Transition from Poisson to circular unitary ensemble

Transitions to universality classes of random matrix ensembles have been useful in the study of weakly-broken symmetries in quantum chaotic systems. Transitions involving Poisson as the initial ensemble have been particularly interesting. The exact two-point correlation function was derived by one of the present authors for the Poisson to circular unitary ensemble (CUE) transition with uniform initial density. This is given in terms of a rescaled symmetry breaking parameter Λ. The same result was obtained for Poisson to Gaussian unitary ensemble (GUE) transition by Kunz and Shapiro, using the contour-integral method of Brezin and Hikami. We show that their method is applicable to Poisson to CUE transition with arbitrary initial density. Their method is also applicable to the more general ℓCUE to CUE transition where ℓCUE refers to the superposition of ℓ independent CUE spectra in arbitrary ratio.     

Statistical theory of nuclear reactions and the Gaussian orthogonal ensemble

Using methods developed in field theory and statistical mechanics, especially in the context of the Anderson model as generalised by Wegner, a novel approach to the statistical theory of nuclear reactions is developed. A finite set of N bound states, coupled to each other by an ensemble of Gaussian orthogonal matrices, is considered and coupled to a set of channels via fixed coupling matrix elements. The ensemble average and the variance of the elements of the nuclear scattering matrix are evaluated, using the method of a generating function combined with the replica trick, followed by the Hubbard-Stratonovitch transformation and a modified loop expansion. In the limit N → ∞, it is shown quite generally that, aside from a trivial dependence on average S-matrix elements, the variance depends only on the transmission coefficients, and that the correlation width of a pair of S-matrix elements is given by a universal function of the transmission coefficients. A modified loop expansion yields an asymptotic series valid for strong absorption. The terms in this series are partly novel, and partly coincide with results obtained earlier in the framework of a model which did not take account of the GOE eigenvalue fluctuations. This suggests that average cross sections are mainly sensitive to the stiffness of the GOE spectrum. Fluctuation properties are also derived, and the link to Ericson fluctuation theory is established.     

The integrable discrete analogues of orthogonal coordinate systems are multi-dimensional circular lattices

We show that the integrable discrete analogues of the Lamé orthogonal systems of coordinates are given by multidimensional circular lattices, i.e. by multidimensional lattices whose elementary quadrilaterals are inscribed in circles.     

一种直角转弯圆波导模式转换器设计

设计了一种尺寸紧凑并具有高功率容量的圆波导TE₁₁-TM₀₁模式转换器,结构呈直角转弯形状。该转换器利用传输TE₁₁模式的圆波导与其E面分支耦合进行模式转换,并在TM₀₁输出端口的反向传输短路面加入调配螺钉来拓宽频带。设计结果表明,转换器在工作频率12.7 GHz处的转换效率为99.6%,大于90%的带宽约20%,填充SF₆绝缘气体工作时可获得12 MW的功率容量。     

冷原子系综中两正交光场偏振模高效率存储的实验研究

高效率光量子信息存储是可扩展光量子信息处理的一个重要工具.本文对一个冷原子系综中两正交光场偏振模的高效率存储进行了实验研究.通过在雪茄型冷原子系统上施加一个中等强度的磁场,消除了原子Zeeman子能级的简并性,从而使磁敏感自旋波从电磁感应透明系统中被移出,由此完成了两正交光场偏振模高效率、长寿命的量子存储.实验测量了两偏振模存储效率与存储时间以及实验重复频率的关系,结果表明,随着重复频率的增加,存储效率逐渐降低,在10 Hz时,测量得到两偏振模存储效率为30%,同时存储寿命达到3 ms.测量结果为偏振纠缠在冷原子系统中的存储提供了重要的实验基础.     

Reflective thin-film device for generating spatial binary patterns of orthogonal circular polarization states

A novel device is described that generates, by reflection, polarized optical wavefronts of juxtaposed fields of alternating orthogonal circular polarization states. It consists of a dielectric substrate coated by a transparent thin film of certain refractive index and of thickness that alternates between two discrete values over adjacent areas of the substrate, in a pattern that corresponds to the desired binary polarization pattern of the reflected wave. Devices that use Ge and Si substrates at wavelengths of 10.6 and 0.6328 μm, respectively, are presented as examples.     

Transition curves for the variance of the nearest neighbor spacing distribution for Poisson to Gaussian orthogonal and unitary ensemble transitions

Using an appropriate 2x2 random matrix ensemble, transition curves for the variance of the nearest neighbor spacing distribution are constructed for the Poisson to Gaussian orthogonal and unitary ensemble transitions in terms of an easily identifiable transition parameter.     

The classicality and quantumness of a quantum ensemble

In this Letter, we investigate the classicality and quantumness of a quantum ensemble. We define a quantity called ensemble classicality based on classical cloning strategy (ECCC) to characterize how classical a quantum ensemble is. An ensemble of commuting states has a unit ECCC, while a general ensemble can have a ECCC less than 1. We also study how quantum an ensemble is by defining a related quantity called quantumness. We find that the classicality of an ensemble is closely related to how perfectly the ensemble can be cloned, and that the quantumness of the ensemble used in a quantum key distribution (QKD) protocol is exactly the attainable lower bound of the error rate in the sifted key.     

The ensemble approach to understand genetic regulatory networks

Understanding the genetic regulatory network comprising genes, RNA, proteins and the network connections and dynamical control rules among them, is a major task of contemporary systems biology. I focus here on the use of the ensemble approach to find one or more well-defined ensembles of model networks whose statistical features match those of real cells and organisms. Such ensembles should help to explain and predict features of real cells and organisms.     

The complex Laguerre symplectic ensemble of non-Hermitian matrices

We solve the complex extension of the chiral Gaussian symplectic ensemble, defined as a Gaussian two-matrix model of chiral non-Hermitian quaternion real matrices. This leads to the appearance of Laguerre polynomials in the complex plane and we prove their orthogonality. Alternatively, a complex eigenvalue representation of this ensemble is given for general weight functions. All k-point correlation functions of complex eigenvalues are given in terms of the corresponding skew orthogonal polynomials in the complex plane for finite-N, where N is the matrix size or number of eigenvalues, respectively. We also allow for an arbitrary number of complex conjugate pairs of characteristic polynomials in the weight function, corresponding to massive quark flavours in applications to field theory. Explicit expressions are given in the large-N limit at both weak and strong non-Hermiticity for the weight of the Gaussian two-matrix model. This model can be mapped to the complex Dirac operator spectrum with non-vanishing chemical potential. It belongs to the symmetry class of either the adjoint representation or two colours in the fundamental representation using staggered lattice fermions.     

The orthogonal projection method in scattering theory

This work gives a detailed account of the orthogonal projection method in the theory of two- and three-body scattering, which is based on the employment of orthogonal projecting pseudopotentials. The method is applied to a number of physical problems, of which the following the most important: the improvement of convergence and the rearragement of Born series to make them convergent at low energies in the presence of bound states in a system, as well as the consideration of the Pauli exclusion principle in the scattering of composite particles and in the integral theory of direct nuclear reactions. The properties of eigenvalues of kernels of the equations obtained are investigated and the conditions for the convergence of their iterations are derived. For the three-body problem, the general case of three different particles is considered, as well as two particular cases, namely, two particles in the field of a heavy core and three identical particles. The proven theorems are illustrated by numerical examples. Other useful applications of the proposed approach are listed and discussed, in particular, those in solid-state physics and in the theory of electromagnetic transitions. The approach suggested is compared with those of the other authors and the prospects of using the developed formalism are discussed.     

The dark-state polaritons of a double-Λ atomic ensemble

We study the interaction of two quantized fields with a double-Λ system driven by two classical control fields with variable complex Rabi frequencies. There exists one normal mode of the quantum fields that propagates without absorption. In the two-mode case of dark-state polaritons, we discuss the possibility of storing and retrieving the quantum state in this normal mode. This system can be also used to generate entangled state and, furthermore, it can act as a controllable beam splitter.     

The entropy of an ensemble of quantum mechanical systems

A mathematical result about a positive self-sdjoint operator of unit trace is proved whose physical interpretation is that when an observation is made on a mixed state of a quantum system leading to a change in its state, the entropy increases as it must.     

The conditional entropy in the microcanonical ensemble: The quantum lattice

The existence of the conditional entropy in the thermodynamic limit for a class of long range compatible observables operating on a quantum lattice is exhibited for the microcanonical ensemble. This limit is demonstrated first along a special sequence of cubes with a fixed contraction parameter. Properties of the parameter dependent limit are utilized to remove the parameter, and the results are extended to van Hove sequences approximable by cubes.     

Observation of a circular dichroism of an ensemble of triplet metastable helium atoms in a Na-He gas-discharge plasma with laser-oriented sodium atoms

We describe an experiment on the observation of a circular dichroism of an ensemble of triplet metastable helium atoms in a sodium-helium gas-discharge plasma where Na atoms are optically oriented with circularly polarized radiation of a laser tunable around the resonant sodium doublet (with wavelength of 589.0 and 589.6 nm, corresponding to the 3² S _1/2 ⇄ 3² P _1/2 and 3² S _1/2 ⇄ 3² P _3/2 transitions). Conditions of observation and the polarization degree of 2³ S ₁ atoms are determined.     

Adiabatic interaction between a dark soliton and a cnoidal wave with orthogonal circular polarizations in an isotropic gyrotropic nonlinear medium

An analytical solution to the one-dimensional (plane waves) nonintegrable problem of interaction (collision) of a dark soliton with a cnoidal wave (control and information signals with orthogonal circular polarizations) in an isotropic gyrotropic medium with Kerr nonlinearity and second-order groupvelocity dispersion is obtained in the adiabatic approximation. The asymptotic behavior of the obtained solution is considered. It is shown that the role of the control signal is reduced to strong amplitude and frequency modulation, which is localized only in the region of variation in the control signal intensity.