1,720,977 research outputs found
Non-Hermitian skin effect as an impurity problem
No full textA striking feature of non-Hermitian tight-binding Hamiltonians is the high sensitivity of both spectrum and eigenstates to boundary conditions. Indeed, if the spectrum under periodic boundary conditions is point gapped by opening the lattice the non-Hermitian skin effect will necessarily occur. Finding the exact skin eigenstates may be demanding in general, and many methods in the literature are based on recurrence equations for the eigenstates’ components. Here we devise a general procedure based on the Green’s function method to calculate the eigenstates of non-Hermitian tight-binding Hamiltonians under open boundary conditions. We apply it to the Hatano-Nelson and non-Hermitian Su-Schrieffer-Heeger models and finally we contrast the edge states localization with that of bulk states
Modeling epidemics through ladder operators
Full text linkWe propose a simple model of spreading of some infection in an originally healthy population which is different from other models existing in the literature. In particular, we use an operator technique which allows us to describe in a natural way the possible interactions between healthy and un-healthy populations, and their transformation into recovered and to dead people. After a rather general discussion, we apply our method to the analysis of Chinese data for the SARS-2003 (Severe acute respiratory syndrome; SARS-CoV-1) and the Coronavirus COVID-19 (Corona Virus Disease; SARS-CoV-2) and we show that the model works very well in reproducing the long-time behaviour of the disease, and in particular in finding the number of affected and dead people in the limit of large time. Moreover, we show how the model can be easily modified to consider some lockdown measure, and we deduce that this procedure drastically reduces the asymptotic value of infected individuals, as expected, and observed in real life
A no-go result for the quantum damped harmonic oscillator
Full text linkIn this letter we show that it is not possible to set up a canonical quantization for the damped harmonic oscillator using the Bateman Lagrangian. In particular, we prove that no square integrable vacuum exists for the natural ladder operators of the system, and that the only vacua can be found as distributions. This implies that the procedure proposed by some authors is only formally correct, and requires a much deeper analysis to be made rigorous
Tridiagonality, supersymmetry and non self-adjoint Hamiltonians
Full text linkIn this paper we consider some aspects of tridiagonal, non self-adjoint, Hamiltonians and of their supersymmetric counterparts. In particular, the problem of factorization is discussed, and it is shown how the analysis of the eigenstates of these Hamiltonians produce interesting recursion formulas giving rise to biorthogonal families of vectors. Some examples are proposed, and a connection with bi-squeezed states is analyzed
Some remarks on few recent results on the damped quantum harmonic oscillator
No full textIn a recent paper, Deguchi et al. (2019), the authors proposed an analysis of the damped quantum harmonic oscillator in terms of ladder operators. This approach was shown to be partly incorrect in Bagarello et al. (2019), via a simple no-go theorem. More recently, (Deguchi and Fujiwara, 2019), Deguchi and Fujiwara claimed that our results in Bagarello et al. (2019) are wrong, and compute what they claim is the square integrable vacuum of their annihilation operators. In this brief note, we show that their vacuum is indeed not a vacuum, and we try to explain what is behind their mistakes in Deguchi et al. (2019) and Deguchi and Fujiwara (2019). We also propose a very simple example clarifying the core of the problem
Diagnosing non-Hermitian many-body localization and quantum chaos via singular value decomposition
No full textStrong local disorder in interacting quantum spin chains can turn delocalized eigenmodes into localized eigenstates, giving rise to many-body localized phases. This is accompanied by distinct spectral statistics: chaotic for the delocalized phase and integrable for the localized phase. In isolated systems, localization and chaos are defined through a web of relations among eigenvalues, eigenvectors, and real-time dynamics. These may change as the system is made open. We ask whether random dissipation (without random disorder) can induce chaotic or localized behavior in an otherwise integrable system. The dissipation is described using non-Hermitian Hamiltonians, which can effectively be obtained from Markovian dynamics conditioned on null measurement. In this non-Hermitian setting, we argue in favor of the use of the singular value decomposition. We complement the singular value statistics with different diagnostic tools, namely, the singular form factor and the inverse participation ratio and entanglement entropy of singular vectors. We thus identify a crossover of the singular values from chaotic to integrable spectral features and of the singular vectors from delocalization to localization. Our method is illustrated in an XXZ Hamiltonian with random local dissipation
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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