Zeta measures and Thermodynamic Formalism for temperature zero

Nonadditive Thermodynamic Formalism: Equilibrium and Gibbs Measures

The nonadditive thermodynamic formalism is a generalization of the classical thermodynamic formalism, in which the topological pressure of a single function φ is replaced by the topological pressure of a sequence of functions Φ = (φn)n. The theory also includes a variational principle for the topological pressure, although with restrictive assumptions on Φ. Our main objective is to provide a ne...

Thermodynamic analogy for quantum phase transitions at zero temperature

We propose a relationship between thermodynamic phase transitions and groundstate quantum phase transitions in systems with variable Hamiltonian parameters. It is based on a link between zeros of the canonical partition function at complex temperatures and exceptional points of a quantum Hamiltonian in the complexextended parameter space. This approach is applied in the interacting boson model,...

An Extension of the Thermodynamic Formalism Approach to Selberg's Zeta Function for General Modular Groups

The Thermodynamic Formalism Approach to Selberg's Zeta Function for Psl(2, Z)

Besides the classical approach to Selberg's zeta function for cofinite Fuchsian groups [S] through the trace formula [V] there has been developed recently another one based on the thermodynamic formalism [R2] applied to the dynamical zeta function of Smale and Ruelle [F] which for geodesic flows on surfaces of constant negative curvature (c.n.c.) is closely related to Selberg's function for the...

Weighted Thermodynamic Formalism and Applications

Let (X, T ) and (Y, S) be two subshifts so that Y is a factor of X. For any asymptotically sub-additive potential Φ on X and a = (a, b) ∈ R with a > 0, b ≥ 0, we introduce the notions of a-weighted topological pressure and a-weighted equilibrium state of Φ. We setup the weighted variational principle. In the case that X, Y are full shifts with one-block factor map, we prove the uniqueness and G...