Diffusion in disordered systems under iterative measurement

Abstract

We consider a sequence of idealized measurements of time-separation $\Delta t$ onto a discrete one-dimensional disordered system. A connection with Markov chains is found. For a rapid sequence of measurements, a diffusive regime occurs and the diffusion coefficient $D$ is analytically calculated. In a general point of view, this result suggests the possibility to break the Anderson localization due to decoherence effects. Quantum Zeno effect emerges because the diffusion coefficient $D$ vanishes at the limit $\Delta t \to 0$.Comment: 8 pages, 0 figures, LATEX. accepted in Phys.Rev.

Mesoscopic circuits with charge discreteness: Quantum transmission lines

“…In this case, it seems interesting to study the role of disorder and the nonlinearity due to charge discreteness. On the other hand, it is known that decoherence effects break localization [16,17] then the role of environment and resistance on the transmission line must also break localization.…”

Coherent transport

“…It is easily checked that this is the transport equation (13), taking into account the relation between the scaled and non-scaled noise spectra ηl …”

Phase-coherence time saturation in mesoscopic systems: Wave-function collapse

“…(v) Random independent measurements intervals ∆t n , with small fluctuations [19], do not change the definition (12). So, a similar definition for the coherence time would be made here.…”

“…The measurements are separated by a bounded interval of time ∆t. Let ρ be the density operator describing the state of the system with Hamiltonian H. Using (2), the mapping between two consecutive measurement is given by (see for instance [19,20]) ρ…”

“…The evolution equation (3) can be written like to a Markov-chain [19][20] for the probability W , explicitly,…”