In the present work we study transmission of electron through vibrat- ing molecular junction interacting with leads using a method of nonequilibrium Green functions. Our Green functions use combination of first quantization to treat vibrational levels and second quantization to treat electron processes. We treat the change of vibrational potential of junction induced by charging of junc- tion, we find a spectral function and a magnitude of current through the junction. We confirm the effect of Fermi sea and Frack-Condon factors on sharpening of peaks. We study these processes on model motivated by biphenyl molecule, in- troducing double well potential and study an effect of quasidegenerate energy levels. We present the shift of peaks, resulting from an increase of moment of inertia, to positions determined by Franck-Condon factors.

No description available.

Relations between propagators and Green functions of Hamiltonians which are SUSY partners have been obtained. New exact propagators for the family of multi-well, time-dependent and non-hermitian potentials have been calculated. Non-conservative SUSY transformation has been studied in the case of multichannel Schrodinger equation with different thresholds. Spectrum (bound/virtual states and resonances) of the non-conservative SUSY partner of zero potential has been founded. Exactly solvable model of the magnetic induced Feshbach resonance has been constructed. This model was tested in the case of Rb$^{85}$. Conservative SUSY transformations of the first and the second order have been studied in the case of multichannel Schrodinger equation with equal thresholds. Transformations which introduce non-trivial coupling between scattering channels have been founded. The first order SUSY transformation which preserves $S$-matrix eigen-phase shifts and modifies mixing parameter has been founded in the case of two channel scattering with partial waves of different parities. In the case of coinciding parities we have found the second order SUSY transformation which preserves $S$-matrix eigen-phase shifts and modifies mixing parameter. Phenomenological two channel $^3S_1-^3D_1$ neutron-proton potential has been obtained by using single channel, phase equivalent and coupling SUSY transformations applied to zero potential.

In this work, the Dyson's equation formalism is outlined and applied toseveral open quantum systems. These systems are composed of a core,quantum-mechanical set of discrete states and several continua, representing macroscopic systems. The macroscopic systems introducedecoherence, as well as allowing the total particlenumber in the system to change.Dyson's equation, an expansion in terms of proper self-energy terms, isderived. The hybridization of two quantum levelsis reproduced in this formalism, and it is shown that decoherence followsnaturally when one of the levels is replaced by a continuum.The work considers three physical systems in detail. The first,quantum dots coupled in series with two leads, is presented in a realistic two-level model. Dyson's equation is used to account for the leads exactly to all ordersin perturbation theory, and the time dynamics of a single electron in the dotsis calculated. It is shown that decoherence from the leads damps the coherentRabi oscillations of the electron. Several regimes of physical interest areconsidered, and it is shown that the difference in couplings of the two leadsplays a central role in the decoherence processes.The second system relates to the decay-out ofsuperdeformed nuclei. In this case, decoherence is provided by coupling to theelectromagnetic field. Two, three, and infinite-level models are consideredwithin the discrete system. It is shown that the two-level model is usuallysufficient to describe decay-out for the classic regions of nuclearsuperdeformation. Furthermore, a statistical model for the normal-deformedstates allows extraction of parameters of interest to nuclear structure fromthe two-level model. An explanation for the universality of decayprofiles is also given in that model.The final system is a proposed small molecular transistor. TheQuantum Interference Effect Transistor is based on a single monocyclic aromatic annulene molecule, with twoleads arranged in the meta configuration. This device is shown to be completely opaque to charge carriers, due to destructive interference. Thiscoherence effect can be tunably broken by introducing new paths with a real orimaginary self-energy, and an excellentmolecular transistor is the result.

I consider Dirichlet eigenvalues for an elliptic system in a region that consists of two domains joined by a thin tube. Under quite general conditions, I am able to give a rate on the convergence of the eigenvalues as the tube shrinks away. I make no assumption on the smoothness of the coefficients and only mild assumptions on the boundary of the domain. Also, I consider the Green function associated with the mixed problem on a Lipschitz domain with a general decomposition of the boundary. I show that the Green function is Hölder continuous, which shows how a solution to the mixed problem behaves.

In this thesis, anisotropic Heisenberg magnets with arbitrary spin are investigated within the second-order Green-function theory. Three models are considered. First, the second-order Green-fuction theory for one-dimensional and two-dimensional Heisenberg ferromagnets with arbitrary spin S in a magnetic field is developed. For the determination of the introduced vertex parameters sum rules, higher-derivative sum rules, and regularity conditions are derived, and the equality of the isothermal and the longitudinal uniform static Kubo susceptibilities is required. Thermodynamic quantities, such as the specific heat, magnetic susceptibility, transverse and longitudinal correlation lengths are calculated. Empirical formulas describing the dependence of the position and height of the susceptibility maximum on the magnetic field are given. An anomal behavior of the longitudinal correlation length is observed. The appearance of two maxima in the temperature dependence of the specific heat is discussed. Further, as an example of a system with an anisotropy in the spin space, the S=1 ferromagnetic chain with easy-axis single-ion anisotropy is studied. Justified by the up-down symmetry of the model with respect to $S_i^z -> -S_i^z$, $\\langle S_i^z \\rangle=0$ is set. Two different ways of the determination of the introduced vertex parameters are presented. The transverse nearest-neighbor correlation function, spin-wave spectrum and longitudinal correlation length are analyzed. The effects of the single-ion anisotropy on the transverse and longitudinal uniform static susceptibilities as well as on the appearance of two maxima in the temperature dependence of the specific heat are examined. Finally, as examples of spatial anisotropic spin systems,layered Heisenberg ferromagnets and antiferromagnets with arbitrary spin are studied within the rotation-invariant Green-function theory. The long-range order is described by the condensation term, which is determined from the requirement that in the ordered state the static susceptibility has to diverge at the ordering wave vector. For determination of the introduced vertex parameters, the sum rule and the isotropy condition are used and also assumptions regarding the temperature dependence of some parameters are made. The main focus is put on the calculation of the specific heat, the Curie temperature, and the Néel temperature in dependence on the interlayer coupling and the spin-quantum number. Empirical formulas describing the dependence of the transition temperatures on the ratio of interlayer and intralayer couplings are given. For all three models, the results of the Green-function theory are compared to available results of exact approaches (Quantum Monte Carlo, exact diagonalization, Bethe-ansatz method) and to available experimental data.

Low-energy electron scattering was used as a tool to study electron-stimulated processes at complex interfaces. The electron diffraction in each complex interface is theoretically treated by a multiple scattering formalism for quantitative analysis. Mathematical descriptions of electron-stimulated processes and a multiple scattering expansion extended from the single-scattering case are presented. This analysis method was applied in three research topics: These are 1) electron-stimulated desorption of Cl+ from Si surfaces, 2) characterization of epitaxial graphene on Si-terminated SiC(0001), and 3) low-energy electron induced DNA damage. Zone-specific desorption of Cl+ from Si(111)- 7X7:Cl surfaces was demonstrated. Graphene epitaxially grown on SiC(0001) surfaces was analyzed using Auger electron diffraction and Raman scattering spectroscopy. Finally, the roles of interfacial water and dissociative electron attachment resonances in low-energy electron-induced DNA damage were revealed. Electron scattering calculations using the "path approach" were applied in all of the above mentioned studies. The combination of theory and experiment has lead to insight regarding electron scattering with complex targets.

Made available in DSpace on 2014-10-09T12:31:37Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T14:00:43Z (GMT). No. of bitstreams: 1 12885.pdf: 941021 bytes, checksum: 89af8f7af86b94c2e39f9dcd1cdcfa0b (MD5) / Dissertacao (Mestrado) / IEA/D / Escola Politecnica, Universidade de Sao Paulo - POLI/USP

Made available in DSpace on 2014-10-09T12:31:37Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T14:00:43Z (GMT). No. of bitstreams: 1 12885.pdf: 941021 bytes, checksum: 89af8f7af86b94c2e39f9dcd1cdcfa0b (MD5) / Dissertacao (Mestrado) / IEA/D / Escola Politecnica, Universidade de Sao Paulo - POLI/USP

New quantitative methods are developed for analyser-based phase contrast imaging (ABI) with hard X-rays. In the first instance we show that quantitative ABI may be implemented using an extended incoherent source. Next, we outline how complex Green’s functions may be reconstructed from phase contrast images and we apply this method to reconstruct the thick perfect crystal Green’s function associated with an ABI imaging system. The use of quantitative ABI with incoherent X-ray sources is not widespread and the first set of results pertains to the feasibility of quantitative ABI imaging and phase retrieval using a rotating anode X-ray source. The necessary conditions for observation of ABI phase contrast are deduced from elementary coherence considerations and numerical simulations. We then focus on the problem of extracting quantitative information from ABI images recorded using an extended incoherent X-ray source. The results of an experiment performed at Friedrich-Schiller University, Germany using a rotating anode X-ray source demonstrate the validity of our approach. It is shown that quantitative information may be extracted from such images under quite general and practicable conditions. We then develop a new use for phase contrast imaging systems that allows the Green’s function associated with a linear shift-invariant imaging system to be deduced from two phase contrast images of a known weak object. This new approach is applied to X-ray crystallography where the development of efficient methods of inferring the phase of rocking curves is an important open problem. We show how the complex Green’s function describing Bragg reflection of a coherent scalar X-ray wavefield from a crystal may be recovered from a single image over a wide range of reciprocal space simultaneously. The solution we derive is fast, non-iterative and deterministic. When applied to crystalline structures for which the kinematic scattering approximation is valid, such as thin crystalline films, our technique is shown to solve the famous one-dimensional phase retrieval problem which allows us to directly invert the Green’s function to retrieve the depth-dependent interplanar spacing. Finally we implement our Green’s function retrieval method on experimental data collected at the SPring-8 synchrotron in Hyogo, Japan. In the experiment we recorded analyser-based phase contrast images of a known weak object using a thick perfect silicon analyser crystal. It is then demonstrated that these measurements can be inverted to recover the complex Green’s function associated with the analyser crystal Bragg peak. The reconstructed Green’s function is found to be in good agreement with the prediction of dynamical diffraction theory.