Related papers: Local spectral estimates and quantitative weak mix…
We consider quantum systems with a Hamiltonian containing a weak perturbation i.e. $\boldsymbol{H=H_0} + \boldsymbol{\lambda} \cdot \boldsymbol{\tilde{H}}$, $\boldsymbol{\lambda}= \{\lambda_1, \lambda_2,...\}$, $\boldsymbol{\tilde{H}}$ $=…
Returning to a classical question in Harmonic Analysis we strengthen an old result of Walter Rudin. We show that there exists a weakly almost periodic function on the group of integers Z which is not in the norm-closure of the algebra B(Z)…
The average result of a weak measurement of some observable $A$ can, under post-selection of the measured quantum system, exceed the largest eigenvalue of $A$. The nature of weak measurements, as well as the presence of post-selection and…
In this article, we give a few examples of local rings in relation to weak normality and seminormality in mixed characteristic. It is known that two concepts can differ in the equal prime characteristic case, while they coincide in the…
We consider mixed local and nonlocal quasilinear parabolic equations of $p$-Laplace type and discuss several regularity properties of weak solutions for such equations. More precisely, we establish local boundeness of weak subsolutions,…
Let $(X,\omega)$ be a compact Hermitian manifold and let $\{\beta\}\in H^{1,1}(X,\mathbb R)$ be a real $(1,1)$-class with a smooth representative $\beta$, such that $\int_X\beta^n>0$. Assume that there is a bounded $\beta$-plurisubharmonic…
The weak mixing angle is a probe of the vector-axial coupling structure of electroweak interactions. It has been measured precisely at the $Z$-pole by experiments at the LEP and SLD colliders, but its energy dependence above $M_Z$ remains…
Linear (spectro) polarimetry is usually performed using separate photon flux measurements after spatial or temporal polarization modulation. Such classical polarimeters are limited in sensitivity and accuracy by systematic effects and…
We study the mixing properties of a class of nonuniformly expanding maps when the return time to the basis has a weak moment of order p >1, up to a slowly varying function. From these computations, we deduce an invariance principle in…
We find a combinatorial formula for the Haar functional of the orthogonal and unitary quantum groups. As an application, we consider diagonal coefficients of the fundamental representation, and we investigate their spectral measures.
We continue to study regularity results for weak solutions of the large class of second order degenerate quasilinear equations of the form \begin{eqnarray} \text{div}\big(A(x,u,\nabla u)\big) = B(x,u,\nabla u)\text{ for }x\in\Omega\nonumber…
We show that the Hamiltonian action satisfies the Palais-Smale condition over a "mixed regularity" space of loops in cotangent bundles, namely the space of loops with regularity $H^s$, $s\in (\frac 12, 1)$, in the base and $H^{1-s}$ in the…
Absorption spectra of small molecular aggregates (oligomers) are considered. The dipole-dipole interaction between the monomers leads to shifts of the oligomer spectra with respect to the monomer absorption. The line-shapes of monomer as…
The unitarity of the lepton mixing matrix is a critical assumption underlying the standard neutrino-mixing paradigm. However, many models seeking to explain the as-yet-unknown origin of neutrino masses predict deviations from unitarity in…
A general approach to the measurement of an observable with pre- and post-selection is presented. The limit of weak measurement is studied in detail, and it is shown that the phase of the probe, including a Hamiltonian contribution to it,…
We investigate the asymptotic behavior of solutions to semi-classical Schroedinger equations with nonlinearities of Hartree type. For a weakly nonlinear scaling, we show the validity of an asymptotic superposition principle for slowly…
We show that for any given solenoidal initial data in $L^2$ and any solenoidal external force in $L_{\text{loc}}^q \bigcap L^{3/2}$ with $q>3$, there exist partially regular weak solutions of the Navier-Stokes equations in $\R^4 \times…
Spectral averaging techniques for one-dimensional discrete Schroedinger operators are revisited and extended. In particular, simultaneous averaging over several parameters is discussed. Special focus is put on proving lower bounds on the…
Noncommutative spectral geometry offers a purely geometric explanation for the standard model of strong and electroweak interactions, including a geometric explanation for the origin of the Higgs field. Within this framework, the…
The late stages of large-scale structure evolution are treated semi-analytically within the framework of modified halo model. We suggest simple yet accurate approximation for relating the non-linear amplitude to linear one for spherical…