| 1. |
- Atkin, Max R., et al.
(författare)
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On the ratio probability of the smallest eigenvalues in the Laguerre unitary ensemble
- 2018
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Ingår i: Nonlinearity. - : IOP PUBLISHING LTD. - 0951-7715 .- 1361-6544. ; 31:4, s. 1155-1196
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Tidskriftsartikel (refereegranskat)abstract
- We study the probability distribution of the ratio between the second smallest and smallest eigenvalue in the n x n Laguerre unitary ensemble. The probability that this ratio is greater than r > 1 is expressed in terms of an n x n Hankel determinant with a perturbed Laguerre weight. The limiting probability distribution for the ratio as n -> infinity is found as an integral over (0, infinity) containing two functions q(1)(x) and q(2)(x). These functions satisfy a system of two coupled Painleve V equations, which are derived from a Lax pair of a Riemann-Hilbert problem. We compute asymptotic behaviours of these functions as rx -> 0(+) and (r - 1)x -> infinity, as well as large n asymptotics for the associated Hankel determinants in several regimes of r and x.
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| 2. |
- Charlier, Christophe, et al.
(författare)
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Asymptotics for Hankel Determinants Associated to a Hermite Weight with a Varying Discontinuity
- 2018
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Ingår i: Symmetry, Integrability and Geometry. - : NATL ACAD SCI UKRAINE, INST MATH. - 1815-0659. ; 14
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Tidskriftsartikel (refereegranskat)abstract
- We study n x n Hankel determinants constructed with moments of a Hermite weight with a Fisher-Hartwig singularity on the real line. We consider the case when the singularity is in the bulk and is both of root-type and jump-type. We obtain large n asymptotics for these Hankel determinants, and we observe a critical transition when the size of the jumps varies with n. These determinants arise in the thinning of the generalised Gaussian unitary ensembles and in the construction of special function solutions of the Painleve IV equation.
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| 3. |
- Salemi, Leandro, et al.
(författare)
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Spin-dependent properties in zigzag graphene nanoribbons with phenyl-edge defects
- 2018
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Ingår i: Physical Review B. - : AMER PHYSICAL SOC. - 2469-9950 .- 2469-9969. ; 98:21
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Tidskriftsartikel (refereegranskat)abstract
- Recent outbreaks in bottom-up chemical techniques have demonstrated the synthesis of atomically perfect zigzag graphene nanoribbons (ZGNRs) and of their corresponding analogs with phenyl-edge functionalization [P. Ruffieux et al., Nature 531, 489 (2016)]. Since spin-polarized currents can be generated at the edges of the ZGNRs, the control of phenyl decoration at the zigzag edges could accurately tune the electronic properties of these carbon-based nanoribbons. In the present paper, using first-principles calculations and a Landauer-Buttiker approach, the electronic and magnetic properties as well as the spin-resolved transmissions are investigated in various phenyl-edge-modified ZGNRs. The understanding of the spin-dependent transport properties in relation to the atomic structure opens the way to design devices such as spin valves for future spintronics applications.
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