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

Chinese Physics Letters

Approximate Scaling Behaviour of Local Spectral Density of States at Relatively Weak Perturbation: a Schematic Shell Model

Wen-ge Wang

Published May 3, 2001• 0 citations
Publisher

Abstract

For a schematic shell model, we show numerically that, contrary to the behaviour of eigenfunctions, the shapes of the so-called local spectral density of states become close to their forms at extremely strong perturbation (after rescaling) even when the perturbation is relatively weak. The same phenomenon is also found for the random version of the schematic shell model. We suggest that this property of the local spectral density of states may be common to models in which the Hamiltonian matrices in independent particle states have a banded and regular structure.

DOI
10.1088/0256-307x/18/6/306

Related papers

Structure of eigenstates and local spectral density of states: A three-orbital schematic shell model

Wen-ge Wang, Felix M. Izrailev, Giulio Casati

The average shape of the spectral local density of states (LDOS) and eigenfunctions (EFs) has been studied numerically for a conservative dynamical model (three-orbital Lipkin-Meshkov-Glick model) that can exhibit strong chaos in the classical limit. Attention is paid to the comparison of the shape of the LDOS with that known for random matrix models, as well as to the shape of the EFs, for different values of the perturbation strength. The classical counterparts of the LDOS has also been studied and found to be in remarkable agreement with the quantum calculations. Finally, by making use of a generalization of Brillouin-Wigner perturbation expansion, the form of the long tails of the LDOS and EFs is given analytically and confirmed numerically.

arXiv:chao-dyn/9708020•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jan 1, 1998•53 citations

Fluctuations of wavefunctions about their classical average

Luis Benet, J Flores, Hen A +3 more

Quantum–classical correspondence for the average shape of eigenfunctions and the local spectral density of states are well-known facts. In this paper, the fluctuations of the quantum wavefunctions around the classical value are discussed. A simple random matrix model leads to a Gaussian distribution of the amplitudes whose width is determined by the classical shape of the eigenfunction. To compare this prediction with numerical calculations in chaotic models of coupled quartic oscillators, we develop a rescaling method for the components. The expectations are broadly confirmed, but deviations due to scars are observed. This effect is much reduced when both Hamiltonians have chaotic dynamics.

arXiv:nlin/0207039•Journal of Physics A Mathematical and General•Jan 22, 2003•18 citations

Statistical Study for Eigenfunctions of 1-dimensional Tight Binding Model

Wen-ge Wang, Bambi Hu

For energy eigenfunctions of 1-dimensional tight binding model, the distribution of ratio of their nearest components, denoted by f(p), gives information for their fluctuation properties. The shape of f(p) is studied numerically for three versions of the 1D tight binding model. It is found that when perturbation is strong the shape of f(p) is usually quite close to that of the Lorentzian distribution. In the case of weak perturbation the shape of the central part of f(p) is model-dependent while tails of f(p) are still close to the Lorentzian form.

arXiv:cond-mat/9806268•Jun 23, 1998•0 citations

Perturbation theory of the electronic properties in strongly correlated solids

M. M. Steiner, Robert C. Albers, Douglas J. Scalapino +1 more

In an attempt to obtain a better description than the local-density approximation (LDA) for the electronic structure of realistic narrow-band systems, we have studied a perturbation-theory method for the self-energy and have tested it on the electronic properties of the periodic one-dimensional Anderson model. For a number of models we have calculated a wide range of properties such as quasiparticle energies, spectral densities, reduced hybridizations, and various magnetic correlation functions. For two different models we were able to compare with Monte Carlo results and found good agreement. In general, we have obtained a description of narrow-band systems that is more reasonable than the one given by the LDA.

Physical review. B, Condensed matter•Jan 15, 1991•43 citations

Ergodic properties of local spectral density for a conservative system of coupled quantum states

Vladimir S. Starovoitov

The shape and the inverse participation ratio (IPR) of local spectral density (LSD) are studied for a generic isolated system of coupled quantum states, the Hamiltonian of which is represented by a band random matrix with disordered leading diagonal. We find for the matrices with arbitrary small band that the lack of ergodicity for LSD can be associated with an exponential increase in IPR with the ratio v /Δ c ( v is the root of the mean square for off-diagonal matrix elements and Δ c is the energy spacing between directly coupled basis states). Criteria specifying transition to localization and ergodicity for LSD are considered.

arXiv:quant-ph/0203071•Journal of Physics A Mathematical and General•Apr 12, 2002•1 citation

Spectral density of a one-dimensional quantum Ising model: Gaussian and multi-Gaussian approximations

Y. Y. Atas, E. Bogomolny

The spectral density of a quantum Ising model in transverse and longitudinal fields for a large but finite number of spins N is discussed in detail. When both fields are of the same order, the spectral densities in the bulk are well approximated by a Gaussian function, which is typical behaviour for many-body models with short-range interactions. The main part of the paper is devoted to the investigation of a different characteristic case where spectral densities have peaks related with strong degeneracies of unperturbed states in certain limits of field amplitudes. In the strict limit peaks overlap and disappear but for values of N accessible in numerical calculations they often strongly influence spectral densities as well as other quantities. A simple method is developed that permits us to find general approximation formulae for the multi-peak structure of spectral density, which is in good agreement with numerics.

Journal of Physics A Mathematical and Theoretical•Aug 4, 2014•20 citations
For a schematic shell model, we show numerically that, contrary to the behaviour of eigenfunctions, the shapes of the so-called local spectral density of states become close to their forms at extremely strong perturbation (after rescaling) even when the perturbation is relatively weak. The same phenomenon is also found for the random version of the schematic shell model. We suggest that this property of the local spectral density of states may be common to models in which the Hamiltonian matrices in independent particle states have a banded and regular structure.
The average shape of the spectral local density of states (LDOS) and eigenfunctions (EFs) has been studied numerically for a conservative dynamical model (three-orbital Lipkin-Meshkov-Glick model) that can exhibit strong chaos in the classical limit. Attention is paid to the comparison of the shape of the LDOS with that known for random matrix models, as well as to the shape of the EFs, for different values of the perturbation strength. The classical counterparts of the LDOS has also been studied and found to be in remarkable agreement with the quantum calculations. Finally, by making use of a generalization of Brillouin-Wigner perturbation expansion, the form of the long tails of the LDOS and EFs is given analytically and confirmed numerically.
Quantum–classical correspondence for the average shape of eigenfunctions and the local spectral density of states are well-known facts. In this paper, the fluctuations of the quantum wavefunctions around the classical value are discussed. A simple random matrix model leads to a Gaussian distribution of the amplitudes whose width is determined by the classical shape of the eigenfunction. To compare this prediction with numerical calculations in chaotic models of coupled quartic oscillators, we develop a rescaling method for the components. The expectations are broadly confirmed, but deviations due to scars are observed. This effect is much reduced when both Hamiltonians have chaotic dynamics.
For energy eigenfunctions of 1-dimensional tight binding model, the distribution of ratio of their nearest components, denoted by f(p), gives information for their fluctuation properties. The shape of f(p) is studied numerically for three versions of the 1D tight binding model. It is found that when perturbation is strong the shape of f(p) is usually quite close to that of the Lorentzian distribution. In the case of weak perturbation the shape of the central part of f(p) is model-dependent while tails of f(p) are still close to the Lorentzian form.
In an attempt to obtain a better description than the local-density approximation (LDA) for the electronic structure of realistic narrow-band systems, we have studied a perturbation-theory method for the self-energy and have tested it on the electronic properties of the periodic one-dimensional Anderson model. For a number of models we have calculated a wide range of properties such as quasiparticle energies, spectral densities, reduced hybridizations, and various magnetic correlation functions. For two different models we were able to compare with Monte Carlo results and found good agreement. In general, we have obtained a description of narrow-band systems that is more reasonable than the one given by the LDA.
The shape and the inverse participation ratio (IPR) of local spectral density (LSD) are studied for a generic isolated system of coupled quantum states, the Hamiltonian of which is represented by a band random matrix with disordered leading diagonal. We find for the matrices with arbitrary small band that the lack of ergodicity for LSD can be associated with an exponential increase in IPR with the ratio v /Δ c ( v is the root of the mean square for off-diagonal matrix elements and Δ c is the energy spacing between directly coupled basis states). Criteria specifying transition to localization and ergodicity for LSD are considered.
The spectral density of a quantum Ising model in transverse and longitudinal fields for a large but finite number of spins N is discussed in detail. When both fields are of the same order, the spectral densities in the bulk are well approximated by a Gaussian function, which is typical behaviour for many-body models with short-range interactions. The main part of the paper is devoted to the investigation of a different characteristic case where spectral densities have peaks related with strong degeneracies of unperturbed states in certain limits of field amplitudes. In the strict limit peaks overlap and disappear but for values of N accessible in numerical calculations they often strongly influence spectral densities as well as other quantities. A simple method is developed that permits us to find general approximation formulae for the multi-peak structure of spectral density, which is in good agreement with numerics.