AC-Conductivity Measure from Heat Production of Free Fermions in Disordered Media

We extend (Bru et al. in J Math Phys 56:051901-1-51, 2015) in order to study the linear response of free fermions on the lattice within a (independently and identically distributed) random potential to a macroscopic electric field that is time- and space-dependent. We obtain the notion of a macroscopic AC-conductivity measure which only results from the second principle of thermodynamics. The latter corresponds here to the positivity of the heat production for cyclic processes on equilibrium states. Its Fourier transform is a continuous bounded function which is naturally called (macroscopic) conductivity. We additionally derive Green–Kubo relations involving time-correlations of bosonic fields coming from current fluctuations in the system. This is reminiscent of non-commutative central limit theorems

Macroscopic conductivity of free fermions in disordered media

We conclude our analysis of the linear response of charge transport in lattice systems of free fermions subjected to a random potential by deriving general mathematical properties of its conductivity at the macroscopic scale. The present paper belongs to a succession of studies on Ohm and Joule's laws from a thermodynamic viewpoint starting with [1-3]. We show, in particular, the existence and finiteness of the conductivity measure μΣ for macroscopic scales. Then we prove that, similar to the conductivity measure associated to Drude's model, μΣ converges in the weak*-topology to the trivial measure in the case of perfect insulators (strong disorder, complete localization), whereas in the limit of perfect conductors (absence of disorder) it converges to an atomic measure concentrated at frequency ν = 0. However, the AC-conductivity μΣ| ℝ\{0} does not vanish in general: We show that μΣ(ℝ\{0}) > 0, at least for large temperatures and a certain regime of small disorder

Microscopic Conductivity of Lattice Fermions at Equilibrium - Part I: Non-Interacting Particles

We consider free lattice fermions subjected to a static bounded potential and a time- and space-dependent electric field. For any bounded convex region $\mathcal{R}\subset \mathbb{R}^{d}$ ($d\geq 1$) of space, electric fields $\mathcal{E}$ within $\mathcal{R}$ drive currents. At leading order, uniformly with respect to the volume $\left| \mathcal{R}\right|$ of $\mathcal{R}$ and the particular choice of the static potential, the dependency on $\mathcal{E}$ of the current is linear and described by a conductivity distribution. Because of the positivity of the heat production, the real part of its Fourier transform is a positive measure, named here (microscopic) conductivity measure of $\mathcal{R}$, in accordance with Ohm's law in Fourier space. This finite measure is the Fourier transform of a time-correlation function of current fluctuations, i.e., the conductivity distribution satisfies Green-Kubo relations. We additionally show that this measure can also be seen as the boundary value of the Laplace-Fourier transform of a so-called quantum current viscosity. The real and imaginary parts of conductivity distributions satisfy Kramers-Kronig relations. At leading order, uniformly with respect to parameters, the heat production is the classical work performed by electric fields on the system in presence of currents. The conductivity measure is uniformly bounded with respect to parameters of the system and it is never the trivial measure $0\,\mathrm{d}\nu$. Therefore, electric fields generally produce heat in such systems. In fact, the conductivity measure defines a quadratic form in the space of Schwartz functions, the Legendre-Fenchel transform of which describes the resistivity of the system. This leads to Joule's law, i.e., the heat produced by currents is proportional to the resistivity and the square of currents

Irrelevant Interactions without Composite Operators - A Remark on the Universality of Second Order Phase Transitions

We study the critical behaviour of symmetric $\phi^4_4$ theory including irrelevant terms of the form $\phi^{4+2n}/\Lambda_0^{2n}$ in the bare action, where $\Lambda_0$ is the UV cutoff (corresponding e.g. to the inverse lattice spacing for a spin system). The main technical tool is renormalization theory based on the flow equations of the renormalization group which permits to establish the required convergence statements in generality and rigour. As a consequence the effect of irrelevant terms on the critical behaviour may be studied to any order without using renormalization theory for composite operators. This is a technical simplification and seems preferable from the physical point of view. In this short note we restrict for simplicity to the symmetry class of the Ising model, i.e. one component $\phi^4_4$ theory. The method is general, however.Comment: 13 page

Large Deviations in Weakly Interacting Fermions - Generating Functions as Gaussian Berezin Integrals and Bounds on Large Pfaffians

We prove that the G\"{a}rtner--Ellis generating function of probability distributions associated with KMS states of weakly interacting fermions on the lattice can be written as the limit of logarithms of Gaussian Berezin integrals. The covariances of the Gaussian integrals are shown to have a uniform Pfaffian bound and to be summable in general cases of interest, including systems that are \emph{not} translation invariant. The Berezin integral representation can thus be used to obtain convergent expansions of the generating function in terms of powers of its parameter. The derivation and analysis of the expansions of logarithms of Berezin integrals are the subject of the second part of the present work. Such technical results are also useful, for instance, in the context of quantum information theory, in the computation of relative entropy densities associated with fermionic Gibbs states, and in the theory of quantum normal fluctuations for weakly interacting fermion systems.FAPESP (2017/22340-9) CNPq (309723/2020-5) by the Basque Government through the grant IT641-13 MTM2017-82160-C2-2-P

Double shunt technique for hybrid palliation of hypoplastic left heart syndrome: a case report

We report a technique to palliate hypoplastic left heart syndrome, with no PDA stenting, but with double polytetrafluoroethylene shunt from pulmonary artery to ascending and descending aorta by combined thoracotomies. A 30-day-old female was operated with this technique. Five months after first operation, the child was submitted to Norwood/Glenn operation. Good hemodinamic recovery and initial clinical evolution was observed. The child was extubated in 8th post operatory day and reentubated in the next day due to pulmonary infection. Despite antibiotic treatment, the child died after systemic infectious complications

Transcatheter pulmonary valve implantation: systematic literature review

Surgical repair of some complex congenital heart diseases involves reconstruction of the right ventricular outflow tract using homografts, bioprostheses, bovine jugular grafts or other valved conduits between the right ventricle and the main pulmonary artery. Although these surgical procedures may be performed with low mortality rates, the life span of these implanted valves or conduits is usually short (< 10 years) due to either degeneration and/or calcification. Variable degrees of pulmonary stenosis, often associated with pulmonary insufficiency, are consequences of conduit degeneration. In 2000, Bonhoeffer et al. were the first to report the transcatheter pulmonary valve implantation (TPVI) of a bioprosthetic pulmonary valve later named Melody® valve (Medtronic, Minneapolis, USA). The technique was initially developed to limit the need for multiple surgical procedures, and, ultimately, to work as a surrogate of a new surgical valve replacement. Subsequent clinical studies in Europe and the United States confirmed the safety and efficacy of this technique in a larger number of patients. Since the National Sanitary Surveillance Agency (Agência Nacional de Vigilância Sanitária - Anvisa) granted approval for clinical use of the Melody® transcatheter pulmonary biological valve in February 2103, we deemed that a judicious assessment of this new technology was timely and necessary before the widespread use in our country. The objective of this study was to perform a systematic literature review on the use of TPVI in patients with dysfunctional homografts, valved conduits and bioprostheses implanted surgically in the right ventricular outflow tract.A correção cirúrgica de algumas cardiopatias congênitas complexas envolve a reconstrução da via de saída do ventrículo direito com a interposição de homoenxertos, biopróteses, enxertos de jugular bovina ou outros condutos valvulados entre o ventrículo direito e o tronco da artéria pulmonar. Apesar de essas cirurgias poderem ser realizadas com baixa mortalidade, a vida útil das válvulas ou dos condutos implantados é normalmente pequena (< 10 anos), seja por degeneração e/ou calcificação. Graus variáveis de estenose pulmonar na maioria das vezes associada a insuficiência pulmonar são consequências da degeneração dos condutos. Em 2000, Bonhoeffer et al. foram os primeiros a relatar o implante transcateter de bioprótese valvular pulmonar (ITVP) com um dispositivo que posteriormente foi denominado de válvula Melody® (Medtronic, Minneapolis, Estados Unidos). A técnica foi inicialmente desenvolvida para limitar a necessidade de múltiplos procedimentos cirúrgicos, substituindo, em última análise, uma nova troca cirúrgica valvular. Estudos subsequentes na Europa e Estados Unidos atestaram para a segurança e eficácia dessa técnica em um número maior de pacientes. Como a Agência Nacional de Vigilância Sanitária (Anvisa) concedeu a aprovação para o uso clínico da válvula biológica pulmonar transcateter Melody® em fevereiro de 2013, consideramos necessária e oportuna a avaliação judiciosa da utilização dessa nova tecnologia antes que ela fosse aplicada em larga escala em nosso país. O objetivo deste estudo foi realizar uma revisão sistemática da literatura sobre o ITVP em pacientes com disfunções de homoenxertos, condutos valvulados e biopróteses implantados cirurgicamente na via de saída do ventrículo direito.Evidências - Credibilidade CientíficaHospital da Unimed João PessoaFundação Universitária de Cardiologia Instituto de Cardiologia Setor de Cardiologia Intervencionista em Cardiopatias CongênitasComplexo Hospitalar Santa Casa de Porto Alegre Serviço de Cardiologia Pediátrica e Cardiologia IntervencionistaHospital Beneficência Portuguesa de São Paulo Setor de Intervenções em Cardiopatias CongênitasUniversidade Federal de São Paulo (UNIFESP) Escola Paulista de Medicina Setor de Cardiologia PediátricaInstituto Dante Pazzanese de Cardiologia Seção Médica de Intervenções em Valvopatias AdquiridasUniversidade Federal de Minas Gerais Hospital de Clinicas Departamento de Cardiopatias CongênitasHospital Laranjeiras Instituto Nacional de Cardiologia Serviço de Cardiologia da Criança e do AdolescenteHospital Federal dos Servidores do Estado Setor de Cardiologia Intervencionista dos Defeitos Estruturais e CongênitosInstituto de Medicina Integral Prof. Fernando Figueira Setor de Hemodinâmica em Cardiopatias CongênitasHospital Biocor Departamento de Cardiologia Pediátrica IntervencionistaInstituto Dante Pazzanese de Cardiologia Seção Médica de Intervenções em Cardiopatias CongênitasUNIFESP, EPM, Setor de Cardiologia PediátricaSciEL