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Title: Solvable Hydrodynamics of Quantum Integrable Systems

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Publication Date:
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
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Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 119; Journal Issue: 22; Related Information: CHORUS Timestamp: 2017-11-30 16:32:36; Journal ID: ISSN 0031-9007
American Physical Society
Country of Publication:
United States

Citation Formats

Bulchandani, Vir B., Vasseur, Romain, Karrasch, Christoph, and Moore, Joel E.. Solvable Hydrodynamics of Quantum Integrable Systems. United States: N. p., 2017. Web. doi:10.1103/PhysRevLett.119.220604.
Bulchandani, Vir B., Vasseur, Romain, Karrasch, Christoph, & Moore, Joel E.. Solvable Hydrodynamics of Quantum Integrable Systems. United States. doi:10.1103/PhysRevLett.119.220604.
Bulchandani, Vir B., Vasseur, Romain, Karrasch, Christoph, and Moore, Joel E.. 2017. "Solvable Hydrodynamics of Quantum Integrable Systems". United States. doi:10.1103/PhysRevLett.119.220604.
title = {Solvable Hydrodynamics of Quantum Integrable Systems},
author = {Bulchandani, Vir B. and Vasseur, Romain and Karrasch, Christoph and Moore, Joel E.},
abstractNote = {},
doi = {10.1103/PhysRevLett.119.220604},
journal = {Physical Review Letters},
number = 22,
volume = 119,
place = {United States},
year = 2017,
month =

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on November 30, 2018
Publisher's Accepted Manuscript

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  • Solvable quantum versions of the classical dynamical system characterized by the Hamiltonian {ital H}={summation}{sup {ital n}}{sub {ital j},{ital k}=1}{ital p}{sub {ital jp}}{sub {ital k}}[{lambda}+{mu}cos({ital q}{sub {ital j}}{minus}{ital q}{sub {ital k}}) ] are presented. The eigenvalues of the quantum Hamiltonians are exhibited, as well as the corresponding eigenfunctions. {copyright} {ital 1996 American Institute of Physics.}
  • The review presents a constructive investigation of exactly integrable one- and two-dimensional quantum systems that possess a nontrivial internal symmetry group.
  • An equivalence of two quantum integrable systems with a complete set of quadratic integrals of motion is established.
  • We study quantum integrable systems of interacting particles from the point of view proposed by A. Gorsky and N. Nekrasov. We obtain the Sutherland system by a Hamiltonian reduction of an integrable system on the cotangent bundles to an affine su(N) algebra and show that it coincides with the Yang-Mills theory on a cylinder. We point out that there exists a tower of 2d quantum field theories. The top of this tower is the gauged G/C WZW model on a cylinder with an inserted Wilson line in an appropriate representation, which in our approach corresponds to Ruijsenaars` relativistic Calogero model.more » Its degeneration yields the 2d Yang-Mills theory, whose small radius limit is the Calogero model itself. We make some comments about the spectra and eigenstates of the models, which one can get from their equivalence with the field theories. Also we point out some possibilities of elliptic deformations of these constructions.« less
  • For the example of the generalized Toda chain in two-dimensional space it is shown that in the quantum domain the semisimple algebras of the classical problem go over into the associative Hopf algebras described by Drinfel'd as quantum algebras. In terms of the quantum algebras, the Heisenberg operators of the interacting field can be expressed as functions of the in fields by means of the formulas of the classical theory, and the expressions obtained earlier for them acquire a simple algebraic meaning.