65 research outputs found
Complex spectral analysis and test function spaces
We consider complex eigenstates of unstable Hamiltonian and its physically
meaningful regions. Starting from a simple model of a discrete state
interacting with a continuum via a general potential, we show that its
Lippmann-Schwinger solution set can be decomposed into a free-field set, a set
containing lower half plane pole of Green's function and a set containing upper
half pole of Green's function. From here distinctive complex eigenstates
corresponding to each pole are constructed. We note that on the real line
square integrable functions can be decomposed into Hardy class above and below
functions which behave well in their respective complex half planes. Test
function restriction formulas which remove unphysical growth are given. As a
specific example we consider Friedrichs model which solutions and complex
eigenstates are known, and compare numerically calculated total time evolution
with test function restricted complex eigenstates for various cases. The
results shows that test function restricted complex eigenstates capture the
essence of decay phenomena quite well.Comment: 32 page
A game-theoretic analysis of Inter-Korean transboundary rivers
Thesis(Master) --KDI School:Master of Public Management,2018.The purpose of this research is to establish a management strategy for the reasonable and equitable utilization of the inter-Korean transboundary rivers through the case of the Imnam Dam on the Bukhan River and the Hwanggang Dam on the Imjin River. As a methodology, game theoretic approach was deployed to explore a solution to the problems of the transboundary rivers between North Korea and South Korea. The existing studies dealing with the inter-Korean negotiations on the transboundary rivers have focused primarily on establishing counter-strategies under non-cooperative circumstances. However, in this research, the possibility of collaboration between the two Koreas was set up by analyzing the scenarios as cooperative games that link rewards. Besides, a methodology is presented that can quantify and evaluate the conditions of cooperation and reward for the best benefits of the two Koreas. The most favorable way for the two Koreas to enjoy the best benefits is that North Korea allocates river flow to South Korea and South Korea actively invests in joint development projects as a reward for it, such as the modernization of North Korea''s deteriorating hydroelectric power facilities, etc.I. Introduction
II. Literature Review
III. Research Method
IV. Analysis and Findings
VI. ConclusionmasterpublishedSungyun, KIM
Stable finite element methods for the Stokes problem
The mixed finite element scheme of the Stokes problem with
pressure stabilization is analyzed for the cross-grid Pk−Pk−1elements, k≥1, using discontinuous pressures. The Pk+−Pk−1 elements are also analyzed. We prove the stability of the scheme using the
macroelement technique. The order of convergence follows from the standard
theory of mixed methods. The macroelement technique can also be applicable
to the stability analysis for some higher order methods using continuous
pressures such as Taylor-Hood methods, cross-grid methods, or iso-grid
methods
Complex collective states in a one-dimensional two-atom system
We consider a pair of identical two-level atoms interacting with a scalar
field in one dimension, separated by a distance . We restrict our
attention to states where one atom is excited and the other is in the ground
state, in symmetric or anti-symmetric combinations. We obtain exact collective
decaying states, belonging to a complex spectral representation of the
Hamiltonian. The imaginary parts of the eigenvalues give the decay rates, and
the real parts give the average energy of the collective states. In one
dimension there is strong interference between the fields emitted by the atoms,
leading to long-range cooperative effects. The decay rates and the energy
oscillate with the distance . Depending on , the decay rates
will either decrease, vanish or increase as compared with the one-atom decay
rate. We have sub- and super-radiance at periodic intervals. Our model may be
used to study two-cavity electron wave-guides. The vanishing of the collective
decay rates then suggests the possibility of obtaining stable configurations,
where an electron is trapped inside the two cavities.Comment: 14 pages, 14 figures, submitted to Phys. Rev.
Decay modes of two repulsively interacting bosons
We study the decay of two repulsively interacting bosons tunneling through a
delta potential barrier by direct numerical solution of the time-dependent
Schr\"odinger equation. The solutions are analyzed according to the regions of
particle presence: both particles inside the trap (in-in), one particle in and
one particle out (in-out), and both particles outside (out-out). It is shown
that the in-in probability is dominated by exponential decay, and its decay
rate is predicted very well from outgoing boundary conditions.
Up to a certain range of interaction strength the decay of in-out probability
is dominated by the single particle decay mode.
The decay mechanisms are adequately described by simple models.Comment: 18 pages, 13 figure
surface reconstruction and electronic structure of BaSnO film
We studied surface and electronic structures of barium stannate (BaSnO)
thin-film by low energy electron diffraction (LEED), and angle-resolved
photoemission spectroscopy (ARPES) techniques.
BaSnO/BaLaSnO/SrTiO (10 nm/100 nm/0.5 mm) samples
were grown using pulsed-laser deposition (PLD) method and were \emph{ex-situ}
transferred from PLD chamber to ultra-high vacuum (UHV) chambers for annealing,
LEED and ARPES studies. UHV annealing starting from 300C up to
550C, followed by LEED and ARPES measurements show 11
surfaces with non-dispersive energy-momentum bands. The 11 surface
reconstructs into a one at the annealing
temperature of 700C where the ARPES data shows clear dispersive bands
with valence band maximum located around 3.3 eV below Fermi level. While the
surface reconstruction is stable under
further UHV annealing, it is reversed to 11 surface by annealing the
sample in 400 mTorr oxygen at 600C. Another UHV annealing at
600C followed by LEED and ARPES measurements, suggests that LEED
surface reconstruction and ARPES
dispersive bands are reproduced. Our results provide a better picture of
electronic structure of BaSnO surface and are suggestive of role of oxygen
vacancies in the reversible surface
reconstruction.Comment: 7 pages, 4 figures, Journa
Computability of entropy and information in classical Hamiltonian systems
We consider the computability of entropy and information in classical
Hamiltonian systems. We define the information part and total information
capacity part of entropy in classical Hamiltonian systems using relative
information under a computable discrete partition.
Using a recursively enumerable nonrecursive set it is shown that even though
the initial probability distribution, entropy, Hamiltonian and its partial
derivatives are computable under a computable partition, the time evolution of
its information capacity under the original partition can grow faster than any
recursive function. This implies that even though the probability measure and
information are conserved in classical Hamiltonian time evolution we might not
actually compute the information with respect to the original computable
partition
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