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Single-Shot Visualization Of Evolving Laser- Or Beam-Driven Plasma Wakefield Accelerators
We introduce Frequency-Domain Tomography (FDT) for visualizing sub-ps evolution of light-speed refractive index structures in a single shot. As a prototype demonstration, we produce single-shot tomographic movies of self-focusing, filamenting laser pulses propagating in a transparent Kerr medium. We then discuss how to adapt FDT to visualize evolving laser-or beam-driven plasma wakefields of current interest to the advanced accelerator community. For short (L similar to 1 cm), dense (n(e) similar to 10(19) cm(-3)) plasmas, the key challenge is broadening probe bandwidth sufficiently to resolve plasma-wavelength-size structures. For long (L similar to 10 to 100 cm), tenuous (n(e) similar to 10(17) cm(-3)) plasmas, probe diffraction from the evolving wake becomes the key challenge. We propose and analyze solutions to these challenges.Physic
Quantum Thetas on Noncommutative T^4 from Embeddings into Lattice
In this paper we investigate the theta vector and quantum theta function over
noncommutative T^4 from the embedding of R x Z^2. Manin has constructed the
quantum theta functions from the lattice embedding into vector space (x finite
group). We extend Manin's construction of the quantum theta function to the
embedding of vector space x lattice case. We find that the holomorphic theta
vector exists only over the vector space part of the embedding, and over the
lattice part we can only impose the condition for Schwartz function. The
quantum theta function built on this partial theta vector satisfies the
requirement of the quantum theta function. However, two subsequent quantum
translations from the embedding into the lattice part are non-additive,
contrary to the additivity of those from the vector space part.Comment: 20 pages, LaTeX, version to appear in J. Phys.
Density of states of a graphene in the presence of strong point defects
The density of states near zero energy in a graphene due to strong point
defects with random positions are computed. Instead of focusing on density of
states directly, we analyze eigenfunctions of inverse T-matrix in the unitary
limit. Based on numerical simulations, we find that the squared magnitudes of
eigenfunctions for the inverse T-matrix show random-walk behavior on defect
positions. As a result, squared magnitudes of eigenfunctions have equal {\it a
priori} probabilities, which further implies that the density of states is
characterized by the well-known Thomas-Porter type distribution. The numerical
findings of Thomas-Porter type distribution is further derived in the
saddle-point limit of the corresponding replica field theory of inverse
T-matrix. Furthermore, the influences of the Thomas-Porter distribution on
magnetic and transport properties of a graphene, due to its divergence near
zero energy, are also examined.Comment: 6 figure
The magnetic dipole transitions in the binding system
The magnetic dipole transitions between the vector mesons and their
relevant pseudoscalar mesons (, , , ,
and etc, the binding states of system) of
the family are interesting. To see the `hyperfine' splitting due to
spin-spin interaction is an important topic for understanding the spin-spin
interaction and the spectrum of the the binding system. The
knowledge about the magnetic dipole transitions is also very useful for
identifying the vector boson mesons experimentally, whose masses are
just slightly above the masses of their relevant pseudoscalar mesons
accordingly. Considering the possibility to observe the vector mesons via the
transitions at factory and the potentially usages of the theoretical
estimate on the transitions, we fucus our efforts on calculating the magnetic
dipole transitions, i.e. precisely to calculate the rates for the transitions
such as decays and , and particularly
work in the Behte-Salpeter framework. In the estimate, as a typical example, we
carefully investigate the dependance of the rate
on the mass difference as well.Comment: 10 pages, 2 figures, 1 tabl
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