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16
Singular solutions for geodesic flows of Vlasov moments
, 2006
"... For Henry McKean, on the occasion of his 75th birthday The Vlasov equation for the collisionless evolution of the singleparticle probability distribution function (PDF) is a wellknown example of coadjoint motion. Remarkably, the property of coadjoint motion survives the process of taking moments. ..."
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For Henry McKean, on the occasion of his 75th birthday The Vlasov equation for the collisionless evolution of the singleparticle probability distribution function (PDF) is a wellknown example of coadjoint motion. Remarkably, the property of coadjoint motion survives the process of taking moments. That is, the evolution of the moments of the Vlasov PDF is also coadjoint motion. We find that geodesic coadjoint motion of the Vlasov moments with respect to powers of the singleparticle momentum admits singular (weak) solutions concentrated on embedded subspaces of physical space. The motion and interactions of these embedded subspaces are governed by canonical Hamiltonian equations for their geodesic evolution. Contents 1
Thermal and quantum fluctuations in chains of ultracold
, 903
"... polar molecules ..."
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of Vlasov moments
"... For Henry McKean, on the occasion of his 75th birthday ABSTRACT. The Vlasov equation for the collisionless evolution of the singleparticle probability distribution function (PDF) is a wellknown example of coadjoint motion. Remarkably, the property of coadjoint motion survives the process of taking ..."
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For Henry McKean, on the occasion of his 75th birthday ABSTRACT. The Vlasov equation for the collisionless evolution of the singleparticle probability distribution function (PDF) is a wellknown example of coadjoint motion. Remarkably, the property of coadjoint motion survives the process of taking moments. That is, the evolution of the moments of the Vlasov PDF is also a form of coadjoint motion. We find that geodesic coadjoint motion of the Vlasov moments with respect to powers of the singleparticle momentum admits singular (weak) solutions concentrated on embedded subspaces of physical space. The motion and interactions of these embedded subspaces are governed by canonical Hamiltonian equations for their geodesic evolution. 1.
c ○ Rinton Press HIGHFIDELITY QUANTUM CONTROL USING ION CRYSTALS IN A PENNING TRAP
, 2009
"... We provide an introduction to the use of ion crystals in a Penning trap [1, 2, 3, 4] for experiments in quantum information. Macroscopic Penning traps allow for the containment of a few to a few million atomic ions whose internal states may be used in quantum information experiments. Ions are laser ..."
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We provide an introduction to the use of ion crystals in a Penning trap [1, 2, 3, 4] for experiments in quantum information. Macroscopic Penning traps allow for the containment of a few to a few million atomic ions whose internal states may be used in quantum information experiments. Ions are laser Doppler cooled [1], and the mutual Coulomb repulsion of the ions leads to the formation of crystalline arrays [5, 6, 7, 8]. The structure and dimensionality of the resulting ion crystals may be tuned using a combination of control laser beams and external potentials [9, 10]. We discuss the use of twodimensional 9Be + ion crystals for experimental tests of quantum control techniques. Our primary qubit is the 124 GHz groundstate electron spin flip transition, which we drive using microwaves [11, 12]. An ion crystal represents a spatial ensemble of qubits, but the effects of inhomogeneities across a typical crystal are small, and as such we treat the ensemble as a single effective spin. We are able to initialize the qubits in a simple state and perform a projective measurement [1] on the system. We demonstrate full control of the qubit Bloch vector, performing arbitrary highfidelity rotations (τπ ∼200 µs). Randomized Benchmarking [13] demonstrates an error per gate (a Paulirandomized π/2 and π pulse pair) of 8±1×10−4. Ramsey interferometry and spinlocking [14] measurements are used to elucidate the limits of qubit coherence in the system, yielding a typical freeinduction decay coherence time of T2 ∼2 ms, and a limiting T1ρ ∼688 ms. These experimental specifications make ion crystals in a Penning trap ideal candidates for novel experiments in quantum control. As such, we briefly describe recent efforts aimed at studying the errorsuppressing capabilities of dynamical
TOWARD OPTIMAL BEAM BRIGHTNESS FROM HIGH VOLTAGE DC PHOTOELECTRON SOURCES
, 2015
"... High voltage DC photoelectron guns generating beams of 100s of kV are the sources of choice for a wide array of linear accelerators. The beam’s brightness is the principal figure of merit for DC gundriven, GeVscale synchrotron light sources and meterscale ultrafast electron diffraction beamlines ..."
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High voltage DC photoelectron guns generating beams of 100s of kV are the sources of choice for a wide array of linear accelerators. The beam’s brightness is the principal figure of merit for DC gundriven, GeVscale synchrotron light sources and meterscale ultrafast electron diffraction beamlines alike. Irrespective of the machine size, the beam brightness is limited by the parameters of the source: the extraction field and voltage, the drive laser 3D pulse shape, and the intrinsic momentum spread of the electrons leaving the photoemitting material. This thesis describes a new experimental DC gun and beamline constructed at Cornell which has demonstrated the state of the art in each of these parameters. Concepts to allow next generation photoguns to simultaneously achieve higher photocathode fields and total voltages are discussed. To conclude the thesis, a calculation of the fundamental limit on photoemitted beam brightness is given, which arises in cold, dense beams for which strong individual electron interactions result in beam heating. Biographical Sketch
Geometric dynamics of Vlasov kinetic theory
, 804
"... April 2008“La nature est un temple où de vivants pilliers Laissent parfois sortir de confuses paroles; L’homme y passe à travers des forêts de symboles Qui l’observent avec des regards familiers.” (C. Baudelaire, Correspondences, Les fleurs du mal) The Vlasov equation of kinetic theory is introduced ..."
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April 2008“La nature est un temple où de vivants pilliers Laissent parfois sortir de confuses paroles; L’homme y passe à travers des forêts de symboles Qui l’observent avec des regards familiers.” (C. Baudelaire, Correspondences, Les fleurs du mal) The Vlasov equation of kinetic theory is introduced and the Hamiltonian structure of its moments is presented. Then we focus on the geodesic evolution of the Vlasov moments. As a first step, these moment equations generalize the CamassaHolm equation to its multicomponent version. Subsequently, adding electrostatic forces to the geodesic moment equations relates them to the Benney equations and to the equations for beam dynamics in particle accelerators. Next, we develop a kinetic theory for self assembly in nanoparticles. Darcy’s law is introduced as a general principle for aggregation dynamics in friction dominated systems (at different scales). Then, a kinetic equation is introduced for the dissipative motion of isotropic
Ultracold Neutral Plasmas
, 2006
"... Ultracold neutral plasmas, formed by photoionizing lasercooled atoms near the ionization threshold, have electron temperatures in the 11000 kelvin range and ion temperatures from tens of millikelvin to a few kelvin. They represent a new frontier in the study of neutral plasmas, which traditionally ..."
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Ultracold neutral plasmas, formed by photoionizing lasercooled atoms near the ionization threshold, have electron temperatures in the 11000 kelvin range and ion temperatures from tens of millikelvin to a few kelvin. They represent a new frontier in the study of neutral plasmas, which traditionally deals with much hotter systems, but they also blur the boundaries of plasma, atomic, condensed matter, and low temperature physics. Modelling these plasmas challenges computational techniques and theories of nonequilibrium systems, so the field has attracted great interest from the theoretical and computational physics communities. By varying laser intensities and wavelengths it is possible to accurately set the initial plasma density and energy, and chargedparticledetection and optical diagnostics allow precise measurements for comparison with theoretical predictions. Recent experiments using optical probes demonstrated that ions in the plasma equilibrate in a strongly coupled fluid phase. Strongly coupled plasmas, in which the electrical interaction energy between charged particles exceeds the average kinetic
Complex nonequilibrium dynamics in plasmas
, 903
"... In this contribution we will discuss two new forms of strongly coupled plasmas which have become possible to create and observe in the laboratory only recently. They exhibit a wealth of intriguing complex behavior which can be studied, in many cases for the first time, experimentally. Plasmas, gases ..."
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In this contribution we will discuss two new forms of strongly coupled plasmas which have become possible to create and observe in the laboratory only recently. They exhibit a wealth of intriguing complex behavior which can be studied, in many cases for the first time, experimentally. Plasmas, gases of charged particles, are universal in the sense that certain
London SW7 2AZ, UK,
, 2006
"... For Henry McKean, on the occasion of his 75th birthday The Vlasov equation for the collisionless evolution of the singleparticle probability distribution function (PDF) is a wellknown example of coadjoint motion. Remarkably, the property of coadjoint motion survives the process of taking moments. ..."
Abstract
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For Henry McKean, on the occasion of his 75th birthday The Vlasov equation for the collisionless evolution of the singleparticle probability distribution function (PDF) is a wellknown example of coadjoint motion. Remarkably, the property of coadjoint motion survives the process of taking moments. That is, the evolution of the moments of the Vlasov PDF is also coadjoint motion. We find that geodesic coadjoint motion of the Vlasov moments with respect to powers of the singleparticle momentum admits singular (weak) solutions concentrated on embedded subspaces of physical space. The motion and interactions of these embedded subspaces are governed by canonical Hamiltonian equations for their geodesic evolution. Contents 1