For most black holes in string theory, the Schwarzschild radius in string units decreases as the string coupling is reduced. We formulate a correspondence principle, which states that (i) when the size of the horizon drops below the size of a string, the typical black hole state becomes a typical state of strings and D-branes with the same charges, and (ii) the mass does not change abruptly dur...

Violation of correspondence principle may occur for very macroscopic but isolated quantum systems on rather short timescales as illustrated by the case of Hyperion, the chaotically tumbling moon of Saturn, for which quantum and classical predictions are expected to diverge on a timescale of approximately 20 years. Motivated by Hyperion, we review salient features of “quantum chaos” and show tha...

The oracle model of computation is believed to allow a rigorous proof of quantum over classical computational superiority. Since quantum and classical oracles are essentially different, a correspondence principle is commonly implicitly used as a platform for comparison of oracle complexity. Here, we question the grounds on which this correspondence is based. Obviously, results on quantum speed-...

We offer a new proof of the Furstenberg-Katznelson multiple recurrence theorem for several commuting probability-preserving transformations T1, T2, . . . , Td : Z y (X,Σ, μ) ([5]), and so, via the Furstenberg correspondence principle introduced in [4], a new proof of the multi-dimensional Szemerédi Theorem. We bypass the detailed analysis of certain towers of factors of a probability-preserving...

The classical McKay correspondence for finite subgroups G of SL(2,C) gives a bijection between isomorphism classes of nontrivial irreducible representations of G and irreducible components of the exceptional divisor in the minimal resolution of the quotient singularity A2C/G. Over non algebraically closed fields K there may exist representations irreducible over K which split over K. The same i...

We study the configuration of a typical highly excited string as one slowly increases the string coupling. The dominant interactions are the long range dilaton and gravitational attraction. In four spacetime dimensions, the string slowly contracts from its initial (large) size until it approaches the string scale where it forms a black hole. In higher dimensions, the string stays large until th...