Implications of Spin-Unitary Spin Independence

M. A. B. Bég, Virendra Pratap Singh

Lukas Rammelmüller, Y. Hou, Joaquín E. Drut +1 more

We theoretically study the pairing behavior of the unitary Fermi gas in the normal phase. Our analysis is based on the static spin susceptibility, which characterizes the response to an external magnetic field. We obtain this quantity by means of the complex Langevin approach and compare our calculations to available literature data in the spin-balanced case. Furthermore, we present results for polarized systems, where we complement and expand our analysis at high temperature with high-order virial expansion results. The implications of our findings for the phase diagram of the spin-polarized unitary Fermi gas are discussed in the context of the state of the art.

Herbert Joseph Bernstein

A conjecture that the (n −1)2 independent moduli and (2n −1) unphysical phases completely specify all n-dimensional unitary matrices is shown to be true in two and three dimensions, but false in four or more. The implications for quantum theory are discussed.

Sebastian Saner

P. Bruno

Jaroslav Novotný, G. Alber, Igor Jex

Abstract We analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic dynamics is described by a diagonalizable superoperator. We prove that this asymptotic dynamics takes place in a typically low dimensional attractor space which is independent of the probability distribution of the unitary operations applied. This vector space is spanned by all eigenvectors of the unitary operations involved which are associated with eigenvalues of unit modulus. Implications for possible asymptotic dynamics of iterated random unitary operations are presented and exemplified in an example involving random controlled-not operations acting on two qubits.