Extended Derivative Dispersion Relations

It is shown that, for a wide class of functions with physical interest as forward scattering amplitudes, integral dispersion relations can be replaced by derivative forms without any high-energy approximation. The applicability of these extended derivative relations, in the investigation of forward proton-proton and antiproton-proton elastic scattering, is exemplified by means of a Pomeron-Reggeon model with totally nondegenerate trajectories.Comment: 7 pages, 1 figure, contribution to "Sense of Beauty in Physics", Miniconference in Honor of Adriano Di Giacomo on his 70th Birthday, Pisa, Italy, Jan. 26-27, 200

Derivative dispersion relations above the physical threshold

We discuss some formal and practical aspects related to the replacement of Integral Dispersion Relations (IDR) by derivative forms, without high-energy approximations. We first demonstrate that, for a class of functions with physical interest as forward scattering amplitudes, this replacement can be analytically performed, leading to novel Extended Derivative Dispersion Relations (EDDR), which, in principle, are valid for any energy above the physical threshold. We then verify the equivalence between the IDR and EDDR by means of a popular parametrization for total cross sections from proton-proton and antiproton-proton scattering and compare the results with those obtained through other representations for the derivative relations. Critical aspects on the limitations of the whole analysis, from both formal and practical points of view, are also discussed in some detail.Comment: Final version, published in Brazilian Journal of Physics, V. 37, 358 (2007

High-Energy Proton-Proton Forward Scattering and Derivative Analyticity Relations

We present the results of several parametrizations to two different ensemble of data on $pp$ total cross sections $\sigma_{tot}^{pp}$ at the highest center-of-mass energies (including cosmic-ray information). The results are statistically consistent with two distinct scenarios at high energies. From one ensemble the prediction for the LHC ($\sqrt s = 14$ TeV) is $\sigma_{tot}^{pp} = 113 \pm 5$ mb and from the other, $\sigma_{tot}^{pp}=140 \pm 7$ mb. From each parametrization, and making use of derivative analyticity relations (DAR), we determine $\rho(s)$ (ratio between the forward real and imaginary parts of the elastic scattering amplitude). A discussion on the optimization of the DAR in terms of a free parameter is also presented.In all cases good descriptions of the experimental data are obtained.Comment: One formula added, one unit changed, small misprints corrected, final version to be published in Brazilian Journal of Physics; 13 pages, 8 figures, aps-revte

Non-hermitian topology as a unifying framework for the Andreev versus Majorana states controversy

Zero-energy Andreev levels in hybrid semiconductor-superconductor nanowires mimic all expected Majorana phenomenology, including 2 e2∕ h conductance quantisation, even where band topology predicts trivial phases. This surprising fact has been used to challenge the interpretation of various transport experiments in terms of Majorana zero modes. Here we show that the Andreev versus Majorana controversy is clarified when framed in the language of non-Hermitian topology, the natural description for quantum systems open to the environment. This change of paradigm allows one to understand topological transitions and the emergence of zero modes in more general systems than can be described by band topology. This is achieved by studying exceptional point bifurcations in the complex spectrum of the system’s non-Hermitian Hamiltonian. Within this broader topological classification, Majoranas from both conventional band topology and a large subset of Andreev levels at zero energy are in fact topologically equivalent, which explains why they cannot be distinguishedWe thank J. Cayao for useful discussions in the early stages of this work. Research supported by the Spanish Ministry of Science, Innovation and Universities through Grants PGC2018-097018-B-I00, FIS2015-65706-P, FIS2015-64654-P, FIS2016-80434-P (AEI/FEDER, EU), the FPI programme BES-2016-078122, the Ramón y Cajal programme Grants RYC-2011-09345, RYC-2013-14645, the María de Maeztu Programme for Units of Excellence in R&D (MDM-2014-0377), and the European Union’s Horizon 2020 research and innovation programme under the FETOPEN Grant Agreement No. 828948. We also acknowledge support from CSIC Research Platform on Quantum Technologies PTI-00

Anisotropic superconducting properties of aligned MgB2 crystallites

Samples of aligned MgB2 crystallites have been prepared, allowing for the first time the direct identification of an upper critical field anisotropy Hc2^{ab}/Hc2^{c}= xi_{ab}/xi_{c} ~ 1.73; with xi_{o,ab} ~ 70 A, xi_{o,c} ~ 40 A, and a mass anisotropy ratio m_{ab}/m_{c} ~ 0.3. A ferromagnetic background signal was identified, possibly related to the raw materials purity.Comment: 4 pages, 4 figures; Revised version to appear in Phys. Rev. Let

Irreversible magnetization under rotating fields and lock-in effect on ErBa_2Cu_3O_7 single crystal with columnar defects

We have measured the irreversible magnetization M_i of an ErBa_2Cu_3O_7 single crystal with columnar defects (CD), using a technique based on sample rotation under a fixed magnetic field H. This method is valid for samples whose magnetization vector remains perpendicular to the sample surface over a wide angle range - which is the case for platelets and thin films - and presents several advantages over measurements of M_L(H) loops at fixed angles. The resulting M_i(\Theta) curves for several temperatures show a peak in the CD direction at high fields. At lower fields, a very well defined plateau indicative of the vortex lock-in to the CD develops. The H dependence of the lock-in angle \phi_L follows the H^{-1} theoretical prediction, while the temperature dependence is in agreement with entropic smearing effects corresponding to short range vortex-defects interactions.Comment: 7 pages, 6 figures, to be published in Phys. Rev.

Exponential dynamical localization for the almost Mathieu operator

We prove that the exponential moments of the position operator stay bounded for the supercritical almost Mathieu operator with Diophantine frequency

Teoria dos Fatos Jurídicos Processuais no Processo Civil do Estado Democrático Constitucional Brasileiro

O fato jurídico processual é tema controverso, sendo conceito tradicionalmente pouco quisto pelos processualistas. Uma explicação plausível para esse preconceito é que a terminologia fato jurídico surgiu entre os estudiosos do direito privado, circunstância que limitou a importação para o ramo (público) do processo, principalmente numa época (fase processualística) em que se buscava a autonomia didático-científica do direito processual face ao direito material. Superada essa ideologia, as amarras que impediam a construção de uma teoria dos fatos jurídicos processuais ficam removidas. Aliás, uma corrente de juristas brasileiros vai assumindo a responsabilidade de edificar a tal teoria. O problema é que a mencionada elaboração teórica, situada nos meandros da propedêutica processual, toma por base a teoria do fato jurídico de Pontes de Miranda, pensada para uma realidade anterior à Constituição de 1988, que precede até mesmo o Código de Processo Civil de 1973 e que possui, destacadamente, viés de aplicação para o direito privado. Eis que, assim, surgem contradições com o processo civil do Estado Democrático Constitucional brasileiro, na atual fase do formalismo-valorativo, sobretudo porque a peça-chave da teoria dos fatos jurídicos processuais é o conceito ponteano de incidência automática e infalível da norma jurídica, o que se choca com as concepções hermenêuticas contemporâneas, as quais situam a norma jurídica como resultado da interpretação e que colocam a jurisprudência como fonte do direito. Para causar ainda mais perplexidade, a teoria dos fatos jurídicos processuais trabalha com categorias que classicamente eram ou mal vistas pela doutrina do processo ou desconhecidas pelos processualistas, como o caso dos negócios jurídicos processuais e dos atos-fatos jurídicos processuais. Assim, importar tais espécies para o processo civil pode ser um tabu de difícil superação. Ver-se-á, porém, que esses choques são meramente aparentes, porque existem elementos na teoria dos fatos jurídicos processuais que fazem dessa construção um instrumento possível de ser aplicado em especial, ao serem feitos alguns necessários ajustes ao processo civil do Estado Democrático Constitucional brasileiro, inclusive com o novo Código de Processo Civil (de 2015). Palavras-chave: Teoria dos fatos jurídicos processuais. Incidência normativa. Processo civil. Formalismo-valorativo. Estado Democrático Constitucional brasileiro