Two-time correlation functions and the Lee-Yang zeros for an interacting Bose gas

Two-time correlation functions of a system of Bose particles are studied. We find a relation of zeros of the correlation functions with the Lee-Yang zeros of the partition function of the system. The obtained relation gives the possibility to observe the Lee-Yang zeros experimentally. A particular case of Bose particles on two levels is examined, and zeros of two-time correlation functions and Lee-Yang zeros of the partition function of the system are analyzed.

Figure 1

Zeros of the correlation function (marked by crosses) and Lee-Yang zeros (marked by circles) in the limit $\beta \to 0$ for (a) $N=50$, (b) $N=100$.

Figure 2

Zeros of correlation function (26) (marked by crosses) and zeros of partition function (24) (marked by circles) for (a) $N=50, 2\beta \gamma =-1$; (b) $N=100, 2\beta \gamma =-1$.

Figure 3

Zeros of correlation function (26) (marked by crosses) and zeros of partition function (24) (marked by circles) for (a) $N=50, 2\beta \gamma =-0.01$; (b) $N=100, 2\beta \gamma =-0.01$.

Figure 4

Zeros of correlation function (26) (marked by crosses) and zeros of partition function (24) (marked by circles) for (a) $N=50, 2\beta \gamma =0.01$; (b) $N=100, 2\beta \gamma =0.01$.

Figure 5

Zeros of correlation function (26) (marked by crosses) and zeros of partition function (24) (marked by circles) for (a) $N=50, 2\beta \gamma =0.1$; (b) $N=100, 2\beta \gamma =0.1$.

Figure 6

Zeros of correlation function (26) (marked by crosses) and zeros of partition function (24) (marked by circles) for $N=20, 2\beta \gamma =ln2$ (a) in the complex plane $q$; (b) in logarithmic scale.