A Family of Exact, Analytic Time Dependent Wave Packet Solutions to a Nonlinear Schroedinger Equation

We obtain time dependent $q$-Gaussian wave-packet solutions to a non linear Schr\"odinger equation recently advanced by Nobre, Rego-Montero and Tsallis (NRT) [Phys. Rev. Lett. 106 (2011) 10601]. The NRT non-linear equation admits plane wave-like solutions ($q$-plane waves) compatible with the celebrated de Broglie relations connecting wave number and frequency, respectively, with energy and momentum. The NRT equation, inspired in the $q$-generalized thermostatistical formalism, is characterized by a parameter $q$, and in the limit $q \to 1$ reduces to the standard, linear Schr\"odinger equation. The $q$-Gaussian solutions to the NRT equation investigated here admit as a particular instance the previously known $q$-plane wave solutions. The present work thus extends the range of possible processes yielded by the NRT dynamics that admit an analytical, exact treatment. In the $q \to 1$ limit the $q$-Gaussian solutions correspond to the Gaussian wave packet solutions to the free particle linear Schr\"odinger equation. In the present work we also show that there are other families of nonlinear Schr\"odinger-like equations, besides the NRT one, exhibiting a dynamics compatible with the de Broglie relations. Remarkably, however, the existence of time dependent Gaussian-like wave packet solutions is a unique feature of the NRT equation not shared by the aforementioned, more general, families of nonlinear evolution equations

New features of quantum discord uncovered by q-entropies

The notion of quantum discord introduced by Ollivier and Zurek [Phys. Rev. Lett 88, 017901 (2001)] (see also Henderson and Vedral [J. Phys. A 34, 6899 (2001)]) has attracted increasing attention, in recent years, as an entropic quantifier of non-classical features pertaining to the correlations exhibited by bipartite quantum systems. Here we generalize the notion so as to encompass power-law q-entropies (that reduce to the standard Shannon entropy in the limit $q \to 1$) and study the concomitant consequences. The ensuing, new discord-like measures we advance describe aspects of non-classicality that are different from those associated with the standard quantum discord. A particular manifestation of this difference concerns a feature related to order. Let $D_1$ stand for the standard, Shannon-based discord measure and $D_q$ for the $q \ne 1$ one. If two quantum states $A$, $B$ are such that $D_1(A) > D_1(B)$, this order-relation does not remain invariant under a change from $D_1$ to $D_q$.Comment: 11 pages, 8 figure

Quantifying Quantum Correlations in Fermionic Systems using Witness Operators

We present a method to quantify quantum correlations in arbitrary systems of indistinguishable fermions using witness operators. The method associates the problem of finding the optimal entan- glement witness of a state with a class of problems known as semidefinite programs (SDPs), which can be solved efficiently with arbitrary accuracy. Based on these optimal witnesses, we introduce a measure of quantum correlations which has an interpretation analogous to the Generalized Robust- ness of entanglement. We also extend the notion of quantum discord to the case of indistinguishable fermions, and propose a geometric quantifier, which is compared to our entanglement measure. Our numerical results show a remarkable equivalence between the proposed Generalized Robustness and the Schliemann concurrence, which are equal for pure states. For mixed states, the Schliemann con- currence presents itself as an upper bound for the Generalized Robustness. The quantum discord is also found to be an upper bound for the entanglement.Comment: 7 pages, 6 figures, Accepted for publication in Quantum Information Processin

Prognostic Factors Affecting Outcome after Allogeneic Transplantation for Hematological Malignancies from Unrelated Donors : Results from a Randomized Trial

Several prognostic factors for the outcome after allogeneic hematopoietic stem-cell transplant (HSCT) from matched unrelated donors have been postulated from registry data; however, data from randomized trials are lacking. We present analyses on the effects of patient-related, donor-related, and treatment-related prognostic factors on acute GVHD (aGVHD), chronic GVHD (cGVHD), relapse, nonrelapse mortality (NRM), disease-free survival (DFS), and overall survival (OS) in a randomized, multicenter, open-label, phase III trial comparing standard graft-versus-host-disease (GVHD) prophylaxis with and without pretransplantation ATG-Fresenius (ATG-F) in 201 adult patients receiving myeloablative conditioning before HSCT from HLA-A, HLA-B antigen, HLA-DRB1, HLA-DQB1 allele matched unrelated donors. High-resolution testing (allele) of HLA-A, HLA-B, and HLA-C were obtained after study closure, and the impact of an HLA 10/10 4-digit mismatch on outcome and on the treatment effect of ATG-F versus control investigated. Advanced disease was a negative factor for relapse, DFS, and OS. Donor age ≥40 adversely affected the risk of aGVHD III-IV, extensive cGVHD, and OS. Younger donors are to be preferred in unrelated donor transplantation. Advanced disease patients need special precautions to improve outcome. The degree of mismatch had no major influence on the positive effect of ATG-F on the reduction of aGVHD and cGVHD. © 2012 American Society for Blood and Marrow Transplantation