[show abstract][hide abstract] ABSTRACT: We consider a toy model of pointer interacting with a 1/2-spin system, whose σx variable is measured by the environment, according to the prescription of decoherence theory. If the environment measuring the variable σx yields ordinary statistical mechanics, the pointer sensitive to the 1/2-spin system undergoes the same, exponential, decoherence regardless of whether real collapses or an entanglement with the environment, mimicking the effect of real collapses, occur. In the case of non-ordinary statistical mechanics the occurrence of real collapses make the pointer still relax exponentially in time, while the equivalent picture in terms of reduced density matrix generates an inverse power law decoherence.
[show abstract][hide abstract] ABSTRACT: We study the entropy time evolution of a quantum mechanical model, which is frequently used as a prototype for Anderson's localization. Recently Latora and Baranger [Phys. Rev. Lett. 82, 520 (1999)] found that there exist three entropy regimes, a transient regime of passage from dynamics to thermodynamics, a linear-in-time regime of entropy increase, that is, a thermodynamic regime of Kolmogorov kind, and a saturation regime. We use the nonextensive entropic indicator advocated by Tsallis [J. Stat. Phys. 52, 479 (1988)] with a mobile entropic index q, and we find that the adoption of the "magic" value q=Q=1/2, compared to the traditional entropic index q=1, reduces the length of the transient regime and makes earlier the emergence of the Kolmogorov regime. We adopt a two-site model to explain these properties by means of an analytical treatment and we argue that Q=1/2 might be a typical signature of the occurrence of Anderson localization.
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 10/2000; 62(3 Pt A):3429-36.
[show abstract][hide abstract] ABSTRACT: We study the time evolution of a quantum system without classical counterpart, undergoing a process of entropy increase due to the environment influence. We show that if the environment-induced decoherence is interpreted in terms of wave-function collapses, a symbolic sequence can be generated. We prove that the Kolmogorov-Sinai entropy of this sequence coincides with rate of von Neumann entropy increase. Comment: 5 pages, 2 figures