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A theoretical physicist who studied quantum correlations in ideal gases with Takafumi Kita. Their fixed-particle-number treatment reproduces fermion antibunching from the Pauli exclusion principle and boson bunching associated with the Hanbury Brown and Twiss effect. It also follows how correlations change through Bose-Einstein condensation, connecting particle statistics to measurable pair-detection behavior.^[ref]

There is a state-assumption issue. For a number-conserving Gaussian quantum state with no anomalous contractions, put ${\psi }_i=\psi ({\mathbf{r}}_i)$, $n_i=⟨{\psi }_i^{†}{\psi }_i⟩$ and the one-body density matrix $g_{ij}=⟨{\psi }_i^{†}{\psi }_j⟩$. Wick's theorem pairs each creation operator with an annihilation operator. The direct pairing gives $n_1{n}_2$; the exchanged pairing gives $ϵg_{12}{g}_{21}$, with $ϵ=+1$ for bosons and $-1$ for fermions. Hencenormal ordering removes the equal-position delta-function self-counting term. Fermionic occupation-number product states are Slater determinants and obey this Wick theorem. Independent thermal bosonic modes also obey it, with $N_{\alpha }$ understood as mean occupations.

A bosonic Fock product state does not generally obey the asserted identity. The bosonic number-state corrections to Gaussian density correlations follow from $⟨a_{\alpha }^{†2}{a}_{\alpha }^2⟩=N_{\alpha }(N_{\alpha }-1)$ and giveFor one occupied mode this is $N(N-1)|{\phi }_1{|}^2|{\phi }_2{|}^2$, whereas the uncorrected Gaussian expression gives $2N^2|{\phi }_1{|}^2|{\phi }_2{|}^2$. This counterexample disproves the asserted identity for arbitrary bosonic number-product states. The formulas below give both the Gaussian result, with its additional state assumption, and the exact bosonic number-state alternative. The ensemble distinction is also explicit in a later primary treatment of ideal-gas correlations.^[ref]

A theoretical physicist who, with Kazumasa Tsutsui, derived reduced density matrices for ideal Bose gas and Fermi gas systems with fixed particle number. Their 2016 analysis distinguishes the canonical ensemble from familiar grand canonical ensemble applications of Wick's theorem, making explicit which particle-number assumptions enter calculations of quantum correlations.^[ref]