منابع مشابه
Integrable matrix theory: Level statistics.
We study level statistics in ensembles of integrable N×N matrices linear in a real parameter x. The matrix H(x) is considered integrable if it has a prescribed number n>1 of linearly independent commuting partners H^{i}(x) (integrals of motion) [H(x),H^{i}(x)]=0, [H^{i}(x),H^{j}(x)]=0, for all x. In a recent work [Phys. Rev. E 93, 052114 (2016)2470-004510.1103/PhysRevE.93.052114], we developed ...
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We give a reinterpretation of the matrix theory discussed by Moore, Nekrasov and Shatashivili (MNS) in terms of the second quantized operators which describes the homology class of the Hilbert scheme of points on surfaces. It naturally relate the contribution from each pole to the inner product of orthogonal basis of free boson Fock space. These basis can be related to the eigenfunctions of Cal...
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The number of levels with energy less than E of an integrable quantum system with two degrees of freedom is equal to XE+sE', where A, is a constant and s a Auctuating quantity with a non-Gaussian distribution. The probability distribution of s decreases roughly like exp( —s ) when s is large. The number of levels between E and E+zJE is equal to kz JE+rE 'I where r is another lluctuating quantit...
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By extending the approach of Berry and Robnik, the limiting level spacing distribution of a system consisting of infinitely many independent components is investigated. The limiting level spacing distribution is characterized by a single monotonically increasing function μ̄(S) of the level spacing S. Three cases are distinguished: (i) Poissonian if μ̄(+∞) = 0, (ii) Poissonian for large S, but pos...
متن کاملRandom Matrix Theory , Interacting Particle Systems and Integrable Systems Percy
The proposal sought a five-year renewal of NSF funding to support the Institute’s fundamental mission to advance scientific research and collaboration among mathematicians hosted through MSRI’s programs and workshops. The proposal made a strong case for a substantial increase in funding over the level of the past ten years of the NSF Core Grant. It was written by the Directorate in consultation...
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ژورنال
عنوان ژورنال: Physical Review E
سال: 2016
ISSN: 2470-0045,2470-0053
DOI: 10.1103/physreve.94.032106