Singularity Analysis and Integrability of a Burgers-Type System of Foursov [PDF]
, 2011 We apply the Painleve test for integrability of partial differential equations to a system of two coupled Burgers-type equations found by Foursov, which was recently shown by Sergyeyev to possess infinitely many commuting local generalized symmetries ...
Sakovich, Sergei
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From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity. [PDF]
Physical Review Letters, 2016 Using shortcuts to adiabaticity, we solve the time-dependent Schrödinger equation that is reduced to a classical nonlinear integrable equation. For a given time-dependent Hamiltonian, the counterdiabatic term is introduced to prevent nonadiabatic ...
Manaka Okuyama, Kazutaka Takahashi
semanticscholar +1 more source
Signatures of quantum integrability and exactly solvable dynamics in an infinite-range many-body Floquet spin system [PDF]
Physical review BIn a recent work Sharma and Bhosale [Phys. Rev. B, 109, 014412 (2024)], $N$-spin Floquet model having infinite range Ising interaction was introduced. In this paper, we generalized the strength of interaction to $J$, such that $J=1$ case reduces to the ...
Harshit Sharma, Udaysinh T. Bhosale
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Hypergeometric $\tau$ Functions of the $q$-Painlev\'e Systems of Types $A_4^{(1)}$ and $(A_1+A_1')^{(1)}$ [PDF]
, 2016 We consider $q$-Painlev\'e equations arising from birational representations of the extended affine Weyl groups of $A_4^{(1)}$- and $(A_1+A_1)^{(1)}$-types.
Nakazono, Nobutaka
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Three magnons in an isotropic S = 1 ferromagnetic chain as an exactly solvable non-integrable system [PDF]
, 2015 It is shown that a generalization of the Bethe ansatz based on a utilization of degenerative discrete-diffractive wave functions solves the three-magnon problem for the S = 1 isotropic ferromagnetic infinite chain.
P. Bibikov
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Properties of Stark Resonant States in Exactly Solvable Systems
, 2015 Properties of Stark resonant states are studied in two exactly solvable systems. These resonances are shown to form a biorthogonal system with respect to a pairing defined by a contour integral that selects states with outgoing wave boundary conditions ...
J. Brown, M. Kolesik
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Quasi-classical expansion of the star-triangle relation and integrable systems on quad-graphs [PDF]
, 2016 In this paper we give an overview of exactly solved edge-interaction models, where the spins are placed on sites of a planar lattice and interact through edges connecting the sites.
V. Bazhanov, A. P. Kels, S. Sergeev
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Exactly solvable `discrete' quantum mechanics; shape invariance, Heisenberg solutions, annihilation-creation operators and coherent states [PDF]
, 2008 Various examples of exactly solvable `discrete' quantum mechanics are explored explicitly with emphasis on shape invariance, Heisenberg operator solutions, annihilation-creation operators, the dynamical symmetry algebras and coherent states.
Odake, Satoru, Sasaki, Ryu
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Quasi-Exactly Solvable N-Body Spin Hamiltonians with Short-Range Interaction Potentials [PDF]
, 2006 We review some recent results on quasi-exactly solvable spin models presenting near-neighbors interactions. These systems can be understood as cyclic generalizations of the usual Calogero-Sutherland models.
Enciso, A. +3 more
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Noncommutative Root Space Witt, Ricci Flow, and Poisson Bracket Continual Lie Algebras [PDF]
, 2009 We introduce new examples of mappings defining noncommutative root space generalizations for the Witt, Ricci flow, and Poisson bracket continual Lie ...
Zuevsky, Alexander
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