Moments of the auto-correlation function and the KMS-condition

Fannes, Mark; Martens, R; Verbeure, André

doi:10.1007/bf01941661

Cited by 5 publications

(2 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, it is rarely possible to obtain the susceptibility from the defining equation (8). For our model, using (4), we show in Appendix A that gi(co') jz(co) = ( -1/ir)P f dco' (15) where co and co' are real variables and P denotes the Cauchy principal value. Sirice yz(co) is odd in co, (14) may also be expressed as co gz(co ) j, (co)=(2/ir)P f dco' CO CO (16) The above has the advantage in that yz(co) is now limited to positive values of co.…”

Section: Dynamic Susceptibilitymentioning

confidence: 99%

Dynamic response function and bounds of the susceptibility of a semiclassical gas and Kramers-Kronig relations in optic-data inversion

1992

Phys. Rev. A

View full text Add to dashboard Cite

The frequency-dependent density-density response function for a semiclassical gas has been calculated from its defining equation of linear-response theory. The particular form of the response function appears to be relevant to optic-data inversion using Kramers-Kronig relations. Also the zero-frequency limit of the response function, being the static susceptibility, is a bounded function. The susceptibilityfor the semiclassical gas model provides a unique opportunity to test the bounds analytically. This study further suggests a slightly different derivation of the lower bounds, perhaps less abstract than by convexity theory via Jensen's inequality.PACS number(s): 05.20. -y, 05.90.+m, 61.20.Lc

show abstract

Section: Dynamic Susceptibilitymentioning

confidence: 99%

Dynamic response function and bounds of the susceptibility of a semiclassical gas and Kramers-Kronig relations in optic-data inversion

1992

Phys. Rev. A

View full text Add to dashboard Cite

show abstract

“…For instance, various characterisation related to correlation inequalities and to variational principles have been derived (see e.g. [13,6,9]). Other perspectives have also been explored related for instance to the Tomita-Takasaki theory and to the Heck algebra and number theory (see e.g.…”

mentioning

confidence: 99%

High temperature convergence of the KMS boundary conditions: The Bose-Hubbard model on a finite graph

Ammari

Ratsimanetrimanana

2019

Preprint

View full text Add to dashboard Cite

The Kubo-Martin-Schwinger condition is a widely studied fundamental property in quantum statistical mechanics which characterises the thermal equilibrium states of quantum systems. In the seventies, G. Gallavotti and E. Verboven, proposed an analogue to the KMS condition for classical mechanical systems and highlighted its relationship with the Kirkwood-Salzburg equations and with the Gibbs equilibrium measures. In the present article, we prove that in a certain limiting regime of high temperature the classical KMS condition can be derived from the quantum condition in the simple case of the Bose-Hubbard dynamical system on a finite graph. The main ingredients of the proof are Golden-Thompson inequality, Bogoliubov inequality and semiclassical analysis.

show abstract

Completely positive linear mappings, non-Hamiltonian evolution, and quantum stochastic processes

Oseledets¹

1984

J Math Sci

View full text Add to dashboard Cite

Moments of the auto-correlation function and the KMS-condition

Abstract: Abstract.Inequalities between successive moments of the time dependent auto-correlation function are derived. Furthermore, we prove that they provide an infinite set of characterizations of an equilibrium state.

Cited by 5 publications

References 13 publications

Dynamic response function and bounds of the susceptibility of a semiclassical gas and Kramers-Kronig relations in optic-data inversion

Dynamic response function and bounds of the susceptibility of a semiclassical gas and Kramers-Kronig relations in optic-data inversion

High temperature convergence of the KMS boundary conditions: The Bose-Hubbard model on a finite graph

Completely positive linear mappings, non-Hamiltonian evolution, and quantum stochastic processes

Contact Info

Product

Resources

About