Equilibrium and Nonequilibrium States of the Model Fröhlich–Peierls Hamiltonian
The model Fröhlich–Peierls Hamiltonian for electrons interacting with phonons only in some infinite discrete modes is considered. It is shown that, in the equilibrium case, this model is thermodynamically equivalent to the model of electrons with periodic potential and free phonons. In the one-dimen...
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| Date: | 2003 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2003
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| Series: | Український математичний журнал |
| Subjects: | |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Equilibrium and Nonequilibrium States of the Model Fröhlich–Peierls Hamiltonian / D.Ya. Petrina // Український математичний журнал. — 2003. — Т. 55, № 8. — С. 1069–1086. — Бібліогр.: 10 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | The model Fröhlich–Peierls Hamiltonian for electrons interacting with phonons only in some infinite discrete modes is considered. It is shown that, in the equilibrium case, this model is thermodynamically equivalent to the model of electrons with periodic potential and free phonons. In the one-dimensional case, the potential is determined exactly in terms of the Weierstrass elliptic function, and the eigenvalue problem can also be solved exactly. Nonequilibrium states are described by the nonlinear Schrödinger and wave equations, which have exact soliton solutions in the one-dimensional case. |
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