Massey Documents by Type

Permanent URI for this communityhttps://mro.massey.ac.nz/handle/10179/294

Browse

Filters

2017 - 20192

Settings

Subject: search.filters.subject.Many-body problem

Search Results

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Convergence properties of Fock-space based approaches in strongly correlated Fermi gases : a dissertation presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Physics at Massey University, Albany, New Zealand
    (Massey University, 2019) Jeszenszki, Peter
    The main objective of this thesis is the effcient numerical description of strongly correlated quantum gases. Due to the complex many-body structure of the wave function, usually, numerical methods are required for its computation. The exact diagonalization approach is considered, where the energies and the wave functions are obtained by diagonalizing the Hamiltonian in a many-body basis. The dimension of the space increases combinatorially with the number of particles and the number of single-particle basis functions, which limits the characterization of fewbody systems to intermediate interactions. One of the main components of the convergence rate originates from the particle-particle interaction itself. The bare contact interaction introduces a singularity in the wave function at the particleparticle coalescence point. This is responsible for the slow convergence in the nite basis expansion in one dimension and it even causes pathological behavior in higher dimensions. Firstly, the Gaussian interaction potential is examined as an alternative pseudopotential. After the description of the accurate calculation of the s-wave scattering length of this potential, the convergence properties are investigated. As this function is smooth, by construction the wave function is free from any singularity implying an exponentially fast convergence rate. If the resolution of the basis set is not fine enough, the finite-range pseudopotential is indistinguishable from the pathological contact potential. Through the example of few particles in a two-dimensional harmonic trap, we show that in order to reach the necessary resolution, the number of harmonic-oscillator single-particle basis functions must increase quadratically with the inverse characteristic length of the pseudopotential. This scaling property combined with the combinatorial growth of the many-body space makes the physically realistic short-range potentials computationally inaccessible. We have also applied the so-called transcorrelated approach, where the singular part of the wave function is isolated in a Jastrow-type factor. This factor can be transformed into the Hamiltonian reducing the irregularity of the eigenfunction and improving the convergence rate. We will show through the example of the homogeneous gas in one dimension that this transformation efficiently improves the convergence from M⁻¹ to M⁻³, where M is the number of the single-particle plane-wave basis functions.
  • Thumbnail Image
    Item
    Non-equilibrium dynamics from few- to many-body systems : a thesis presented in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics at Massey University, Albany, New Zealand
    (Massey University, 2017) Cosme, Jayson Gutierrez
    We study different nonequilibrium phenomena of isolated quantum systems ranging from few- to many-body interacting bosons. Firstly, we have suggested the dynamics of the center-of-mass motion to sensitively detect unconverged numerical many-body dynamics in potential with separable quantum motion of the center of mass. As an example, we consider the time evolution of attractive bosons in a homogenous background and use it to benchmark a specific numerical method based on variational multimode expansion of the many-body wave function - the Multicon gurational time-dependent Hartree for bosons (MCTDHB). We demonstrate that the simplified convergence criterion based on a threshold value for the least occupied mode function fails to assure qualitatively correct result while our suggested convergence test based on the center-of-mass motion correctly detects the deviation of numerical results from the exact results. Recent technological progress in manipulating low-entropy quantum states has motivated us to study the phenomenon of interaction blockade in bosonic systems. We propose an experimental protocol to observe the expected bosonic enhancement factor in this blockade regime. Specifically, we suggest the use of an asymmetric double-well potential constructed by superposition of multiple optical tweezer laser beams. Numerical simulations using the MCTDHB method predict that the relevant states and the expected enhancement factor can be observed. In the second half of the thesis, we have investigated the onset of quantum thermalization in a two-level generalization of the Bose-Hubbard dimer. To this end, the relaxation dynamics following a quench is studied using two numerical methods: We study different nonequilibrium phenomena of isolated quantum systems ranging from few- to many-body interacting bosons. Firstly, we have suggested the dynamics of the center-of-mass motion to sensitively detect unconverged numerical many-body dynamics in potential with separable quantum motion of the center of mass. As an example, we consider the time evolution of attractive bosons in a homogenous background and use it to benchmark a specific numerical method based on variational multimode expansion of the many-body wave function - the Multicon gurational time-dependent Hartree for bosons (MCTDHB). We demonstrate that the simplified convergence criterion based on a threshold value for the least occupied mode function fails to assure qualitatively correct result while our suggested convergence test based on the center-of-mass motion correctly detects the deviation of numerical results from the exact results. Recent technological progress in manipulating low-entropy quantum states has motivated us to study the phenomenon of interaction blockade in bosonic systems. We propose an experimental protocol to observe the expected bosonic enhancement factor in this blockade regime. Specifically, we suggest the use of an asymmetric double-well potential constructed by superposition of multiple optical tweezer laser beams. Numerical simulations using the MCTDHB method predict that the relevant states and the expected enhancement factor can be observed. In the second half of the thesis, we have investigated the onset of quantum thermalization in a two-level generalization of the Bose-Hubbard dimer. To this end, the relaxation dynamics following a quench is studied using two numerical methods: (1) full quantum dynamics and (2) semiclassical phase-space method. We rely on arguments based on the eigenstate thermalization hypothesis (ETH), quantum chaos as seen from the distribution of level spacings, and the concept of chaotic eigenstates in demonstrating equilibration dynamics of local observables in the system after an integrability-breaking quench. The same issue on quantum thermalization can be viewed from a different perspective using semiclassical phase-space methods. In particular, we employ the truncated Wigner approximation (TWA) to simulate the quantum dynamics. In this case, we show that the marginal distributions of the individual trajectories which sample the initial Wigner distribution are in good agreement with the corresponding microcanonical distribution.