Cosine and Sine Operators Related with Orthogonal Polynomial Sets on the Intervall [-1,1]

The quantization of phase is still an open problem. In the approach of Susskind and Glogower so called cosine and sine operators play a fundamental role. Their eigenstates in the Fock representation are related with the Chebyshev polynomials of the second kind. Here we introduce more general cosine and sine operators whose eigenfunctions in the Fock basis are related in a similar way with arbitrary orthogonal polynomial sets on the intervall [-1,1]. To each polynomial set defined in terms of a weight function there corresponds a pair of cosine and sine operators. Depending on the symmetry of the weight function we distinguish generalized or extended operators. Their eigenstates are used to define cosine and sine representations and probability distributions. We consider also the inverse arccosine and arcsine operators and use their eigenstates to define cosine-phase and sine-phase distributions, respectively. Specific, numerical and graphical results are given for the classical orthogonal polynomials and for particular Fock and coherent states.Comment: 1 tex-file (24 pages), 11 figure

Examining electron-boson coupling using time-resolved spectroscopy

Nonequilibrium pump-probe time domain spectroscopies can become an important tool to disentangle degrees of freedom whose coupling leads to broad structures in the frequency domain. Here, using the time-resolved solution of a model photoexcited electron-phonon system we show that the relaxational dynamics are directly governed by the equilibrium self-energy so that the phonon frequency sets a window for "slow" versus "fast" recovery. The overall temporal structure of this relaxation spectroscopy allows for a reliable and quantitative extraction of the electron-phonon coupling strength without requiring an effective temperature model or making strong assumptions about the underlying bare electronic band dispersion.Comment: 23 pages, 4 figures + Supplementary Material and movies, to appear in PR

Quantenmechanische Phasenoperatoren im Zusammenhang mit orthogonalen Polynomsystemen

Der Ansatz von Susskind und Glogower für das quantenmechanische Phasenproblem definiert hermitesche Operatoren, die als Kosinus- und Sinusoperatoren interpretierbar sind. Deren Eigenzustände in der Fock-Darstellung sind die Chebyshev- Polynome zweiter Art. Auf dieser Grundlage werden allgemeinere Kosinus- und Sinusoperatoren eingeführt, deren Eigenzustände in der Fock-Darstellung mit beliebigen Polynomen gebildet sind, die im Intervall [−1,+1] bezüglich einer Gewichtsfunktion ein Orthogonalsystem bilden. Jedem Satz Polynome ist ein Paar Kosinus- und Sinusoperatoren zugeordnet. Je nachdem ob die Gewichtsfunktionen symmetrisch oder unsymmetrisch sind, wird zwischen verallgemeinerten und erweiterten Kosinus- und Sinusoperatoren unterschieden. Es werden auch korrespondierende Arcuskosinus- und Arcussinusoperatoren vom verallgemeinerten und erweiterten Type eingeführt. Die Eigenzustände der trigonometrischen und inversen trigonometrischen Operatoren werden untersucht und dazu verwendet, um Darstellungen beliebiger Quantenzustände sowie entsprechende Wahrscheinlichkeitsverteilungen zu definieren. Für die klassischen orthogonalen Polynome werden Beispiele explizit angegeben. Weiterhin werden Exponentialoperatoren als Verallgemeinerung der exponentiellen Phasenoperatoren von Susskind und Glogower eingeführt, die mit den verallgemeinerten bzw. erweiterten Kosinus- und Sinusoperatoren in Beziehung stehen. Die Eigenzustände der als Absteigeoperatoren wirkenden Exponentialoperatoren sind innerhalb des Einheitskreises definiert und bilden, sofern sie die Darstellung des Einheitsoperators ermoglichen, verallgemeinerte kohärente Zustände. In diesem Fall konnen damit zweidimensionale Wahrscheinlichkeitsverteilungen innerhalb des Einheitskreises und daraus resultierende Phasenverteilungen definiert werden. Im Fall der klassischen orthogonalen Polynome haben die Eigenzustände der verallgemeinerten und erweiterten Exponentialoperatoren als Normierungsfunktionen die hypergeometrischen 2 F 1 - bzw. 4 F 3 -Funktionen. Die Darstellung des Einheitsoperators erfordert eine spezielle Grenzbetrachtung. Schließlich werden die Eigenzustände der Exponentialoperatoren, die mit den klassischen orthogonalen Polynomen im Zusammenhang stehen, erweitert, indem verallgemeinerte hypergeometrische Zustände eingeführt werden, deren Normierungsfunktionen die verallgemeinerten hypergeometrischen Funktionen p F q sind. In Abhängigkeit vom Konvergenzradius der verallgemeinerten hypergeometrischen Funktionen wird zwischen verallgemeinerten hypergeometrischen Zuständen in der gesamten Ebene, innerhalb des Einheitskreises und auf dem Einheitskreis unterschieden. Diejenigen verallgemeinerten hypergeometrischen Zustände, die die Darstellung des Einheitsoperators ermoglichen, werden als kohärente verallgemeinerte hypergeometrische Zustände definiert. Diese konnen als Basis zur Darstellung beliebiger Zustände im Bargmann- bzw. Hardy-Raum verwendet werden und definieren verallgemeinerte hypergeometrische Husimi-Verteilungen und daraus resultierende Phasenverteilungen.The approach of Susskind and Glogower to the quantum phase problem defines Hermitian operators, which may be interpreted as cosine and sine operators. Their eigenstates in the Fock representation are the Chebyshev polynomials of the second kind. On the basis of this approach more general cosine and sine operators are introduced, whose eigenstates in the Fock representation are given by arbitrary orthogonal polynomial sets on the interval [−1,+1] with respect to a weight function. To every polynomial set there corresponds a pair of cosine and sine operators. Depending on the symmetry of the weight function one distinguishes between generalized and extended cosine and sine operators. Corresponding arccosine and arcsine operators of the generalized and extended type are introduced. The eigenstates of the trigonometric and inverse trigonometric operators are studied and used to define corresponding representations of an arbitrary quantum state as well as corresponding probability distributions. Explicit examples are given for the classical orthogonal polynomials. Further, exponential operators generalizing the Susskind-Glogower exponential phase operators are introduced in terms of the cosine and sine operators. The eigenstates of the lowering exponential operators are defined on the unit disk and yield generalized coherent states if they admit a resolution of unity. In this case they can be used to define two-dimensional probability distributions (Q-functions) on the unit disk and corresponding phase distributions as marginal distributions. In the case of the classical orthogonal polynomials the eigenstates of the generalized (extended) operators are normalized to the hypergeometric functions 2 F 1 ( 4 F 3 ); the resolution of unity needs a special treatment as a limiting case. Finally, extending the class of states encounted above, generalized hypergeometric states normalized to the generalized hypergeometric functions p F q are introduced. Depending on the radius of convergence of p F q , one distinguishes between generalized hypergeometric states on the (whole) plane, on the unit disk and on the unit circle. The states yielding a resolution of unity define the generalized hypergeometric coherent states. They can be used to define representations of an arbitrary state in the appropriate Bargmann and Hardy spaces, respectively, as well as corresponding generalized hypergeometric Husimi distributions and (marginal) phase distributions

The Next Generation Photoinjector

This dissertation will elucidate the design, construction, theory, and operation of the Next Generation Photoinjector (NGP). This photoinjector is comprised of the BNL/SLAC/UCLA 1.6 cell symmetrized S-band photocathode radio frequency (rf) electron gun and a single emittance-compensation solenoidal magnet. This photoinjector is a prototype for the Linear Coherent Light Source X-ray Free Electron Laser operating in the 1.5 {angstrom} range. Simulations indicate that this photoinjector is capable of producing a 1nC electron bunch with transverse normalized emittance less than 1 {pi} mm mrad were the cathode is illuminated with a 10 psec longitudinal flat top pulse. Using a Gaussian longitudinal laser profile with a full width half maximum (FWHM) of 10 psec, simulation indicates that the NGP is capable of producing a normalized rms emittance of 2.50 {pi} mm mrad at 1 nC. Using the removable cathode plate we have studied the quantum efficiency (QE) of both copper and magnesium photo-cathodes. The Cu QE was found to be 4.5 x 10{sup -5} with a 25% variation in the QE across the emitting surface of the cathode, while supporting a field gradient of 125 MV/m. At low charge, the transverse normalized rms emittance, {epsilon}{sub n,rms}, produced by the NGP is {epsilon}{sub n,rms} = 1.2 {pi} mm mrad for Q{sub T} = 0.3 nC. The 95% electron beam bunch length was measured to 10.9 psec. The emittance due to the finite magnetic field at the cathode has been studied. The scaling of this magnetic emittance term as a function of cathode magnetic field was found to be 0.01 {pi} mm mrad per Gauss. The 1.6 cell rf gun has been designed to reduce the dipole field asymmetry of the longitudinal accelerating field. Low level rf measurements show that this has in fact been accomplished, with an order of magnitude decrease in the dipole field. High power beam studies also show that the dipole field has been decreased. An upper limit of the intrinsic non-reducible thermal emittance of a photocathode under high field gradient was found to be {epsilon}{sub n,rms} = 0.8 {pi} mm mrad. Agreement is found between the theoretical calculation of the thermal emittance, {epsilon}{sub 0} = 0.62 {pi} mm mrad, and the experimental results, after taking into account all of the emittance contribution terms. The 1 nC emittance was found to be {epsilon}{sub n,rms} = 4.75 {pi} mm mrad with a 95% electron beam bunch length of 14.7 psec. Systematic bunch length measurements showed electron beam bunch lengthening due the electron beam charge. They will show that the discrepancy between measurement and simulation is due to three effects. The major effect is due to the variation of the QE in the photo-emitting area of the Cu cathode. Also, space charge emittance blowup in the transport line will be shown to be a significant effect because the electron beam is still in the space charge dominated regime. The last effect, which has been observed experimentally, is the electron bunch lengthening as a function of total electron bunch charge

Spontaneous in vitro transformation of adult neural precursors into stem-like cancer cells

Recent studies have found that cellular self-renewal capacity in brain cancer is heterogeneous, with only stem-like cells having this property. A link between adult stem cells and cancer stem cells remains, however, to be shown. Here, we describe the emergence of cancer stem-like cells from in vitro cultured brain stem cells. Adult rat subventricular zone (SVZ) stem cells transformed into tumorigenic cell lines after expansion in vitro. These cell lines maintained characteristic features of stem-like cells expressing Nestin, Musashi-1 and CD133, but continued to proliferate upon differentiation induction. Karyotyping detected multiple acquired chromosomal aberrations, and syngeneic transplantation into the brain of adult rats resulted in malignant tumor formation. Tumors revealed streak necrosis and displayed a neural as well as an undifferentiated phenotype. Deficient downregulation of platelet-derived growth factor (PDGF) receptor alpha was identified as candidate mechanism for tumor cell proliferation, and its knockdown by siRNA resulted in a reduction of cell growth. Our data point to adult brain precursor cells to be transformed in malignancies. Furthermore, in vitro expansion of adult neural stem cells, which will be mandatory for therapeutic strategies in neurological disorders, also harbors the risk for amplifying precursor cells with acquired genetic abnormalities and induction of malignant tumors after transplantation