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glS
glS
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When this Can the characteristic function is$\chi_\rho(\beta)={\rm tr}[\rho D(\beta)]$ be an indicator function?

Given the characteristic function defined as: $$\chi(\beta)=\text{tr}[\rho D(\beta)],$$ with $D(\alpha)$$D(\alpha)=e^{\alpha a^\dagger-\bar\alpha a}$ the displacement operator. Is it possible that for some $\rho$ we have $$\chi(\beta)=\textbf{1}_A,$$ for $\textbf{1}_A$ the indicator function of some area $A$ in phase-space?

When this characteristic function is an indicator function?

Given the characteristic function defined as: $$\chi(\beta)=\text{tr}[\rho D(\beta)],$$ with $D(\alpha)$ the displacement operator. Is it possible that for some $\rho$ we have $$\chi(\beta)=\textbf{1}_A,$$ for $\textbf{1}_A$ the indicator function of some area $A$ in phase-space?

Can the characteristic function $\chi_\rho(\beta)={\rm tr}[\rho D(\beta)]$ be an indicator function?

Given the characteristic function defined as: $$\chi(\beta)=\text{tr}[\rho D(\beta)],$$ with $D(\alpha)=e^{\alpha a^\dagger-\bar\alpha a}$ the displacement operator. Is it possible that for some $\rho$ we have $$\chi(\beta)=\textbf{1}_A,$$ for $\textbf{1}_A$ the indicator function of some area $A$ in phase-space?

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Qmechanic ♦
Qmechanic ♦
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Nicolas Medina Sanchez
Nicolas Medina Sanchez
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When this characteristic function is an indicator function?

Given the characteristic function defined as: $$\chi(\beta)=\text{tr}[\rho D(\beta)],$$ with $D(\alpha)$ the displacement operator. Is it possible that for some $\rho$ we have $$\chi(\beta)=\textbf{1}_A,$$ for $\textbf{1}_A$ the indicator function of some area $A$ in phase-space?