Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One Dimensional Bose Gases

Real-time dynamics in a quantum many-body system are inherently complicated and hence difficult to predict. There are, however, a special set of systems where these dynamics are theoretically tractable: integrable models. Such models possess non-trivial conserved quantities beyond energy and momentum. These quantities are believed to control dynamics and thermalization in low dimensional atomic gases as well as in quantum spin chains. But what happens when the special symmetries leading to the existence of the extra conserved quantities are broken? Is there any memory of the quantities if the breaking is weak? Here, in the presence of weak integrability breaking, we show that it is possible to construct residual quasi-conserved quantities, so providing a quantum analog to the KAM theorem and its attendant Nekhoreshev estimates. We demonstrate this construction explicitly in the context of quantum quenches in one-dimensional Bose gases and argue that these quasi-conserved quantities can be probed experimentally.Comment: 21 pages with appendices; 13 figures; version accepted by PR

Quench Dynamics in Randomly Generated Extended Quantum Models

We analyze the thermalization properties and the validity of the Eigenstate Thermalization Hypothesis in a generic class of quantum Hamiltonians where the quench parameter explicitly breaks a Z_2 symmetry. Natural realizations of such systems are given by random matrices expressed in a block form where the terms responsible for the quench dynamics are the off-diagonal blocks. Our analysis examines both dense and sparse random matrix realizations of the Hamiltonians and the observables. Sparse random matrices may be associated with local quantum Hamiltonians and they show a different spread of the observables on the energy eigenstates with respect to the dense ones. In particular, the numerical data seems to support the existence of rare states, i.e. states where the observables take expectation values which are different compared to the typical ones sampled by the micro-canonical distribution. In the case of sparse random matrices we also extract the finite size behavior of two different time scales associated with the thermalization process.Comment: 30 pages, 44 figure

Utilização de índices de vegetação na avaliação da cobertura vegetal do projeto de assentamento José Emídio dos Santos, Capela-SE.

Este trabalho tem como objetivo realizar uma avaliação da cobertura vegetal no Projeto de Assentamento José Emídio dos Santos, a partir dos índices de vegetação: SR, NDVI, SAVI e EVI. Foi utilizada uma imagem de satélite Landsat 5 TM (Thematic Mapper) com data de passagem 03/04/2009. Todos os índices de vegetação foram eficientes na separação de classes de cobertura vegetal, no entanto, o SR apresentou valores elevados com relação aos demais

Aplicação da classificação supervisionada na análise temporal do uso da terra no projeto de assentamento José Emídio dos Santos, Capela/Sergipe, 199-2009.

Este trabalho tem como objetivo realizar uma análise das modificações ocorridas no Projeto de Assentamento José Emídio dos Santos, antiga Usina Santa Clara a partir da evolução temporal do uso da terra em dois períodos distintos. Para a avaliação foram utilizadas duas imagens de satélite Landsat 5 TM (Thematic Mapper) e posteriormente, a classificação supervisionada através do software ArcGIS, pelo método da máxima verossimilhança. A análise dos mapas temáticos com a evolução temporal do uso da terra no assentamento possibilitou melhor visualização das mudanças ocorridas no espaço geográfico em função das atividades antrópicas. As principais mudanças observadas referem-se à pressão demográfica e, a substituição de áreas anteriormente utilizadas com o monocultivo da cana de açúcar por uma diversificação de cultura de subsistência pelos assentados

Remarks on the notion of quantum integrability

We discuss the notion of integrability in quantum mechanics. Starting from a review of some definitions commonly used in the literature, we propose a different set of criteria, leading to a classification of models in terms of different integrability classes. We end by highlighting some of the expected physical properties associated to models fulfilling the proposed criteria.Comment: 22 pages, no figures, Proceedings of Statphys 2

Zamolodchikov-Faddeev Algebra and Quantum Quenches in Integrable Field Theories

We analyze quantum quenches in integrable models and in particular the determination of the initial state in the basis of eigenstates of the post-quench hamiltonian. This leads us to consider the set of transformations of creation and annihilation operators that respect the Zamolodchikov-Faddeev algebra satisfied by integrable models. We establish that the Bogoliubov transformations hold only in the case of quantum quenches in free theories. In the most general case of interacting theories, we identify two classes of transformations. The first class induces a change in the S-matrix of the theory but not of its ground state, whereas the second class results in a "dressing" of the operators. As examples of our approach we consider the transformations associated with a change of the interaction in the Sinh-Gordon and the Lieb-Liniger model.Comment: v2: published version (typos corrected

UvA-DARE (Digital Academic Repository) Competing interactions in semiconductor quantum dots

Competing interactions in semiconductor quantum dots van den Berg, R.; Brandino, G.P.; El Araby, O.; Konik, R.M.; Gritsev, V.; Caux, J.S. General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. We introduce an integrability-based method enabling the study of semiconductor quantum dot models incorporating both the full hyperfine interaction as well as a mean-field treatment of dipole-dipole interactions in the nuclear spin bath. By performing free-induction decay and spin-echo simulations we characterize the combined effect of both types of interactions on the decoherence of the electron spin, for external fields ranging from low to high values. We show that for spin-echo simulations the hyperfine interaction is the dominant source of decoherence at short times for low fields, and competes with the dipole-dipole interactions at longer times. On the contrary, at high fields the main source of decay is due to the dipole-dipole interactions. In the latter regime an asymmetry in the echo is observed. Furthermore, the nondecaying fraction previously observed for zero-field free-induction decay simulations in quantum dots with only hyperfine interactions, is destroyed for longer times by the mean-field treatment of the dipolar interactions