Related papers: Faraday effect revisited: sum rules and convergenc…
This paper is the second in a series revisiting the (effect of) Faraday rotation. We formulate and prove the thermodynamic limit for the transverse electric conductivity of Bloch electrons, as well as for the Verdet constant. The main…
This paper is the first in a series revisiting the Faraday effect, or more generally, the theory of electronic quantum transport/optical response in bulk media in the presence of a constant magnetic field. The independent electron…
A flow invariant in quantum field theory is a quantity that does not depend on the flow connecting the UV and IR conformal fixed points. We study the flow invariance of the most general sum rule with correlators of the trace Theta of the…
In the context of boundary conformal field theory, we derive a sum rule that relates two and three point functions of the displacement operator. For four dimensional conformal field theory with a three dimensional boundary, this sum rule in…
Power-law uniform (in the operator norm) convergence on vector subspaces with their own norms in von Neumann's ergodic theorem with continuous time is considered. All possible exponents of the considered power-law convergence are found; for…
The sum rule for the moments of the spectral density is discussed for the single-band Hubbard model. It is shown that respecting the sum rule up to the order m=3 is conceptually important for a qualitatively correct description of the…
A formula for the Hall response of interacting multi-band systems with arbitrary band topology and spin-orbit coupling is derived. The formula is valid at finite frequency, which is relevant for Faraday rotation, and it takes into account…
We present a complete derivation of the granular analogue to Drude conductivity using diagrammatic methods. The convergence issues arising when changing the order of momentum and frequency summation are more severe than in the homogeneous…
We consider a spherical variant of the Faraday problem, in which a spherical drop is subjected to a time-periodic body force, as well as surface tension. We use a full three-dimensional parallel front-tracking code to calculate the…
The strength of fluctuations, as measured by their variance, is paramount in the quantitative description of a large class of physical systems, ranging from simple and complex liquids to active fluids and solids. Fluctuations originate from…
Sum rules are elegant formulas that relate entropy functionals to coefficients associated with orthogonal polynomials [Sim11]. In a series of paper (see for example [GNR16], [GNR17], [BSZ18a], [BSZ18b]), interesting connections have been…
Sum rules have played an important role in the development of many branches of physics since the earliest days of quantum mechanics. We present examples of one-dimensional quantum mechanical sum rules and apply them in two familiar systems,…
The dispersion relation of vertically oscillating fluid surfaces has been a subject extensively studied in the past, as well as surface instabilities produced by electrohydrodynamic (EHD) waves in similar configurations. In the present work…
We establish a set of exact sum rules that relate the interatomic force constants to the frequency-dependent electromagnetic susceptibility of a solid or molecule, thereby generalizing the long-established principles of rototranslational…
In traditional QCD sum rules, the simple hadron spectral density model of ``delta-function-type ground state + theta-function-type continuous spectrum" determines that there is no perfect parameter selection. In recent years, inverse…
We analyze the transformation properties of Faraday law in an empty space and its relationship with Maxwell equations. In our analysis we express the Faraday law via the four-potential of electromagnetic field and the field of…
Using unitarity, analyticity and crossing symmetry, we derive universal sum rules for scattering amplitudes in theories invariant under an arbitrary symmetry group. The sum rules relate the coefficients of the energy expansion of the…
Noether invariance in statistical mechanics provides fundamental connections between the symmetries of a physical system and its conservation laws and sum rules. The latter are exact identities that involve statistically averaged forces and…
We study the inverse scattering problem for electric potentials and magnetic fields in $\ere^d, d\geq 3$, that are asymptotic sums of homogeneous terms at infinity. The main result is that all these terms can be uniquely reconstructed from…
In this article, we study the Faraday effect in a binary composite consisting of a dielectric matrix with metallic inclusions. We first use the replica trick together with a variational method in order to compute the effective permittivity…