15,075 research outputs found
A beginner's introduction to Fukaya categories
The goal of these notes is to give a short introduction to Fukaya categories
and some of their applications. The first half of the text is devoted to a
brief review of Lagrangian Floer (co)homology and product structures. Then we
introduce the Fukaya category (informally and without a lot of the necessary
technical detail), and briefly discuss algebraic concepts such as exact
triangles and generators. Finally, we mention wrapped Fukaya categories and
outline a few applications to symplectic topology, mirror symmetry and
low-dimensional topology. This text is based on a series of lectures given at a
Summer School on Contact and Symplectic Topology at Universit\'e de Nantes in
June 2011.Comment: 42 pages, 13 figure
Quantum coherent transport in a three-arm beam splitter and a Braess paradox
The Braess paradox encountered in classical networks is a counterintuitive
phenomenon when the flow in a road network can be impeded by adding a new road
or, more generally, the overall net performance can degrade after addition of
an extra available choice. In this work, we discuss the possibility of a
similar effect in a phase-coherent quantum transport and demonstrate it by
example of a simple Y-shaped metallic fork. To reveal the Braess-like partial
suppression of the charge flow in such device, it is proposed to transfer two
outgoing arms into a superconducting state. We show that the differential
conductance-vs-voltage spectrum of the hybrid fork structure varies
considerably when the extra link between the two superconducting leads is added
and it can serve as an indicator of quantum correlations which manifest
themselves in the quantum Braess paradox.Comment: 9 pages, 3 figures, the author version presented at the Quantum 2017
Workshop (Torino, Italy, 7-13 May 2017) and submitted to the International
Journal of Quantum Information; v2: reference 9 added and the introduction
extende
THz-range free-electron laser ESR spectroscopy: techniques and applications in high magnetic fields
The successful use of picosecond-pulse free-electron-laser (FEL) radiation
for the continuous-wave THz-range electron spin resonance (ESR) spectroscopy
has been demonstrated. The combination of two linac-based FELs (covering the
wavelength range of 4 - 250 m) with pulsed magnetic fields up to 70 T
allows for multi-frequency ESR spectroscopy in a frequency range of 1.2 - 75
THz with a spectral resolution better than 1%. The performance of the
spectrometer is illustrated with ESR spectra obtained in the
2,2-diphenyl-1-picrylhydrazyl (DPPH) and the low-dimensional organic material
(CHN)CuCl.Comment: 9 pages, 9 figures. Rev. Sci. Instrum., accepte
Transverse-Longitudinal Coupling by Space Charge in Cyclotrons
A method is presented that enables to compute the parameters of matched beams
with space charge in cyclotrons with emphasis on the effect of the
transverse-longitudinal coupling. Equations describing the
transverse-longitudinal coupling and corresponding tune-shifts in first order
are derived for the model of an azimuthally symmetric cyclotron. The
eigenellipsoid of the beam is calculated and the transfer matrix is transformed
into block-diagonal form. The influence of the slope of the phase curve on the
transverse-longitudinal coupling is accounted for. The results are generalized
and numerical procedures for the case of an AVF cyclotron are presented. The
algorithm is applied to the PSI Injector II and Ring cyclotron and the results
are compared to TRANSPORT.Comment: 8 pages, 2 figure
Symplectic cohomology and q-intersection numbers
Given a symplectic cohomology class of degree 1, we define the notion of an
equivariant Lagrangian submanifold. The Floer cohomology of equivariant
Lagrangian submanifolds has a natural endomorphism, which induces a grading by
generalized eigenspaces. Taking Euler characteristics with respect to the
induced grading yields a deformation of the intersection number. Dehn twists
act naturally on equivariant Lagrangians. Cotangent bundles and Lefschetz
fibrations give fully computable examples. A key step in computations is to
impose the "dilation" condition stipulating that the BV operator applied to the
symplectic cohomology class gives the identity. Equivariant Lagrangians mirror
equivariant objects of the derived category of coherent sheaves.Comment: 32 pages, 9 figures, expanded introduction, added details of example
7.5, added discussion of sign
Beam Dynamics in High Intensity Cyclotrons Including Neighboring Bunch Effects: Model, Implementation and Application
Space charge effects, being one of the most significant collective effects,
play an important role in high intensity cyclotrons. However, for cyclotrons
with small turn separation, other existing effects are of equal importance.
Interactions of radially neighboring bunches are also present, but their
combined effects has not yet been investigated in any great detail. In this
paper, a new particle in cell based self-consistent numerical simulation model
is presented for the first time. The model covers neighboring bunch effects and
is implemented in the three-dimensional object-oriented parallel code
OPAL-cycl, a flavor of the OPAL framework. We discuss this model together with
its implementation and validation. Simulation results are presented from the
PSI 590 MeV Ring Cyclotron in the context of the ongoing high intensity upgrade
program, which aims to provide a beam power of 1.8 MW (CW) at the target
destination
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