The DOI matches its Crossref record; 33 of the 33 references it cites were found in a registry or an index.
Statistical mechanics of one-dimensional solitary-wave-bearing scalar fields: Exact results and ideal-gas phenomenology
Abstract
The statistical mechanics of one-dimensional scalar fields governed by nonlinear wave equations having solitary-wave (soliton) solutions are discussed in detail. Previously neglected "phase-shift" interactions between phonons and solitary waves (kinks) are taken into account and it is shown that these interactions provide the mechanism for sharing of energy and degrees of freedom among the "elementary" excitations of the nonlinear system. In particular, the ideal-gas phenomenology proposed by Krumhansl and Schrieffer for the $``{\ensuremath{\varphi}}^{4}''$ model is corrected and extended to the entire class of nonlinear Klein-Gordon models having solitary-wave solutions (e.g., ${\ensuremath{\varphi}}^{4}$, sine-Gordon, double-quadratic, etc.). By a comparison of the results of the phenomenological approach to those obtained via the exact transfer-operator method, it is found that the ideal-gas phenomenology gives exact results for the various low-temperature thermodynamic functions and correlation lengths.
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Cites
Methods of Theoretical Physics
Morse, P. M., Feshbach, H., & Hill, E. L. (1954) · American Journal of Physics · doi:10.1119/1.1933765 · Cited by 13,197
Ordering, metastability and phase transitions in two-dimensional systems
Kosterlitz, J. M., & Thouless, D. J. (1973) · Journal of Physics C: Solid State Physics · doi:10.1088/0022-3719/6/7/010 · Cited by 9,538
Handbook of Mathematical Functions
(2018) · A Century of Excellence in MEASUREMENTS, STANDARDS, and TECHNOLOGY · doi:10.1201/9781351069397-39 · Cited by 9,062
Zur Theorie der Metalle: I. Eigenwerte und Eigenfunktionen der linearen Atomkette
Bethe, H. (1931) · Zeitschrift f�r Physik · doi:10.1007/bf01341708 · Cited by 3,768
The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
Ablowitz, M. J., Kaup, D. J., Newell, A. C., & Segur, H. (1974) · Studies in Applied Mathematics · doi:10.1002/sapm1974534249 · Cited by 3,187
On the theory of metals. 1. Eigenvalues and eigenfunctions for the linear atomic chain
Bethe, H. A. (1931) · Cited by 1,934
Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model
José, J. V., Kadanoff, L. P., Kirkpatrick, S., & Nelson, D. R. (1977) · Physical Review B · doi:10.1103/physrevb.16.1217 · Cited by 1,928
The soliton: A new concept in applied science
Scott, A. C., Chu, F. Y. F., & McLaughlin, D. W. (1973) · Proceedings of the IEEE · doi:10.1109/proc.1973.9296 · Cited by 1,679
Molecular-dynamics study of a three-dimensional one-component model for distortive phase transitions
Schneider, T., & Stoll, E. (1978) · Physical Review B · doi:10.1103/physrevb.17.1302 · Cited by 1,592
XIV. The distribution of electrons round impurities in monovalent metals
Friedel, J. (1952) · The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science · doi:10.1080/14786440208561086 · Cited by 1,068
Metadata
- Authors
- Currie, J. F., Krumhansl, J. A., Bishop, A. R., & Trullinger, S. E.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 1980-07-15
- Volume
- 22
- Issue
- 2
- Pages
- 477-496
- ISSN
- 0163-1829 (ISSN-L)
- OpenAlex
- W1974753876
- Cited by
- 517
- References
- 33
- FWCI
- 39.61
- Type
- journal article
- Language
- en
- Open access
- closed
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- Currie, J. F., Krumhansl, J. A., Bishop, A. R., & Trullinger, S. E. (1980). Statistical mechanics of one-dimensional solitary-wave-bearing scalar fields: Exact results and ideal-gas phenomenology. Physical Review B. https://doi.org/10.1103/physrevb.22.477
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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