2014/09/14 by Serdar Elhatisari, Elhatisari, Serdar
Physics and Astronomy · #Atomic Physics (physics.atom-ph) #Atomic and Subatomic Physics Research #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #Nuclear Theory (nucl-th) #Quantum Chromodynamics and Particle Interactions #Quantum Gases (cond-mat.quant-gas) #cond-mat.quant-gas #hep-lat #nucl-th #physics.atom-ph
paper · pdf · doi:10.48550/arxiv.1409.4048
Ph.D. thesis, 201 pages, 19 figures, 17 tables
arxiv created 2014/09/14 · openalex publication_date 2014/09/14 · arxiv updated 2014/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the first part of the thesis we consider the constraints of causality and unitarity for particles interacting via strictly finite-range interactions. We generalize Wigner's causality bound to the case of non-vanishing partial-wave mixing. Specifically we analyze the system of the low-energy interactions between protons and neutrons. We also analyze low-energy scattering for systems with arbitrary short-range interactions plus an attractive 1/rα tail for α≥2. In particular, we focus on the case of α=6 and we derive the constraints of causality and unitarity also for these systems and find that the van der Waals length scale dominates over parameters characterizing the short-distance physics of the interaction. This separation of scales suggests a separate universality class for physics characterizing interactions with an attractive 1/r6 tail. We argue that a similar universality class exists for any attractive potential 1/rα for α≥2. In the second part of the thesis we present lattice Monte Carlo calculations of fermion-dimer scattering in the limit of zero-range interactions using the adiabatic projection method. The adiabatic projection method uses a set of initial cluster states and Euclidean time projection to give a systematically improvable description of the low-lying scattering cluster states in a finite volume. We use Lüscher's finite-volume relations to determine the s-wave, p-wave, and d-wave phase shifts. For comparison, we also compute exact lattice results using Lanczos iteration and continuum results using the Skorniakov-Ter-Martirosian equation. For our Monte Carlo calculations we use a new lattice algorithm called impurity lattice Monte Carlo. This algorithm can be viewed as a hybrid technique which incorporates elements of both worldline and auxiliary-field Monte Carlo simulations.