Daniel Braun et al 1997 J. Phys. A: Math. Gen. 30 L117 doi:10.1088/0305-4470/30/6/002
Time-reversal symmetry and random polynomials
Daniel Braun
, Marek Kus,
and Karol Zyczkowski,§
LETTER TO THE EDITOR
We analyse the density of roots of random polynomials where each complex coefficient is constructed of a random modulus and a fixed, deterministic phase. The density of roots is shown to possess a singular component only in the case for which the phases increase linearly with the index of coefficients. This means that, contrary to earlier belief, eigenvectors of a typical quantum chaotic system with some antiunitary symmetry will not display a clustering curve in the stellar representation. Moreover, a class of time-reverse invariant quantum systems is shown, for which spectra display fluctuations characteristic of orthogonal ensemble, while eigenvectors confer to predictions of unitary ensemble.
- PACS
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02.10.De Algebraic structures and number theory
- MSC
- Subjects
- Dates
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Issue 6 (21 March 1997)
Received 21 November 1996
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Time-reversal symmetry and random polynomials
Daniel Braun et al 1997 J. Phys. A: Math. Gen. 30 L117
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