Related papers: Quasicrystal Scattering and the Riemann Zeta Funct…
The meromorphic function $W(s)$ introduced in the Riemann-Zeta function $\zeta(s) = W(s) \zeta(1-s)$ maps the line of $s = 1/2 + it$ onto the unit circle in $W$-space. $|W(s)| = 0$ gives the trivial zeroes of the Riemann-Zeta function…
Interactions between elementary excitations in quasi-one dimensional antiferromagnets are of experimental relevance and their quantitative theoretical treatment has been a theoretical challenge for many years. Using matrix product states,…
Superscaling in electron scattering from nuclei is re-examined paying special attention to the definition of the averaged single-nucleon responses. The validity of the extrapolation of nucleon responses in the Fermi gas has been examined,…
We consider a dimer formed by two particles with an attractive contact interaction in one dimension, colliding with a hard wall. We compute the scattering phase shifts and the reflection coefficients for various collision energies and…
We investigate the extent to which the nuclear transverse response to electron scattering in the quasielastic region, evaluated in the random-phase approximation can be described by ring approximation calculations. Different effective…
As for the Fourier transforms of positive and integrable functions supported in the unit interval, we make a list of improvements for P\'olya's results on the distribution of their positive zeros and give new sufficient conditions under…
The cuprate high-temperature superconductors are known to host a wide array of effects due to interactions and disorder. In this work, we look at some of the consequences of these effects which can be visualized by scanning tunneling…
Topological superconductors, such as noncentrosymmetric superconductors with strong spin-orbit coupling, exhibit protected zero-energy surface states, which possess an intricate helical spin structure. We show that this nontrival spin…
A model for nonequilibrium dynamical mean-field theory is constructed for the infinite dimensional Hubbard lattice. We impose nonequilibrium by expressing the physical orbital as a superposition of a left-($L$) moving and right-($R$) moving…
The Riemann zeta function at integer arguments can be written as an infinite sum of certain hypergeometric functions and more generally the same can be done with polylogarithms, for which several zeta functions are a special case. An…
In this paper, we prove the existence of the scattering operator for the fractional magnetic Schrodinger operators. For this, we construct the fractional distorted Fourier transforms with magnetic potentials. Applying the properties of the…
We describe a way to obtain a two-dimensional quasiperiodic tiling with eight-fold symmetry using cold atoms. A series of such optical tilings, related by scale transformations, is obtained for a series of specific values of the chemical…
We extend beyond the Euler scales the hydrodynamic theory for quantum and classical integrable models developed in recent years, accounting for diffusive dynamics and local entropy production. We review how the diffusive scale can be…
A real potential Hamiltonian has real energy bound states below the scattering threshold and complex energy resonances above it. Scattering states are not square integrable, being instead delta function normalized. This lack of square…
We introduce a new method to detect the zeros of the Riemann zeta function which is sensitive to the vertical distribution of the zeros. This allows us to prove there are few `half-isolated' zeros. By combining this with classical methods,…
These notes describe a new method to investigate the spectral properties if quantum scattering Hamiltonians, developed in collaboration with J. Sj\"ostrand and M.Zworski. This method consists in constructing a family of "quantized transfer…
We propose a means to realize two-dimensional quasiperiodic structures by trapping atoms in an optical potential. The structures have eight-fold symmetry and are closely related to the well-known quasiperiodic octagonal (Ammann-Beenker)…
It is known that the limiting gap distribution of the directions to visible points in planar quasicrystals of cut-and-project type exists as a continuous function $F(s)$. In this article we study the asymptotic behaviour of said limiting…
We study an integrable vertex model with a periodic boundary condition associated with U_q(A_n^{(1)}) at the crystallizing point q=0. It is an (n+1)-state cellular automaton describing the factorized scattering of solitons. The dynamics…
Model sets play a fundamental role in structure analysis of quasicrystals. The diffraction diagram of a quasicrystal admits as symmetry group a finite group G, and there is a G-cluster C (union of orbits of G) such that the quasicrystal can…