Universal Quantum Viscosity in a Unitary Fermi Gas | Science
Mutually unbiased bases and trinary operator sets for N A compete orthonormal basis of N -qutrit unitary operators drawn from the Pauli group consists of the identity and 9 N -1 traceless operators. The traceless ones partition into 3 N +1 maximally commuting subsets (MCS’s) of 3 N -1 operators each, whose joint eigenbases are mutually unbiased. We prove that Pauli factor groups of order 3N are isomorphic to all MCS’s and show how SOME UNCOMMON MA TRIX THEOR Y - Reed College In particular, w e ha ve this sp ectral decomp osition of the unitary matrix ÒgeneratedÓ b y the an tihermitian matrix iA : U " ei A = (d k =1 |a k)ei a k (a k | I h ave b elab ored this familiar material in order to facilitate discussion of some closely related material whic h, b ecause only rarely called up on in ph ysical arXiv:1309.2921v1 [hep-th] 11 Sep 2013 In four dimensions, if a SFT is unitary, the condition that the theory is conformal (1.6) can be simplified (this follows from the unitarity bound on operator dimensions [19], see appendix A) to Vµ = ∂µL, i.e., Tµ µ = L . (1.8) Equation (1.8) is a necessary and sufficient condition for a unitary … Unitary Irreducible Representations of SL (3, R): Journal
¯h ∆ϕ is a unitary operation which rotates by ∆ϕabout the z axis. (Proof:Rˆ z(∆ϕ) is exactly e−i Hˆ h¯ t for t =∆ϕ/ω 0.) Being unitary means Rˆ z(∆ϕ)† =Rˆ z(∆ϕ)−1 =Rˆ z(−∆ϕ). So aligning B with the z axis results in rotation of the spin about the z axis. Each state is restricted to the line of latitude it
UNIT AR Y B ASES - reed.edu ¥ eac h of the ! -matrices is unitary ; ¥ the ! -matrices are trace -wise orthonormal : 1 2 tr)!i j * = )ij F rom the latter circumstance it follo ws moreo ver that ¥ eac h of the ! -matrices (with the exception only of ! 0) is traceless ; Ev ery 2 ! 2 matrix can b e dev elop ed A =!3 k =0 a k! k with a k = 1 2 tr) A ! … Addendum: Observation of an anti-PT-symmetric exceptional
• SU(2) = group of 2×2 unitary matrices with determinant = 1 • Structure constants: ϵijk • Aside: SU(2) is sometimes used as name for the more general rotation group, not just the 2×2 unitary traceless matrices. I will do that from now on because it’s shorter than writing “rotation group”.
¥ eac h of the ! -matrices is unitary ; ¥ the ! -matrices are trace -wise orthonormal : 1 2 tr)!i j * = )ij F rom the latter circumstance it follo ws moreo ver that ¥ eac h of the ! -matrices (with the exception only of ! 0) is traceless ; Ev ery 2 ! 2 matrix can b e dev elop ed A =!3 k =0 a k! k with a k = 1 2 tr) A ! … Addendum: Observation of an anti-PT-symmetric exceptional May 30, 2019 CiteSeerX — ZERO PATTERNS AND UNITARY SIMILARITY