P. G. Silvestrov

Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo

The overlap of two wave packets evolving in time with slightly different Hamiltonians decays exponentially approximate to e(-gammat), for perturbation strengths U greater than the level spacing Delta. We present numerical evidence for a dynamical system that the decay rate gamma is given by the smallest of the Lyapunov exponent lambda of the classical chaotic dynamics and the level broadening U(2)/Delta that follows from the golden rule of quantum mechanics. This implies the range of validity U > the square root of [lambdaDelta] for the perturbation-strength independent decay rate discovered by Jalabert and Pastawski [Phys. Rev. Lett. 86, 2490 (2001)].

Towards an explanation of the mesoscopic double-slit experiment: A new model for charging of a quantum Dot

For a quantum dot (QD) in the intermediate regime between integrable and fully chaotic, the widths of single-particle levels naturally differ by orders of magnitude. In particular, the width of one strongly coupled level may be larger than the spacing between other, very narrow, levels. In this case many consecutive Coulomb blockade peaks are due to occupation of the same broad level. Between the peaks the electron jumps from this level to one of the narrow levels, and the transmission through the dot at the next resonance essentially repeats that at the previous one. This offers a natural explanation to the recently observed behavior of the transmission phase in an interferometer with a QD.

Theory of directed localization in one dimension.

We present an analytical solution of the delocalization transition that is induced by an imaginary vector potential in a disordered chain [N. Hatano and D. R. Nelson, Phys. Rev. Lett. 77, 570 (1996)]. We compute the relation between the real and imaginary parts of the energy in the thermodynamic limit, as well as finite-size effects. The results are in good agreement with numerical simulations for weak disorder (in which the mean free path is large compared to the wavelength).

Adiabatic quantization of Andreev quantum billiard levels

We identify the time

Ehrenfest times for classically chaotic systems

T

Limits to Error Correction in Quantum Chaos

between Andreev reflections as a classical adiabatic invariant in a ballistic chaotic cavity (Lyapunov exponent

Spin effects and transport in quantum dots with overlapping resonances

\lambda

Enhanced sensitivity of the transmission phase of a quantum dot to Kondo correlations

), coupled to a superconductor by an

Noiseless scattering states in a chaotic cavity

N

Effect of inelastic scattering on the average Coulomb-blockade peak height in quantum dots .

-mode point contact. Quantization of the adiabatically invariant torus in phase space gives a discrete set of periods