Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. B, Condensed matter

Orthogonality exponent and the friction coefficient of an electron gas

Kurt Schönhammer

Published May 1, 1991• 11 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.43.11323

Related papers

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

Károly Vladár

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.

Progress of Theoretical Physics•Jul 1, 1993•4 citations

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 Physics•Sep 1, 1987•3 citations

Orthogonality theorem for a one-dimensional-electron gas with a bounded spectrum

Vladimir Georgievich Marikhin

The overlap between the ground-state wave functions of a one-dimensional electron gas with the Hamiltonians Ĥ 0 and $$\hat H_0 $$ , where $$\hat H_0 + \hat V$$ is the impurity potential, is calculated. It is shown that in the limit of an infinite potential the overlap vanishes as M −1/8 as M→∞, where M is the number of filled levels, while in the case of a weak potential this overlap differs little from 1. A relation is found between the magnitude of the overlap and the behavior of the density of states near the Fermi energy (statistics of the levels). The possibility of linearization of the spectrum and the possibility of performing a bosonization procedure are discussed in light of the results obtained.

Journal of Experimental and Theoretical Physics Letters•Jul 1, 1996•0 citations

Anderson’s orthogonality catastrophe in one dimension induced by a magnetic field

Hans Konrad Knörr, Peter Otte, Wolfgang Spitzer

According to Anderson's orthogonality catastrophe, the overlap of the N -particle ground states of a free Fermi gas with and without an (electric) potential decays in the thermodynamic limit. For the finite one-dimensional system various boundary conditions are employed. Unlike the usual setup the perturbation is introduced by a magnetic (vector) potential. Although such a magnetic field can be gauged away in one spatial dimension there is a significant and interesting effect on the overlap caused by the phases. We study the leading asymptotics of the overlap of the two ground states and the two-term asymptotics of the difference of the ground-state energies. In the case of periodic boundary conditions our main result on the overlap is based upon a well-known asymptotic expansion by Fisher and Hartwig on Toeplitz determinants with a discontinuous symbol. In the case of Dirichlet boundary conditions no such result is known to us and we only provide an upper bound on the overlap, presumably of the right asymptotic order.

arXiv:1502.07507•Journal of Physics A Mathematical and Theoretical•Jul 24, 2015•7 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 Physics•Apr 1, 1978•21 citations

The exponent in the orthogonality catastrophe for Fermi gases

Martin Gebert, Heinrich Küttler, Peter Müller +1 more

We quantify the asymptotic vanishing of the ground-state overlap of two non-interacting Fermi gases in d -dimensional Euclidean space in the thermodynamic limit. Given two one-particle Schrödinger operators in finite-volume which differ by a compactly supported bounded potential, we prove a power-law upper bound on the ground-state overlap of the corresponding non-interacting N -Fermion systems. We interpret the decay exponent \gamma in terms of scattering theory and find \gamma = \pi^{-2}\|\mathrm {arcsin}|T_E/2|\|_{\mathrm {HS}}^2 , where T_E is the transition matrix at the Fermi energy E . This exponent reduces to the one predicted by Anderson [Phys. Rev. 164, 352–359 (1967)] for the exact asymptotics in the special case of a repulsive point-like perturbation.

arXiv:1407.2512•Journal of Spectral Theory•Sep 15, 2016•9 citations
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.
The overlap between the ground-state wave functions of a one-dimensional electron gas with the Hamiltonians Ĥ 0 and H^0\hat H_0 H^0​ , where H^0+V^\hat H_0 + \hat VH^0​+V^ is the impurity potential, is calculated. It is shown that in the limit of an infinite potential the overlap vanishes as M −1/8 as M→∞, where M is the number of filled levels, while in the case of a weak potential this overlap differs little from 1. A relation is found between the magnitude of the overlap and the behavior of the density of states near the Fermi energy (statistics of the levels). The possibility of linearization of the spectrum and the possibility of performing a bosonization procedure are discussed in light of the results obtained.
According to Anderson's orthogonality catastrophe, the overlap of the N -particle ground states of a free Fermi gas with and without an (electric) potential decays in the thermodynamic limit. For the finite one-dimensional system various boundary conditions are employed. Unlike the usual setup the perturbation is introduced by a magnetic (vector) potential. Although such a magnetic field can be gauged away in one spatial dimension there is a significant and interesting effect on the overlap caused by the phases. We study the leading asymptotics of the overlap of the two ground states and the two-term asymptotics of the difference of the ground-state energies. In the case of periodic boundary conditions our main result on the overlap is based upon a well-known asymptotic expansion by Fisher and Hartwig on Toeplitz determinants with a discontinuous symbol. In the case of Dirichlet boundary conditions no such result is known to us and we only provide an upper bound on the overlap, presumably of the right asymptotic order.
We quantify the asymptotic vanishing of the ground-state overlap of two non-interacting Fermi gases in d -dimensional Euclidean space in the thermodynamic limit. Given two one-particle Schrödinger operators in finite-volume which differ by a compactly supported bounded potential, we prove a power-law upper bound on the ground-state overlap of the corresponding non-interacting N -Fermion systems. We interpret the decay exponent \gamma in terms of scattering theory and find \gamma = \pi^{-2}\|\mathrm {arcsin}|T_E/2|\|_{\mathrm {HS}}^2 , where T_E is the transition matrix at the Fermi energy E . This exponent reduces to the one predicted by Anderson [Phys. Rev. 164, 352–359 (1967)] for the exact asymptotics in the special case of a repulsive point-like perturbation.