1,721,004 research outputs found
Improved energy estimates for a class of time-dependent perturbed Hamiltonians
Full text linkWe consider time-dependent perturbations which are relatively bounded with
respect to the square root of an unperturbed Hamiltonian operator, and whose
commutator with the latter is controlled by the full perturbed Hamiltonian. The
perturbation is modulated by two auxiliary parameters, one regulates its
intensity as a prefactor and the other one controls its time-scale via a
regular function, whose derivative is compactly supported in a finite interval.
We introduce a natural generalization of energy conservation in the case of
time-dependent Hamiltonians: the boundedness of the two-parameter unitary
propagator for the physical evolution with respect to the -th power energy
norm for all . We provide bounds of the -th power energy
norms, uniformly in time and in the time-scale parameter, for the unitary
propagators, generated by the time-dependent perturbed Hamiltonian and by the
unperturbed Hamiltonian in the interaction picture. The physically interesting
model of Landau-type Hamiltonians with an additional weak and
time-slowly-varying electric potential of unit drop is included in this
framework.Comment: 22 pages; in the Introduction and in Sect. 5 presentation of the
results improved, Remark 2.6 adde
Purely linear response of the quantum Hall current to space-adiabatic perturbations
No full textUsing recently developed tools from space-adiabatic perturbation theory, in particular the construction of a non-equilibrium almost-stationary state, we give a new proof that the Kubo formula for the Hall conductivity remains valid beyond the linear response regime. In particular, we prove that, in quantum Hall systems and Chern insulators, the transverse response current is quantized up to any order in the strength of the inducing electric field. The latter is introduced as a perturbation to a periodic, spectrally gapped equilibrium Hamiltonian by means of a linear potential; existing proofs of the exactness of Kubo formula rely instead on a time-dependent magnetic potential. The result applies to both continuum and discrete crystalline systems modelling the quantum (anomalous) Hall effect
From charge to spin: Analogies and differences in quantum transport coefficients
No full textWe review some recent results from the mathematical theory of transport of charge and spin in gapped crystalline quantum systems. The emphasis will be on transport coefficients, such as conductivities and conductances. As for the former, those are computed as appropriate expectations of current operators in a non-equilibrium almost-stationary state (NEASS), which arises from the perturbation of an equilibrium state by an external electric field. While for charge transport the usual double-commutator Kubo formula is recovered (also beyond linear response), we obtain formulas for appropriately defined spin conductivities, which are still explicit but more involved. Certain "Kubo-like " terms in these formulas are also shown to agree with the corresponding contributions to the spin conductance. In addition to that, we employ similar techniques to show a new result, namely that even in systems with non-conserved spin, there is no generation of spin torque, that is, the spin torque operator has an expectation in the NEASS which vanishes faster than any power of the intensity of the perturbing field
A Multiscale Approach to the Elastic Moduli of Biomembrane
Full text linkWe develop equilibrium fluctuation formulae for the isothermal elastic moduli of discrete biomembrane models at different scales. We account for the coupling of large stretching and bending strains of triangulated network models endowed with harmonic and dihedral angle potentials, on the basis of the discrete-continuum approach presented in Schmidt and Fraternali (J Mech Phys Solids 60:172–180, 2012). We test the proposed equilibrium fluctuation formulae with reference to a coarse-grained molecular dynamics model of the red blood cell (RBC) membrane (Marcelli et al. in Biophys J 89:2473–2480, 2005; Hale et al. in Soft Matter 5:3603–3606, 2009), employing a local maximum-entropy regularization of the fluctuating configurations (Fraternali et al. in J Comput Phys 231:528–540, 2012). We obtain information about membrane stiffening/softening due to stretching, curvature, and microscopic undulations of the RBC model. We detect local dependence of the elastic moduli over the RBC membrane, establishing comparisons between the present theory and different approaches available in the literature
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
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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