The Toda lattice, introduced by Morikazu Toda (1967), is a simple model for a one-dimensional crystal in solid state physics. It is famous because it is one of the earliest examples of a non-linear completely integrable system.
It is given by a chain of particles with nearest neighbor interaction, described by the Hamiltonian
and the equations of motion
where is the displacement of the -th particle from its equilibrium position,
The Todalattice, introduced by Morikazu Toda (1967), is a simple model for a one-dimensional crystal in solid state physics. It is famous because it...
toda in Wiktionary, the free dictionary. Toda may refer to: Toda people Toda language Toda Embroidery TodalatticeToda field theory Oscillator Toda Toda...
Schrödinger equation, and certain integrable many-body systems, such as the Todalattice. The modern theory of integrable systems was revived with the numerical...
of field theory and partial differential equations, a Toda field theory, named after Morikazu Toda, is specified by a choice of Lie algebra and a specific...
Volterra lattice also behaves like a discrete version of the KdV equation. The Volterra lattice is an integrable system, and is related to the Todalattice. It...
Morikazu Toda (戸田 盛和, Toda Morikazu, 20 October 1917 – 6 October 2010) was a Japanese physicist, best known for the discovery of the Todalattice. His main...
Vries equation, Kadomtsev–Petviashvili equation, the Ishimori equation, Todalattice equation, and the Dym equation. This approach has also been applied to...
introduction of the theory of prequantization has led to the theory of quantum Todalattices. The Kostant partition function is named after him. With Gerhard Hochschild...
interaction theory is introduced by Steven Weinberg. The Todalattice is introduced by Morikazu Toda as a simple model for a one-dimensional crystal in solid...
one-dimensional Schrödinger operator. It also arises in: The Lax pair of the Todalattice. The three-term recurrence relationship of orthogonal polynomials, orthogonal...
0 {\displaystyle \displaystyle iv_{t}+u+v|u|^{2}=0} Dirac field, QFT Todalattice any ∇ 2 log u n = u n + 1 − 2 u n + u n − 1 {\displaystyle \displaystyle...
extensions, AMS, 1992 with K. T-R McLaughlin: A continuum limit of the Todalattice, AMS, 1998 Orthogonal polynomials and random matrices: a Riemann-Hilbert...
Teschl, Gerald (2001), "Almost everything you always wanted to know about the Toda equation", Jahresbericht der Deutschen Mathematiker-Vereinigung, 103 (4):...
contributions to the theory of completely integrable systems in particular the Todalattice and the Korteweg–de Vries equation. In 1980 he co-founded Physica D:...
are to the fields of Sturm–Liouville theory, Jacobi operators and the Todalattice. He also works in biomathematics, in particular in the novel area of...
maximal volume of a polytope in a d-dimensional integer lattice with k ≥ 1 interior lattice points is at most k ⋅ ( 8 d ) d ⋅ 15 d ⋅ 2 2 d + 1 , {\displaystyle...
This means that the Toda field theory is not a continuous limit of the Toda chain. Toda, M. (1975). "Studies of a non-linear lattice". Physics Reports....
2307/1971140 with Roe Goodman: Classical and quantum mechanical systems of Todalattice type, 3 Parts, Comm. Math. Phys., Part I, vol. 83, 1982, pp. 355–386...
relations between numerical analysis and integrable systems have been found (Todalattice and numerical linear algebra, discrete soliton equations and series acceleration)...
; Mahon, M. E. (1994), "Relaxation and Stochasticity in a Truncated TodaLattice", Physical Review E, 49 (1): 3735–3747, Bibcode:1994PhRvE..49.3735K,...
It is related to the prototypical Ising model, where at each site of a lattice, a spin σ i ∈ { ± 1 } {\displaystyle \sigma _{i}\in \{\pm 1\}} represents...