Spectral anomalies and spectral switches of partially coherent and polychromatic light diffracted at an aperture

Inrecentyearsanewbranchofmodernphysicalopticscalledsingularoptics[1]hasbeendeveloped.In2002theworkinsingularopticswasextendedfrommonochromaticlighttospatiallyfullycoherentandpolychromaticlightbyGburetal.[2—4].Itwasfoundthat,whenaconverging,spatiallyfullycoherentandpolychromaticsphericalwaveisdiffractedatanaperture,anomalousspectralchangestakeplaceclosetozerosoftheintensityinthefarfield;i.e.thespectrumisredshiftedatsomepoints,blueshiftedatothers,andsplitintotwolineselsewhere.Thepredictionsofsp…     

Generalized optical theorems for the reconstruction of Green's function of an inhomogeneous elastic medium

This paper investigates the reconstruction of elastic Green's function from the cross-correlation of waves excited by random noise in the context of scattering theory. Using a general operator equation-the resolvent formula-Green's function reconstruction is established when the noise sources satisfy an equipartition condition. In an inhomogeneous medium, the operator formalism leads to generalized forms of optical theorem involving the off-shell T-matrix of elastic waves, which describes scattering in the near-field. The role of temporal absorption in the formulation of the theorem is discussed. Previously established symmetry and reciprocity relations involving the on-shell T-matrix are recovered in the usual far-field and infinitesimal absorption limits. The theory is applied to a point scattering model for elastic waves. The T-matrix of the point scatterer incorporating all recurrent scattering loops is obtained by a regularization procedure. The physical significance of the point scatterer is discussed. In particular this model satisfies the off-shell version of the generalized optical theorem. The link between equipartition and Green's function reconstruction in a scattering medium is discussed.     

Relationship between spectral properties and spatial coherence properties in one-dimensional free fields

Some consequences of a recently derived relationship between the spectral properties and the spatial coherence properties of a stationary optical field are studied for the case when the field is one-dimensional. It is found that the spectrum may be determined from the knowledge of the spatial coherence of the field at all pairs of points that lie within an interval whose length is at least as great as the coherence length of the light.     

Renormalized perturbation theory for a multiplicative noise system

We study an anharmonic overdamped oscillator driven by both additive and multiplicative Gaussian white noise. Within the Martin-Siggia-Rose formalism we employ renormalized perturbation theory to calculate the stationary correlation function and the response function of the oscillator variable. Due to the absence of a simple fluctuation-dissipation theorem renormalization cannot make use of exact stationary moments, but is perormed with the help of renormalization conditions.     

Operator formalism on general algebraic curves

The usual Laurent expansion of the analytic tensors on the complex plane is generalized to any closed and orientable Riemann surface represented as an affine algebraic curve. As an application, the operator formalism for the b − c systems is developed. The physical states are expressed by means of creation and annihilation operators as in the complex plane and the correlation functions are evaluated starting from simple normal ordering rules. The Hilbert space of the theory exhibits an interesting internal structure, being splitted into n (n is the number of branches of the curve) independent Hilbert spaces. In this way we are able to realize new kinds of conformal field theories at genus zero with symmetry group Virⁿ ⊗ G, Vir being the Virasoro group and G denoting a discrete and nonabelian crystallographic group. Exploiting the operator formalism a large collection of explicit formulas of string theory is derived. Finally, we develop as an important byproduct new methods in order to handle differential equations related to monodromy, like the Riemann monodromy problem.     

The Schwinger model and its axial anomaly

The Schwinger model (quantum electrodynamics with massless fermions in one spatial dimension) is solved, supposing that space is a circle. This clarifies aspects of the usual version of the model, where space is a line, without changing the physics. The Hamiltonian formalism is used. On a circle, an abelian gauge field has one physical degree of freedom, and the gauge covariant Dirac operator, which couples the fermions to this degree of freedom, exhibits spectral flow. The relationship between the spectral flow and the axial anomaly is explained. Some variants of the Schwinger model are also discussed.     

Gamow Vectors and Time Asymmetry

We prove that Gamow vectors are important toolsin the quantum theory of irreversibility. We use themathematical formalism of rigged Hilbert spaces. Wediscuss some spectral formulas that include Gamow vectors as well as some results concerningGamow vectors. The role of the time-reversal operator isstudied. The formalism can be applied to formulate asense of irreversibility in cosmology.     

Review on the theory of the dielectric dispersion of insulators

The theory of the dielectric dispersion of insulators is reviewed with special emphasis on the infrared and submillimeter-wave spectral regions. The concepts of linear response, causality, local field, correlation, etc., are described with a uniform advanced mathematical formalism which gives insight into the merits and disadvantages of the present models. The models and formulas presented are supplemented by experimental data.     

Star Products and Perturbative Quantum Field Theory

We discuss the deformation quantization approach to perturbative quantum field theory. The various forms of Wick's theorem are shown to be a direct consequence of the structure of the star products. The scattering function for a scalar field in interaction with a spacetime-dependent source is derived. The translation of the results to the operator formalism reproduces known relations which lead to the derivation of the Feynman rules.     

Relaxation to Stationary Nonequilibrium States in Stochastic Ginzburg–Landau Models

We propose an approach to investigate properties of the time relaxation to stationary nonequilibrium states of correlation functions of stochastic Ginzburg–Landau models with noise (temperature of the reservoirs in contact with the system) changing in space. The formalism relates the stochastic expectations to correlation functions of an imaginary time field theory, and it allows us to study the nonlinear dynamics in terms of a field theory given by a perturbation of a Gaussian measure related to the (easier) linear dynamical problem. To show the usefulness of the formalism, we argue that a perturbative analysis within the integral representation is enough to give us the time relaxation rates of the correlations in some situations.     

Random systems,turbulence and disordering fields

The statistical theory of random processes is cast into a Lagrangian form. The formalism requires the existence of an arbitrarily weak random stirring force, playing the role of a disordering field. In scale invariant systems the coupling strength of the weak stirring force can be scaled out and it disappears from the theory. The formalism is applied to the turbulent flow of an incompressible fluid; in particular, we derive the Feynman rules by means of which the distribution of fluctuations around an average flow can be determined. The formalism is further illustrated on the example of a stationary fluid flow between parallel planes: an approximate formula for the correlation function of vorticities is obtained, which is expected to be valid at large Reynolds numbers.     

Relations Between Characteristic Function,Positive P-Representation and Coherent Thermal State

We employ the coherent thermal states (a kind of entangled states) in thermal field dynamics to establish a complete entangled state formalism expressing pseudo-classical representations of density operator for light field. Especially, the relationship between the coherent thermal state and the characteristic function and the positive P representation in quantum optics theory are obtained.     

Relations Between Characteristic Function, Positive P-Representation and Coherent Thermal State

We employ the coherent thermal states (a kind of entangled states) in thermal field dynamics to establish a complete entangled state formalism expressing pseudo-classical representations of density operator for light field.Especially, the relationship between the coherent thermal state and the characteristic function and the positive P representation in quantum optics theory are obtained.     

Scattering of scalar light wave from a Gaussianben Schell model medium

The scattering of scalar light wave from a random medium with a correlation function of Gaussian–Schell model distribution is studied. It is shown that the properties of the scattered field, i.e., the spectral density and the spectral degree of coherence of the scattered field, are closely related to the properties of the scattering medium, including the scaled effective radius and the scaled correlation length of the correlation function.     

Rotationally symmetric scattering from anisotropic media

It is reported that the rotationally symmetric distributions of the spectral density and the spectral degree of coherence of the scattered field in the far zone can be produced by appropriate choices of the effective radius and the correlation length of the scatterer, when a polychromatic plane light wave is incident upon a Gaussian-correlated, quasi-homogeneous, anisotropic medium. The necessary and sufficient conditions are presented. Our results are illustrated by numerical examples.     

Thermodynamical properties of the transverse Ising model

A new effective field theory is proposed and used to derive the thermodynamical properties of the transverse Ising model. The formalism is based on an exact formal spin identity for the two-state transverse Ising model and utilizes an exponential operator technique. The method, which can explicitly and systematically include correlation effects, is illustrated in several lattice structures by employing its simplest approximation version (in which spin-spin correlations are neglected). The lines of critical points in the Ω-T plane as well as the thermal behaviour of both transverse and longitudinal magnetizations are analysed for square and simple cubic lattices. It is shown that the present formalism, in spite of its simplicity, yields results which represent a remarkable improvement on the standard mean field treatment (MFA).     

Reciprocity relations for scattering from quasi-homogeneous anisotropic media

Valid within the accuracy of the first-order Born approximation, we obtain the analytical expressions of the three-dimensional spatial Fourier transforms, which show the reciprocity relations for the scattering of a polychromatic plane wave incident upon a Gaussian-correlated, quasi-homogeneous, anisotropic scatterer. We find that the spectral degree of coherence of the scattered field is only related with the effective radius of the scatterer and the normalized spectral density of the scattered field is only related with the correlation length of the scatterer.     

光纤环相干性分析

运用部分相干光理论,得到了光纤环自相关函数,并利用自相关函数推导出了光谱透射因子,它把光纤环输入、输出光场的光谱密度函数直接联系起来,代表了光纤环的相干性.应用光谱透过因子,结合光纤环耦合输出系数、光学长度、损耗分析讨论了光纤环相干性.     

Verallgemeinerung der Methode der singulären Normallösungen für isotherme irreversible Vlasov-Systeme

Irreversible Vlasov systems, i.e. systems governed by a Vlasov-type kinetic equation including entropy-producing collision terms, are treated by the techniques of singular normal modes and singular integral equations using a new indirect method which renders possible a straightforward generalization of the Case formalism as developed originally for collision-free Vlasov plasmas. This method is in contrast to a more complex method given by the present authors for the first application of the singular normal mode expansion to irreversible Vlasov systems (1970). The linearized Vlasov operator supplemented by complete Bhatnagar-Gross-Krook collision integrals as the most important model collision terms is analyzed in detail for a nonrelativistic, nondegenerate, stationary electron gas with neutralizing positive ions and neutral particles without a magnetic field at constant temperature, generalizations for more complex irreversible Vlasov systems being possible. The key of the indirect method given is the introduction of a transformed electron distribution function containing as an additive term an integral over the usual distribution function.