We compute the Hochschild homology of the crossed product $\Bbb C[S_n]\ltimes A^{\otimes n}$ in terms of the Hochschild homology of the associative algebra $A$ (over $\Bbb C$). It allows us to compute the Hochschild (co)homology of $\Bbb C[W]\ltimes A^{\otimes n}$ where $A$ is the $q$-Weyl algebra or any its degeneration and $W$ is the Weyl group of type $A_{n-1}$ or $B_n$. For a deformation quantization $A_+$ of an affine symplectic variety $X$ we show that the Hochschild homology of $S^n A$, $A=A_+[\hbar^{-1}]$ is additively isomorphic to the Chen-Ruan orbifold cohomology of $S^nX$ with coefficients in $\Bbb C((\hbar))$. We prove that for $X$ satisfying $H^1(X,\Bbb C)=0$ (or $A\in VB(d)$) the deformation of $S^nX$ ($\Bbb C[S_n]\ltimes A^{\otimes n}$) which does not come from deformations of $X$ ($A$) exists if and only if $\dim X=2$ ($d=2$). In particular if $A$ is $q$-Weyl algebra (its trigonometric or rational degeneration) then the corresponding nontrivial deformations yield the double affine Hecke algebras of type $A_{n-1}$ (its trigonometric or rational versions) introduced by Cherednik.

Pavel Etingof Alexei Oblomkov

This paper generalizes D. Burago and S. Ivanov's work on filling volume minimality and boundary rigidity of almost real hyperbolic metrics. We show that regions with metrics close to a negatively curved symmetric metric are strict minimal fillings and hence boundary rigid. This includes perturbations of complex, quaternionic and Cayley hyperbolic metrics.

Yuping Ruan

Let X be a compact connected Riemann surface of genus at least two. Let r be a prime number and \xi a holomorphic line bundle on it such that r is not a divisor of degree(\xi). Let {\mathcal M}_\xi(r) denote the moduli space of stable vector bundles over X of rank r and determinant \xi. By \Gamma we will denote the group of line bundles L over X such that $L^{\otimes r}$ is trivial. This group \Gamma acts on {\mathcal M}_\xi(r). We compute the Chen-Ruan cohomology of the corresponding orbifold.

Indranil Biswas Mainak Poddar

A low-background neutron detector array was developed to measure the cross section of the $^{13}$C($\alpha$,n)$^{16}$O reaction, which is the neutron source for the $s$-process in AGB stars, in the Gamow window ($E_{c.m.}$ = 190 $\pm$ 40 keV) at the China Jinping Underground Laboratory (CJPL). The detector array consists of 24 $^{3}$He proportional counters embedded in a polyethylene cube. Due to the deep underground location and a borated polyethylene shield around the detector array, a low background of 4.5(2)/hour was achieved. The $^{51}$V(p, n)$^{51}$Cr reaction was used to determine the neutron detection efficiency of the array for neutrons with energy $E_n$ $<$ 1 MeV. Geant4 simulations, which were shown to well reproduce experimental results, were used to extrapolate the detection efficiency to higher energies for neutrons emitted in the $^{13}$C($\alpha$,n) $^{16}$O reaction. The theoretical angular distributions of the $^{13}$C($\alpha$,n)$^{16}$O reaction were shown to be important in estimating the uncertainties of the detection efficiency.

Y. T. Li W. P. Lin B. Gao H. Chen H. Huang Y. Huang T. Y. Jiao K. A. Li X. D. Tang X. Y. Wang X. Fang H. X. Huang J. Ren L. H. Ru X. C. Ruan N. T. Zhang Z. C. Zhang

For the Laplacian $\Delta$ defined on a p.c.f. self-similar fractal, we give an explicit formula for the resolvent kernel of the Laplacian with Dirichlet boundary conditions, and also with Neumann boundary conditions. That is, we construct a symmetric function $G^{(\lambda)}$ which solves $(\lambda \mathbb{I} - \Delta)^{-1} f(x) = \int G^{(\lambda)}(x,y) f(y) d\mu(y)$. The method is similar to Kigami's construction of the Green kernel in \cite[\S3.5]{Kig01} and is expressed as a sum of scaled and "translated" copies of a certain function $\psi^{(\lambda)}$ which may be considered as a fundamental solution of the resolvent equation. Examples of the explicit resolvent kernel formula are given for the unit interval, standard Sierpinski gasket, and the level-3 Sierpinski gasket $SG_3$.

Marius Ionescu Erin P. J. Pearse Luke G. Rogers Huo-Jun Ruan Robert S. Strichartz

Dimensional effects in particle-in-cell (PIC) simulation of target normal sheath acceleration (TNSA) of protons are considered. As the spatial divergence of the laser-accelerated hot sheath electrons and the resulting space-charge electric field on the target backside depend on the spatial dimension, the maximum energy of the accelerated protons obtained from three-dimensional (3D) simulations is usually much less that from two-dimensional (2D) simulations. By closely examining the TNSA of protons in 2D and 3D PIC simulations, we deduce an empirical ratio between the maximum proton energies obtained from the 2D and 3D simulations. This ratio may be useful for estimating the maximum proton energy in realistic (3D) TNSA from the results of the corresponding 2D simulation. It is also shown that the scaling law also applies to TNSA from structured targets.

K. D. Xiao C. T. Zhou K. Jiang Y. C. Yang R. Li H. Zhang B. Qiao T. W. Huang J. M. Cao T. X. Cai M. Y. Yu S. C. Ruan X. T. He

The adiabatic evolution is the dynamics of an instantaneous eigenstate of a slowly varing Hamiltonian. Recently, an interesting phenomenon shows up that white noises can enhance and even induce adiabaticity, which is in contrast to previous perception that environmental noises always modify and even ruin a designed adiabatic passage. We experimentally realized a noise-induced adiabaticity in a nuclear magnetic resonance system. Adiabatic Hadamard gate and entangled state are demonstrated. The effect of noise on adiabaticity is experimentally exhibited and compared with the noise-free process. We utilized a noise-injected method, which can be applied to other quantum systems.

B X Wang T Xin X Y Kong Sh J Wei D Ruan G L Long

Production of the huge longitudinal magnetic fields by using an ultraintense laser pulse irradiating a solenoid target is considered. Through three-dimensional particle-in-cell simulations, it is shown that the longitudinal magnetic field up to ten kilotesla can be observed in the ultraintense laser-solenoid target interactions. The finding is associated with both fast and return electron currents in the solenoid target. The huge longitudinal magnetic field is of interest for a number of important applications, which include controlling the divergence of laser-driven energetic particles for medical treatment, fast-ignition in inertial fusion, etc., as an example, the well focused and confined directional electron beams are realized by using the solenoid target.

K. D. Xiao C. T. Zhou H. Zhang T. W. Huang R. Li B. Qiao J. M. Cao T. X. Cai S. C. Ruan X. T. He

For a finite group G acting on a smooth projective variety X, we construct two new G-equivariant rings: first the stringy K-theory of X, and second the stringy cohomology of X. For a smooth Deligne-Mumford stack Y we also construct a new ring called the full orbifold K-theory of Y. For a global quotient Y=[X/G], the ring of G-invariants of the stringy K-theory of X is a subalgebra of the full orbifold K-theory of the the stack Y and is linearly isomorphic to the ``orbifold K-theory'' of Adem-Ruan (and hence Atiyah-Segal), but carries a different, ``quantum,'' product, which respects the natural group grading. We prove there is a ring isomorphism, the stringy Chern character, from stringy K-theory to stringy cohomology, and a ring homomorphism from full orbifold K-theory to Chen-Ruan orbifold cohomology. These Chern characters satisfy Grothendieck-Riemann-Roch for etale maps. We prove that stringy cohomology is isomorphic to Fantechi and Goettsche's construction. Since our constructions do not use complex curves, stable maps, admissible covers, or moduli spaces, our results simplify the definitions of Fantechi-Goettsche's ring, of Chen-Ruan's orbifold cohomology, and of Abramovich-Graber-Vistoli's orbifold Chow. We conclude by showing that a K-theoretic version of Ruan's Hyper-Kaehler Resolution Conjecture holds for symmetric products. Our results hold both in the algebro-geometric category and in the topological category for equivariant almost complex manifolds.

Tyler J. Jarvis Ralph Kaufmann Takashi Kimura

The stellar (n, $\gamma$) cross section data for the mass numbers around A $\approx$ 160 are of key importance to nucleosynthesis in the main component of the slow neutron capture process, which occur in the thermally pulsing asymptotic giant branch (TP--AGB). The new measurement of (n, $\gamma$) cross sections for $^{159}$Tb was performed using the C$_6$D$_6$ detector system at the back streaming white neutron beam line (Back-n) of the China spallation neutron source (CSNS) with neutron energies ranging from 1 eV to 1 MeV. Experimental resonance capture kernels were reported up to 1.2 keV neutron energy with this capture measurement. Maxwellian-averaged cross sections (MACS) were derived from the measured $^{159}$Tb (n, $\gamma$) cross sections at $kT$ = 5 $\sim$ 100 keV and are in good agreement with the recommended data of KADoNiS-v0.3 and JEFF-3.3, while KADoNiS-v1.0 and ENDF-VIII.0 significantly overestimate the present MACS up to 40$\%$ and 20$\%$, respectively. A sensitive test of the s-process nucleosynthesis was also performed with the stellar evolution code MESA. Significant changes in abundances around A $\approx$ 160 were observed between the ENDF/B-VIII.0 and present measured rate of $^{159}$Tb(n, $\gamma$)$^{160}$Tb in the MESA simulation.

S. Zhang G. Li W. Jiang D. X. Wang J. Ren E. T. Li M. Huang J. Y. Tang X. C. Ruan H. W. Wang Z. H. Li Y. S. Chen L. X. Liu X. X. Li Q. W. Fan R. R. Fan X. R. Hu J. C. Wang X. Li 1D. D. Niu N. Song M. Gu