1,720,962 research outputs found
Localization of Generalized Wannier Bases Implies Chern Triviality in Non-periodic Insulators
No full textWe investigate the relation between the localization of generalized Wannier bases and the topological properties of two-dimensional gapped quantum systems of independent electrons in a disordered background, including magnetic fields, as in the case of Chern insulators and quantum Hall systems. We prove that the existence of a well-localized generalized Wannier basis for the Fermi projection implies the vanishing of the Chern character, which is proportional to the Hall conductivity in the linear response regime. Moreover, we state a localization dichotomy conjecture for general non-periodic gapped quantum systems
The Haldane model and its localization dichotomy
No full textGapped periodic quantum systems exhibit an interesting Localization Dichotomy, which emerges when one looks at the localization of the optimally localized Wannier functions associated to the Bloch bands below the gap. As recently proved, either these Wannier functions are exponentially localized, as it happens whenever the Hamiltonian operator is time-reversal symmetric, or they are delocalized in the sense that the expectation value of |x| 2 diverges. Intermediate regimes are forbidden. Following the lesson of our Maestro, to whom this contribution is gratefully dedicated, we find useful to explain this subtle mathematical phenomenon in the simplest possible model, namely the discrete model proposed by Haldane [10]. We include a pedagogical introduction to the model and we explain its Localization Dichotomy by explicit analytical arguments. We then introduce the reader to the more general, model-independent version of the dichotomy proved in [19]
Středa formula for charge and spin currents
Full text linkWe consider a 2-dimensional Bloch-Landau-Pauli Hamiltonian for a spinful electron in a constant magnetic field subject to a periodic background potential. Assuming that the z-component of the spin operator is conserved, we compute the linear response of the associated spin density of states to a small change in the magnetic field, and identify it with the spin Hall conductivity. This response is in the form of a spin Chern marker, which is in general quantized to a half-integer, and to an integer under the further assumption of time-reversal symmetry. Our result is thus a generalization to the context of the quantum spin Hall effect of the well-known formula by Středa, which is formulated instead for charge transport
The Haldane model and its localization dichotomy
No full textGapped periodic quantum systems exhibit an interesting Localization Dichotomy, which emerges when one looks at the localization of the optimally localized Wannier functions associated to the Bloch bands below the gap. As recently proved, either these Wannier functions are exponentially localized, as it happens whenever the Hamiltonian operator is time-reversal symmetric, or they are delocalized in the sense that the expectation value of |x|^2 diverges. Intermediate regimes are forbidden.
Following the lesson of our Maestro, to whom this contribution is gratefully dedicated, we find useful to explain this subtle mathematical phenomenon in the simplest possible model, namely the discrete model proposed by Haldane (Phys. Rev. Lett. 61, 2017 (1988)). We include a pedagogical introduction to the model and we explain its Localization Dichotomy by explicit analytical arguments. We then introduce the reader to the more general, model-independent version of the dichotomy proved in (Commun. Math. Phys. 359, 61-100 (2018)), and finally we announce further generalizations to non-periodic models
Spectral and scattering theory of one-dimensional coupled photonic crystals
Full text linkWe study the spectral and scattering theory of light transmission in a system consisting of two asymptotically periodic waveguides, also known as one-dimensional photonic crystals, coupled by a junction. Using analyticity techniques and commutator methods in a two-Hilbert spaces setting, we determine the nature of the spectrum and prove the existence and completeness of the wave operators of the system
Bulk-edge correspondence for unbounded Dirac-Landau operators
Full text linkWe consider two-dimensional unbounded magnetic Dirac operators, either
defined on the whole plane, or with infinite mass boundary conditions on a
half-plane. Our main results use techniques from elliptic PDEs and integral
operators, while their topological consequences are presented as corollaries of
some more general identities involving magnetic derivatives of local traces of
fast decaying functions of the bulk and edge operators. One of these
corollaries leads to the so-called St\v{r}eda formula: if the bulk operator has
an isolated compact spectral island, then the integrated density of states of
the corresponding bulk spectral projection varies linearly with the magnetic
field as long as the gaps between the spectral island and the rest of the
spectrum are not closed, and the slope of this variation is given by the Chern
character of the projection. The same bulk Chern character is related to the
number of edge states which appear in the gaps of the bulk operator.Comment: Final version, 25 pages, appeared in JM
Ultra-generalized Wannier bases: Are they relevant to topological transport?
Full text linkWe generalize Prodan's construction of radially localized generalized Wannier bases [E. Prodan, J. Math. Phys. 56(11), 113511 (2015)] to gapped quantum systems without time-reversal symmetry, including, in particular, magnetic Schrodinger operators, and we prove some basic properties of such bases. We investigate whether this notion might be relevant to topological transport by considering the explicitly solvable case of the Landau operator
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
- …
