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Introduction to ‘Quantum Integrability in Out of Equilibrium Systems’

Pasquale Calabrese, Fabian H. L. Eßler, Giuseppe Mussardo

Introduction to the field of quantum integrable models

Journal of Statistical Mechanics Theory and ExperimentJun 1, 2016358 citations

Bethe vectors and form factors for two-component bose gas

E. Ragoucy

This short note presents works done in collaboration with S. Pakuliak (JINR, Dubna) and N. Slavnov (Steklov Math. Inst., Moscow). It is a summary of the articles arXiv:1412.6037, arXiv:1501.07566, arXiv:1502.01966 and arXiv:1503.00546. Here are mentioned only references used for our calculations. A detailed list of references can be found in our articles mentionned here.

arXiv:1609.08951Physics of Particles and Nuclei LettersMar 1, 20170 citations

Generalized Coordinate Bethe Ansatz for open spin chains with non-diagonal boundaries

E. Ragoucy

We introduce a generalization of the original Coordinate Bethe Ansatz that allows to treat the case of open spin chains with non-diagonal boundary matrices. We illustrate it on two cases: the XXX and XXZ chains. Short review on a joint work with N. Crampe (L2C) and D. Simon (LPMA), see arXiv:1009.4119, arXiv:1105.4119 and arXiv:1106.3264.

arXiv:1109.6189Journal of Physics Conference SeriesFeb 8, 20123 citations

\textbf{Non-equilibrium Aspects of Quantum Integrable Systems}

Natan Andrei

Bulletin of the American Physical SocietyMar 14, 20160 citations

Non-equilibrium Aspects of Quantum Integrable Systems

Natan Andrei

APSJan 1, 20160 citations

Construction of a coordinate Bethe ansatz for the asymmetric simple exclusion process with open boundaries

Damien Simon

The asymmetric simple exclusion process with open boundaries, which is a very simple model of out-of-equilibrium statistical physics, is known to be integrable. In particular, its spectrum can be described in terms of Bethe roots. The large deviation function of the current can be obtained as well by diagonalizing a modified transition matrix, which is still integrable: the spectrum of this new matrix can also be described in terms of Bethe roots for special values of the parameters. However, due to the algebraic framework used to write the Bethe equations in previous works, the nature of the excitations and the full structure of the eigenvectors remained unknown. This paper explains why the eigenvectors of the modified transition matrix are physically relevant, gives an explicit expression for the eigenvectors and applies it to the study of atypical currents. It also shows how the coordinate Bethe ansatz developed for the excitations leads to a simple derivation of the Bethe equations and of the validity conditions of this ansatz. All the results obtained by de Gier and Essler are recovered and the approach gives a physical interpretation of the exceptional points. The overlap of this approach with other tools such as the matrix ansatz is also discussed. The method that is presented here may be not specific to the asymmetric exclusion process and may be applied to other models with open boundaries to find similar exceptional points.The asymmetric simple exclusion process with open boundaries, which is a very simple model of out-of-equilibrium statistical physics, is known to be integrable. In particular, its spectrum can be described in terms of Bethe roots. The large deviation function of the current can be obtained as well by diagonalizing a modified transition matrix, which is still integrable: the spectrum of this new matrix can also be described in terms of Bethe roots for special values of the parameters. However, due to the algebraic framework used to write the Bethe equations in previous works, the nature of the excitations and the full structure of the eigenvectors remained unknown. This paper explains why the eigenvectors of the modified transition matrix are physically relevant, gives an explicit expression for the eigenvectors and applies it to the study of atypical currents. It also shows how the coordinate Bethe ansatz developed for the excitations leads to a simple derivation of the Bethe equations and of the validity conditions of this ansatz. All the results obtained by de Gier and Essler are recovered and the approach gives a physical interpretation of the exceptional points. The overlap of this approach with other tools such as the matrix ansatz is also discussed. The method that is presented here may be not specific to the asymmetric exclusion process and may be applied to other models with open boundaries to find similar exceptional points.

arXiv:0903.4968Journal of Statistical Mechanics Theory and ExperimentJul 8, 2009109 citations

Integrability in out-of-equilibrium systems

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Integrability in out-of-equilibrium systems

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