Joule expansion of a pure many-body state

We derive the Joule expansion of an isolated perfect gas from the principles of quantum mechanics. Contrary to most studies of irreversible processes which consider composite systems, the interesting and ignored degrees of freedom are here described by operators acting in the same many-body Hilbert space. Moreover, the expansion of the gas into the entire accessible volume is obtained for pure states. Still, the number particle density is characterized by a chemical potential and a temperature. We discuss the special case of a boson gas below the Bose condensation temperature.     

Phase Effect on Guided Resonance in Photonic Crystal Slabs

Phase effect on the guided resonances in photonic crystal slabs is analysed. We present an analysis in the case of a mirror symmetric system and an asymmetric system irradiated from both sides, as well as the more realistic and interesting case of a system bounded from one side by a perfect mirror. Gain is incorporated in the system, mainly to exemplify the results. Finally we find that phase effects persist in the asymmetric system resulting in a periodic response for the reflectivity versus the distance from the mirror, which is the main parameter controlling the phase relationship between the two incident waves.     

A new form of symplectically invariant multimode uncertainty relations

We derive symplectically invariant uncertainty relations for a set of canonically conjugated variables. The uncertainty relations obtained are multimode analogs of the Robertson–Schrödinger inequalities. Our uncertainty relations are equivalent to the necessary and sufficient conditions for a matrix to be a correlation matrix of some quantum state, obtained by R. Simon and coauthors. The advantage of our inequalities, compared to that suggested by Simon, consists in its simplicity and more obvious symplectic invariance. We derive our inequalities for the case of a two-mode system in explicit form. Particular cases of small and large degrees of correlation between the first and second modes are analyzed in detail.     

Dynamics of locally rotationally symmetric Bianchi type VIII cosmologies with anisotropic matter

This paper is a study of the effects of anisotropic matter sources on the qualitative evolution of spatially homogenous cosmologies of Bianchi type VIII. The analysis is based on a dynamical system approach and makes use of an anisotropic matter family developed by Calogero and Heinzle which generalises perfect fluids and provides a measure of deviation from isotropy. Thereby the role of perfect fluid solutions is put into a broader context. The results of this paper concern the past and future asymptotic dynamics of locally rotationally symmetric solutions of type VIII with anisotropic matter. It is shown that solutions whose matter source is sufficiently close to being isotropic exhibit the same qualitative dynamics as perfect fluid solutions. However a high degree of anisotropy of the matter model can cause dynamics to differ significantly from the vacuum and perfect fluid case.     

Field squeeze operators in optical cavities with atomic ensembles

We propose a method of generating unitarily single and two-mode field squeezing in an optical cavity with an atomic cloud. Through a suitable laser system, we are able to engineer a squeeze field operator decoupled from the atomic degrees of freedom, yielding a large squeeze parameter that is scaled up by the number of atoms, and realizing degenerate and nondegenerate parametric amplification. By means of the input-output theory we show that ideal squeezed states and perfect squeezing could be approached at the output. The scheme is robust to decoherence processes.     

Analysis of multi-configuration density functional theory methods: theory and model application to bond-breaking

We consider the extension of the standard single-determinant Kohn–Sham method to the case of a multi-configuration auxiliary wave function. By applying the rigorous Kohn–Sham method to this case, we construct the proper interacting and auxiliary energy functionals. Following the Hohenberg–Kohn theorem for both energy functionals, we derive the corresponding multi-configuration Kohn–Sham equations, based on a local effective potential. At the end of the analysis we show that, at the ground state, the auxiliary wavefunction must collapse into a single-determinant wave function, equal to the regular KS wavefunction. We also discuss the stability of the wavefunction in multi-configuration density functional theory methods where the auxiliary system is partially interacting, and the remaining (residual) correlation is evaluated as a functional of the density. As an example showing both the challenges and the possibilities, we implement such a procedure for the perfect pairing wavefunction, using a residual correlation functional that is based on the Lee–Yang–Parr functional, and present results for an elementary bond-breaking process.     

Fock space construction of the massless dipole field

We construct the Fock space representation of the free massless scalar dipole field in terms of creation and annihilation operators for the eigenvectors of the momentum operator. The Poincaré group is implemented unitarily only on a subspace of the full (positive metric) Hilbert space. The subspace possesses a hermitean, local, irreducible scalar field constructed out of the (non-hermitean) dipole field. Thus this subspace is a perfect candidate for a physical subspace of observable particles. We show that this possibility is however excluded by the fact that these particles interact with an external c-number source in a manner that violates unitarity. We illustrate our construction by applying it to the linearized Higgs model with external c-number source and examine the (non-trivial) dynamics of the dipole degrees of freedom in this case. An explicit separation of the physical degrees of freedom from the unphysical ones is presented for this interacting model.     

Photoconductivity of a two-dimensional electron system with spin-orbit coupling in AC magnetic field

The response of an electron system to a dc probe field is analyzed in the case when an initial deviation of conduction-electron spin degrees of freedom from equilibrium in a microwave magnetic field induces combined resonance transitions in the electron system. It is shown that a perturbation of spin degrees of freedom is converted into kinetic energy and modifies transport coefficients, leading to oscillations of diagonal components of the conductivity tensor.     

Cyclic integrals and reduction of rotational relativistic Birkhoffian system

The order reduction method of the rotational relativistic Birkhoffian is studied.For a rotational relativistic Birkhoffian system.the cyclic integrals can be found by using the perfect differential method.Through these cyclic integrals,the order of the system can be reduced.If the rotational relativistic Birkhoffian system has a cyclic integral,then the Birkhoffian equations can be reduced at least two degrees and the Birkhoffian form can be kept.An example is given to illustrate the application of the results.     

Application of time delay spectrometry for rough surface characterization

This paper describes the design and performance of an ultrasound measurement system, utilizing a swept frequency excitation signal, for analyzing the backscattered signal from planar rough surfaces. The implementation is in the form of a time delay spectrometry (TDS) system operating in reflection mode whose advantages are improved signal-to-noise ratio even with low peak power relative to conventional pulse-echo methods. Because of simultaneous transmission and reception, the TDS system requires two transducers. The TDS measurement system uses a swept frequency spectrum analyzer as the central analog processing unit. Both planar piston and focused transducers in the low MHz range were used for the measurements. Due to the statistical nature of rough surface backscatter, the mean of several statistically uncorrelated measurements is required to characterize the scattering behavior of a given rough surface. Backscatter data are obtained for a series of planar rough surfaces, in the form of scattering magnitude vs. frequency and vs. incident (=backscattered) angle. Analysis of the results reveals a good correlation between the root-mean-square (RMS) height and mean backscatter magnitude at 0 degrees incident angle, and between the ratio of RMS height to correlation length and the difference in mean backscatter magnitude between 0 degrees and 5 degrees.     

Perfect imaging of hypersurfaces via transformation optics

Conventional optical imaging systems suffer from the presence of many imperfections, such as spherical aberrations, astigmatism, or coma. If the imaging system is corrected for spherical aberrations and fulfills the Abbe sine condition, perfect imaging is guaranteed between two parallel planes but only in a small neighborhood of the optical axis. It is therefore worth asking for optical systems that would allow for perfect imaging between arbitrary smooth surfaces without restrictions in shape or extension. In this Letter, we describe the application of transformation optics to design refractive index distributions that allow perfect, aberration-free imaging for various imaging configurations in R(n). A special case is the imaging between two extended parallel lines in R(2), which leads to the well-known hyperbolic secant index distribution that is used for the fabrication of gradient index lenses.     

Photon antibunching in the fluorescence of a single dye molecule embedded in a thin polymer film

We used scanning confocal microscopy to study the fluorescence from a single terrylene molecule embedded in a thin polymer film of polymethyl methacrylate, at room temperature, with a high signal-to-background ratio. The photon-pair correlation function g((2))(tau) exhibits perfect photon antibunching at tau = 0 and a limit of 1.3, compatible with bunching associated with the molecular triplet state. Application of this molecular system to a triggered single-photon source based on single-molecule fluorescence is investigated.     

一种广义三模腔光机械系统的相干完美吸收与透射

提出了一种广义的三模式腔光机械系统,系统的中间是一个反射率为100%的可移动的全反射机械振子,两侧均由一个部分透射的固定光学腔镜构成.其中两个光学腔由一束较强的控制场和一束较弱的信号场驱动与同一个机械振子实现耦合.较弱的信号场将会被该系统完全吸收而不产生任何能量输出,并且当相干完美吸收产生时,输入信号场的能量将由两个腔场和机械模共同分担;较弱的输入信号场由一个腔完美透视到另一个腔而不产生任何的能量损耗.分析与数值结果显示,在不同参数机制下,在该三模光机械系统中可以实现相干完美吸收、相干完美透射和相干完美合成的量子现象.此外,改变腔与腔之间的耦合度,可以实现输出探测场在相干完美吸收和相干完美透射之间转换;通过简单的相位调制,可以实现探测场左腔-右腔的输出和输入方向的互换.这些动态控制在量子信息网络可用来构造光子开关、光子路由、光子交换机等一些特殊功能的光子学器件.     

(1+2)维各向同性介质中的旋转椭圆空间光孤子

从(1+2)维非局域非线性薛定谔方程出发, 通过坐标变换得到了旋转坐标系下的非局域非线性薛定谔方程. 假设响应函数为高斯型, 用虚时间法数值求解了旋转坐标系下的非局域非线性薛定谔方程的静态孤子解, 迭代出了不同非局域程度条件下的静态椭圆孤子数值解. 最后采用分步傅里叶算法, 以迭代的孤子解作为初始输入波形, 模拟了在不同的非局域程度条件下, (1+2)维椭圆空间光孤子的旋转传输特性. 强非局域时, 椭圆光孤子的长轴方向和短轴方向波形都是高斯型, 其他的非局域程度下, 不是高斯型. 由此表明：(1+2)维椭圆光孤子对非局域程度依赖性很强. 旋转角速度和功率均与非局域程度以及孤子的椭圆度有关.     

An approach for characterizing coupling in dynamical systems

The study of coupling in dynamical systems dates back to Christian Hyugens who, in 1665, discovered that pendulum clocks with the same length pendulum synchronize when they are near to each other. In that case the observed synchronous motion was out of phase. In this paper we propose a new approach for measuring the degree of coupling and synchronization of a dynamical system consisting of interacting subsystems. The measure is based on quantifying the active degrees of freedom (e.g. correlation dimension) of the coupled system and the constituent subsystems. The time-delay embedding scheme is extended to coupled systems and used for attractor reconstruction of the coupled dynamical system. We use the coupled Lorenz, Rossler and Hénon model systems with a coupling strength variable for evaluation of the proposed approach. Results show that we can measure the active degrees of freedom of the coupled dynamical systems and can quantify and distinguish the degree of synchronization or coupling in each of the dynamical systems studied. Furthermore, using this approach the direction of coupling can be determined.     

The ballistic resonance of transversal mechanical waves in random-dimer systems

The propagation of transversal mechanical waves in one-dimensional disordered system is studied in presence of the short-range correlation. The dimer and host unit cells are constructed within a particular way that provides perfect unity transmission resonances over all of the system length. Moreover, while dealing with the on-site correlation this interesting configuration also supplies the ballistic vibration propagating modes for any amount of the mass disorder in opposition with the well-known conventional diffusive random dimer model. This process is appropriate to design better mechanical filters with very high adjustable ballistic transmission quality.     

Concrete Hilbert spaces for quantum systems with infinitely many degrees of freedom

We demonstrate a method to describe quantum systems with infinitely many degrees of freedom in concrete Hilbert spaces, using the electromagnetic radiation field as a well-known example of such a system. Since our method is not only applicable to the case of countably many but even to the case of uncountably many degrees of freedom, there is no need for a finite quantization volume in radiation theory.     

Complete correlation,detection loophole and Bell's theorem

Two new formulations of Bell's theorem are given here. First, we consider a definite set of two entangled photons with only two polarization directions, for which Bell's locality assumption is violated for the case of perfect correlation. Then, using a different approach, we prove an efficient Bell‐type inequality which is violated by some quantum mechanical predictions, independent of the efficiency factors.     

A data-analysis method for decomposing synchronization variability of anticipatory systems into stochastic and deterministic components

Synchronization has been shown to be a valuable concept in the field of nonlinear dynamics and dynamical systems in general. Deviation from perfect synchronization results from an interplay of deterministic coupling forces and stochastic fluctuating forces. When the exact details of these two sources of variance are unknown, it becomes useful to estimate them directly from data. To this end, we develop a data analysis method for estimating parameters associated with these deterministic and stochastic components. The method relies on separating their respective contributions to synchronization error. We focus on the case where a slave system synchronizes with the future of a master system, so-called anticipating synchronization.