Poincare Recurrences and Topological Diversity
نویسنده
چکیده
Finite entropy thermal systems undergo Poincaré recurrences. In the context of field theory, this implies that at finite temperature, timelike two-point functions will be quasi-periodic. In this note we attempt to reproduce this behavior using the AdS/CFT correspondence by studying the correlator of a massive scalar field in the bulk. We evaluate the correlator by summing over all the SL(2, Z) images of the BTZ spacetime. We show that all the terms in this sum receive large corrections after at certain critical time, and that the result, even if convergent, is not quasiperiodic. We present several arguments indicating that the periodicity will be very difficult to recover without an exact re-summation, and discuss several toy models which illustrate this. Finally, we consider the consequences for the information paradox. e-mail: [email protected], [email protected], [email protected]
منابع مشابه
Topological Evolution of Classical Electromagnetic Fields and the Photon
The theory of classical electromagnetism is constructed in terms of two exterior differential systems, F − dA = 0, and J − dG = 0, which act as topological constraints on the variety of independent variables {x, y, z, t}. These two fundamental constraints lead to two other independent concepts of topological torsion, A^F, and topological spin, A^G, which are explicitly dependent upon the potent...
متن کاملCombinatorial Cell Complexes and Poincare Duality
We define and study a class of finite topological spaces, which model the cell structure of a space obtained by gluing finitely many Euclidean convex polyhedral cells along congruent faces. We call these finite topological spaces, combinatorial cell complexes (or c.c.c). We define orientability, homology and cohomology of c.c.c’s and develop enough algebraic topology in this setting to prove th...
متن کاملPi Spaces with Analytic Dimension 1 and Arbitrary Topological Dimension
For every n, we construct a metric measure space that is doubling, satisfies a Poincare inequality in the sense of HeinonenKoskela, has topological dimension n, and has a measurable tangent bundle of dimension 1.
متن کاملTorsion and Spin as Topological Coherent structures in Plasmas
Classical electromagnetism de ̄ned in terms of the Fields fE;B;D;Hg and the Potentials fA; Ág implies that the domain of support for ̄nite non-zero electromagnetic ̄eld intensities, and ̄nite non-zero electromagnetic currents, in most cases cannot be compact without boundary. The existence of Potentials leads to the independent concepts of topological Torsion (with the magnetic helicity as a fou...
متن کاملComplicated Poincare Half-Maps in a Linear System
Poincare half-maps can be used to characterize the behavior of recurrent dynamical systems. Their usefulness is demonstrated for a linear three-dimensional single-loop feedback system. In this example everything can be calculated analytically. The resulting half-maps are "benign" endomorphic maps with a complicated topological structure. This is surprising since the combination of two such half...
متن کامل