Matches in SemOpenAlex for { <https://semopenalex.org/work/W1991101850> ?p ?o ?g. }
- W1991101850 abstract "We consider $Nifmmodetimeselsetexttimesfi{}N$ Gaussian random matrices, whose average density of eigenvalues has the Wigner semicircle form over $[ensuremath{-}sqrt{2},sqrt{2}]$. For such matrices, using a Coulomb gas technique, we compute the large $N$ behavior of the probability ${mathcal{P}}_{N,L}({N}_{L})$ that ${N}_{L}$ eigenvalues lie within the box $[ensuremath{-}L,L]$. This probability scales as ${mathcal{P}}_{N,L}({N}_{L}={ensuremath{kappa}}_{L}N)ensuremath{approx}mathrm{exp}mathbf{(}ensuremath{-}ensuremath{beta}{N}^{2}{ensuremath{psi}}_{L}({ensuremath{kappa}}_{L})mathbf{)}$, where $ensuremath{beta}$ is the Dyson index of the ensemble and ${ensuremath{psi}}_{L}({ensuremath{kappa}}_{L})$ is a $ensuremath{beta}$-independent rate function that we compute exactly. We identify three regimes as $L$ is varied: (i) ${N}^{ensuremath{-}1}ensuremath{ll}L<sqrt{2}$ (bulk), (ii) $Lensuremath{sim}sqrt{2}$ on a scale of $mathcal{O}({N}^{ensuremath{-}2/3})$ (edge), and (iii) $L>sqrt{2}$ (tail). We find a dramatic nonmonotonic behavior of the number variance ${V}_{N}(L)$ as a function of $L$: after a logarithmic growth $ensuremath{propto}mathrm{ln}(NL)$ in the bulk (when $Lensuremath{sim}mathcal{O}(1/N)$), ${V}_{N}(L)$ decreases abruptly as $L$ approaches the edge of the semicircle before it decays as a stretched exponential for $L>sqrt{2}$. This ``dropoff'' of ${V}_{N}(L)$ at the edge is described by a scaling function ${stackrel{texttildelow{}}{V}}_{ensuremath{beta}}$ that smoothly interpolates between the bulk (i) and the tail (iii). For $ensuremath{beta}=2$ we compute ${stackrel{texttildelow{}}{V}}_{2}$ explicitly in terms of the Airy kernel. These analytical results, verified by numerical simulations, directly provide for $ensuremath{beta}=2$ the full statistics of particle-number fluctuations at zero temperature of 1D spinless fermions in a harmonic trap." @default.
- W1991101850 created "2016-06-24" @default.
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- W1991101850 date "2014-06-26" @default.
- W1991101850 modified "2023-10-18" @default.
- W1991101850 title "Phase Transitions and Edge Scaling of Number Variance in Gaussian Random Matrices" @default.
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- W1991101850 doi "https://doi.org/10.1103/physrevlett.112.254101" @default.
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