scholarly journals Classical Thermodynamics of the Toda Lattice: --As a Classical Limit of the Two-Component Bethe Ansatz Scheme--

1986 ◽  
Vol 76 (4) ◽  
pp. 820-836 ◽  
Author(s):  
H. Takayama ◽  
M. Ishikawa
Keyword(s):  
Bethe Ansatz ◽  
Classical Limit ◽  
Toda Lattice ◽  
Two Component ◽  
Classical Thermodynamics

Wave kinetic description of quantum pair plasmas

2008 ◽  
Vol 74 (1) ◽  
pp. 91-97 ◽  
Author(s):  
J. T. MENDONÇA ◽  
J. E. RIBEIRO ◽  
P. K. SHUKLA
Keyword(s):  
Dispersion Relation ◽  
Classical Limit ◽  
Landau Damping ◽  
Quantum Plasma ◽  
Kinetic Description ◽  
Electrostatic Waves ◽  
Pair Plasma ◽  
Electron Positron ◽  
Two Component ◽  
Electron Positron Pair

AbstractThe dispersion relation for a quantum pair plasma is derived, by using a wave kinetic description. A general form of the kinetic dispersion relation for electrostatic waves in a two-component quantum plasma is established. The particular case of an electron–positron pair plasma is considered in detail. Exact expressions for Landau damping are derived, and the quasi-classical limit is discussed.

Classical thermodynamics of the Heisenberg chain in a field by generalized Bethe ansatz method

1990 ◽  
Vol 145 (4) ◽  
pp. 154-158 ◽  
Author(s):  
R.K. Bullough ◽  
Y.-z. Chen ◽  
J. Timonen ◽  
V. Tognetti ◽  
R. Vaia
Keyword(s):  
Bethe Ansatz ◽  
Heisenberg Chain ◽  
Ansatz Method ◽  
Classical Thermodynamics

scholarly journals R-MATRICES AND HAMILTONIAN STRUCTURES FOR CERTAIN LAX EQUATIONS

2013 ◽  
Vol 25 (03) ◽  
pp. 1350005 ◽  
Author(s):  
CHAO-ZHONG WU
Keyword(s):  
Lie Algebra ◽  
Toda Lattice ◽  
Hamiltonian Structures ◽  
Two Component ◽  
Lax Equations

In this paper a list of R-matrices on a certain coupled Lie algebra is obtained. With one of these R-matrices, we construct infinitely many bi-Hamiltonian structures for each of the two-component BKP and the Toda lattice hierarchies. We also show that, when such two hierarchies are reduced to their subhierarchies, these bi-Hamiltonian structures are reduced correspondingly.

Classical limit of sine-Gordon thermodynamics using the Bethe ansatz

1986 ◽  
Vol 34 (11) ◽  
pp. 7851-7865 ◽  
Author(s):  
Michael D. Johnson ◽  
Niu-Niu Chen ◽  
Michael Fowler
Keyword(s):  
Bethe Ansatz ◽  
Classical Limit

Angular momentum coherent states

1971 ◽  
Vol 321 (1546) ◽  
pp. 321-340 ◽  
Keyword(s):  
Angular Momentum ◽  
Coherent State ◽  
Harmonic Oscillator ◽  
Classical Limit ◽  
Coherent States ◽  
Uncertainty Relations ◽  
Mean Square ◽  
Expectation Values ◽  
Angular Momenta ◽  
Two Component

The work of Carruthers & Nieto on the harmonic oscillator coherent states is combined with Schwinger’s construction of angular momentum to produce the angular momentum coherent states. It is shown that these states become the vector representatives of angular momentum in the classical limit, and so are particularly useful for discussing the transition from quantum to classical angular momentum. The uncertainty relations for angle and angular momentum are described and are compatible with the classical limit. Under rotations the coherent states transform in a manner that in the classical limit is equivalent to the transformation of vectors, and in the same limit the root mean square variation of the expectation values of the components of angular momentum become negligible in comparison with the expectation values themselves. The coupling of two angular momenta in the classical limit is investigated: it is shown that although the product of two coherent states is not itself a coherent state, it does represent a packet similar to a true coherent state, and centred on the direction of the classical resultant of the two component vectors. The properties and implications of hyperbolic angular momentum space are discussed.

scholarly journals Faces of Relativistic Toda Chain

1997 ◽  
Vol 12 (15) ◽  
pp. 2675-2724 ◽  
Author(s):  
S. Kharchev ◽  
A. Mironov ◽  
A. Zhedanov
Keyword(s):  
Orthogonal Polynomial ◽  
Toda Lattice ◽  
Toda Chain ◽  
Polynomial Systems ◽  
Function Approach ◽  
Unitary Matrix ◽  
Lax Representation ◽  
Two Dimensional ◽  
Two Component ◽  
Toda Lattice Hierarchy

We demonstrate that the generalization of the relativistic Toda chain (RTC) is a special reduction of two-dimensional Toda lattice hierarchy (2DTL). This reduction implies that the RTC is gauge equivalent to the discrete AKNS hierarchy and, which is the same, to the two-component Volterra hierarchy while its forced (semi-infinite) variant is described by the unitary matrix integral. The integrable properties of the RTC hierarchy are revealed in different frameworks of the Lax representation, orthogonal polynomial systems, and τ-function approach. Relativistic Toda molecule hierarchy is also considered, along with the forced RTC. Some applications to biorthogonal polynomial systems are discussed.

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