Unstable States: From Quantum Mechanics to Statistical Physics

Ivana Paidarová (1) , Philippe Durand (2)

1 J. Heyrovský Institute of Physical Chemistry of the ASCR
2 GMO - Groupe THEO (LCPQ)

Influenced by the ideas of Jaynes and Prigogine from the mid-1950s, we present a unified formulation of dynamics and thermodynamics of irreversible processes. Our approach originates in the quantum theory of resonances described by effective Hamiltonians. The concept of effective Hamiltonian is extended to the concept of effective Liouvillian that deals with macroscopic observables and brings insight into the dissipative nonequilibrium thermodynamics. The time-energy/frequency Fourier-Laplace transformation and the use of projectors focus on the variables of interest. The line profiles and dynamics in quantum mechanics are treated on the same footing. The long macroscopic times in statistical physics are derived from short microscopic times by means of hierarchies of effective Liouvillians and perturbation theory in the complex plane. The theory is illustrated on solvable models of quasi-continua and continua related to fluctuations and dissipation and on a model of kinetics of a chemical reaction implying a short-lived (resonance) transition state.

Ivana Paidarová, Philippe Durand. Unstable States: From Quantum Mechanics to Statistical Physics. Cleanthes A. Nicolaides and Erkki Brändas. Unstable States in the Continuous Spectra, Part I: Analysis, Concepts, Methods, and Results, Elsevier, pp.1-49, 2010, Advances in Quantum Chemistry, 978-0-12-380900-1. ⟨10.1016/S0065-3276(10)60001-9⟩. ⟨hal-00880139⟩