Completely integrable systems and groups generated by reflections.
Eugene Gutkin,Bill Sutherland +1 more
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TLDR
A class of quantum Hamiltonian systems with delta-function potential, related to groups generated by reflections, are introduced and it is shown that these systems are completely integrable and they integrate explicitly.Abstract:
We introduce a class of quantum Hamiltonian systems with δ-function potential, related to groups generated by reflections. They generalize the system of equal elastic particles on the line. We show that these systems are completely integrable and we integrate them explicitly. Then we apply our technique to obtain identities for groups generated by reflections.read more
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Quantum Integrable Systems Related to Lie Algebras
TL;DR: In this article, a review of quantum integrable finite-dimensional systems related to Lie algebras is presented, which contains results such as the forms of spectra, wave functions, S-matrices and quantum integrals of motion.
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The Bethe Wavefunction
TL;DR: Gaudin's La fonction d'onde de Bethe as discussed by the authors is a uniquely influential masterpiece on exactly solvable models of quantum mechanics and statistical physics and is available in English for the first time.
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Periodic Integrable Systems with Delta-Potentials
TL;DR: In this paper, the root system generalization of the quantum Bose-gas on the circle with pairwise delta function interactions is studied, and the underlying symmetry structures are governed by the associated graded algebra of Cherednik's degenerate double affine Hecke algebra, acting by Dunkl-type differential-reflection operators.
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Directed random polymers via nested contour integrals
TL;DR: In this article, the authors studied the partition function of two versions of the continuum directed polymer in 1 + 1 dimension, and derived exact formulas for the Laplace transforms of the partition functions.
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TL;DR: In this paper, Newtonian mechanics: experimental facts investigation of the equations of motion, variational principles Lagrangian mechanics on manifolds oscillations rigid bodies, differential forms symplectic manifolds canonical formalism introduction to pertubation theory.
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TL;DR: Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements as mentioned in this paper.
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