Probability distributions of linear statistics in chaotic cavities and associated phase transitions
- Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste (Italy)
We establish large deviation formulas for linear statistics on the N transmission eigenvalues (T{sub i}) of a chaotic cavity, in the framework of random matrix theory. Given any linear statistics of interest A=SIGMA{sub i=1}{sup N}a(T{sub i}), the probability distribution P{sub A}(A,N) of A generically satisfies the large deviation formula lim{sub N-}>{sub i}nfinity[-2 log P{sub A}(Nx,N)/betaN{sup 2}]=PSI{sub A}(x), where PSI{sub A}(x) is a rate function that we compute explicitly in many cases (conductance, shot noise, and moments) and beta corresponds to different symmetry classes. Using these large deviation expressions, it is possible to recover easily known results and to produce new formulas, such as a closed form expression for v(n)=lim{sub N-}>{sub i}nfinity var(T{sub n}) (where T{sub n}=SIGMA{sub i}T{sub i}{sup n}) for arbitrary integer n. The universal limit v*=lim{sub n-}>{sub i}nfinity v(n)=1/2pibeta is also computed exactly. The distributions display a central Gaussian region flanked on both sides by non-Gaussian tails. At the junction of the two regimes, weakly nonanalytical points appear, a direct consequence of phase transitions in an associated Coulomb gas problem. Numerical checks are also provided, which are in full agreement with our asymptotic results in both real and Laplace space even for moderately small N. Part of the results have been announced by Vivo et al. [Phys. Rev. Lett. 101, 216809 (2008)].
- OSTI ID:
- 21366696
- Journal Information:
- Physical Review. B, Condensed Matter and Materials Physics, Vol. 81, Issue 10; Other Information: DOI: 10.1103/PhysRevB.81.104202; (c) 2010 The American Physical Society; ISSN 1098-0121
- Country of Publication:
- United States
- Language:
- English
Similar Records
Measurements of interfacial area concentration in two-phase bubbly flow
A comprehensive laboratory study on the immersion freezing behavior of illite NX particles. A comparison of 17 ice nucleation measurement techniques