52,233 research outputs found
Pseudo-random operators of the circular ensembles
We demonstrate quantum algorithms to implement pseudo-random operators that
closely reproduce statistical properties of random matrices from the three
universal classes: unitary, symmetric, and symplectic. Modified versions of the
algorithms are introduced for the less experimentally challenging quantum
cellular automata. For implementing pseudo-random symplectic operators we
provide gate sequences for the unitary part of the time-reversal operator.Comment: 5 pages, 4 figures, to be published PR
Pseudo-unitary symmetry and the Gaussian pseudo-unitary ensemble of random matrices
Employing the currently discussed notion of pseudo-Hermiticity, we define a
pseudo-unitary group. Further, we develop a random matrix theory which is
invariant under such a group and call this ensemble of pseudo-Hermitian random
matrices as the pseudo-unitary ensemble. We obtain exact results for the
nearest-neighbour level spacing distribution for (2 X 2) PT-symmetric
Hamiltonian matrices which has a novel form, s log (1/s) near zero spacing.
This shows a level repulsion in marked distinction with an algebraic form in
the Wigner surmise. We believe that this paves way for a description of varied
phenomena in two-dimensional statistical mechanics, quantum chromodynamics, and
so on.Comment: 9 pages, 2 figures, LaTeX, submitted to the Physical Review Letters
on August 20, 200
Entanglement of pseudo-Hermitian random states
In a recent paper (arXiv:1905.07348v1), Dyson scheme to deal with density
matrix of non-Hermitian Hamiltonians has been used to investigate the
entanglement of states of a PT-symmetric bosonic system. They found that von
Neumann entropy can show a different behavior in the broken and unbroken
regime. We show that their results can be recast in terms of an abstract model
of pseudo-Hermitian random matrices. It is found however that, although the
formalism is practically the same, the entanglement is not of Fock states but
of Bell states.Comment: 15 pages, 2 figure
Gaussian-random Ensembles of Pseudo-Hermitian Matrices
Attention has been brought to the possibility that statistical fluctuation
properties of several complex spectra, or, well-known number sequences may
display strong signatures that the Hamiltonian yielding them as eigenvalues is
PT-symmetric (Pseudo-Hermitian). We find that the random matrix theory of
pseudo-Hermitian Hamiltonians gives rise to new universalities of level-spacing
distributions other than those of GOE, GUE and GSE of Wigner and Dyson. We call
the new proposals as Gaussian Pseudo-Orthogonal Ensemble and Gaussian
Pseudo-Unitary Ensemble. We are also led to speculate that the enigmatic
Riemann-zeros ( would rather correspond to some
PT-symmetric (pseudo-Hermitian) Hamiltonian.Comment: Invited Talk Delivered in II International Workshop on
`Pseudo-Hermitian Hanmiltonians in Physics' at Prague, June 14-16, 200
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