Zur Theorie von Oberflächenzuständen an Festkörpern

Using the Green's function technique for the calculation of surface states of thin films derived in an earlier work¹, we examine in detail to what extent this method is valid in comparison to an exact calculation. As a model potential we limit ourself to a one dimensional array of δ-functions.     

Slave bosons in radial gauge: A bridge between path integral and Hamiltonian language

We establish a correspondence between the resummation of world lines and the diagonalization of the Hamiltonian for a strongly correlated electronic system. For this purpose, we analyze the functional integrals for the partition function and the correlation functions invoking a slave boson representation in the radial gauge. We show in the spinless case that the Green's function of the physical electron and the projected Green's function of the pseudofermion coincide. Correlation and Green's functions in the spinful case involve a complex entanglement of the world lines which, however, can be obtained through a strikingly simple extension of the spinless scheme. As a toy model we investigate the two-site cluster of the single impurity Anderson model which yields analytical results. All expectation values and dynamical correlation functions are obtained from the exact calculation of the relevant functional integrals. The hole density, the hole auto-correlation function and the Green's function are computed, and a comparison between spinless and spin 1/2 systems provides insight into the role of the radial slave boson field. In particular, the exact expectation value of the radial slave boson field is finite in both cases, and it is not related to a Bose condensate.     

Perturbation theory for QED bound states

A new method is presented for deriving a systematic perturbative expansion for QED bound states, which does not rely upon solving any new or old equation. The starting point is a given nonperturbative zeroth order Green's function, obtained by a suitable “relativistic dressing” of the nonrelativistic Green's function for the Schrödinger equation with Coulomb potential, which embodies the Coulombic bound states and is known. The comparison with the complete Green's function as given by standard perturbative QED gives a perturbative kernel which is then used for the expansion of the QED Green's function in terms of the given non-perturbative zeroth order Green's function.     

Influence of Majorana Bound States in Quantum Rings

A quantum ring coupled to a 1D topological superconductor hosting Majorana bound states (MBSs) is investigated. The MBSs effects over the spectrum and persistent current along the quantum ring are studied. The spectra of the system are obtained by an exact numerical diagonalization of the Bogoliubov-de Gennes Hamiltonian in the Majorana representation. In addition, Green's function formalism is implemented for analytical calculations and obtained a switching condition in the MBSs fermionic parity. Three different patterns that could be obtained for the spatial separation of the MBSs, named: bowtie, diamond, and asymmetric, are reported here, which are present only in odd parity in the quantum ring, while only a single pattern (bowtie) is obtained for even parity. Those patterns are subject strictly to the switching condition for the MBSs. Besides, quantum ring with the presence of a Majorana zero mode presents gapped/gapless spectra in odd/even parity showing in the even case a subtle signature in the persistent current.     

Single fermion Green's function in the quantum ordered Fermi-system: Analytic solution

An exact self-consistent solution for a finite temperature quantum-ordered state of correlated electron system found previously (8 and 1) is used to derive the fermionic single-particle Green's function. The quantum order parameter (QOP) found in the form of a periodic (elliptic Jacoby) function of the Matsubara's imaginary time (Mukhin, 2009), plays the role of effective scattering potential seen by electrons. The analytic solution for the Green's function demonstrates the following new features: (1) the pseudo-gap behavior of the single-electron density of states (DOS) near the (shifted) Fermi-level;(2) the side-bands of decreasing intensity away from the Fermi-level; (3) scaling of the quasi-particle energies with the QOP amplitude; (4) fermionic quasi-particles in the QOP state are combined from two confined “odd” and “even” fermions that separately would be unstable. The false-color plot of single-fermion DOS in the limit of a periodic kink-like Matsubara time-dependence of QOP is presented and could be used as prediction for the ARPES experiments. The plot of the DOS transfer between different energies at the “fermi-surface” momentum for a given kink-like QOP is also presented. Some possibly observable consequences of the found finger-prints are discussed.     

Impurity binding energies in quantum dots with parabolic confinement

We present an effective numerical procedure to calculate the binding energies and wave functions of the hydrogen-like impurity states in a quantum dot (QD) with parabolic confinement. The unknown wave function was expressed as an expansion over one-dimensional harmonic oscillator states, which describes the electron's movement along the defined z-axis. Green's function technique used to obtain the solution of Schredinger equation for electronic states in a transverse plane. Binding energy of impurity states is defined as poles of the wave function. The dependences of the binding energy on the position of an impurity, the size of the QD and the magnetic field strength are presented and discussed.     

Quantum Theory of Solid State Plasma Dielectric Response

We review the quantum mechanical derivation of the random phase approximation (RPA) for solid state plasmas, starting from the Hamilton equations for canonically paired “second quantized” creation and annhilation field operators of interacting quantum many‐body systems. Discussing variational differentiation, the coupled equations of motion for the quantum field operators are derived. The concept of Green's functions is reviewed and interpreted, first for retarded Green's functions, and their equations of motion are developed from the equations of motion for the field operators. Thermodynamic Green's functions are discussed, and their periodicity/antiperiodicity properties in imaginary time are carefully examined with discussion of Matsubara Fourier series and representation in terms of a spectral weight function. The analytic continuation from imaginary time to real time is treated. Finally, we define nonequilibrium Green's functions and discuss the linearized timedependent Hartree approximation leading to the random phase approximation. An interesting application to the case of Graphene in a perpendicular magnetic field is discussed in detail, along with applications to normal systems, in terms of attendant phenomenology involving electron‐hole pair excitations and plasmons (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Density of states in a cylindrical GaAs/AlxGa1−xAs quantum well wire under tilted laser field

Within the effective-mass approximation the subband electronic levels and density of states in a semiconductor quantum well wire under tilted laser field are investigated. The energies and wave functions are obtained using a finite element method, which accurately takes into account the laser-dressed confinement potential. The density of states obtained in a Green's function formalism is uniformly blueshifted under the laser's axial field whereas the transverse component induces an additional non-uniform increase of the subband levels. Our results confirm that the tilted laser field destroys the cylindrical symmetry of the quantum confinement potential and breaks down the electronic states' degeneracy. Axial and transversal effects of the non-resonant laser field on the density of states compete, bringing the attention to a supplementary degree of freedom for controlling the optoelectronic properties: the angle between the polarization direction of the laser and the quantum well wire axis.     

Numerical evaluation of the one-loop effective action in static backgrounds with spherical symmetry

The problem of evaluating the one-loop quantum corrections to the energy of classical solution is ubiquitous in elementary particle physics. In many cases already the classical solution is known only numerically so that methods based on exact wave functions for the quantum excitations cannot be applied. We propose here a numerical method based on the use of Euclidean Green's functions which allows to extract the finite parts after Lorentz covariant regularization and renormalization.     

Harmonic Green's functions for flexural waves in semi-infinite plates with arbitrary boundary conditions and high-frequency approximation for convex polygonal plates

This paper provides a method for obtaining the harmonic Green's function for flexural waves in semi-infinite plates with arbitrary boundary conditions and a high frequency approximation of the Green's function in the case of convex polygonal plates, by using a generalised image source method. The classical image source method consists in describing the response of a point-driven polygonal plate as a superposition of contributions from the original source and virtual sources located outside of the plate, which represent successive reflections on the boundaries. The proposed approach extends the image source method to plates including boundaries that induce coupling between propagating and evanescent components of the field and on which reflection depends on the angle of incidence. This is achieved by writing the original source as a Fourier transform representing a continuous sum of propagating and evanescent plane waves incident on the boundaries. Thus, the image source contributions arise as continuous sums of reflected plane waves. For semi-infinite plates, the exact Green's function is obtained for an arbitrary set of boundary conditions. For polygonal plates, a high-frequency approximation of the Green's function is obtained by neglecting evanescent waves for the second and subsequent reflections on the edges. The method is compared to exact and finite element solutions and evaluated in terms of its frequency range of applicability.     

Green's function and scattering matrix in a discrete oscillator basis

Convenient analytic finite-dimensional approximations for basic operators of scattering theory-specifically, the Green's function and the off-shell T matrix—are constructed in an oscillator basis for real-and complex-valued local and nonlocal interaction potentials. It is shown that the approximate operators converge smoothly to their exact counterparts as the dimensions of the oscillator basis are increased step by step. The simple and rather accurate formulas obtained in this study can be widely used in various applications of quantum scattering theory.     

A boundary integral method to compute Green's functions for the radiative transport equation

The Green's function for the time-independent radiative transport equation in the whole space can be computed as an expansion in plane wave solutions. Plane wave solutions are a general class of solutions for the radiative transport equation. Because plane wave solutions are not known analytically in general, we calculate them numerically using the discrete ordinate method. We use the whole space Green's function to derive boundary integral equations. Through the solution of the boundary integral equations, we compute the Green's function for bounded domains. In particular we compute the Green's function for the half space, the slab, and the two-layered half space. The boundary conditions used here are in their most general form. Hence, this theory can be applied to boundaries with any kind of reflection and transmission law.     

T型双量子点分子Aharonov-Bohm干涉仪的电输运

利用非平衡格林函数方法, 理论研究T型双量子点分子Aharonov-Bohm (A-B)干涉仪的电荷及其自旋输运性质. 通过控制T型双量子点分子内量子点间有无耦合, 能够实现在同一电子能级位置处分别出现共振和反共振状态, 根据此性质, 能将体系设计成量子开关器件. 当将两个完全相同的T型双量子点分子分别嵌入A-B干涉仪两臂中时, 磁通取适当数值, 能够出现完全的量子相消干涉. 通过调节量子点能级、左右两电极间的偏压和Rashba自旋轨道相互作用强度, 可对体系自旋流进行调控. 关键词： 非平衡格林函数 T型双量子点分子 Aharonov-Bohm干涉仪 自旋输运     

Infrared problem in QED and electric charge renormalization

The electric charge renormalization in quantum electrodynamics is discussed, by taking into account the fact that an “infrared dressing transformation” is needed to go from the local states occurring in the Green's functions, to the (physical) charged states which obey Gauss' law. Apparent difficulties discussed in the literature are resolved. The construction of physical multicharged states is discussed explicitly.     

Equivalence betweenS-matrix and Green's function approach to the kondo problem

We prove the complete equivalence of Suhl'sS-matrix approach and Nagaoka's Green's functions approach to the Kondo problem. This proof is established quite generally for any density of states function of the electrons. In particular we solve Suhl's equations and show that Nagaoka's equations as well as their solutions can be derived from Suhl's approach. Vice versa it is shown that the solutions of the Nagaoka equations satisfy Suhl's equations uniquely.     

Exact function of the equations of quantum mechanics in an electromagnetic field. II

The zero term of the quasiclassical asymptotic (?→ 0) of the Klein-Gordon-Fock equation as symmetrized by Feynman (V. V. Belov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 11, 45 (1975)), giving the exact Green's function of the Cauchy problem in arbitrary (nonparallel) steady homogeneous electric and magnetic fields, is constructed. The exact Green's function for the Dirae equation in an arbitrary, steady electromagnetic field and for the Pauli equation (semirelativistic Schrödinger equation) in the nonsteady-state case is constructed in an analogous manner.     

Theory of the excitonic lineshape in low-dimensional structures with rough interfaces

A quantum mechanical theory of single-particle motion under the influence of a stochastic potential is presented. By solving the Dyson equation, the one-particle Green's function can be determined approximately. Assuming a Gaussian distribution, an explicit expression is derived for the spectral function. The analytical results are in good agreement with numerically calculated data. The theory is applied to excitons on rough interfaces. The optical absorption of excitons on rough surfaces can be traced back to the one-particle Green's function for the center-of-mass motion. In contrast to the classical treatment, the asymmetry of the lines and the redshift of the maxima can be explained. The coefficients for linewidth and asymmetry can be expressed in terms of the excitonic wavefunction and the binary correlation function of the stochastic potential.PACS: 61.43.Bn; 71.35 + z; 73.20.Dx; 78.66.Fd.     

Field of a point source in a semi-infinite elastic medium

An exact solution for the tensor Green's function of a harmonic field for a semi-infinite elastic medium is presented in an easy-to-use form in the theory of wave scattering. The solution is derived in the form of a sum of the Green's functions for an infinite medium and the term satisfying the homogeneous wave equation for a semi-infinite elastic medium. The results reproduce the known far-field asymptotics containing longitudinal, transversal and surface Rayleigh-type wave modes. The near-field asymptotic is essentially different for the regions far and near the boundary.     

Transition from the Kondo effect to a Coulomb blockade in an electron shuttle

We investigate the effect of the mechanical motion of a quantum dot on the transport properties of a quantum dot shuttle.Employing the equation of motion method for the nonequilibrium Green’s function,we show that the oscillation of the dot,i.e.,the time-dependent coupling between the dot’s electron and the reservoirs,can destroy the Kondo effect.With the increase in the oscillation frequency of the dot,the density of states of the quantum dot shuttle changes from the Kondo-like to a Coulomb-blockade pattern.Increasing the coupling between the dot and the electrodes may partly recover the Kondo peak in the spectrum of the density of states.Understanding of the effect of mechanical motion on the transport properties of an electron shuttle is important for the future application of nanoelectromechanical devices.