An analogue of the Wiener Tauberian Theorem for the Heisenberg Motion group

We show that the Wiener Tauberian property holds for the Heisenberg Motion group TnB

Density matrix renormalization group algorithm for Bethe lattices of spin-1/2 or spin-1 sites with Heisenberg antiferromagnetic exchange

A density matrix renormalization group (DMRG) algorithm is presented for the Bethe lattice with connectivity Z = 3 and antiferromagnetic exchange between nearest-neighbor spins s = 1/2 or 1 sites in successive generations g. The algorithm is accurate for s = 1 sites. The ground states are magnetic with spin S(g) = 2(g)s, staggered magnetization that persists for large g > 20, and short-range spin correlation functions that decrease exponentially. A finite energy gap to S > S(g) leads to a magnetization plateau in the extended lattice. Closely similar DMRG results for s = 1/2 and 1 are interpreted in terms of an analytical three-site model.

ENTANGLEMENT IN A 3-SPIN HEISENBERG-XY CHAIN WITH NEAREST-NEIGHBOR INTERACTIONS, SIMULATED IN AN NMR QUANTUM SIMULATOR

The evolution of entanglement in a 3-spin chain with nearest-neighbor Heisenberg-XY interactions for different initial states is investigated here. In an NMR experimental implementation, we generate multipartite entangled states starting from initial separable pseudo-pure states by simulating nearest-neighbor XY interactions in a 3-spin linear chain of nuclear spin qubits. For simulating XY interactions, we follow algebraic method of Zhang et al. Phys. Rev. A 72 (2005) 012331]. Bell state between end qubits has been generated by using only the unitary evolution of the XY Hamiltonian. For generating W-state and GHZ-state a single qubit rotation is applied on second and all the three qubits, respectively after the unitary evolution of the XY Hamiltonian.

Analyticity of the Schrodinger propagator on the Heisenberg group

We discuss the analytic extension property of the Schrodinger propagator for the Heisenberg sublaplacian and some related operators. The result for the sublaplacian is proved by interpreting the sublaplacian as a direct integral of an one parameter family of dilated special Hermite operators.

Revisiting Riesz transforms on Heisenberg groups

We characterise higher order Riesz transforms on the Heisenberg group and also show that they satisfy dimension-free bounds under some assumptions on the multipliers. Using transference theorems, we deduce boundedness theorems for Riesz transforms on the reduced Heisenberg group and hence also for the Riesz transforms associated to multiple Hermite and Laguerre expansions.

Quantum phases of dimerized and frustrated Heisenberg spin chains with s=1/2, 1 and 3/2: an entanglement entropy and fidelity study

We study here different regions in phase diagrams of the spin-1/2, spin-1 and spin-3/2 one-dimensional antiferromagnetic Heisenberg systems with frustration (next-nearest-neighbor interaction J(2)) and dimerization (delta). In particular, we analyze the behaviors of the bipartite entanglement entropy and fidelity at the gapless to gapped phase transitions and across the lines separating different phases in the J(2)-delta plane. All the calculations in this work are based on numerical exact diagonalizations of finite systems.

On the images of Sobolev spaces under the heat kernel transform on the Heisenberg group

The aim of this paper is to obtain certain characterizations for the image of a Sobolev space on the Heisenberg group under the heat kernel transform. We give three types of characterizations for the image of a Sobolev space of positive order H-m (H-n), m is an element of N-n, under the heat kernel transform on H-n, using direct sum and direct integral of Bergmann spaces and certain unitary representations of H-n which can be realized on the Hilbert space of Hilbert-Schmidt operators on L-2 (R-n). We also show that the image of Sobolev space of negative order H-s (H-n), s(> 0) is an element of R is a direct sum of two weighted Bergman spaces. Finally, we try to obtain some pointwise estimates for the functions in the image of Schwartz class on H-n under the heat kernel transform. (C) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Revisiting the Fourier transform on the Heisenberg group

A recent theorem of S. Alesker, S. Artstein-Avidan and V. Milman characterises the Fourier transform on R-n as essentially the only transform on the space of tempered distributions which interchanges convolutions and pointwise products. In this note we study the image of the Schwartz space on the Heisenberg group under the Fourier transform and obtain a similar characterisation for the Fourier transform on the Heisenberg group.

Studies on a frustrated Heisenberg spin chain with alternating ferromagnetic and antiferromagnetic exchanges

We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (J(1)(F)) and antiferromagnetic (J(1)(A)) nearest-neighbor interactions and a ferromagnetic next-nearest-neighbor interaction (J(2)(F)). In this model frustration is present due to the non-zero J(2)(F). The model with site spin s behaves like a Haldane spin chain, with site spin 2s in the limit of vanishing J(2)(F) and large J(1)(F)/J(1)(A). We show that the exact ground state of the model can be found along a line in the parameter space. For fixed J(1)(F), the phase diagram in the space of J(1)(A)-J(2)(F) is determined using numerical techniques complemented by analytical calculations. A number of quantities, including the structure factor, energy gap, entanglement entropy and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and potentially important feature of this model is that it can exhibit a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.

Mixed norm estimates for the Riesz transforms on the Heisenberg group

In this paper we prove weighted mixed norm estimates for Riesz transforms on the Heisenberg group and Riesz transforms associated to the special Hermite operator. From these results vector-valued inequalities for sequences of Riesz transforms associated to generalised Grushin operators and Laguerre operators are deduced.

Sapientia, 1976, Vol. XXXI, nº 122 (número completo)

Contenido: Verdad, historia y hermenéutica / Octavio N. Derisi – El lumen naturale en Santo Tomás y el essere ideale en Rosmini / William R. Darós – El constitutivo esencial de la persona / Octavio N. Derisi – Filosofía y desarrollo integral / Alberto Caturelli – La respuesta del hombre frente a lo existente : intuición y palabra / Osvaldo Francella – Notas y comentarios -- Bibliografía

Teoría y práctica de la poesía cinética en Composición de lugar (1976) de Amanda Berenguer

Resumen: Este trabajo propone un análisis de Composición de lugar (1976), el volumen que mejor representa la faceta experimental de la poesía de Amanda Berenguer (Montevideo, 1921-2010). Nos interesa examinar el texto a la luz de la noción de “poesía cinética” que desarrolló la autora y, a partir de esta coincidencia de teoría y praxis, rastrear sus vínculos con las búsquedas estéticas de otros autores y grupos de neovanguardia.

Teología, 1976, Tomo XIII nº 027-028 (número completo)

San Cipriano y el Donatismo, en la polémica antidonatista de san Agustín. Estudio histórico-patrístico / Rubén D. García -- La Iglesia y la existencia cristiana en la teología de San Buenaventura. II° parte / José Rovai -- Renovación de la Iglesia Ortodoxa Rusa a principios de este siglo / Domingo Krpan -- Pueblo, religión del pueblo e Iglesia / Lucio Gera -- El plan de la Epístola a los Gálatas / Luis H. Rivas -- Sagrada Congregación para la Educación Católica: La formación teológica de los futuros sacerdotes -- Notas bibliográficas

Mons. Enrique Angelelli, obispo de La Rioja (1968-1976) : recepción diocesana de su muerte: testimonios y valoraciones

Resumen: Este aporte intenta lograr una mirada sincrónica de la tragedia que se llevó de este mundo a Mons. Enrique Angelelli. La trama humana en su conjunto se desarrolla entre tristezas y alegrías y, también, lógicamente, la historia de la Iglesia posee los mismos condimentos. Pero, la clave está en la luz con la cual miramos estos acontecimientos que, en este caso, no sólo será científica o meramente sociológica sino, fundamentalmente, teológica. Así, al recoger los testimonios del pueblo de Dios, presentamos un hecho histórico reflejado a través del prisma de la fe.

[Discurso do Deputado Aldo Fagundes : Sessão da Câmara dos Deputados de 13 de setembro de 1976]

Dá conhecimento à Camara dos Deputados do inteiro teor do documento divulgado pelo Instituto dos Arquitetos do Brasil, onde se analisam as distorções sofridas pelo plano original de Brasília. Discorre sobre a importância da presença do homem no Planalto Central brasileiro, reverenciando a memória do ex-Presidente Juscelino Kubitschek na oportunidade em que evoca episódios ligados à fundação da cidade. Manifesta apreensão ante a ameaça de desumanização que paira sobre a comunidade brasiliense, conforme denuncia o referido documento. Enfatiza a necessidade da imediata institucionalização da ação comunitária em Brasília, que auxilie o Poder Público na solução dos problemas sociais que a cidade vem enfrentando. Traz à baila a questão da participação política do povo brasiliense, expondo as tendências que se vão esboçando, de um lado, pela criação de um Conselho Comunitário e, de outro, pela criação de um órgão de representação política propriamente dito, seja Câmara de Vereadores, seja Assembléia Legislativa. Reproduz em síntese as disposições gerais de projeto que apresentou propondo a criação do Conselho Comunitário de Brasília - COBRAS. Divulga o inteiro teor do parecer das Comissões Técnicas da Casa que já se manifestaram sobre o mencionado projeto. Anuncia a posição assumida pelo Presidente da Associação Comercial, Vicente de Paula Araújo, em favor da participação de Brasília nas decisões políticas e administrativas de interesse da cidade.