The extended loop group: An infinite dimensional manifold associated with the loop space

A set of coordinates in the non-parametric loop-space is introduced. We show that these coordinates transform under infinite dimensional linear representations of the diffeomorphism group. An extension of the group of loops in terms of these objects is proposed. The enlarged group behaves locally as an infinite dimensional Lie group. Ordinary loops form a subgroup of this group. The algebraic properties of this new mathematical structure are analyzed in detail. Applications of the formalism to field theory, quantum gravity and knot theory are considered.     

基于动态模态分解的长江口海表温度时空分布特征重构研究

河口近海海域的海表温度分布特征对于深入理解海洋热力、动力过程及海气相互作用等自然过程及综合效应具有重要意义。卫星数据重构是精确获取动态大面积海表温度数据的重要手段,采用非线性系统的动态模态分解（dynamic mode decomposition,DMD）数据分析方法,利用2003年1月至2016年7月的MODIS\SST数据,经剔除异常数据、填补空白数据后,重构了2016年8月至2019年12月长江口海洋表面温度数据,并评估了重构效果。研究结果表明,在时序数据充足的情况下,DMD算法能很好地解决动态系统的采样问题。DMD结合正交三角（orthogonal right triangular,QR）分解算法能有效重构长江口的海表温度数据,平均均方根误差（root mean square error,RMSE）为0.007 6。进一步分析发现,无论是DMD算法还是DMD结合QR分解算法,还原结果精度都较高。     

Shallow donor states induced by in-diffused Cu in ZnO: a combined HREELS and hybrid DFT study

A combined experimental and first principles study of Cu defects in bulk ZnO is presented. Cu particles are epitaxially deposited on the polar O-ZnO(0001) surface at room temperature. Upon heating, a broadening of the quasielastic peak in high resolution electron energy loss spectra is observed, corresponding to an electronic doping effect of Cu atoms in bulk ZnO with an ionization energy of 88 meV. Cu impurities in ZnO, although commonly acting as acceptors, are presently observed to induce shallow donor states. We assign these to interstitial Cu species on the basis of a hybrid density functional study.     

Multipoint holographic optical velocimetry in microfluidic systems

We show how holographic optical trapping can be used for the multipoint measurement of fluid flow in microscopic geometries. An array of microprobes can be simultaneously trapped and used to map out the fluid flow in a microfluidic device. The optical traps are alternately turned on and off such that the probe particles are displaced by the flow of the surrounding fluid and then retrapped. The particles' displacements are monitored by digital video microscopy and directly converted into velocity field values. This technique enables the measurement of a two-dimensional flow field at points arbitrarily distributed in a three-dimensional volume. The validity of the technique is demonstrated for the case of the flow around a spinning sphere and the flow at the outlet of a microchannel.     

Charge-fluctuation contribution to the Raman response in superconducting cuprates

We calculate the Raman response contribution due to soft collective modes, finding a strong dependence on the photon polarizations and on the characteristic wave vectors of the modes. We compare our results with recent Raman spectroscopy experiments in underdoped cuprates, La2-xSrxCuO4 and (Y1.97Ca0.3)Ba2CuO6.05, where anomalous low-energy peaks are observed, which soften upon lowering the temperature. We show that the specific dependence on doping and on photon polarizations of these peaks can naturally arise from charge collective excitations at finite wavelength.     

Engineering massive quantum memories by topologically time-modulated spin rings

We introduce a general scheme to realize perfect storage of quantum information in systems of interacting qubits. This novel approach is based on global external controls of the Hamiltonian that yield time-periodic inversions in the dynamical evolution allowing a perfect periodic quantum state reconstruction. We illustrate the method in the particularly interesting and simple case of spin systems affected by XY residual interactions with or without static imperfections. The global control is achieved by step time inversions of an overall topological phase of the Aharonov-Bohm type. Such a scheme holds both at finite size and in the thermodynamic limit, thus enabling the massive storage of arbitrarily large numbers of local states, and is stable against several realistic sources of noise and imperfections.     

Looking at Fokker-Planck dynamics with a noisy instrument

We consider the class of experiments which can be characterized by a Fokker-PIanck dynamics corresponding to the overdamped motion of a state point in a suitable stochastic potential. We assume that the general form of the potential is known (or can be guessed with reasonable accuracy), but that its parameters are to be determined experimentally by measurements made with a noisy instrument. This possible method for determining the potential parameters, which exploits the system's own internal stochastic motion in order to explore rapidly its available parameter space, is substantially more efficient than traditional methods involving time averages of single point measurements, and yet does not appear to have been previously considered. The method could be important when, for example, the experiment must be completed in a limited time owing either to the expense of the experimental materials or to the temporary stationarity of the preparation, situations which are commonly encountered in experimental biochemistry and biology.