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Autor:
FYODOROV, Y. V.1 yan.fyodorov@kcl.ac.uk
Publikováno v:
Acta Physica Polonica: A. Dec2023, Vol. 144 Issue 6, p447-455. 9p.
Publikováno v:
Annals of Probability 2016, Vol. 44, No. 4, 2980-3031
The goal of this paper is to establish a relation between characteristic polynomials of $N\times N$ GUE random matrices $\mathcal{H}$ as $N\to\infty$, and Gaussian processes with logarithmic correlations. We introduce a regularized version of fractio
Externí odkaz:
http://arxiv.org/abs/1312.0212
Autor:
Fyodorov, Y. V., Savin, D. V.
Publikováno v:
Phys. Rev. Lett. 108, 184101 (2012)
We consider an open (scattering) quantum system under the action of a perturbation of its closed counterpart. It is demonstrated that the resulting shift of resonance widths is a sensitive indicator of the non-orthogonality of resonance wavefunctions
Externí odkaz:
http://arxiv.org/abs/1201.3357
Publikováno v:
J. Stat. Mech. (2011) L03001
We calculate perturbatively the multifractality spectrum of wave-functions in critical random matrix ensembles in the regime of weak multifractality. We show that in the leading order the spectrum is universal, while the higher order corrections are
Externí odkaz:
http://arxiv.org/abs/1101.4532
Autor:
Fyodorov, Y. V., Savin, D. V.
Publikováno v:
The Oxford Handbook of Random Matrix Theory, edited by G. Akemann, J. Baik, and P. Di Francesco (Oxford University Press, Oxford, 2011): pp. 703-722
This is a brief overview of RMT applications to quantum or wave chaotic resonance scattering, focusing mainly on theoretical results obtained via non-perturbative methods starting from mid-nineties.
Comment: 22 pages, chapter for the Oxford Hand
Comment: 22 pages, chapter for the Oxford Hand
Externí odkaz:
http://arxiv.org/abs/1003.0702
Publikováno v:
J. Stat. Mech. (2009) L12001
We demonstrate that by considering disordered single-particle Hamiltonians (or their random matrix versions) on ultrametric spaces one can generate an interesting class of models exhibiting Anderson metal-insulator transition. We use the weak disorde
Externí odkaz:
http://arxiv.org/abs/0909.4704
Publikováno v:
J. Math. Phys. 49, 053507 (2008)
We revisit a long standing issue in the theory of disordered electron systems and their effective description by a non-linear sigma model: the hyperbolic Hubbard-Stratonovich (HS) transformation in the bosonic sector. For time-reversal invariant syst
Externí odkaz:
http://arxiv.org/abs/0801.4960
Autor:
Wei, Y., Fyodorov, Y. V.
Publikováno v:
J. Phys. A, Vol 40 (2007) 13587-13605
Rigorous justification of the Hubbard-Stratonovich transformation for the Pruisken-Sch\"afer type of parameterisations of real hyperbolic O(m,n)-invariant domains remains a challenging problem. We show that a naive choice of the volume element invali
Externí odkaz:
http://arxiv.org/abs/math-ph/0703001
Publikováno v:
Phys. Rev. Lett. 97, 046803 (2006)
Two exact relations between mutlifractal exponents are shown to hold at the critical point of the Anderson localization transition. The first relation implies a symmetry of the multifractal spectrum linking the multifractal exponents with indices $q<
Externí odkaz:
http://arxiv.org/abs/cond-mat/0603378