Abstract
In spite of the remarkable success of classical statistic mechanics [1, 2] in describing correctly the crossover behavior of one-dimensional systems with degenerate vacuum from the high-temperature topologically disordered phase to the low-temperature ordered phase, the classical theory becomes inadequate in the low-temperature region where the energy associated with fluctuation quanta becomes comparable to the temperature. Furthermore, the question of renormalizations of the boson mass and the soliton energy and bound states of fluctuations (e.g., the breathers in the sine-Gordon system) are only handled in the framework of the quantum statistics.
Supported by the National Science Foundation, under Grant Number DMR76–21032
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
D.J. Scalapino, M. Sears, R.A. Ferrell: Phys. Rev. B 6, 3409 (1972)
N. Gupta, B. Sutherland: Phys. Rev. A 14, 1790 (1976)
H.A. Bethe: Z. Phys. 71, 205 (1931)
E. Lieb, W. Liniger: Phys. Rev. 103, 1605 (1963)
C.N. Yang, C.P. Yang: J. Math. Phys. (NY) 7, 1115 (1969)
H. Bergkoff, H.B. Thacker: Phys. Rev. Lett. 42, 135 (1979); Phys. Rev. D 19, 3666 (1979)
R.F. Dashen, B. Hasslacher, A. Neveu: Phys. Rev. D 10, 4114 (1974); ibid 10, 4130 (1974)
R.F. Dashen, B. Hasslacher, A. Neveu: Phys. Rev. D 11, 3424 (1975)
K. Maki, H. Takayama: Phys. Rev. B 20, 3223 (1979)
K. Maki, H. Takayama: Phys. Rev. B 20, 5002 (1979)
H. Takayama, K. Maki: Phys. Rev. B 20, 5009 (1979)
H. Takayama, K. Maki: Phys. Rev. B 22, 4558 (1980)
S. Coleman: Phys. Rev. D 15, 2929 (1977)
H.J. Mikeska: J. Phys. C 11, L29 (1978)
K. Maki: J. Low. Temp. Phys. 41, 327 (1980)
K. Maki: Solitons in Low Temperature Physics, in Prog. of Low Temperature Physics, ed. by D.F. Brewer (North Holland, Amsterdam) to be published
J.A. Krumhansl, J.R. Schrieffer: Phys. Rev. B 11, 3535 (1975)
J.F. Currie, J.A. Krumhansl, A.R. Bishop, S.E. Trullinger: Phys. Rev. B (1980), in press
S.E. Trullinger: Solid State Commun. 29, 27 (1979)
A. Seeger, H. Donth, A. Kochendörfer: Z. Phys. 134, 173 (1953)
J.K. Perring, T.H.R. Skyrme: Nucl. Phys. 31, 550 (1962)
A. Luther: Phys. Rev. B 14, 2153 (1976)
J.B. McGuire: J. Math. Phys. (NY) 5, 622 (1964)
C.N. Yang: Phys. Rev. 168, 1920 (1968)
K. Maki, H. Takayama: Phys. Rev. B (1980) in press
J.K. Kjems, M. Steiner: Phys. Rev. Lett. 41, 1137 (1978)
K.M. Leung, D.W. Hone, D.L. Mills, P.S. Riseborough, S.E. Trullinger: Phys. Rev. B 21, 4017 (1980)
H.J. Mikeska: J. Phys. C. 13, 2913 (1980)
J.P. Boucher, L.P. Regnault, J. Rossat-Mignod, J.P. Renard, J. Bouillot, W.G. Stirling: Solid State Commun. 33, 171 (1980)
K. Kawasaki, Prog. Theor. Phys. 55, 2029 (1976)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1981 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Maki, K. (1981). Quantum Statistics of Solitons. In: Bernasconi, J., Schneider, T. (eds) Physics in One Dimension. Springer Series in Solid-State Sciences, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81592-8_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-81592-8_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-81594-2
Online ISBN: 978-3-642-81592-8
eBook Packages: Springer Book Archive