On a q-analog of the Wallach-Okounkov formula

We obtain a $q$-analog of the well known Wallach-Okounkov result on a joint spectrum of invariant differential operators with polynomial coefficients on a prehomogeneous vector space of complex $n \times n$-matrices. We are motivated by applications to the problems of harmonic analysis in the quantum matrix ball: our main theorem can be used while proving the Plancherel formula (to be published). This paper is dedicated to our friend and colleague Dmitry Shklyarov who celebrates his 30-th birthday on April 8, 2006.Comment: 10 pages, corrected minor misprint

On gauge-invariant Green function in 2+1 dimensional QED

Both the gauge-invariant fermion Green function and gauge-dependent conventional Green function in $2+1$ dimensional QED are studied in the large $N$ limit. In temporal gauge, the infra-red divergence of gauge-dependent Green function is found to be regulariable, the anomalous dimension is found to be $\eta= \frac{64}{3 \pi^{2} N}$. This anomalous dimension was argued to be the same as that of gauge-invariant Green function. However, in Coulomb gauge, the infra-red divergence of the gauge-dependent Green function is found to be un-regulariable, anomalous dimension is even not defined, but the infra-red divergence is shown to be cancelled in any gauge-invariant physical quantities. The gauge-invariant Green function is also studied directly in Lorentz covariant gauge and the anomalous dimension is found to be the same as that calculated in temporal gauge.Comment: 8 pages, 6 figures, to appear in Phys. Rev.

Topological Quantum Phase Transition in Synthetic Non-Abelian Gauge Potential

The method of synthetic gauge potentials opens up a new avenue for our understanding and discovering novel quantum states of matter. We investigate the topological quantum phase transition of Fermi gases trapped in a honeycomb lattice in the presence of a synthetic non- Abelian gauge potential. We develop a systematic fermionic effective field theory to describe a topological quantum phase transition tuned by the non-Abelian gauge potential and ex- plore its various important experimental consequences. Numerical calculations on lattice scales are performed to compare with the results achieved by the fermionic effective field theory. Several possible experimental detection methods of topological quantum phase tran- sition are proposed. In contrast to condensed matter experiments where only gauge invariant quantities can be measured, both gauge invariant and non-gauge invariant quantities can be measured by experimentally generating various non-Abelian gauges corresponding to the same set of Wilson loops

Ultrasensitive detections in atomic and molecular physics: demonstration in molecular overtone spectroscopy

We consider several highly sensitive techniques commonly used in detection of atomic and molecular absorptions. Their basic operating principles and corresponding performances are summarized and compared. We then present our latest results on the ultrasensitive detection of molecular overtone transitions to illustrate the principle and application of the cavity-enhanced frequency-modulation (FM) spectroscopy. An external cavity is used to enhance the molecular response to the light field, and an FM technique is applied for shot-noise-limited signal recovery. A perfect match between the FM sideband frequency and the cavity free spectral range makes the detection process insensitive to the laser-frequency noise relative to the cavity, and, at the same time, overcomes the cavity bandwidth limit. Working with a 1.064-µm Nd:YAG laser, we obtained sub-Doppler overtone resonances of C2HD, C2H2, and CO2 molecules. A detection sensitivity of 5 x 10^-13 of integrated absorption (1 x 10^-14/cm) over 1-s averaging time has been achieved

Discriminative Cooperative Networks for Detecting Phase Transitions

The classification of states of matter and their corresponding phase transitions is a special kind of machine-learning task, where physical data allow for the analysis of new algorithms, which have not been considered in the general computer-science setting so far. Here we introduce an unsupervised machine-learning scheme for detecting phase transitions with a pair of discriminative cooperative networks (DCN). In this scheme, a guesser network and a learner network cooperate to detect phase transitions from fully unlabeled data. The new scheme is efficient enough for dealing with phase diagrams in two-dimensional parameter spaces, where we can utilize an active contour model -- the snake -- from computer vision to host the two networks. The snake, with a DCN "brain", moves and learns actively in the parameter space, and locates phase boundaries automatically

Medium effects in the production and decay of vector mesons in pion-nucleus reactions

The $\omega$-, $\rho$- and $\phi$-resonance production and their dileptonic decay in $\pi^- A$ reactions at 1.1 - 1.7 GeV/c are calculated within the intranuclear cascade (INC) approach. The invariant mass distribution of the dilepton pair for each resonance can be decomposed in two components which correspond to their decay 'inside' the target nucleus and in the vacuum, respectively. The first components are strongly distorted by the nuclear medium due to resonance-nucleon scattering and a possible mass shift at finite baryon density. These medium modifications are compared to background sources in the dilepton spectrum from $\pi N$ bremsstrahlung as well as the Dalitz decays of $\omega$ and $\eta$ mesons produced in the reaction. Detailed predictions for $\pi^- Pb$ reactions at 1.3 and 1.7 GeV/c are made within several momentum bins for the lepton pair.Comment: 29 pages, LaTeX, including 12 postscript figures, UGI-97-07, Nucl. Phys. A., in pres

The influences of the galactic cosmic ray on the atmospheric ozone

The relationship between the yearly variations of cosmic ray intensity and ozone in the atmosphere, and the ozone disturbance initiated by the Forbush decrease of 1965-1976 is analyzed. The data on cosmic ray intensity were selected from the records of the super neutron monitor at Deep River station and the ionization chamber at Beijing station. Ozone data were taken from Resolute (Canada), Bismark (N. Dakota, USA), Kagoshima (Japan), and Kodaikanal (India). The statistical results show that ozone is prominently modulated and disturbed by the 11 year variation and the Forbush decrease in the galactic cosmic ray