October  2015, 35(10): 4831-4838. doi: 10.3934/dcds.2015.35.4831

Ergodicity of two particles with attractive interaction

1. 

Institut für Statistik und Wahrscheinlichkeitstheorie, TU Wien, 1040 Wien, Austria

2. 

Institut für Theoretische Physik, TU Wien, 1040 Wien, Austria

Received  January 2014 Revised  January 2015 Published  April 2015

We study the ergodic properties of a classical two-particle system with square-well pair potential in an interval.
Citation: Karl Grill, Christian Tutschka. Ergodicity of two particles with attractive interaction. Discrete & Continuous Dynamical Systems - A, 2015, 35 (10) : 4831-4838. doi: 10.3934/dcds.2015.35.4831
References:
[1]

V. I. Arnold, Mathematical Methods of Classical Mechanics,, Springer, (1989).  doi: 10.1007/978-1-4757-2063-1.  Google Scholar

[2]

R. J. Baxter, Exactly solved models in statistical mechanics,, Academic Press, (1982).   Google Scholar

[3]

L. Boltzmann, Vorlesungen Über Gastheorie,, Barth, (1896).   Google Scholar

[4]

M. Boshernitzan, A condition for minimal interval exchange maps to be uniquely ergodic,, Duke Mathematical Journal, 52 (1985), 723.  doi: 10.1215/S0012-7094-85-05238-X.  Google Scholar

[5]

G. R. Brannock and J. K. Percus, Wertheim cluster development of free energy functionals for general nearest-neighbor interactions in $D=1$,, The Journal of Chemical Physics, 105 (1996), 614.  doi: 10.1063/1.471920.  Google Scholar

[6]

J. A. Cuesta and C. Tutschka, Overcomplete free energy functional for $D=1$ particle systems with next neighbor interactions,, Journal of Statistical Physics, 111 (2003), 1125.  doi: 10.1023/A:1023096031180.  Google Scholar

[7]

K. F. Herzfeld and M. Goeppert-Mayer, On the states of aggregation,, The Journal of Chemical Physics, 2 (1934), 38.  doi: 10.1063/1.1749355.  Google Scholar

[8]

M. Keane, Interval exchange transformations,, Mathematische Zeitschrift, 141 (1975), 25.  doi: 10.1007/BF01236981.  Google Scholar

[9]

S. Kerckhoff, H. Masur and J. Smillie, Ergodicity of billiard flows and quadratic differentials,, Annals of Mathematics, 124 (1986), 293.  doi: 10.2307/1971280.  Google Scholar

[10]

A. I. Khinchin, Mathematical Foundations of Statistical Mechanics,, Dover, (1949).   Google Scholar

[11]

H. Masur, Interval exchange transformations and measured foliations,, Annals of Mathematics, 115 (1982), 169.  doi: 10.2307/1971341.  Google Scholar

[12]

A. van der Poorten, Fermat's four squares theorem,, 2007. Available from: , ().   Google Scholar

[13]

D. Ruelle, Statistical Mechanics: Rigorous Results,, Benjamin, (1969).   Google Scholar

[14]

W. A. Veech, Gauss measures for transformations on the space of interval exchange maps,, Annals of Mathematics, 115 (1982), 201.  doi: 10.2307/1971391.  Google Scholar

show all references

References:
[1]

V. I. Arnold, Mathematical Methods of Classical Mechanics,, Springer, (1989).  doi: 10.1007/978-1-4757-2063-1.  Google Scholar

[2]

R. J. Baxter, Exactly solved models in statistical mechanics,, Academic Press, (1982).   Google Scholar

[3]

L. Boltzmann, Vorlesungen Über Gastheorie,, Barth, (1896).   Google Scholar

[4]

M. Boshernitzan, A condition for minimal interval exchange maps to be uniquely ergodic,, Duke Mathematical Journal, 52 (1985), 723.  doi: 10.1215/S0012-7094-85-05238-X.  Google Scholar

[5]

G. R. Brannock and J. K. Percus, Wertheim cluster development of free energy functionals for general nearest-neighbor interactions in $D=1$,, The Journal of Chemical Physics, 105 (1996), 614.  doi: 10.1063/1.471920.  Google Scholar

[6]

J. A. Cuesta and C. Tutschka, Overcomplete free energy functional for $D=1$ particle systems with next neighbor interactions,, Journal of Statistical Physics, 111 (2003), 1125.  doi: 10.1023/A:1023096031180.  Google Scholar

[7]

K. F. Herzfeld and M. Goeppert-Mayer, On the states of aggregation,, The Journal of Chemical Physics, 2 (1934), 38.  doi: 10.1063/1.1749355.  Google Scholar

[8]

M. Keane, Interval exchange transformations,, Mathematische Zeitschrift, 141 (1975), 25.  doi: 10.1007/BF01236981.  Google Scholar

[9]

S. Kerckhoff, H. Masur and J. Smillie, Ergodicity of billiard flows and quadratic differentials,, Annals of Mathematics, 124 (1986), 293.  doi: 10.2307/1971280.  Google Scholar

[10]

A. I. Khinchin, Mathematical Foundations of Statistical Mechanics,, Dover, (1949).   Google Scholar

[11]

H. Masur, Interval exchange transformations and measured foliations,, Annals of Mathematics, 115 (1982), 169.  doi: 10.2307/1971341.  Google Scholar

[12]

A. van der Poorten, Fermat's four squares theorem,, 2007. Available from: , ().   Google Scholar

[13]

D. Ruelle, Statistical Mechanics: Rigorous Results,, Benjamin, (1969).   Google Scholar

[14]

W. A. Veech, Gauss measures for transformations on the space of interval exchange maps,, Annals of Mathematics, 115 (1982), 201.  doi: 10.2307/1971391.  Google Scholar

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