 15 pages, no fig
Entanglement, non-Markovianity, and causal non-separability
Quantum mechanics, in principle, allows for processes with indefinite causal
order. However, most of these causal anomalies have not yet been detected
experimentally. We show that every such process can be simulated experimentally
by means of non-Markovian dynamics with a measurement on additional degrees of
freedom. Explicitly, we provide a constructive scheme to implement arbitrary
acausal processes. Furthermore, we give necessary and sufficient conditions for
open system dynamics with measurement to yield processes that respect causality
locally, and find that tripartite entanglement and nonlocal unitary
transformations are crucial requirements for the simulation of causally
indefinite processes. These results show a direct connection between three
counter-intuitive concepts: non-Markovianity, entanglement, and causal
indefiniteness.Comment: 14 pages, 8 figure
Dynamic criticality at the jamming transition
We characterize vibrational motion occurring at low temperatures in dense
suspensions of soft repulsive spheres over a broad range of volume fractions
encompassing the jamming transition at (T = 0, phi = phi_J). We find that
characteristic time and length scales of thermal vibrations obey critical
scaling in the vicinity of the jamming transition. We show in particular that
the amplitude and the time scale of dynamic fluctuations diverge symmetrically
on both sides of the transition, and directly reveal a diverging correlation
length. The critical region near phi_J is divided in three different regimes
separated by a characteristic temperature scale T*(phi) that vanishes
quadratically with the distance to phi_J. While two of them, (T < T*(phi), phi
> phi_J) and (T < T*(phi), phi < phi_J), are described by harmonic theories
developed in the zero temperature limit, the third one for T > T*(phi) is
inherently anharmonic and displays new critical properties. We find that the
quadratic scaling of T*(phi) is due to nonperturbative anharmonic
contributions, its amplitude being orders of magnitude smaller than the
perturbative prediction based on the expansion to quartic order in the
interactions. Our results show that thermal vibrations in colloidal assemblies
directly reveal the critical nature of the jamming transition. The critical
region, however, is very narrow and has not yet been attained experimentally,
even in recent specifically-dedicated experiments.Comment: 18 pages; submitted to J. Chem. Phys. for "Special Topic Issue on the
Glass Transition
Genericity of blackhole formation in the gravitational collapse of homogeneous self-interacting scalar fields
The gravitational collapse of a wide class of self-interacting homogeneous
scalar fields models is analyzed. The class is characterized by certain general
conditions on the scalar field potential, which, in particular, include both
asymptotically polynomial and exponential behaviors. Within this class, we show
that the generic evolution is always divergent in a finite time, and then make
use of this result to construct radiating star models of the Vaidya type. It
turns out that blackholes are generically formed in such models.Comment: 18 pages, 4 figure
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