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
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2017
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Massey University
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Abstract
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.
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Bosons, Few-body problem, Many-body problem, Quantum theory, Research Subject Categories::NATURAL SCIENCES::Physics