Spontaneous magnetization of quantum XYXY spin model in joint presence of quenched and annealed disorder

We investigate equilibrium statistical properties of the quantum XY spin-1/2 model in an external magnetic field when the interaction and field parts are subjected to quenched or/and annealed disorder. The randomness present in the system are termed annealed or quenched depending on the relation between two different time scales - the time scale associated with the equilibriation of the randomness and the time of observation. Within a mean-field framework, we study the effects of disorders on spontaneous magnetization, both by perturbative and numerical techniques. Our primary interest is to understand the differences between quenched and annealed cases, and also to investigate the interplay when both of them are present in a system. We observe in particular that when interaction and field terms are respectively quenched and annealed, critical temperature for the system to magnetize in the direction parallel to the applied field does not depend on any of the disorders. Further, an annealed disordered interaction neither affects the magnetizations nor the critical temperatures. We carry out a comparative study of the different combinations of the disorders in the interaction and field terms, and point out their generic features.Comment: 9 pages, 2 figures, 1 tabl

Memory effects displayed in the evolution of continuous variable system

We analyze non-Markovian memory effects displayed by the quantum Brownian motion modelled as quantum harmonic oscillators coupled to a bath consisting of harmonic oscillators. We study the time evolution of fidelity, Petz-R\'enyi relative entropy and quantum entanglement for a family of 1-, 2- and 3-mode Gaussian states.Comment: 16 pages, 7 figure

A class of optimal positive maps in MnM_n

It is proven that a certain class of positive maps in the matrix algebra $M_n$ consists of optimal maps, i.e. maps from which one cannot subtract any completely positive map without loosing positivity. This class provides a generalization of a seminal Choi positive map in $M_3$.Comment: 13 pages, comments are welcom