Abstract
A new and elementary method is proposed for obtaining the equations of state of the classical and quantum CSM models as solutions of first-order nonlinear differential equations satisfied by auxiliary functions constructed from the corresponding canonical partition functions. For the classical case, the differential equation (18) is new. For the quantum case the differential equation (34) is shown to be equivalent with Yang—Yang’s type of solution obtained by Sutherland. This equivalence provides an explanation for the local character, in momentum space, of our differential equation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. J. Baxter, Statistical mechanics of a one-dimensional Coulomb system with a uniform charge background, Proc. Cambridge Philos. Soc. 59 (1963), 779–787.
P. Choquard, On the statistical mechanics of one-dimensional Coulomb systems, Helv. Phys. Acta 48 (1975), No. 4, 585–598.
M. Hénon, Integrals of the Toda lattice, Phys. Rev. B 9 (1974), 1921–1923.
J. Moser, Three integrable Hamiltonian systems connected to isospectral deformations, Adv. Math. 16 (1975), 197–220.
S. N. M. Ruijsenaars, Action-angle maps and scattering theory for some finite-dimensional integrable systems. III. Sutherland type systems and their duals, Publ. Res. Inst. Math. Sci. 31 (1995), No. 2, 247–353.
B. Sutherland, Quantum many-body problem in one dimension: thermodynamics, J. Math. Phys. 12 (1971), 251–256.
B. Sutherland, Exact results for a quantum many-body problem in one dimension. II, Phys. Rev. A 5 (1972), 1372–1376.
B. Sutherland, A microscopic theory of exclusion statistics, Phys. Rev. B 56 (1997), No. 8, 4422–4431.
C. M. Yang and C. P. Yang, Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction, J. Math. Phys. 10 (1969), 1115–1122.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media New York
About this chapter
Cite this chapter
Choquard, P. (2000). Classical and Quantum Partition Functions of the Calogero—Moser—Sutherland Model. In: van Diejen, J.F., Vinet, L. (eds) Calogero—Moser— Sutherland Models. CRM Series in Mathematical Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1206-5_8
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1206-5_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7043-0
Online ISBN: 978-1-4612-1206-5
eBook Packages: Springer Book Archive