Correlations and dynamics in many-body non-Hermitian systems

Abstract

Ovaj rad istražuje međuigru temeljnih aspekata nehermitske kvantne mehanike i međudjelovanja čestica primjenom Bose-Hubbard modela s asimetričnim amplitudama preskoka i odbojnim interakcijama. U prvom dijelu analiziramo sustav s malim brojem bozona te pomoću računa smetnje i numeričkih metoda istražujemo razlike u odnosu na hermitski i jednočestični nehermitski slučaj. U nastavku proučavamo suprafluid-Mott izolator fazni prijelaz te ispitujemo kako nehermitska priroda sustava utječe na kritičnu vrijednost interakcije potrebnu za taj prijelaz.This thesis investigates the interplay between fundamental aspects of non-Hermitian quantum mechanics and particle interactions through the Bose-Hubbard model with asymmetric hopping and repulsive interaction. In the first part, we analyze a system with a small number of bosons and use perturbation theory and numerical methods to explore the differences compared to the Hermitian and single-particle non-Hermitian case. In the second part, we study the superfluid–Mott insulator phase transition and examine how system's non-Hermicity affects the critical value of interaction required for the transition to happen