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Dynamical correlation functions for an impenetrable Bose gas with Neumann or Dirichlet boundary conditions

Takeo Kojima
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Abstract

We study the time and temperature dependent correlation functions for an impenetrable Bose gas with Neumann or Dirichlet boundary conditions $\langle \psi(x_1,0)\psi^\dagger(x_2,t)\rangle _{\pm,T}$. We derive the Fredholm determinant formulae for the correlation functions, by means of the Bethe Ansatz. For the special case $x_1=0$, we express correlation functions with Neumann boundary conditions $\langle\psi(0,0)\psi^\dagger(x_2,t)\rangle _{+,T}$, in terms of solutions of nonlinear partial differential equations which were introduced in \cite{kojima:Sl} as a generalization of the nonlinear Schr\"odinger equations. We generalize the Fredholm minor determinant formulae of ground state correlation functions $\langle\psi(x_1)\psi^\dagger(x_2)\rangle _{\pm,0}$ in \cite{kojima:K}, to the Fredholm determinant formulae for the time and temperature dependent correlation functions $\langle\psi(x_1,0)\psi^\dagger(x_2,t)\rangle _{\pm,T}$, $t \in {\bf R}$, $T \geq 0$.

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Takeo Kojima. 1999-01-01. Dynamical correlation functions for an impenetrable Bose gas with Neumann or Dirichlet boundary conditions. https://doi.org/10.2991/jnmp.1999.6.1.7

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