The one-dimensional Bose-Hubbard Model with nearest-neighbor interaction

We study the one-dimensional Bose-Hubbard model using the Density-Matrix Renormalization Group (DMRG).For the cases of on-site interactions and additional nearest-neighbor interactions the phase boundaries of the Mott-insulators and charge density wave phases are determined. We find a direct phase transition between the charge density wave phase and the superfluid phase, and no supersolid or normal phases. In the presence of nearest-neighbor interaction the charge density wave phase is completely surrounded by a region in which the effective interactions in the superfluid phase are repulsive. It is known from Luttinger liquid theory that a single impurity causes the system to be insulating if the effective interactions are repulsive, and that an even bigger region of the superfluid phase is driven into a Bose-glass phase by any finite quenched disorder. We determine the boundaries of both regions in the phase diagram. The ac-conductivity in the superfluid phase in the attractive and the repulsive region is calculated, and a big superfluid stiffness is found in the attractive as well as the repulsive region.Comment: 19 pages, 30 figure

Bose-Einstein condensate collapse: a comparison between theory and experiment

We solve the Gross-Pitaevskii equation numerically for the collapse induced by a switch from positive to negative scattering lengths. We compare our results with experiments performed at JILA with Bose-Einstein condensates of Rb-85, in which the scattering length was controlled using a Feshbach resonance. Building on previous theoretical work we identify quantitative differences between the predictions of mean-field theory and the results of the experiments. Besides the previously reported difference between the predicted and observed critical atom number for collapse, we also find that the predicted collapse times systematically exceed those observed experimentally. Quantum field effects, such as fragmentation, that might account for these discrepancies are discussed.Comment: 4 pages, 2 figure

Quantum saturation and condensation of excitons in Cu2_2O: a theoretical study

Recent experiments on high density excitons in Cu$_2$O provide evidence for degenerate quantum statistics and Bose-Einstein condensation of this nearly ideal gas. We model the time dependence of this bosonic system including exciton decay mechanisms, energy exchange with phonons, and interconversion between ortho (triplet-state) and para (singlet-state) excitons, using parameters for the excitonic decay, the coupling to acoustic and low-lying optical phonons, Auger recombination, and ortho-para interconversion derived from experiment. The single adjustable parameter in our model is the optical-phonon cooling rate for Auger and laser-produced hot excitons. We show that the orthoexcitons move along the phase boundary without crossing it (i.e., exhibit a ``quantum saturation''), as a consequence of the balance of entropy changes due to cooling of excitons by phonons and heating by the non-radiative Auger two-exciton recombination process. The Auger annihilation rate for para-para collisions is much smaller than that for ortho-para and ortho-ortho collisions, explaining why, under the given experimental conditions, the paraexcitons condense while the orthoexcitons fail to do so.Comment: Revised to improve clarity and physical content 18 pages, revtex, figures available from G. Kavoulakis, Physics Department, University of Illinois, Urban

Quantum Vacuum Experiments Using High Intensity Lasers

The quantum vacuum constitutes a fascinating medium of study, in particular since near-future laser facilities will be able to probe the nonlinear nature of this vacuum. There has been a large number of proposed tests of the low-energy, high intensity regime of quantum electrodynamics (QED) where the nonlinear aspects of the electromagnetic vacuum comes into play, and we will here give a short description of some of these. Such studies can shed light, not only on the validity of QED, but also on certain aspects of nonperturbative effects, and thus also give insights for quantum field theories in general.Comment: 9 pages, 8 figur

A Phenomenological Analysis of Gluon Mass Effects in Inclusive Radiative Decays of the J/ψ\rm{J/\psi} and $\Upsilon

The shapes of the inclusive photon spectra in the processes \Jp \to \gamma X and \Up \to \gamma X have been analysed using all available experimental data. Relativistic, higher order QCD and gluon mass corrections were taken into account in the fitted functions. Only on including the gluon mass corrections, were consistent and acceptable fits obtained. Values of $0.721^{+0.016}_{-0.068}$ GeV and $1.18^{+0.09}_{-0.29}$ GeV were found for the effective gluon masses (corresponding to Born level diagrams) for the \Jp and \Up respectively. The width ratios \Gamma(V \to {\rm hadrons})/\Gamma(V \to \gamma+ {\rm hadrons}) V=\Jp, \Up were used to determine $\alpha_s(1.5 {\rm GeV})$ and $\alpha_s(4.9 {\rm GeV})$. Values consistent with the current world average $\alpha_s$ were obtained only when gluon mass correction factors, calculated using the fitted values of the effective gluon mass, were applied. A gluon mass $\simeq 1$ GeV, as suggested with these results, is consistent with previous analytical theoretical calculations and independent phenomenological estimates, as well as with a recent, more accurate, lattice calculation of the gluon propagator in the infra-red region.Comment: 50 pages, 11 figures, 15 table

Level Set Method for the Evolution of Defect and Brane Networks

A theory for studying the dynamic scaling properties of branes and relativistic topological defect networks is presented. The theory, based on a relativistic version of the level set method, well-known in other contexts, possesses self-similar ``scaling'' solutions, for which one can calculate many quantities of interest. Here, the length and area densities of cosmic strings and domain walls are calculated in Minkowski space, and radiation, matter, and curvature-dominated FRW cosmologies with 2 and 3 space dimensions. The scaling exponents agree the naive ones based on dimensional analysis, except for cosmic strings in 3-dimensional Minkowski space, which are predicted to have a logarithmic correction to the naive scaling form. The scaling amplitudes of the length and area densities are a factor of approximately 2 lower than results from numerical simulations of classical field theories. An expression for the length density of strings in the condensed matter literature is corrected.Comment: 46pp LaTeX, revtex4(preprint), 1 eps figure, revised for publication. Note title chang

Best practice in active surveillance for men with prostate cancer: a Prostate Cancer UK consensus statement

Objectives To develop a consensus statement on current best practice of active surveillance (AS) in the UK, informed by patients and clinical experts. Subjects and Methods A consensus statement was drafted on the basis of three sources of data: systematic literature search of national and international guidelines; data arising from a Freedom of Information Act request to UK urology departments regarding their current practice of AS; and survey and interview responses from men with localized prostate cancer regarding their experiences and views of AS. The Prostate Cancer UK Expert Reference Group (ERG) on AS was then convened to discuss and refine the statement. Results Guidelines and protocols for AS varied significantly in terms of risk stratification, criteria for offering AS, and protocols for AS between and within countries. Patients and healthcare professionals identified clinical, emotional and process needs for AS to be effective. Men with prostate cancer wanted more information and psychological support at the time of discussing AS with the treating team and in the first 2 years of AS, and a named healthcare professional to discuss any questions

Observation of inverse Compton emission from a long γ-ray burst.

Long-duration γ-ray bursts (GRBs) originate from ultra-relativistic jets launched from the collapsing cores of dying massive stars. They are characterized by an initial phase of bright and highly variable radiation in the kiloelectronvolt-to-megaelectronvolt band, which is probably produced within the jet and lasts from milliseconds to minutes, known as the prompt emission1,2. Subsequently, the interaction of the jet with the surrounding medium generates shock waves that are responsible for the afterglow emission, which lasts from days to months and occurs over a broad energy range from the radio to the gigaelectronvolt bands1-6. The afterglow emission is generally well explained as synchrotron radiation emitted by electrons accelerated by the external shock7-9. Recently, intense long-lasting emission between 0.2 and 1 teraelectronvolts was observed from GRB 190114C10,11. Here we report multi-frequency observations of GRB 190114C, and study the evolution in time of the GRB emission across 17 orders of magnitude in energy, from 5 × 10-6 to 1012 electronvolts. We find that the broadband spectral energy distribution is double-peaked, with the teraelectronvolt emission constituting a distinct spectral component with power comparable to the synchrotron component. This component is associated with the afterglow and is satisfactorily explained by inverse Compton up-scattering of synchrotron photons by high-energy electrons. We find that the conditions required to account for the observed teraelectronvolt component are typical for GRBs, supporting the possibility that inverse Compton emission is commonly produced in GRBs