Abstract. We study the details of the distribution of the entanglement spectrum (eigenvalues of the reduced density matrix) of a disordered spin chain exhibiting a many-body localization (MBL) transition. In the thermalizing region we identify the evolution under increasing system size of the eigenvalue distribution function, whose thermodynamic limit is close to (but possibly different from) the Marchenko-Pastur distribution. From the analysis we extract a correlation length L s (h) determining the minimum system size to enter the asymptotic region. We find that L s (h) diverges at the MBL transition. We discuss the nature of the subleading corrections to the entanglement spectrum distribution and to the entanglement entropy.
arXiv:1610.09316v3 [cond-mat.dis-nn] 30 Oct 2017Entanglement critical length at the many-body localization transition 2 1. Introduction.
We analyze the coherence properties of polarized neutrons, after they have interacted with a magnetic field or a phase shifter undergoing different kinds of statistical fluctuations. We endeavor to probe the degree of disorder of the distribution of the phase shifts by means of the loss of quantum-mechanical coherence of the neutron. We find that the notion of entropy of the shifts and that of decoherence of the neutron do not necessarily agree. In some cases the neutron wave function is more coherent, even though it has interacted with a more disordered medium
We analyze the notion of quantum coherence in an interference experiment. We let the phase shifts fluctuate according to a given statistical distribution and introduce a decoherence parameter, defined in terms of a generalized visibility of the interference pattern. One might naively expect that a particle ensemble suffers a greater loss of quantum coherence by interacting with an increasingly randomized distribution of shifts. As we shall see, this is not always true.
Abstract. We analyze the coherence properties of neutron wave packets, after they have interacted with a phase shifter undergoing different kinds of statistical fluctuations. We give a quantitative (and operational) definition of decoherence and compare it to the standard deviation of the distribution of the phase shifts. We find that in some cases the neutron ensemble is more coherent, even though it has interacted with a wider (i.e. more disordered) distribution of shifts. This feature is independent of the particular definition of decoherence: this is shown by proposing and discussing an alternative definition, based on the Wigner function, that displays a similar behavior. We briefly discuss the notion of entropy of the shifts and find that, in general, it does not correspond to that of decoherence of the neutron.
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