Statistics of random quasi 1D Hamiltonian with slowly varying parameters. Painlev\'{e} again.

The statistics of random band--matrices with width and strength of the band slowly varying along the diagonal is considered. The Dyson equation for the averaged Green function close to the edge of spectrum is reduced to the Painlev\'{e} I equation. The analytical properties of the Green function allow to fix the solution of this equation. The former appears to be the same as that arose within the random--matrix regularization of 2d-gravity.Comment: 9 pages, latex, no figures

Theory of directed localization in one dimension

Wetensch. publicatieFaculteit der Wiskunde en Natuurwetenschappe

Adiabatic quantization of Andreev quantum billiard levels

Wetensch. publicatieFaculteit der Wiskunde en Natuurwetenschappe

Noiseless scattering states in a chaotic cavity

Wetensch. publicatieFaculteit der Wiskunde en Natuurwetenschappe

Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo

Wetensch. publicatieFaculteit der Wiskunde en Natuurwetenschappe

Hypersensitivity to perturbations of quantum-chaotic wave-packet dynamics

Wetensch. publicatieFaculteit der Wiskunde en Natuurwetenschappe

Instanton -- Antiinstanton interaction and asymptotics of perturbation theory expansion in double well oscillator

Instanton -- antiinstanton pair is considered as a source of singularity at the Borel plane for the ground state energy of anharmonic oscillator. The problem of defining the short range instanton -- antiinstanton interaction reduces to calculation of a smooth part of the Borel function, which cannot be found without explicit calculation of several terms of ordinary perturbation theory. On the other hand, the large order terms of perturbative expansion are dominated by large fluctuations in the functional integral like well separated instanton and antiinstanton. The preasymptotics ($\sim 1/n$) of large order perturbation theory contribution to the ground state energy of anharmonic oscillator was found analytically. To this end the subleading long range asymptotics of the classical instanton -- antiinstanton interaction, the one -- loop quantum contribution to instanton -- antiinstanton interaction and the second quantum correction to a single instanton density were considered.Comment: 12 pages, Latex, BUDKERINP 94-2

Instanton--anti-instanton pair induced contributions to Re+e−→hadronsR_{e^+e^-\to hadrons} and Rτ→hadronsR_{\tau \to hadrons}

The instanton--anti-instanton pair induced asymptotics of perturbation theory expansion for the cross section of electron--positron pair annihilation to hadrons and hadronic width of $\tau$-lepton was found. For $N_f = N_c$ the nonperturbative instanton contribution is finite and may be calculated without phenomenological input. The instanton induced peturbative asymptotics was shown to be enhanced as $(n+10)!$ and in the intermediate region $n<15$ may exceed the renormalon contribution. Unfortunately, the analysis of $\sim 1/n$ corrections shows that for $n \sim 10$ the obtained asymptotic expressions are at best only the order of magnitude estimate. The asymptotic series for $R_{e^+ e^- \rightarrow hadrons}$ , though obtained formally for $N_f =N_c$, is valid up to energies $\sim 15$Gev. The instanton--anti-instanton pair nonperturbative contribution to $R_{\tau \rightarrow hadrons}$ blows up. On the one hand, this means that instantons could not be considered {\it ab--initio} at such energies. On the other hand, this result casts a strong doubt upon the possibility to determine the $\alpha_s$ from the $\tau$--lepton width.Comment: 22 pages, latex, no figure

Crossing of two Coulomb-Blockade Resonances

We investigate theoretically the transport of non--interacting electrons through an Aharanov--Bohm (AB) interferometer with two quantum dots (QD) embedded into its arms. In the Coulomb-blockade regime, transport through each QD proceeds via a single resonance. The resonances are coupled through the arms of the AB device but may also be coupled directly. In the framework of the Landauer--Buttiker approach, we present expressions for the scattering matrix which depend explicitly on the energies of the two resonances and on the AB phase. We pay particular attention to the crossing of the two resonances.Comment: 15 pages, 1 figur

Quantum-to-classical crossover of mesoscopic conductance fluctuations

We calculate the system-size-over-wave-length ($M$) dependence of sample-to-sample conductance fluctuations, using the open kicked rotator to model chaotic scattering in a ballistic quantum dot coupled by two $N$-mode point contacts to electron reservoirs. Both a fully quantum mechanical and a semiclassical calculation are presented, and found to be in good agreement. The mean squared conductance fluctuations reach the universal quantum limit of random-matrix-theory for small systems. For large systems they increase $\propto M^2$ at fixed mean dwell time $\tau_D \propto M/N$. The universal quantum fluctuations dominate over the nonuniversal classical fluctuations if $N < \sqrt{M}$. When expressed as a ratio of time scales, the quantum-to-classical crossover is governed by the ratio of Ehrenfest time and ergodic time.Comment: 5 pages, 5 figures: one figure added, references update