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- A.R. Its
- Leningrad Branch of the Steklov Mathematical Institute, Academy of Sciences of the U.S.S.R., Fontanka 27, Lomi, Leningrad U.S.S.R. 191011, U.S.S.R.
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- A.G. Izergin
- Leningrad Branch of the Steklov Mathematical Institute, Academy of Sciences of the U.S.S.R., Fontanka 27, Lomi, Leningrad U.S.S.R. 191011, U.S.S.R.
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- V.E. Korepin
- Leningrad Branch of the Steklov Mathematical Institute, Academy of Sciences of the U.S.S.R., Fontanka 27, Lomi, Leningrad U.S.S.R. 191011, U.S.S.R.
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- N.A. Slavnov
- Leningrad Branch of the Steklov Mathematical Institute, Academy of Sciences of the U.S.S.R., Fontanka 27, Lomi, Leningrad U.S.S.R. 191011, U.S.S.R.
書誌事項
- 公開日
- 1990-04
- DOI
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- 10.1142/s0217979290000504
- 公開者
- World Scientific Pub Co Pte Ltd
この論文をさがす
説明
<jats:p> The quantum nonlinear Schrödinger equation (one dimensional Bose gas) is considered. Classification of representations of Yangians with highest weight vector permits us to represent correlation function as a determinant of a Fredholm integral operator. This integral operator can be treated as the Gelfand-Levitan operator for some new differential equation. These differential equations are written down in the paper. They generalize the fifth Painlève transcendent, which describe equal time, zero temperature correlation function of an impenetrable Bose gas. These differential equations drive the quantum correlation functions of the Bose gas. The Riemann problem, associated with these differential equations permits us to calculate asymp-totics of quantum correlation functions. Quantum correlation function (Fredholm determinant) plays the role of τ functions of these new differential equations. For the impenetrable Bose gas space and time dependent correlation function is equal to τ function of the nonlinear Schrödinger equation itself, For a penetrable Bose gas (finite coupling constant c) the correlator is τ-function of an integro-differentiation equation. </jats:p>
収録刊行物
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- International Journal of Modern Physics B
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International Journal of Modern Physics B 04 (05), 1003-1037, 1990-04
World Scientific Pub Co Pte Ltd
