Non-uniraty evolutios and non hermitina hamiltonians in decoherence of closed systems

MARIO CASTAGNINO; SEBASTIAN FORTIN

Paris

Congreso; PHHQP XI: Non-Hermitian Operators in Quantum Physics; 2012

Universidad de Paris

Non-unitary evolutions are essential to explain and study the phenomena of decoherence, the quantum to the classical limit, and the final equilibrium. These phenomena appear in the evolution of quantum system, where decoherence time and relaxation time can be defined using non-unitary evolutions, pole theory, and non-Hermitic Hamiltonians.As it is indicated in the brief historical summary of paper [6], schematically three periods can be identified in the development of the general program of decoherence:-In the first period the arrival to the equilibrium of irreversible systems was studied. The main problem of this period was that too long decoherence times were found, if compared with the experimental ones. -In a second period decoherence in open systems was studied. The main model for this process was EID that determines, case by case, which is the privileged basis, called usually moving preferred basis where decoherence takes place in a decoherence time  . This is the orthodox position on the subject [7]. In this period, the decoherence times founded were much smaller, solving the problem of the first period.-Recently, in a third period, the study of the arrival to equilibrium of closed systems was studied. Within this period, many formalisms for closed systems were introduced (see [8]). Among them a new approach to decoherence, SID, was presented by Castagnino et al., endowed with a non-Hermitian Hamiltonian and therefore with a non unitary evolution. According to this approach decoherence is a process dependent of the choice of some observables which have a particular physical relevance (the van Hove observables) in a closed system. This process also determines which is the privileged basis, called final preferred basis that defines the observables that acquires classic characteristics (at the relaxation time ) and that can be interpreted like properties that obey a Boolean logic. SID also solves an important problem explaining how closed system reach equilibrium. Relaxation time can be very long but equilibrium is always reached. In fact, Riemann-Lebesgue theorem shows that, in any system with destructive interference, reaches equilibrium in a very long Khalfin: time [9]. This time was experimentally detected in 2006 [10]. Moreover, in this contribution (following [2]) , we will introduce a generic definition of moving preferred basis where the state decoheres in a time  , also solving the main problem of the first period.