Discrete and selective absorption in crystalline molecular nanofilms

Recent research in nano-optical engineering and in nanomedicine as well, seeks for methods of construction of various types of nano-markers, nano-carriers, and ways to deliver drugs to the exactly determined regions of body. In this process it is important to find methods of recognition of certain types of molecules. It is obvious that optical recognition would be the easiest and the most effective way to do it. Our research presents a model of a molecular ultrathin crystalline film and generated exciton system inside it and corresponding methodology of analysis of their optical characteristics. Properties of these spatially very restricted structures are very sensitive to their surrounding surfaces. Using the two-time Green’s functions adapted for crystalline structures with symmetry breaking, and graphical-numerical software, we have calculated the energy spectra and possible exciton states. We have shown that the appearance and the presence of localized states on the surfaces and in the boundary layers of the film depend on the thickness of the film and the film surroundings, presented through the perturbation of parameters on surfaces. Optical properties in these structures demonstrate discrete and very selective resonant absorption spectra, depending on the perturbation on their surfaces.     

Field-theoretic approach to the properties of the solid state

The techniques of quantum field theory are used to investigate the thermodynamic ion displacement correlation function—or Green's function of the phonon field—in a crystal and especially in a metal. The structure of thermodynamic Green's functions is outlined and the method for solving for them at finite temperature is fully discussed.The analytic structure of the phonon Green's function is then considered. This function is shown to be bounded and invertible everywhere off the real axis; a spectral form is derived for its inverse. The symmetries imposed by the point group of the crystal are then discussed.Assuming small ionic oscillations, we find the inverse of the phonon Green's function as a linear function of the electronic contribution to the dielectric response function of the metal. This dielectric function is shown to be simply related to the longitudinal part of the conductivity tensor that gives the response of the electrons to the effective electric field in the metal. The assumption of translational invariance then leads to an explicit expression for the phonon Green's function in terms of this conductivity.The deformations in the lattice induced by an arbitrarily time varying external force are calculated in terms of the retarded phonon Green's function. In the static long wavelength limit the phonon Green's function yields the macroscopic elastic constants of the crystal. Their relation to the conductivity is exhibited, and several elastic constants are estimated. We also see that the complete phonon spectrum and the lifetimes of the phonon states may be calculated from this Green's function. A relation between the long wavelength acoustic attenuation in metals and the de conductivity is derived, which is in good agreement with recent experiments. Furthermore, the ions in a metal are shown to have a high-frequency oscillation along with the electrons, at essentially the electron plasma frequency.     

Anomalous wave interference at Z3-exciton resonance of CuCl

The transmission and the reflection spectra of a thin CuCl single crystal of 0.15μ thickness have been measured in the Z₃-exciton resonance region at 1.6K by using a weak dye-laser light as a light source. Well resolved interference fringes have been obtained over the exciton resonance. In the higher energy region than the longitudinal exciton's energy, the separation of adjacent fringes cannot be explained by interference of the lower branch polariton waves (LBP) or the upper branch polariton waves (UBP). These structures have been explained by the mutual interference effect between the UBP and LBP waves, anomalous waves. This has been confirmed by the measurements of two-photon absorption due to the excitonic molecule via respective polariton states.     

Generating functional approach to the Green's functions diagrammatic technique for spin and pseudospin lattice systems: I. General theory

The theory of the irreducible many-point Green's functions, describing spin and pseudospin lattice systems, is formulated with the help of the generating functional approach. The diagrammatic technique for the generating functional is also developed. Special attention is paid to the construction and summation of the diagrammatic series for the one- and two-point Green's functions. Closed formulae for the one-point Green's function and the generalized Vaks-Larkin- Pikin equation are obtained. The $\text{1}\text{z}$ expansion scheme near the critical temperature of the order-disorder phase transition, is discussed, where z denotes the effective number of nearest- neighbours for a given site in a crystal lattice.     

Comparison of the molecular cluster model with the phonon model for Jahn—Teller active impurities in crystals

For comparing the molecular cluster model with the phonon model in describing the Jahn-Teller interaction for magnetic impurities in crystals, the Jahn-Teller energy and the Ham reduction factors are expressed in terms of the phonon Green's function of the host crystal for an orbital triplet coupled to E_g modes of vibrations. Numerical results for the case of MgO lattice have been obtained using the phonon Green's function derived from the breathing shell model.     

Optical bistability of a layered semiconductor in the exciton absorption region

The effect of specific features of the exciton and phonon spectra of layered semiconductors on the conditions of realization of optical bistability in the exciton absorption region has been theoretically investigated by the Green’s function method. By the example of the 2H polytype of PbI₂, it is shown that effective exciton scattering from low-energy bending-wave vibrations leads to a blue shift of the frequency range of bistability realization and its narrowing; expansion of the temperature range of bistability observation; and a shift of the hysteresis loop to higher intensities, accompanied by a decrease in its height and width. The possibility of observing polarization optical bistability, which is related to the dependence of the exciton energy spectrum on the propagation direction of a light wave in a crystal, is also substantiated.     

Theory of interacting bosons without anomalous propagators

A self-consistent theory of an interacting many-boson system is presented in the framework of the formalism of thermodynamic Green's functions without introducing anomalous propagators referring to the concept of a restricted average or any other symmetry-breaking assumption. Depending on the interaction, the theory comprises both phenomena of Bose-Einstein condensation and of boson pairing without a macroscopic occupation of the zero-momentum single-particle state. The results are discussed with reference to the problem of Bose-Einstein condensation of ⁴He II and to the phenomenon of exciton condensation and exciton pairing in highly excited semiconductors.     

The effective-mass nature of deep-level point-defect states in semiconductors

The basic premise of Effective-Mass Theory (EMT) is that bound-state wavefunctions are constructible from Bloch functions in a small region or regions of k space. In contrast, deep-level wavefunctions are believed to involve Bloch functions from the entire Brillouin zone and several bands. In this paper we analyse the wavefunction of the deep vacancy level in Si obtained recently by self-consistent Green's-function calculations. We find that this wavefunction has a strong EMT character in that it is composed primarily of Bloch functions from the nearest bands and the corresponding coefficients, i.e. the envelope functions, are peaked about the band extrema. As a further check, we have used a spherical average of the self-consistent vacancy potential in the acceptor EMT equations. The resulting energy level is at E_v+0.9 eV, as compared with the Green's-function-theoretic value of E_v+0.8 eV. The resulting wavefunction, on the other hand, does not have the correct form. A check of the correction terms left out by the standard EMT equations reveals that their contributions to the energy level are large and tend to cancel one another.     

Application of the Green's function method to lattice vibrations in thin films

The Green's function method is used to investigate the lattice vibrations in a simple cubic thin film with nearest neighbour interactions. Appropriate Green's functions for the study of the surface waves for (001) and (011) orientations of the surface are determined. For a thin film with two parallel (001) free surfaces the atomic force tensors at the surface are modified in order to satisfy the rotational invariance condition. The surface waves are determined and a detailed discussion is made for the long wave-length limit k_y = 0 and k_x ? 1. For a given k_x there is a critical thickness below which only an antisymmetrical solution can exist. For the (011) orientation only the case of a single free surface is discussed.     

Higher order field equations II; Limit properties of green's functions

In a previous paper wave propagation was studied according to a sixth-order partial differential equation involving a complex mass M. The corresponding Yang-Feldman integral equations (indicated as SM-YF-equations), were formulated using modified Green's functions G^M_R(x) and G^M_A(x), which then incorporate the partial differential equation together with certain boundary conditions. In this paper certain limit properties of these modified Green's functions are derived: (a) It is shown that for |M| → ∞ the Green's functions G^M_R(x) and G^M_A(x) approach the Green's functions Δ_R(x) and Δ_A(x) of the corresponding KG-equation (Klein-Gordon equation). (b) It is further shown that the asymptotic behaviour of G^M_A(x) and G^M_A(x) is the same as of Δ_R(x) and Δ_A(x) - and also the same as for D_R(x) and D_A(x) for t→ ± ∞, where D_R and D_A are the Green n's functions for the KG-equation with mass zero. It is essential to take limits in the sense of distribution theory in both cases (a) and (b). The property (b) indicates that the wave propagation properties of the SM-YF-equations, the KG-equation with finite mass and the KG-equation with mass zero are closely related in an asymptotic sense.     

Theoretical study of acoustic waves supported by a film-substrate interface

By using the Green's function method, we study the dispersion of acoustic waves guided by an anisotropic film-substrate interface when the film thickness changes.     

Calculation of two-time-correlation functions in Liouville space

Starting from the Liouville equation of motion for the density operator, a method analogous to Green's function techniques is developed for the calculation of two-time-correlation functions. The method is applied to the calculation of the optical absorption line shape of excitons in molecular crystals.     

Camel's back excitons in GaP

The influence of the recently proposed camel's back structure of the GaP conduction band edge on the exciton spectrum is investigated theoretically. The results are in good agreement with differential absorption data and strongly support a camel's back structure, with a 4 meV central hump. The computed exciton binding energy is 18.5 meV, and when combined with recent experimental data, indicates a binding of about 32 meV for the electron-hole liquid.     

Derivation and application of the reciprocity relations for radiative transfer with internal illumination

A Green's function formulation is used to derive basic reciprocity relations for planar radiative transfer in a general medium with internal illumination. Reciprocity (or functional symmetry) allows an explicit and generalized development of the equivalence between source and probability functions. Assuming similar symmetry in three-dimensional space, a general relationship is derived between planar-source intensity and point-source total directional energy. These quantities are expressed in terms of standard (universal) functions associated with the planar medium, while all results are derived from the differential equation of radiative transfer.     

Path Integral Solution for the Coulomb Potential in a Curved Space of Constant Positive Curvature

A new path integral treatment of a hydrogen-like atom in a uniformly curved space with a constant positive curvature is presented. By converting the radial path integral into a path integral for the modified Pöschl-Teller potential with the help of the space-time transformation technique, the radial Green’s function is expressed in closed form, from which the energy spectrum and the corresponding normalized wave functions of the bound states are extracted. In the limit of vanishing curvature, the Green’s function, the energy spectra and the correctly normalized wave functions of bound and scattering states for a standard hydrogen-like atom are found.     

Green's functions for gravitational multi-instantons

The Green's functions for scalar fields propagating on the self-dual gravitational multi-instantons and multi-Taub-NUT metrics are given explicitly in closed form. The special cases for flat space, Taub-NUT and the Eguchi-Hanson instanton are listed. A construction is described for obtaining the Green's functions for fields of arbitrary spin.     

A green's function analysis of atomic and molecular (e, 2e) reactions

Investigation of Atomic and molecular (e, 2e) spectra will be discussed in terms of a Green's function approach. The energy, intensity and momentum distribution of energy levels observed by electron coincidence ionization spectroscopy, are directly related to the poles, pole strengths and generalized overlap amplitude of the one particle propagator or Green's function. The theoretical calculation of these observable quantities via the Green's function technique will be discussed. In particular, the position and intensity of satellite (or “shakeup”) lines, relative to the main lines, will be analysed in some detail.     

The intrinsical character of the electronic correlation in an electron gas

By introducing the phase transformation of electron operators, we map the equation of motion of an one-particle Green's function into that of a non-interacting one-particle Green's function where the electrons are moving in a time-depending scalar potential and pure gauge fields for a D-dimensional electron gas, and we demonstrate that the electronic correlation strength strongly depends upon the excitation energy spectrum and collective excitation modes of electrons. It naturally explains that the electronic correlation strength is strong in the one dimension, while it is weak in the three dimensions.     

Elastic distortion of a conducting surface in the vicinity of a point charge

The elastic distortion of a conducting surface when a point charge is brought near the suface is investigated theoretically. The displacement field is calculated with the aid of a Green's function in terms of known functions. General results for surface and bulk displacements are displayed graphically. Numerical results for tungsten and aluminum are presented. Modifications of the image potential due to the distortion are discussed.     

A comment on functional integrals and many-body systems

Green's functions for systems of non-interacting particles at T=0 are obtained through ab initio calculations using functional integral algorithms. It is shown in detail how the correct Green's functions are computed and how one recovers the structure of the ground state (which in the usual derivations is the starting point).