Thermalization of Green functions and quasinormal modes

We develop a new method to study the thermalization of time dependent retarded Green function in conformal field theories holographically dual to thin shell AdS Vaidya space times. The method relies on using the information of all time derivatives of the Green function at the shell and then evolving it for later times. The time derivatives of the Green function at the shell is given in terms of a recursion formula. Using this method we obtain analytic results for short time thermalization of the Green function. We show that the late time behaviour of the Green function is determined by the first quasinormal mode. We then implement the method numerically. As applications of this method we study the thermalization of the retarded time dependent Green function corresponding to a minimally coupled scalar in the AdS 3 and AdS 5 thin Vaidya shells. We see that as expected the late time behaviour is determined by the first quasinormal mode. We apply the method to study the late time behaviour of the shear vector mode in AdS 5 Vaidya shell. At small momentum the corresponding time dependent Green function is expected to relax to equilibrium by the shear hydrodynamic mode. Using this we obtain the universal ratio of the shear viscosity to entropy density from a time dependent process.

Green functions of the Dirac equation with magnetic-solenoid field

Various Green functions of the Dirac equation with a magnetic-solenoid field (the superposition of the Aharonov-Bohm field and a collinear uniform magnetic field) are constructed and studied. The problem is considered in 2+1 and 3+1 dimensions for the natural extension of the Dirac operator (the extension obtained from the solenoid regularization). Representations of the Green functions as proper time integrals are derived. The nonrelativistic limit is considered. For the sake of completeness the Green functions of the Klein-Gordon particles are constructed as well. (C) 2004 American Institute of Physics.

Solutions of Fractional Diffusion-Wave Equations in Terms of H-functions

MSC 2010: 35R11, 42A38, 26A33, 33E12

Many-body effects in electrochemisorption : Part III. Beyond mean field and hartree-fock

Several channels provided by many-body couplings — both fermion-fermion and fermion-boson — for the evolution of the chemisorption system are discussed. This provides an opportunity of a systematic study of the effects of correlations reflected through the intricate pole structure of the absorbate Green functions. The results of Newns, Anda and others in the context of chemisorption are generalized.

Boundedness of weakly singular integral operators on domains

The monograph dissertation deals with kernel integral operators and their mapping properties on Euclidean domains. The associated kernels are weakly singular and examples of such are given by Green functions of certain elliptic partial differential equations. It is well known that mapping properties of the corresponding Green operators can be used to deduce a priori estimates for the solutions of these equations. In the dissertation, natural size- and cancellation conditions are quantified for kernels defined in domains. These kernels induce integral operators which are then composed with any partial differential operator of prescribed order, depending on the size of the kernel. The main object of study in this dissertation being the boundedness properties of such compositions, the main result is the characterization of their Lp-boundedness on suitably regular domains. In case the aforementioned kernels are defined in the whole Euclidean space, their partial derivatives of prescribed order turn out to be so called standard kernels that arise in connection with singular integral operators. The Lp-boundedness of singular integrals is characterized by the T1 theorem, which is originally due to David and Journé and was published in 1984 (Ann. of Math. 120). The main result in the dissertation can be interpreted as a T1 theorem for weakly singular integral operators. The dissertation deals also with special convolution type weakly singular integral operators that are defined on Euclidean spaces.

Localised modes due to impurities in III–V semiconductors

Local mode frequencies due to substitutional impurities in some III–V semiconductors are calculated using Green functions on the mass defect approximation and compared with experimental results.

Curie-temprature of a spin one xy ferromagnet with uniaxial anisotropy

A spin one XY ferromagnet with uniaxial anisotropy has been investigated, using Green's function technique in random phase approximation (RPA). The Green functions associated with the anisotropy energy are treated without decoupling. A set of coupled equations have been obtained to find the critical temperature Tc and left angle bracket(SZ)2right-pointing angle bracket at Tc as function of the uniaxial anisotropy parameter D. Tc and left angle bracket(SZ)2right-pointing angle bracket at Tc are found to increase with D. The results are compared with the earlier results obtained in the Narath type of RPA.

Effects of contact resistance on thermal-conductivity of composite media with a periodic structure

The thermal conductivity of periodic composite media with spherical or cylindrical inclusions embedded in a homogeneous matrix is discussed. Using Green functions, we show that the Rayleigh identity can be generalized to deal with thermal properties ot these systems. A new calculating method for effective conductivity of composite media is proposed. Useful formulae for effective thermal conductivity are derived, and meanings of contact resistance in engineering problems are explained.

Fast numerical methods for mixed, singular Helmholtz boundary value problems and Laplace eigenvalue problems - with applications to antenna design, sloshing, electromagnetic scattering and spectral geometry

This thesis presents a novel class of algorithms for the solution of scattering and eigenvalue problems on general two-dimensional domains under a variety of boundary conditions, including non-smooth domains and certain "Zaremba" boundary conditions - for which Dirichlet and Neumann conditions are specified on various portions of the domain boundary. The theoretical basis of the methods for the Zaremba problems on smooth domains concern detailed information, which is put forth for the first time in this thesis, about the singularity structure of solutions of the Laplace operator under boundary conditions of Zaremba type. The new methods, which are based on use of Green functions and integral equations, incorporate a number of algorithmic innovations, including a fast and robust eigenvalue-search algorithm, use of the Fourier Continuation method for regularization of all smooth-domain Zaremba singularities, and newly derived quadrature rules which give rise to high-order convergence even around singular points for the Zaremba problem. The resulting algorithms enjoy high-order convergence, and they can tackle a variety of elliptic problems under general boundary conditions, including, for example, eigenvalue problems, scattering problems, and, in particular, eigenfunction expansion for time-domain problems in non-separable physical domains with mixed boundary conditions.

Aplicações do formalismo de Keldysh ao transporte e ao bombeamento de calor em nanoestruturas

Num regime balísstico e a baixas temperaturas, a fórmula de Landauer dá uma boa descrição do transporte de calor para nano-junções conectadas a dois fios acoplados a banhos térmicos a temperaturas diferentes. Partindo de um modelo microscópico e utilizando o método de funções de Green fora do equilíbrio, é possível obter uma expressão para a condutância térmica na nano-junção equivalente a fórmula de Landauer. Esta depende dos valores das constantes de acoplamento entre os modos de fônons da região central e dos fios, além do gradiente térmico. A expressão para a condutância térmica é muito semelhante aquela obtida para a condutância elétrica. Neste trabalho nós apresentamos o método para o cálculo de grandezas relacionadas ao transporte térmico em um regime onde não há um gradiente de temperatura entre os reservatórios mas o sistema sofre uma perturbação dependente do tempo. Ou seja, com uma escolha conveniente da parametrização temporal dos termos de acoplamento entre a nano-junção e os fios é possível produzir uma corrente de calor na ausência de diferença de temperaturas entre os banhos térmicos aos quais os fios estão conectados. Esse fenômeno caracteriza o bombeamento de calor. Desenvolvemos uma teoria de transporte dependente do tempo para descrever o bombeamento. A teoria é geral, dependendo da densidade de fônons, da intensidade e dependência temporal do acoplamento. Aplicamos o formalismo em um modelo simples demonstrando que, em princípio, é possível bombear calor através de uma cadeia linear de átomos sem gradiente térmico.

Interaction of linear waves with infinitely long horizontal cylinders studied by boundary element method

The two-dimensional problems concerning the interaction of linear water waves with cylinders of arbitrary shape in two-layer deep water are investigated by use of the Boundary Integral Equation method (BIEM). Simpler new expressions for the Green functions are derived, and verified by comparison of results obtained by BIEM with these by an analytical method. Examined are the radiation and scattering of linear waves by two typical configurations of cylinders in two-layer deep water. Hydrodynamic behaviors including hydrodynamic coefficients, wave forces, reflection and transmission coefficients and energies are analyzed in detail, and some interesting physical phenomena are observed.

Exercise sheet 3

Exercises and solutions in LaTex

Exercise sheet 3 pdf

Exercises and solutions in PDF

Antenas de microfita com patch em anel e múltiplas camadas dielétricas anisotrópicas uniaxiais

This work presents an analysis of the annular ring microstrip antennas printed on uniaxial anisotropic substrates and with superstrate.The analysis uses the full-wave formulation by means of the Hertz vector potentials method, in the Hankel transform domain. The definition of the Hertz vector potentials and the application of the appropriate boundary conditions to the structure allow determining the dyadic Green functions, relating the current densities in the conducting patch to the transforms of the tangential electric field components. Galerkin s method is then used to obtain the matrix equation whose nontrivial solution gives the complex resonant frequency of the antenna. From the modeling, it is possible to obtain results for the resonant frequency, bandwidth and quality factor, as a function of several parameters of the antenna, for different configurations. We have considered annular ring microstrip antennas on a single dielectric layer, antennas with two anisotropic dielectric layers, and annular ring microstrip antennas on suspended substrates. Numerical results for the resonant frequency of the these structures printed on isotropic substrates are also presented and compared with those published by other authors, showing a good agreement