27 research outputs found
How Wigner Functions Transform Under Symplectic Maps
It is shown that, while Wigner and Liouville functions transform in an
identical way under linear symplectic maps, in general they do not transform
identically for nonlinear symplectic maps. Instead there are ``quantum
corrections'' whose hbar tending to zero limit may be very complicated.
Examples of the behavior of Wigner functions in this limit are given in order
to examine to what extent the corresponding Liouville densities are recovered.Comment: 8 pages, 6 figures [RevTeX/epsfig, macro included]. To appear in
Proceedings of the Advanced Beam Dynamics Workshop on Quantum Aspects of Beam
Physics (Monterey, CA 1998
Accurate Transfer Maps for Realistic Beamline Elements: Part I, Straight Elements
The behavior of orbits in charged-particle beam transport systems, including
both linear and circular accelerators as well as final focus sections and
spectrometers, can depend sensitively on nonlinear fringe-field and
high-order-multipole effects in the various beam-line elements. The inclusion
of these effects requires a detailed and realistic model of the interior and
fringe fields, including their high spatial derivatives. A collection of
surface fitting methods has been developed for extracting this information
accurately from 3-dimensional field data on a grid, as provided by various
3-dimensional finite-element field codes. Based on these realistic field
models, Lie or other methods may be used to compute accurate design orbits and
accurate transfer maps about these orbits. Part I of this work presents a
treatment of straight-axis magnetic elements, while Part II will treat bending
dipoles with large sagitta. An exactly-soluble but numerically challenging
model field is used to provide a rigorous collection of performance benchmarks.Comment: Accepted to PRST-AB. Changes: minor figure modifications, reference
added, typos corrected
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ADVANCED METHODS FOR THE COMPUTATION OF PARTICLE BEAM TRANSPORT AND THE COMPUTATION OF ELECTROMAGNETIC FIELDS AND MULTIPARTICLE PHENOMENA
Since 1980, under the grant DEFG02-96ER40949, the Department of Energy has supported the educational and research work of the University of Maryland Dynamical Systems and Accelerator Theory (DSAT) Group. The primary focus of this educational/research group has been on the computation and analysis of charged-particle beam transport using Lie algebraic methods, and on advanced methods for the computation of electromagnetic fields and multiparticle phenomena. This Final Report summarizes the accomplishments of the DSAT Group from its inception in 1980 through its end in 2011
The Moyal-Lie Theory of Phase Space Quantum Mechanics
A Lie algebraic approach to the unitary transformations in Weyl quantization
is discussed. This approach, being formally equivalent to the
-quantization, is an extension of the classical Poisson-Lie formalism
which can be used as an efficient tool in the quantum phase space
transformation theory.Comment: 15 pages, no figures, to appear in J. Phys. A (2001
Quantum logic gates for coupled superconducting phase qubits
Based on a quantum analysis of two capacitively coupled current-biased
Josephson junctions, we propose two fundamental two-qubit quantum logic gates.
Each of these gates, when supplemented by single-qubit operations, is
sufficient for universal quantum computation. Numerical solutions of the
time-dependent Schroedinger equation demonstrate that these operations can be
performed with good fidelity.Comment: 4 pages, 5 figures, revised for publicatio
Multilevel effects in the Rabi oscillations of a Josephson phase qubit
We present Rabi oscillation measurements of a Nb/AlOx/Nb dc superconducting
quantum interference device (SQUID) phase qubit with a 100 um^2 area junction
acquired over a range of microwave drive power and frequency detuning. Given
the slightly anharmonic level structure of the device, several excited states
play an important role in the qubit dynamics, particularly at high power. To
investigate the effects of these levels, multiphoton Rabi oscillations were
monitored by measuring the tunneling escape rate of the device to the voltage
state, which is particularly sensitive to excited state population. We compare
the observed oscillation frequencies with a simplified model constructed from
the full phase qubit Hamiltonian and also compare time-dependent escape rate
measurements with a more complete density-matrix simulation. Good quantitative
agreement is found between the data and simulations, allowing us to identify a
shift in resonance (analogous to the ac Stark effect), a suppression of the
Rabi frequency, and leakage to the higher excited states.Comment: 14 pages, 9 figures; minor corrections, updated reference
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Advanced Computing for 21st Century Accelerator Science and Technology
Dr. Dragt of the University of Maryland is one of the Institutional Principal Investigators for the SciDAC Accelerator Modeling Project Advanced Computing for 21st Century Accelerator Science and Technology whose principal investigators are Dr. Kwok Ko (Stanford Linear Accelerator Center) and Dr. Robert Ryne (Lawrence Berkeley National Laboratory). This report covers the activities of Dr. Dragt while at Berkeley during spring 2002 and at Maryland during fall 2003
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Final Technical Report for the Grant DF-FG02-03ER41236 Partial Support of CPO6, The Sixth International Charged-Particle Optics Conference
The International Conference on Charged Particle Optics, CPO, is held every 4 years, and brings together scientists working in all areas of charged-particle optics including electron microscopy, accelerators, spectrometers, electron and ion sources, and theory. In October 2002 the sixth such conference, CPO6, was held near Washington, DC. This is the report on the Sixth International Charged-Particle Optics Conference. Proceedings of this conference have been published in Nuclear Instruments & Methods in Physics Research, Section A Volume 519, February/March 2004
A Lie connection between Hamiltonian and Lagrangian optics
Introduction In Hamiltonian optics rays are described using the Hamiltonian H # ##n 2 # p 2 # 1#2 (1) The use of a Hamiltonian formulation is advantageous because Hamiltonian flows produce symplectic maps, and there is a well developed calculus, using both characteristic functions and Lie algebraic methods, for handling symplectic maps in an efficient and economical way [1, 2]. However, the use of a Hamiltonian approach has the consequence, perhaps at first surprising, that the map describing simple transit in a uniform medium (free flight in optical parlance, and a drift in accelerator parlance), is nonlinear. Therefore, in a Hamiltonian approach to optics, aberrations (nonlinearities) arise not only from transfer maps associated with lens interfaces, but also from simple transit within and between lenses. This circumstance is perhaps of les