Article

# Reducing nonideal to ideal coupling in random matrix description of chaotic scattering: Application to the time-delay problem

Budker Institute of Nuclear Physics, Novo-Nikolaevsk, Novosibirsk, Russia
(Impact Factor: 2.29). 04/2001; 63(3 Pt 2):035202. DOI: 10.1103/PhysRevE.63.035202
Source: arXiv

ABSTRACT

We write explicitly a transformation of the scattering phases reducing the problem of quantum chaotic scattering for systems with M statistically equivalent channels at nonideal coupling to that for ideal coupling. Unfolding the phases by their local density leads to universality of their local fluctuations for large M. A relation between the partial time delays and diagonal matrix elements of the Wigner-Smith matrix is revealed for ideal coupling. This helped us in deriving the joint probability distribution of partial time delays and the distribution of the Wigner time delay.

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• "If instead the system is studied in the weak magnetic field limit, electronic transport is sensitive to the complex (chaotic) dynamics in the cavity. When the dwell time is much larger than the Thouless time, random matrix theory (RMT) is a powerful approach, which has allowed to obtain several results: for a perfect contact with N conducting channels, the distribution of C q for N = 1 [10], N = 2 [11] and large N [12]. The distribution of R q was found in the case N = 2 in Ref. [13] and the mean value R q h/(e 2 N T ) = R dc for N T 1 [14] [15]. "
##### Article: Capacitance and charge relaxation resistance of chaotic cavities - Joint distribution of two linear statistics in the Laguerre ensemble of random matrices
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ABSTRACT: We consider the AC transport in a quantum RC circuit made of a coherent chaotic cavity with a top gate. Within a random matrix approach, we study the joint distribution for the mesoscopic capacitance $C_\mu=(1/C+1/C_q)^{-1}$ and the charge relaxation resistance $R_q$, where $C$ is the geometric capacitance and $C_q$ the quantum capacitance. We study the limit of a large number of conducting channels $N$ with a Coulomb gas method. We obtain $\langle R_q\rangle\simeq h/(Ne^2)=R_\mathrm{dc}$ and show that the relative fluctuations are of order $1/N$ both for $C_q$ and $R_q$, with strong correlations $\langle \delta C_q\delta R_q\rangle/\sqrt{\langle \delta C_q^2\rangle\,\langle \delta R_q^2\rangle}\simeq+0.707$. The detailed analysis of large deviations involves a second order phase transition in the Coulomb gas. The two dimensional phase diagram is obtained.
EPL (Europhysics Letters) 07/2014; 109(5). DOI:10.1209/0295-5075/109/50004 · 2.10 Impact Factor
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• "= 1, P 1 (τ ) = (β/2) β/2 Γ(β/2) τ −2− β 2 e − β 2τ [17] and N = 2, P 2 (τ ) = β 3β+2 Γ(3(β+1)/2) Γ(β+1)Γ(3β+2) τ −3(β+1) U β+1 2 , 2(β + 1); β/τ e −β/τ [24] "
##### Article: Wigner Time-Delay Distribution in Chaotic Cavities and Freezing Transition
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ABSTRACT: Using the joint distribution for proper time delays of a chaotic cavity derived by Brouwer, Frahm, and Beenakker [Phys. Rev. Lett. 78, 4737 (1997)], we obtain, in the limit of the large number of channels N, the large deviation function for the distribution of the Wigner time delay (the sum of proper times) by a Coulomb gas method. We show that the existence of a power law tail originates from narrow resonance contributions, related to a (second order) freezing transition in the Coulomb gas.
Physical Review Letters 06/2013; 110(25):250602. DOI:10.1103/PhysRevLett.110.250602 · 7.51 Impact Factor
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##### Article: Distribution of Proper Delay Times in Quantum Chaotic Scattering: A Crossover from Ideal to Weak Coupling
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ABSTRACT: The probability distribution of the proper delay times during scattering on a chaotic system is derived in the framework of the random matrix approach and the supersymmetry method. The result obtained is valid for an arbitrary number of scattering channels as well as arbitrary coupling to the energy continuum. The case of statistically equivalent channels is studied in detail. In particular, the semiclassical limit of an infinite number of weak channels is paid appreciable attention.
Physical Review Letters 09/2001; 87(9):094101. DOI:10.1103/PhysRevLett.87.094101 · 7.51 Impact Factor