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RESEARCH PRODUCT
Statistical Mechanics of the Integrable Models
Jussi TimonenD. J. PillingR. K. Bulloughsubject
Coupling constantPhysicsNonlinear Sciences::Exactly Solvable and Integrable SystemsIntegrable systemmedia_common.quotation_subjectStatistical mechanicsQuantum statistical mechanicsInfinitySpace (mathematics)Classical limitmedia_commonMathematical physicsdescription
There is an infinity of classically integrable models. The only ones we can consider here, and these only briefly, are: the sine-Gordon (s-G) model $${\phi _{{\rm{xx}}}}{}^ - {\phi _{{\rm{tt}}}} = {{\rm{m}}^2}\sin \phi ,$$ (1.1) the sinh-Gordon (sinh-G) model $${\phi _{{\rm{xx}}}}{}^ - {\phi _{{\rm{tt}}}} = {{\rm{m}}^2}\sinh \phi ,$$ (1.2) and the repulsive and attractive non-linear Schrodinger (NLS) models $${}^ - {\rm{i}}{\phi _{\rm{t}}} = {\phi _{{\rm{xx}}}}{}^ - 2{\rm{c}}\phi {\left| \phi \right|^2}.$$ (1.3) The “attractive” NLS has real coupling constant c 0; φ is complex. In (1.1) and (1.2) m is a mass (ħ = c = 1) and φ is real. These 4 integrable models are in one space and one time (1+1) dimensions. There are integrable models in 2+1 dimensions we cannot discuss here [1].
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1987-01-01 |