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Entanglement induced fluctuations of cold bosons

Ram Brustein and Amos Yarom

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Figure 1

Figure 1. Shown is a graph of the relative particle number fluctuations (\Delta N_V)^2/\langle
N_V\rangle in a sub-volume of size a of a one-dimensional box of size L with Dirichlet boundary conditions versus the relative size of the sub-volume a/L. Each color corresponds to a different initial state as specified by the legend.



Figure 2

Figure 2. Shown is a graph of the relative particle number fluctuations (\Delta N_V)^2/\langle
N_V\rangle for the case of a harmonic oscillator of mass m and frequency ω. The sub-volume is in the region –a < x < a and the fluctuations are plotted against the relative size of the sub-volume in units of \sqrt {m \omega / \hbar } . Each color corresponds to a different initial state as specified by the legend.



Figure 3

Figure 3. Logarithmic plot of energy fluctuations versus a/L for a one-dimensional box with periodic boundary conditions. Here, the UV cutoff π2Q2 is 10 000, the state is the 20th excited state (k = 20), and the mass has been chosen such that Ek2/(π2k2) = 1.




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