131 research outputs found
On the Convergence to Ergodic Behaviour of Quantum Wave Functions
We study the decrease of fluctuations of diagonal matrix elements of
observables and of Husimi densities of quantum mechanical wave functions around
their mean value upon approaching the semi-classical regime (). The model studied is a spin (SU(2)) one in a classically strongly chaotic
regime. We show that the fluctuations are Gaussian distributed, with a width
decreasing as the square root of Planck's constant. This is
consistent with Random Matrix Theory (RMT) predictions, and previous studies on
these fluctuations. We further study the width of the probability distribution
of -dependent fluctuations and compare it to the Gaussian Orthogonal
Ensemble (GOE) of RMT.Comment: 13 pages Latex, 5 figure
Coherent Destruction of Coulomb Blockade Peaks in Molecular Junctions
Coherent electronic transport in single-molecule junctions is investigated in
the Coulomb blockade regime. Both the transmission phase and probability are
calculated for junctions with various contact symmetries. A dramatic
suppression of the Coulomb blockade peaks is predicted for junctions where
multiple atomic orbitals of the molecule couple to a single electrode although
the charging steps are unaffected.Comment: 6 pages, 4 figure
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[− /τϕ], where is the system-dependent parameter. In the dephasing probe model, coincides with the Ehrenfest time, ∝ 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, ∝ ln[L/ξ] depends on the correlation length ξ of the coupling potential instead of λ
Breit-Wigner width for two interacting particles in one-dimensional random potential
For two interacting particles (TIP) in one-dimensional random potential the
dependence of the Breit-Wigner width , the local density of states and
the TIP localization length on system parameters is determined analytically.
The theoretical predictions for are confirmed by numerical
simulations.Comment: 10 pages Latex, 4 figures included. New version with extended
numerical results and discussions of earlier result
Coherent propagation of interacting particles in a random potential: the Mechanism of enhancement
Coherent propagation of two interacting particles in 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 and are the single and two particle
localization lengths and the exponent 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 ().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, \lt\lt. 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 depends strongly on the source of dephasing. For a voltage probe, is of order the Ehrenfest time . In contrast, for a chaotic environment or a classical source of noise, it has the correlation length of the coupling/noise potential replacing the Fermi wavelength . 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
Decoherence from a Chaotic Environment: An Upside Down "Oscillator" as a Model
Chaotic evolutions exhibit exponential sensitivity to initial conditions.
This suggests that even very small perturbations resulting from weak coupling
of a quantum chaotic environment to the position of a system whose state is a
non-local superposition will lead to rapid decoherence. However, it is also
known that quantum counterparts of classically chaotic systems lose exponential
sensitivity to initial conditions, so this expectation of enhanced decoherence
is by no means obvious. We analyze decoherence due to a "toy" quantum
environment that is analytically solvable, yet displays the crucial phenomenon
of exponential sensitivity to perturbations. We show that such an environment,
with a single degree of freedom, can be far more effective at destroying
quantum coherence than a heat bath with infinitely many degrees of freedom.
This also means that the standard "quantum Brownian motion" model for a
decohering environment may not be as universally applicable as it once was
conjectured to be.Comment: RevTeX, 29 pages, 5 EPS figures. Substantially rewritten analysis,
improved figures, additional references, and errors fixed. Final version (to
appear in PRA
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 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
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