19,165 research outputs found
Tunneling-induced restoration of classical degeneracy in quantum kagome ice
Quantum effect is expected to dictate the behavior of physical systems at low temperature. For quantum magnets with geometrical frustration, quantum fluctuation usually lifts the macroscopic classical degeneracy, and exotic quantum states emerge. However, how different types of quantum processes entangle wave functions in a constrained Hilbert space is not well understood. Here, we study the topological entanglement entropy and the thermal entropy of a quantum ice model on a geometrically frustrated kagome lattice. We find that the system does not show a Z(2) topological order down to extremely low temperature, yet continues to behave like a classical kagome ice with finite residual entropy. Our theoretical analysis indicates an intricate competition of off-diagonal and diagonal quantum processes leading to the quasidegeneracy of states and effectively, the classical degeneracy is restored
The entropy of black holes: a primer
After recalling the definition of black holes, and reviewing their energetics
and their classical thermodynamics, one expounds the conjecture of Bekenstein,
attributing an entropy to black holes, and the calculation by Hawking of the
semi-classical radiation spectrum of a black hole, involving a thermal
(Planckian) factor. One then discusses the attempts to interpret the black-hole
entropy as the logarithm of the number of quantum micro-states of a macroscopic
black hole, with particular emphasis on results obtained within string theory.
After mentioning the (technically cleaner, but conceptually more intricate)
case of supersymmetric (BPS) black holes and the corresponding counting of the
degeneracy of Dirichlet-brane systems, one discusses in some detail the
``correspondence'' between massive string states and non-supersymmetric
Schwarzschild black holes.Comment: 51 pages, 4 figures, talk given at the "Poincare seminar" (Paris, 6
December 2003), to appear in Poincare Seminar 2003 (Birkhauser
Firewall or smooth horizon?
Recently, Almheiri, Marolf, Polchinski, and Sully found that for a
sufficiently old black hole (BH), the set of assumptions known as the
\emph{complementarity postulates} appears to be inconsistent with the
assumption of local regularity at the horizon. They concluded that the horizon
of an old BH is likely to be the locus of local irregularity, a "firewall".
Here I point out that if one adopts a different assumption, namely that
semiclassical physics holds throughout its anticipated domain of validity, then
no inconsistency seems to arise, and the horizon retains its regularity. In
this alternative view-point, the vast portion of the original BH information
remains trapped inside the BH throughout the semiclassical domain of
evaporation, and possibly leaks out later on. This appears to be an inevitable
outcome of semiclassical gravity.Comment: A slightly different version (with small modifications, mostly
semantic, and some updated references) was published in Gen. Relativ. Gravi
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