63 research outputs found
Level statistics and eigenfunctions of pseudointegrable systems: dependence on energy and genus number
We study the level statistics (second half moment and rigidity
) and the eigenfunctions of pseudointegrable systems with rough
boundaries of different genus numbers . We find that the levels form energy
intervals with a characteristic behavior of the level statistics and the
eigenfunctions in each interval. At low enough energies, the boundary roughness
is not resolved and accordingly, the eigenfunctions are quite regular functions
and the level statistics shows Poisson-like behavior. At higher energies, the
level statistics of most systems moves from Poisson-like towards Wigner-like
behavior with increasing . Investigating the wavefunctions, we find many
chaotic functions that can be described as a random superposition of regular
wavefunctions. The amplitude distribution of these chaotic functions
was found to be Gaussian with the typical value of the localization volume
. For systems with periodic boundaries we find
several additional energy regimes, where is relatively close to the
Poisson-limit. In these regimes, the eigenfunctions are either regular or
localized functions, where is close to the distribution of a sine or
cosine function in the first case and strongly peaked in the second case. Also
an interesting intermediate case between chaotic and localized eigenfunctions
appears
Renormalization of Hamiltonian Field Theory; a non-perturbative and non-unitarity approach
Renormalization of Hamiltonian field theory is usually a rather painful
algebraic or numerical exercise. By combining a method based on the coupled
cluster method, analysed in detail by Suzuki and Okamoto, with a Wilsonian
approach to renormalization, we show that a powerful and elegant method exist
to solve such problems. The method is in principle non-perturbative, and is not
necessarily unitary.Comment: 16 pages, version shortened and improved, references added. To appear
in JHE
From Gapped Excitons to Gapless Triplons in One Dimension
Often, exotic phases appear in the phase diagrams between conventional
phases. Their elementary excitations are of particular interest. Here, we
consider the example of the ionic Hubbard model in one dimension. This model is
a band insulator (BI) for weak interaction and a Mott insulator (MI) for strong
interaction. Inbetween, a spontaneously dimerized insulator (SDI) occurs which
is governed by energetically low-lying charge and spin degrees of freedom.
Applying a systematically controlled version of the continuous unitary
transformations (CUTs) we are able to determine the dispersions of the
elementary charge and spin excitations and of their most relevant bound states
on equal footing. The key idea is to start from an externally dimerized system
using the relative weak interdimer coupling as small expansion parameter which
finally is set to unity to recover the original model.Comment: 18 pages, 10 figure
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Demonstration of efficient full aperture Type I/Type II third harmonic conversion on Nova
Type I/Type II third harmonic conversion has been implemented at the 74 cm aperture of the Nova laser system. We discuss the performance capabilities and alignment issues of this scheme for Nova relative to conventional Type II/Type II conversion. 3 refs., 2 figs
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