×

Birkhoff’s theorem, many-body response functions, and the ergodic condition. (English) Zbl 1228.82059

Summary: The ergodic hypothesis is viewed as one that is physically measurable through scattering by an external probe. Linear response theory is used to derive a general ergodic condition on the response functions. It is shown that the same condition is also implied by Birkhoff’s theorem. This coincidence allows us to shed light on the abstract terms of the theorem via classical many-body models.

MSC:

82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
70H05 Hamilton’s equations
37A99 Ergodic theory
28D10 One-parameter continuous families of measure-preserving transformations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] I.E. Farquhar, in: Ergodic Theory in Statistical Mechanics (1964)
[2] DOI: 10.1088/0034-4885/31/2/305 · doi:10.1088/0034-4885/31/2/305
[3] DOI: 10.1103/PhysRev.135.A1505 · doi:10.1103/PhysRev.135.A1505
[4] DOI: 10.1088/0034-4885/29/1/306 · doi:10.1088/0034-4885/29/1/306
[5] DOI: 10.1142/S0217979293002900 · doi:10.1142/S0217979293002900
[6] DOI: 10.1103/PhysRevLett.87.250601 · doi:10.1103/PhysRevLett.87.250601
[7] DOI: 10.1088/0305-4470/39/17/S52 · Zbl 1089.82025 · doi:10.1088/0305-4470/39/17/S52
[8] DOI: 10.1016/j.physa.2006.01.014 · doi:10.1016/j.physa.2006.01.014
[9] DOI: 10.1103/PhysRevA.31.3231 · doi:10.1103/PhysRevA.31.3231
[10] , in: Handbook of Mathematical Functions (1972)
[11] DOI: 10.1103/PhysRevE.61.R2172 · doi:10.1103/PhysRevE.61.R2172
[12] T. Prosen, in: Open Problems in Strongly Correlated Electron Systems (2001)
[13] DOI: 10.1103/PhysRevLett.89.100601 · doi:10.1103/PhysRevLett.89.100601
[14] M.H. Vainstein, in: Lecture Notes in Physics (2006)
[15] P. Grigolini, in: Quantum Mechanical Irreversibility and Measurement (1993) · doi:10.1142/1956
[16] DOI: 10.1103/PhysRevE.74.061111 · doi:10.1103/PhysRevE.74.061111
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.