2019/06/30 by Serdar Elhatisari · 5 citations
Chemistry · Physics and Astronomy · #Adiabatic process #Adiabatic quantum computation #Advanced Physical and Chemical Molecular Interactions #Euclidean space #Gaussian #Hamiltonian (control theory) #Nuclear physics research studies #Projection (relational algebra) #Quantum Chromodynamics and Particle Interactions #Subspace topology #Wave function #hep-lat #nucl-th
paper · pdf · doi:10.1140/epja/i2019-12844-9
published in The European Physical Journal A 55(8) (Springer Science+Business Media) · 13 pages, 5 figures, version accepted for publication in EJPA
openalex publication_date 2019/08/01 · arxiv created 2019/08/14 · arxiv updated 2019/09/02 · openalex created_date 2019/09/05 · openalex updated_date 2026/08/05
Euclidean time projection is a powerful tool that uses exponential decay to extract the low-energy information of quantum systems. The adiabatic projection method, which is based on Euclidean time projection, is a procedure for studying scattering and reactions on the lattice. The method constructs the adiabatic Hamiltonian that gives the low-lying energies and wave functions of two-cluster systems. In this paper we seek the answer to the question whether an adiabatic Hamiltonian constructed in a smaller subspace of the two-cluster state space can still provide information on the low-lying spectrum and the corresponding wave functions. We present the results from our investigations on constructing the adiabatic Hamiltonian using Euclidean time projection and extracting details of the low-energy spectrum and wave functions by diagonalizing it. In our analyses we consider systems of fermion-fermion and fermion-dimer interacting via a zero-range attractive potential in one dimension, and fermion-fermion interacting via an attractive Gaussian potential in three dimensions. The results presented here provide a guide for improving the adiabatic projection method and for reducing the computational costs of large-scale calculations of ab initio nuclear scattering and reactions using Monte Carlo methods.