Yang-Mills Theory on a Cylinder Coupled to Point Particles

We study a model of quantum Yang-Mills theory with a finite number of gauge invariant degrees of freedom. The gauge field has only a finite number of degrees of freedom since we assume that space-time is a two dimensional cylinder. We couple the gauge field to matter, modeled by either one or two nonrelativistic point particles. These problems can be solved {\it without any gauge fixing}, by generalizing the canonical quantization methods of Ref.\[rajeev] to the case including matter. For this, we make use of the geometry of the space of connections, which has the structure of a Principal Fiber Bundle with an infinite dimensional fiber. We are able to reduce both problems to finite dimensional, exactly solvable, quantum mechanics problems. In the case of one particle, we find that the ground state energy will diverge in the limit of infinite radius of space, consistent with confinement. In the case of two particles, this does not happen if they can form a color singlet bound state (`meson').Comment: 37 pages, UR-1327 ER-40685-77

An extended model of the quantum free-electron laser

Previous models of the quantum regime of operation of the Free Electron Laser (QFEL) have performed an averaging and the application of periodic boundary conditions to the coupled Maxwell - Schrodinger equations over short, resonant wavelength intervals of the interaction. Here, an extended, one-dimensional model of the QFEL interaction is presented in the absence of any such averaging or application of periodic boundary conditions, the absence of the latter allowing electron diffusion processes to be modeled throughout the pulse. The model is used to investigate how both the steady-state (CW) and pulsed regimes of QFEL operation are affected. In the steady-state regime it is found that the electrons are confined to evolve as a 2-level system, similar to the previous QFEL models. In the pulsed regime Coherent Spontaneous Emission (CSE) due to the shape of the electron pulse current distribution is shown to be present in the QFEL regime for the first time. However, unlike the classical case, CSE in the QFEL is damped by the effects of quantum diffusion of the electron wavefunction. Electron recoil from the QFEL interaction can also cause a diffusive drift between the recoiled and non-recoiled parts of the electron pulse wavefunction, effectively removing the recoiled part from the primary electron-radiation interaction.Comment: Submitted to Optics Expres

An evaluation of the implementation of Georgia's Pre-k program: Report of the findings from the Georgia Early Childhood Study (2002-03)

After ten years, Georgia continues to lead the nation in providing full day, publicly subsidized Pre-K to four-year-olds whose parents choose to enroll them. In this report, we assess the extent to which differences in the way Pre-K is implemented affect children's development. Do teachers with higher levels of education have more positive impacts on children's development? Do teaching styles make a difference in terms of children's outcomes by the end of kindergarten? Do children taught using certain curricula fare better than those taught using others? Answers to questions such as these can assist Pre-K administrators in refining Georgia's program and inform those in other states who are developing or expanding their prekindergarten programs

Engineering entanglement for metrology with rotating matter waves

Entangled states of rotating, trapped ultracold bosons form a very promising scenario for quantum metrology. In order to employ such states for metrology, it is vital to understand their detailed form and the enhanced accuracy with which they could measure phase, in this case generated through rotation. In this work, we study the rotation of ultracold bosons in an asymmetric trapping potential beyond the lowest Landau level (LLL) approximation. We demonstrate that while the LLL can identify reasonably the critical frequency for a quantum phase transition and entangled state generation, it is vital to go beyond the LLL to identify the details of the state and quantify the quantum Fisher information (which bounds the accuracy of the phase measurement). We thus identify a new parameter regime for useful entangled state generation, amenable to experimental investigation

Invariant quantum discord in qubit-qutrit systems under local dephasing

We investigate the dynamics of quantum discord and entanglement for a class of mixed qubit-qutrit states assuming that only the qutrit is under the action of a dephasing channel. We demonstrate that even though the entanglement in the qubit-qutrit state disappears in a finite time interval, partial coherence left in the system enables quantum discord to remain invariant throughout the whole time evolution

High-resolution imaging of ultracold fermions in microscopically tailored optical potentials

We report on the local probing and preparation of an ultracold Fermi gas on the length scale of one micrometer, i.e. of the order of the Fermi wavelength. The essential tool of our experimental setup is a pair of identical, high-resolution microscope objectives. One of the microscope objectives allows local imaging of the trapped Fermi gas of 6Li atoms with a maximum resolution of 660 nm, while the other enables the generation of arbitrary optical dipole potentials on the same length scale. Employing a 2D acousto-optical deflector, we demonstrate the formation of several trapping geometries including a tightly focussed single optical dipole trap, a 4x4-site two-dimensional optical lattice and a 8-site ring lattice configuration. Furthermore, we show the ability to load and detect a small number of atoms in these trapping potentials. A site separation of down to one micrometer in combination with the low mass of 6Li results in tunneling rates which are sufficiently large for the implementation of Hubbard-models with the designed geometries.Comment: 15 pages, 6 figure

Multiparticle Schrodinger operators with point interactions in the plane

We study a system of N bosons in the plane interacting with delta function potentials. After a coupling constant renormalization we show that the Hamiltonian defines a self-adjoint operator and obtain a lower bound for the energy. The same results hold if one includes a regular inter-particle potential.Comment: 17 pages, Late

Discovery of Griffiths phase in itinerant magnetic semiconductor Fe_{1-x}Co_xS_2

Critical points that can be suppressed to zero temperature are interesting because quantum fluctuations have been shown to dramatically alter electron gas properties. Here, the metal formed by Co doping the paramagnetic insulator FeS$_2$, Fe$_{1-x}$Co$_x$S$_2$, is demonstrated to order ferromagnetically at $x>x_c=0.01\pm0.005$ where we observe unusual transport, magnetic, and thermodynamic properties. We show that this magnetic semiconductor undergoes a percolative magnetic transition with distinct similarities to the Griffiths phase, including singular behavior at $x_c$ and zero temperature.Comment: 10 pages, 4 figure

Dynamic organization of DNA replication in mammalian cell nuclei: spatially and temporally defined replication of chromosome-specific alpha-satellite DNA sequences

Five distinct patterns of DNA replication have been identified during S-phase in asynchronous and synchronous cultures of mammalian cells by conventional fluorescence microscopy, confocal laser scanning microscopy, and immunoelectron microscopy. During early S-phase, replicating DNA (as identified by 5-bromodeoxyuridine incorporation) appears to be distributed at sites throughout the nucleoplasm, excluding the nucleolus. In CHO cells, this pattern of replication peaks at 30 min into S-phase and is consistent with the localization of euchromatin. As S-phase continues, replication of euchromatin decreases and the peripheral regions of heterochromatin begin to replicate. This pattern of replication peaks at 2 h into S-phase. At 5 h, perinucleolar chromatin as well as peripheral areas of heterochromatin peak in replication. 7 h into S-phase interconnecting patches of electron-dense chromatin replicate. At the end of S-phase (9 h), replication occurs at a few large regions of electron-dense chromatin. Similar or identical patterns have been identified in a variety of mammalian cell types. The replication of specific chromosomal regions within the context of the BrdU-labeling patterns has been examined on an hourly basis in synchronized HeLa cells. Double labeling of DNA replication sites and chromosome-specific alpha-satellite DNA sequences indicates that the alpha-satellite DNA replicates during mid S-phase (characterized by the third pattern of replication) in a variety of human cell types. Our data demonstrates that specific DNA sequences replicate at spatially and temporally defined points during the cell cycle and supports a spatially dynamic model of DNA replication