Non-Hermitian Aubry-André model with power-law hopping

Localization of Interacting Fermions in the Aubry-André Model.

We consider interacting electrons in a one-dimensional lattice with an incommensurate Aubry-André potential in the regime when the single-particle eigenstates are localized. We rigorously establish the persistence of ground state localization in the presence of weak many-body interaction, for almost all the chemical potentials. The proof uses a quantum many-body extension of methods adopted for...

Disorder-driven transition in a chain with power-law hopping

Almost power-Hermitian rings

In this paper we define a new type of rings ”almost powerhermitian rings” (a generalization of almost hermitian rings) and establish several sufficient conditions over a ring R such that, every regular matrix admits a diagonal power-reduction.

Power Law Model Adaptation to Fingering of Non-newtonian Fluids

The growth rate of fingers of a Newtonian fluid can be modeled by a power law dependence on time. In this experiment, we examine whether the model can be adapted to describe a fluid with changing viscosity. We provide two possible interpretations. For PVA and a PVA/glycerol solution, we show that by assuming a constant exponent, the changing behavior of the fluid can be captured by a coefficien...

The Dynamic Power Law Model

I propose a new measure of common, time-varying tail risk for large cross sections of stock returns. Stock return tails are described by a power law in which the power law exponent is allowed to transition smoothly through time as a function of recent data. It is motivated by asset pricing theory and is estimable via quasi-maximum likelihood. Estimates indicate substantial time variation in sto...