Decoherence time in self-induced decoherence

Abstract

A general method for obtaining the decoherence time in self-induced decoherence is presented. In particular, it is shown that such a time can be computed from the poles of the resolvent or of the initial conditions in the complex extension of the Hamiltonian's spectrum. Several decoherence times are estimated: 10 −13 − 10 −15 s for microscopic systems, and 10 −37 − 10 −39 s for macroscopic bodies. For the particular case of a thermal bath, our results agree with those obtained by the einselection (environment-induced decoherence) approach. PACS number(s) 03.65.Bz

Self-induced decoherence approach: Strong limitations on its validity in a simple spin bath model and on its general physical relevance

“…(23), we considered three different cases for selecting the coefficients α i , β i , ǫ (i) ↑↑ , ǫ (i) ↓↓ , and ǫ (i) ↑↓ , i.e., for choosing the initial state of the environment and the observable. In the completely random case (A), the coefficients α i , β i , and ǫ (i) ↑↓ were taken to be random complex numbers, with magnitudes and phases drawn from a uniform distribution over the intervals [0,1] and [0, 2π], respectively (and such that |β i | 2 = 1 − |α i | 2 ). Similiarly, the coefficients ǫ (i) ↑↑ and ǫ (i) ↓↓ were random real numbers drawn from a uniform distribution over the interval [−1, 1].…”

“…The interpretation of the processes described by these theories is fundamentally different, even though phenomenological effects of EID can manifest themselves in a manner formally similiar to that of SID, i.e., as a disappearance of off-diagonal terms in expectation values. Any proposed derivations of an "equivalence" between SID and EID [1,3,6] can therefore at most claim to describe coincidental formal similiarities in the context of very particular models, and only if the scope of EID is reduced to the influence on expectation values. On the basis of our arguments, we question the justification for labeling the process referred to by SID as "decoherence.…”

“…In a series of papers [1,2,3,4,5,6,7,8,9,10,11,12,13,14], the authors claim to present a "new approach to decoherence" [2], termed "self-induced decoherence" (SID). Their main assertion is that, for systems endowed with a continuous energy spectrum, the expectation value of an observable will become diagonal in the eigenbasis of the Hamiltonian of the system, and that this effect can be viewed as decoherence.…”

The nonrelativistic limit of (central-extended) Poincaré group and some consequences for quantum actualization

“…Then, there is a large number of constants of motion that introduce relevant indices in the energy spectrum, and, according to MHI, all these constants of motion actualize, among them the momenta P i . Moreover, according to [15,16], also well defined classical trajectories appear. Since these trajectories are linear, they are defined by the corresponding momenta P i , and this is a feature that proves that momenta do actualize.…”

Decoherence: A Closed-System Approach

“…Although 'EID' is still considered almost as a synonym for 'decoherence', in the last times other approaches have been proposed to face the conceptual difficulties of EID (Diosi [21], [22], Milburn [23], Penrose [24], Casati and Chirikov [25], [26], Adler [27] [32]), that is, not based on the dissipation of energy from the system to the environment. Among them, the self-induced decoherence (SID) approach shows that a closed quantum system with continuous spectrum may decohere by destructive interference ( [33], [34], [35], [36], [37], [38], [39], [40]). …”