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Full-Text Articles in Physics
Mutually Unbiased Bases And Trinary Operator Sets For N Qutrits, Jay Lawrence
Mutually Unbiased Bases And Trinary Operator Sets For N Qutrits, Jay Lawrence
Dartmouth Scholarship
A complete 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 3^N are isomorphic to all MCS's, and show how this result applies in specific cases. For two qutrits, the 80 traceless operators partition into 10 MCS's. We prove that 4 of the corresponding basis sets must be separable, while 6 must be totally entangled (and Bell-like). For three qutrits, 728 operators …
Vibrational Modes Of Thin Oblate Clouds Of Charge, Thomas G. Jenkins, Ross L. Spencer
Vibrational Modes Of Thin Oblate Clouds Of Charge, Thomas G. Jenkins, Ross L. Spencer
Faculty Publications
A numerical method is presented for finding the eigenfunctions (normal modes) and mode frequencies of azimuthally symmetric non-neutral plasmas confined in a Penning trap whose axial thickness is much smaller than their radial size. The plasma may be approximated as a charged disk in this limit; the normal modes and frequencies can be found if the surface charge density profile sigma(r) of the disk and the trap bounce frequency profile wz(r) are known. The dependence of the eigenfunctions and equilibrium plasma shapes on nonideal components of the confining Penning trap fields is discussed. The results of the calculation are compared …