Anderson Orthogonality Research Articles

Line defects in quasi-one-dimensional systems: Orthogonality exponents and electron density.

Two effects of elastic scattering due to an impurity in a quasi-one-dimensional system are investigated with an exact calculation of the scattering matrix. For this we restricted our interest to line defects V(x,y)=\ensuremath{\delta}(x)v(y), where x is the propagation direction. First the Anderson orthogonality exponents ${\mathit{K}}_{+}$ for inserting a localized potential into an electron gas and K(a) for displacing the localized potential by a vector a are discussed for quasi-one-dimensional constrictions. By this the crossover from one to two dimensions in the large-distance behavior of K(a) is clarified. Also, the electron density around line defects for arbitrary transport current has been studied. All calculations are done within the noninteracting-Fermi-gas approximation.

Overlap Integral between the Ground States of an Electron Gas Corresponding to Two Positions of a Scattering Potential

The exponent K in the Anderson orthogonality theorem is calculated for a heavy particle having two sites, when the electron scattering on one site involves n partial waves. K is given in closed expressions for n=1...4. Small and large translations of the scattering center and the weak scattering are discussed at arbitrary n. The partial wave l cannot contribute by more than l+(1/2) to K

Overlap Integral between the Ground States of an Electron Gas Corresponding to Two Positions of a Scattering Potential

The exponent K in the Anderson orthogonality theorem is calculated for a heavy particle having two sites, when the electron scattering on one site involves n partial waves. K is given in closed expressions for n = 1 …4. Small and large translations of the scattering center and the weak scattering are discussed at arbitrary n. The partial wave l cannot contribute by more than l + (1/2) to K.

Many-electron singularity in aggregate X-ray line and photoelectron spectra

It is generally admitted that the many-electron effects govern the shape of the discrete X-ray line and photoemission spectra. This phenomenon has been studied in bulk metals (Mahan, Nozieres and de Dominicis model) where it is characterized by two effects: the Anderson orthogonality between the initial and final ground states and the $$|E|^{\alpha _H - 1} $$ spectrum behaviour, whereE is the emitted particle energy defect (with respect to the one-electron energy) and α H (with 0<α H <1) and exponent related to the phase shifts δ at the Fermi level due to the localised hole potential. We study these two effects in limited media (closed loop shape withN=10 to 30 atoms). We observe that, asN increases, the ground state overlap tends toward zero in a way which is surprisingly close to the Anderson $$N^{ - \alpha _H /2} $$ behaviour. TheE spectra are also obtained. They are very different from the bulk which will lead to asymmetry parameters smaller for aggregates than for the bulk. A discussion of the experimental results is presented.

Motion of a particle in a Fermi sea: One dimension.

We study the motion of a particle in a degenerate Fermi sea in one dimension by calculating numerically the one-particle spectral function as well as a number of two-particle response functions. The problem is formulated in terms of the eigenstates of the static case, in which the particle is localized at a particular site. In spite of the Anderson orthogonality catastrophe, accurate results for small systems (up to 100 sites and electrons) are obtained with relatively few basis states, i.e., 0 and 1 particle-hole pair excitations. The mobile particle in one dimension does not display ``quasiparticle'' behavior, and most response functions show power-law threshold behavior as in the case of a localized particle, in complete agreement with exact results. We discuss practical applications to optical spectra and to the dynamical mobility of optically generated holes in doped semiconductor quantum wires.

Orthogonality exponent and the friction coefficient of an electron gas.

The Anderson orthogonality exponent K for the overlap of two ground states of a free-electron gas with a local potential at different positions is discussed. In the small-distance limit, it is shown that for arbitrary local potentials K can be expressed in terms of the friction tensor. In the one-dimensional case, K depends on the potential only via the friction coefficient for arbitrary distance, and the exponent is bounded for arbitrary shape of the potential in contrast to the two- or higher-dimensional case. The exact result for K is presented for a short-range potential on a lattice.

Orthogonality Exponents in Low-Dimensional Metals

The Anderson orthogonality exponents K + for introducing a localized perturbation into an electron gas and K(a) for displacing the localized potential by a vector a are discussed for one- and two-dimensional systems. It is shown that the smoothness of the potential enters very differently in the exponents K + and K(a). The controversial point of the boundedness of the two exponents is clarified

Tunneling coherence and localization in a spin-boson system: A dynamic extension of the Anderson orthogonality theorem

We formulate a dynamic theory of the ground state of a spin-boson Hamiltonian. We show that the dynamic contribution from the coherently excited bosons completely compensates the infrared divergence due to the zero-point fluctuation of bosons. Our theory is a dynamic extension of the Anderson orthogonality theorem. We predict novel results of the continuous transition of the tunneling ground state to the localized one at a critical magnitude of the interaction strength.

Anderson Orthogonality Theorem: Overlap Integral between Two Ground States with Differnt Centers of Local Potential

Etude de l'integrale de recouvrement entre deux etats fondamentaux du systeme d'electrons libres possedant un potentiel local a chaque site different

New Formalism for an Overlap Integral of the Anderson Orthogonality Theorem

We propose a simple calculation method for an overlap integral between two ground states of the system with a local potential at each different site. Our formalism is applied to the overlap integral limited to I-wave scattering and the exact result is obtained. We also apply our formalism to the overlap integral for the system with 1- and {'-partial wave components of scattering. The overlap integral in this case is exactly obtained in a closed form as a function of the phase shifts of 1- and {'-waves. Our result covers that of Yamada, Sakurai, Miyazima and Hwang.

Golden-rule approach to the soft-x-ray-absorption problem

The cross section of the soft-x-ray absorption is derived based on the Fermi golden rule, by summing the transition probabilities over all possible final states. It is shown that the factor connected with the Anderson orthogonality catastrophe is canceled in the process of summation, and the spectrum is finally expressed by the core-hole propagator times the open-line propagator, as shown by Nozi\`eres and De Dominicis. Our results are compared with the results obtained by Mahan and collaborators and are shown to improve over theirs in several respects, expecially in the core-hole propagator. With the use of the new integral kernel, the integral equation for the threshold region is treated and the exact form of the edge anomaly, including the analytical form of the prefactor of the power-law spectrum of Nozi\`eres and De Dominicis, is obtained.

Orthogonality Catastrophe for a System of Interacting Electrons. III

The Anderson orthogonality theorem is derived for a general non· separable local potential. It is shown that the overlap integral is given for this general case by exp [ - 2(2~i)' Tr(!nS(It»'log N], where S(It) is the scattering S·matrix at the Fermi energy. This form of the overlap integral is also shown to hold for interacting conduction electrons if local potential V in the final state is replaced by the self· energy difference ;E*(It) due to the local potential.

Exactly soluble x-ray-edge model for nonadiabatic scattering from metal surfaces

One implication of the Anderson orthogonality theorem is that a particle cannot elastically scatter from a metallic surface with unit probability. A simple, but exactly soluble, model (within the usual bounds of x-ray edgeology) is presented which enables transparent and analytic calculation of the no-loss line intensity. Comparison between the dynamic properties of the scattering event and the static properties of the coupled substrate-particle system are made. Commentary on this result, in the light of other recent work, is offered.

Many-Body Contributions to the Auger Line Shapes of Free-Electron Metals

The core-valence-valence Auger line shapes of free-electron metals are evaluated with use of a change of mean-field model for the initial-state interactions. Significant many-body effects are (i) excitonic distortion of the initial-state orbitals, (ii) the Anderson orthogonality effect, (iii) replacement transitions, and (iv) shakeoff transitions. Comparison of the theory with Li data suggests that both many-body effects and band effects play major roles in determining Auger line shapes.

Ground state of the asymmetric Anderson Hamiltonian

General discussion on the ground state of the asymmetric Anderson model is given on the basis of the Anderson orthogonality theorem and the compensation theorem. With the use of a single approximate wave-function for the ground state, the field-dependences of d-electron number, ndσ, and resistivity, ϱ(H), are explicitly calculated showing negative magneto-resistance.

Edge Singularities in Spin-Dependent Final-State Interactions of X-Ray Photoelectron and Absorption Spectra

X-ray edge singularities in the spin-dependent final-state interactions have been calculated perturbationally in the most divergent term approximation for the photoelectron and absorption spectra of the narrow-band metals (and also the simple metals). For the ferromagnetic exchange couplings ( J > 0 ) of conduction electrons with the core-hole or the narrow-band electron spins S , the exchange interaction is found to make the two different contributions: (i) the Mahan threshold singularity is modified by a logarithmic factor ( 1 – 2 ρ J log |ω/ D |) n , and (ii) the Anderson orthogonality exponent is increased by ζ(ρ J ) 2 , where η and ζ depend on the spin S multiplicity, and ρ and D are the density of states and the cut-off width of the conduction band, respectively. A possibility is pointed out that the edge singularities may be suppressed at the absorption threshold of the transition metals.