92,874 research outputs found
Coarse-grained entropy and causal holographic information in AdS/CFT
We propose bulk duals for certain coarse-grained entropies of boundary
regions. The `one-point entropy' is defined in the conformal field theory by
maximizing the entropy in a domain of dependence while fixing the one-point
functions. We conjecture that this is dual to the area of the edge of the
region causally accessible to the domain of dependence (i.e. the `causal
holographic information' of Hubeny and Rangamani). The `future one-point
entropy' is defined by generalizing this conjecture to future domains of
dependence and their corresponding bulk regions. We show that the future
one-point entropy obeys a nontrivial second law. If our conjecture is true,
this answers the question "What is the field theory dual of Hawking's area
theorem?"Comment: 43 pages, 9 figures. v3: minor changes suggested by referee v2: added
a few additional reference
On a notion of maps between orbifolds, I. function spaces
This is the first of a series of papers which are devoted to a comprehensive
theory of maps between orbifolds. In this paper, we define the maps in the more
general context of orbispaces, and establish several basic results concerning
the topological structure of the space of such maps. In particular, we show
that the space of such maps of C^r-class between smooth orbifolds has a natural
Banach orbifold structure if the domain of the map is compact, generalizing the
corresponding result in the manifold case. Motivations and applications of the
theory come from string theory and the theory of pseudoholomorphic curves in
symplectic orbifolds.Comment: Final version, 46 pages. Accepted for publication in Communications
in Contemporary Mathematics. A preliminary version of this work is under a
different title "A homotopy theory of orbispaces", arXiv: math. AT/010202
Variational formulation of hybrid problems for fully 3-D transonic flow with shocks in rotor
Based on previous research, the unified variable domain variational theory of hybrid problems for rotor flow is extended to fully 3-D transonic rotor flow with shocks, unifying and generalizing the direct and inverse problems. Three variational principles (VP) families were established. All unknown boundaries and flow discontinuities (such as shocks, free trailing vortex sheets) are successfully handled via functional variations with variable domain, converting almost all boundary and interface conditions, including the Rankine Hugoniot shock relations, into natural ones. This theory provides a series of novel ways for blade design or modification and a rigorous theoretical basis for finite element applications and also constitutes an important part of the optimal design theory of rotor bladings. Numerical solutions to subsonic flow by finite elements with self-adapting nodes given in Refs., show good agreement with experimental results
First steps in synthetic guarded domain theory: step-indexing in the topos of trees
We present the topos S of trees as a model of guarded recursion. We study the
internal dependently-typed higher-order logic of S and show that S models two
modal operators, on predicates and types, which serve as guards in recursive
definitions of terms, predicates, and types. In particular, we show how to
solve recursive type equations involving dependent types. We propose that the
internal logic of S provides the right setting for the synthetic construction
of abstract versions of step-indexed models of programming languages and
program logics. As an example, we show how to construct a model of a
programming language with higher-order store and recursive types entirely
inside the internal logic of S. Moreover, we give an axiomatic categorical
treatment of models of synthetic guarded domain theory and prove that, for any
complete Heyting algebra A with a well-founded basis, the topos of sheaves over
A forms a model of synthetic guarded domain theory, generalizing the results
for S
Generic absoluteness and boolean names for elements of a Polish space
It is common knowledge in the set theory community that there exists a
duality relating the commutative -algebras with the family of -names
for complex numbers in a boolean valued model for set theory . Several
aspects of this correlation have been considered in works of the late 's
and early 's, for example by Takeuti, and by Jech. Generalizing Jech's
results, we extend this duality so as to be able to describe the family of
boolean names for elements of any given Polish space (such as the complex
numbers) in a boolean valued model for set theory as a space
consisting of functions whose domain is the Stone space of , and
whose range is contained in modulo a meager set. We also outline how this
duality can be combined with generic absoluteness results in order to analyze,
by means of forcing arguments, the theory of .Comment: 27 page
Localized Random Lasing Modes and a New Path for Observing Localization
We demonstrate that a knowledge of the density-of-states and the eigenstates
of a random system without gain, in conjunction with the frequency profile of
the gain, can accurately predict the mode that will lase first. Its critical
pumping rate can be also obtained. It is found that the shape of the
wavefunction of the random system remains unchanged as gain is introduced.
These results were obtained by the time-independent transfer matrix method and
finite-difference-time-domain (FDTD) methods. They can be also analytically
understood by generalizing the semi-classical Lamb theory of lasing in random
systems. These findings provide a new path for observing the localization of
light, such as looking for mobility edge and studying the localized states.
%inside the random systems..Comment: Sent to PRL. 3 figure
Extremely Correlated Quantum Liquids
We formulate the theory of an extremely correlated electron liquid,
generalizing the standard Fermi liquid. This quantum liquid has specific
signatures in various physical properties, such as the Fermi surface volume and
the narrowing of electronic bands by spin and density correlation functions.
We use Schwinger's source field idea to generate equations for the Greens
function for the Hubbard operators. A local (matrix) scale transformation in
the time domain to a quasiparticle Greens function, is found to be optimal.
This transformation allows us to generate vertex functions that are guaranteed
to reduce to the bare values for high frequencies, i.e. are ``asymptotically
free''. The quasiparticles are fractionally charged objects, and we find an
exact Schwinger Dyson equation for their Greens function. We find a hierarchy
of equations for the vertex functions, and further we obtain Ward identities so
that systematic approximations are feasible.
An expansion in terms of the density of holes measured from the Mott Hubbard
insulating state follows from the nature of the theory. A systematic
presentation of the formalism is followed by some preliminary explicit
calculations.Comment: 40 pages, typos remove
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