Progress of Theoretical Physics

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

Károly Vladár

Published Jul 1, 1993• 4 citations

Abstract

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.

DOI: 10.1143/ptp.90.43

Related papers

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

T. Kitamura, Akihide Oguchi, Kei Yosida

The overlap integral between two ground states of the conduction electron system with a local potential at each different site is studied. The overlap integral is obtained for the system with 3 nonzero partial wave components of scattering, and this result is extended to the general case with n nonzero phase shifts. It is shown that the calculation of the exponent of the overlap integral can be reduced to solving an eigenvalue problem.

Progress of Theoretical PhysicsSep 1, 19873 citations

New Formalism for an Overlap Integral of the Anderson Orthogonality Theorem

Akihide Oguchi, Kei Yosida

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 l-wave scattering and the exact result is obtained. We also apply our formalism to the overlap integral for the system with l- and l’-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 l- and l’-waves. Our result covers that of Yamada, Sakurai, Miyazima and Hwang.

Progress of Theoretical PhysicsMay 1, 19867 citations

Orthogonality exponent and the friction coefficient of an electron gas

Kurt Schönhammer

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.

Physical review. B, Condensed matterMay 1, 199111 citations

Orthogonality Catastrophe Due to Local Electron Interaction

K. Yamada, Kei Yosida

The overlap integral between two ground state wave functions of the conduction electron system with different local situations is discussed for a general case in which local electron interaction exists in addition to a local impurity potential. The Anderson theorem which states that the overlap integral is expressed by exp[-δ/π×logN] is proved in this general case.

Progress of Theoretical PhysicsApr 1, 197821 citations

Orthogonality Catastrophe for a System of Interacting Electrons

Kei Yamada, Kei Yosida

The Anderson theorem concerning the overlap integral between two ground-state wave-functions of the electron system with different local potentials is discussed from a general point of view. It is shown that this theorem generally holds in the case where the initial Hamiltonian also includes electron interactions.

Progress of Theoretical PhysicsAug 1, 197814 citations

Orthogonality Catastrophe for a System of Interacting Electrons. III

K. Yamada, Kei Yosida

Journal of the Physical Society of Japan 65 (1996) pp. 2910–2916 An Estimate of the Asymmetry of Ag 3d XPS Lines Takashi Ikeda Progress of Theoretical Physics Vol. 70 No. 1 (1983) pp. 73–84 Application of the Orthogonality Theorem to the Motion of a Charged Particle in Metals Kosaku Yamada, Akio Sakurai and Motomu Takeshige Progress of Theoretical Physics Vol. 72 No. 2 (1984) pp. 195–201 Diffusion of Positive Muon and Orthogonality Theorem Kosaku Yamada Progress of Theoretical Physics Vol. 73 No. 6 (1985) pp. 1342–1351 A Closed Form Solution for the Hopping Rate of Charged Particles in Metals Kosaku Yamada, Akio Sakurai and Sasuke Miyazima Progress of Theoretical Physics Vol. 75 No. 5 (1986) pp. 1030–1043 Application of the Orthogonality Theorem to the Motion of a Charged Particle in Metals. II Kosaku Yamada, Akio Sakurai, Sasuke Miyazima and Hae Sun Hwang Progress of Theoretical Physics Vol. 75 No. 5 (1986) pp. 1048–1057 New Formalism for an Overlap Integral of the Anderson Orthogonality Theorem Akihide Oguchi and Kei Yosida Progress of Theoretical Physics Vol. 76 No. 5 (1986) pp. 999–1007 Ground State of a Tunneling Particle Coupled to Boson Excitaions in a Double-Well Potential Akiko Tanaka and Akio Sakurai Progress of Theoretical Physics Vol. 78 No. 3 (1987) pp. 583–590 Anderson Orthogonality Theorem Takeshi Kitamura, Akihide Oguchi and Kei Yosida Progress of Theoretical Physics Vol. 82 No. 5 (1989) pp. 917–929 Ground State of a Spin-Boson System Toshio Tsuzuki Progress of Theoretical Physics Vol. 90 No. 1 (1993) pp. 43–51 Overlap Integral between the Ground States of an Electron Gas Corresponding to Two Positions of a Scattering Potential K. Vladár Progress of Theoretical Physics Supplement No.106 (1991) pp. 147–156 Orthogonality Exponents in Low-Dimensional Metals K. Schönhammer

Progress of Theoretical PhysicsNov 1, 198255 citations