On free loop spaces of toric spaces

Growth of the Hilbert-Poincar\"e series for the rational homology of the free loop space of a toric space is addressed. In case the toric space is a manifold, the structure of the fan dictates whether the Hilbert-Poincar\"e series has exponential growth. Applications are made to the existence of infinitely many geometrically distinct periodic geodesics

The KO*-rings of BT^m, the Davis-Januszkiewicz Spaces and certain toric manifolds

This paper contains an explicit computation of the KO*-ring structure of an m-fold product of CP^{\infty}, the Davis-Januszkiewicz spaces and toric manifolds which have trivial Sq^2-homology.Comment: 34 page

Proliferation of effective interactions: decoherence-induced equilibration in a closed many-body system

We address the question on how weak perturbations, that are quite ineffective in small many-body systems, can lead to decoherence and hence to irreversibility when they proliferate as the system size increases. This question is at the heart of solid state NMR. There, an initially local polarization spreads all over due to spin-spin interactions that conserve the total spin projection, leading to an equilibration of the polarization. In principle, this quantum dynamics can be reversed by changing the sign of the Hamiltonian. However, the reversal is usually perturbed by non reversible interactions that act as a decoherence source. The fraction of the local excitation recovered defines the Loschmidt echo (LE), here evaluated in a series of closed $N$ spin systems with all-to-all interactions. The most remarkable regime of the LE decay occurs when the perturbation induces proliferated effective interactions. We show that if this perturbation exceeds some lower bound, the decay is ruled by an effective Fermi golden rule (FGR). Such a lower bound shrinks as $N$ increases, becoming the leading mechanism for LE decay in the thermodynamic limit. Once the polarization stayed equilibrated longer than the FGR time, it remains equilibrated in spite of the reversal procedure.Comment: 8 pages, 4 figure