Dephasing in the semiclassical limit is system-dependent

Dephasing in open quantum chaotic systems has been investigated in the limit of large system sizes to the Fermi wavelength ratio, L/λF 〉 1. The weak localization correction g wl to the conductance for a quantum dot coupled to (i) an external closed dot and (ii) a dephasing voltage probe is calculated in the semiclassical approximation. In addition to the universal algebraic suppression g wl ∝ (1 + τD/τϕ)−1 with the dwell time τD through the cavity and the dephasing rate τϕ−1, we find an exponential suppression of weak localization by a factor of ∝ exp[− $$\tilde \tau$$ /τϕ], where $$\tilde \tau$$ is the system-dependent parameter. In the dephasing probe model, $$\tilde \tau$$ coincides with the Ehrenfest time, $$\tilde \tau$$ ∝ ln[L/λF], for both perfectly and partially transparent dot-lead couplings. In contrast, when dephasing occurs due to the coupling to an external dot, $$\tilde \tau$$ ∝ ln[L/ξ] depends on the correlation length ξ of the coupling potential instead of λ

Coherent propagation of interacting particles in a random potential: the Mechanism of enhancement

Coherent propagation of two interacting particles in $1d$ weak random potential is considered. An accurate estimate of the matrix element of interaction in the basis of localized states leads to mapping onto the relevant matrix model. This mapping allows to clarify the mechanism of enhancement of the localization length which turns out to be rather different from the one considered in the literature. Although the existence of enhancement is transparent, an analytical solution of the matrix model was found only for very short samples. For a more realistic situation numerical simulations were performed. The result of these simulations is consistent with l_{2}/l_1 \sim l_1^{\gamma} , where $l_1$ and $l_2$ are the single and two particle localization lengths and the exponent $\gamma$ depends on the strength of the interaction. In particular, in the limit of strong particle-particle interaction there is no enhancement of the coherent propagation at all ($l_{2} \approx l_1$).Comment: 23 pages, REVTEX, 3 eps figures, improved version accepted for publication in Phys. Rev.

Dephasing in quantum chaotic transport : A semiclassical approach

We investigate the effect of dephasing/decoherence on quantum transport through open chaotic ballistic conductors in the semiclassical limit of small Fermi wavelength to system size ratio, $\\lambda_F/L$\lt$$\lt$1$. We use the trajectory-based semiclassical theory to study a two-terminal chaotic dot with decoherence originating from: (i) an external closed quantum chaotic environment, (ii) a classical source of noise, (iii) a voltage probe, i.e. an additional current-conserving terminal. We focus on the pure dephasing regime, where the coupling to the external source of dephasing is so weak that it does not induce energy relaxation. In addition to the universal algebraic suppression of weak localization, we find an exponential suppression of weak-localization \\propto \\exp[-\\tilde{\\tau}/\\tau_\\phi], with the dephasing rate \\tau_\\phi^{-1}. The parameter $\\tilde{\\tau}$ depends strongly on the source of dephasing. For a voltage probe, $\\tilde{\\tau}$ is of order the Ehrenfest time $\\propto \\ln [L/\\lambda_F ]$. In contrast, for a chaotic environment or a classical source of noise, it has the correlation length $\\xi$ of the coupling/noise potential replacing the Fermi wavelength $\\lambda_F$. We explicitly show that the Fano factor for shot noise is unaffected by decoherence. We connect these results to earlier works on dephasing due to electron-electron interactions, and numerically confirm our findings

Interplay between pairing and exchange in small metallic dots

We study the effects of the mesoscopic fluctuations on the competition between exchange and pairing interactions in ultrasmall metallic dots when the mean level spacing is comparable or larger than the BCS pairing energy. Due to mesoscopic fluctuations, the probability to have a non-zero spin ground state may be non-vanishing and shows universal features related to both level statistics and interaction. Sample to sample fluctuations of the renormalized pairing are enlightened.Comment: 10 pages, 5 figure

Loschmidt Echo and Lyapunov Exponent in a Quantum Disordered System

We investigate the sensitivity of a disordered system with diffractive scatterers to a weak external perturbation. Specifically, we calculate the fidelity M(t) (also called the Loschmidt echo) characterizing a return probability after a propagation for a time $t$ followed by a backward propagation governed by a slightly perturbed Hamiltonian. For short-range scatterers we perform a diagrammatic calculation showing that the fidelity decays first exponentially according to the golden rule, and then follows a power law governed by the diffusive dynamics. For long-range disorder (when the diffractive scattering is of small-angle character) an intermediate regime emerges where the diagrammatics is not applicable. Using the path integral technique, we derive a kinetic equation and show that M(t) decays exponentially with a rate governed by the classical Lyapunov exponent.Comment: 9 pages, 7 figure

Scaling near Quantum Chaos Border in Interacting Fermi Systems

The emergence of quantum chaos for interacting Fermi systems is investigated by numerical calculation of the level spacing distribution $P(s)$ as function of interaction strength $U$ and the excitation energy $\epsilon$ above the Fermi level. As $U$ increases, $P(s)$ undergoes a transition from Poissonian (nonchaotic) to Wigner-Dyson (chaotic) statistics and the transition is described by a single scaling parameter given by $Z = (U \epsilon^{\alpha}-u_0) \epsilon^{1/2\nu}$, where $u_0$ is a constant. While the exponent $\alpha$, which determines the global change of the chaos border, is indecisive within a broad range of $0.9 \sim 2.0$, finite value of $\nu$, which comes from the increase of the Fock space size with $\epsilon$, suggests that the transition becomes sharp as $\epsilon$ increases.Comment: 4 pages, 4 figures, to appear in Phys. Rev. E (Rapid Communication