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

Wave packet dynamics for a non-linear Schrödinger equation describing continuous position measurements

International audienc

Entropic entanglement criteria for Fermion systems

Entanglement criteria for general (pure or mixed) states of systems consisting of two identical fermions are introduced. These criteria are based on appropriate inequalities involving the entropy of the global density matrix describing the total system, on the one hand, and the entropy of the one-particle reduced density matrix, on the other hand. A majorization-related relation between these two density matrices is obtained, leading to a family of entanglement criteria based on Rényi’s entropic measure. These criteria are applied to various illustrative examples of parametrized families of mixed states. The dependence of the entanglement detection efficiency on Rényi’s entropic parameter is investigated. The extension of these criteria to systems of N identical fermions is also considered

Entwicklung und klinische Anwendung neuer retroviraler Vektorsysteme fuer somatische Gentherapie. Retrovirale Vektorsysteme fuer somatische Gentherapie Schlussbericht

The aim of the given project was to introduce clinical gene therapeutic studies relying on the use of retroviral vectors in Hamburg. During the period of support we were able to establish the technological basis for the successful execution of the supposed clinical trials. Moreover, the infrastructure to conduct gene transfer in accordance with the rules of 'good manufacturing practice' was created by the foundation of two small German biotech companies. In cooperation with our partner Heinrich-Pette-Institute (HPI) we initiated two clinical studies, which are going to start in 1999 and at the beginning of 2000, respectively. Because of the large interest of other clinics, the clinical study on adoptive immunotherapy with gene-modified T lymphocytes designed during this project will be carried out as an international phase I/II study under the direction of the Hamburg BMT center. During the project, efficient infection protocols for hematopoietic stem and progenitor cells and for the enrichment of gene-modified cells were developed. It was shown for the first time that the matrix protein fibronectin facilitates retroviral gene transfer into T lymphocytes. Recently, the first protocol for clinical gene transfer in the absence of bovine serum has been published by our group. Thereby, an important problem of biological safety during ex vivo transduction has been solved. In cooperation with or partner HPI, new retroviral vectors have been developed, which are characterized by better expression features in hematopoietic cells. (orig.)Available from TIB Hannover: DtF QN1(76,23) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman