Statistics of Wave Functions in Coupled Chaotic Systems

Using the supersymmetry technique, we calculate the joint distribution of local densities of electron wavefunctions in two coupled disordered or chaotic quantum billiards. We find novel spatial correlations that are absent in a single chaotic system. Our exact result can be interpreted for small coupling in terms of the hybridization of eigenstates of the isolated billiards. We show that the presented picture is universal, independent of microscopic details of the coupling.Comment: 4 pages, 2 figures; acknowledgements and references adde

Spins, charges and currents at Domain Walls in a Quantum Hall Ising Ferromagnet

We study spin textures in a quantum Hall Ising ferromagnet. Domain walls between ferro and unpolarized states at $\nu=2$ are analyzed with a functional theory supported by a microscopic calculation. In a neutral wall, Hartree repulsion prevents the appearance of a fan phase provoked by a negative stiffness. For a charged system, electrons become trapped as solitons at the domain wall. The size and energy of the solitons are determined by both Hartree and spin-orbit interactions. Finally, we discuss how electrical transport takes place through the domain wall.Comment: 4 pages, 3 figures include

Quantum Pumping in the Magnetic Field: Role of Discrete Symmetries

We consider an effect of the discrete spatial symmetries and magnetic field on the adiabatic charge pumping in mesoscopic systems. In general case, there is no symmetry of the pumped charge with respect to the inversion of magnetic field Q(B) \neq Q(-B). We find that the reflection symmetries give rise to relations Q(B)=Q(-B) or Q(B)=-Q(-B) depending on the orientation of the reflection axis. In presence of the center of inversion, Q(B) = 0. Additional symmetries may arise in the case of bilinear pumping.Comment: 4 page

Conductance Fluctuations of Open Quantum Dots under Microwave Radiation

We develop a time dependent random matrix theory describing the influence of a time-dependent perturbation on mesoscopic conductance fluctuations in open quantum dots. The effect of external field is taken into account to all orders of perturbation theory, and our results are applicable to both weak and strong fields. We obtain temperature and magnetic field dependences of conductance fluctuations. The amplitude of conductance fluctuations is determined by electron temperature in the leads rather than by the width of electron distribution function in the dot. The asymmetry of conductance with respect to inversion of applied magnetic field is the main feature allowing to distinguish the effect of direct suppression of quantum interference from the simple heating if the frequency of external radiation is larger than the temperature of the leads $\hbar\omega \gg T$.Comment: 7 pages, 5 figure

Conductance fluctuations in a quantum dot under almost periodic ac pumping

It is shown that the variance of the linear dc conductance fluctuations in an open quantum dot under a high-frequency ac pumping depends significantly on the spectral content of the ac field. For a sufficiently strong ac field $\gamma\tau_{\phi}<< 1$, where $1/\tau_{\phi}$ is the dephasing rate induced by ac noise and $\gamma$ is the electron escape rate, the dc conductance fluctuations are much stronger for the harmonic pumping than in the case of the noise ac field of the same intensity. The reduction factor $r$ in a static magnetic field takes the universal value of 2 only for the white--noise pumping. For the strictly harmonic pumping $A(t)=A_{0}\cos\omega t$ of sufficiently large intensity the variance is almost insensitive to the static magnetic field $r-1= 2\sqrt{\tau_{\phi}\gamma} << 1$. For the quasi-periodic ac field of the form $A(t)=A_{0} [\cos(\omega_{1} t)+\cos(\omega_{2} t)]$ with $\omega_{1,2} >> \gamma$ and $\gamma\tau_{\phi} << 1$ we predict the novel effect of enchancement of conductance fluctuations at commensurate frequencies $\omega_{2}/\omega_{1}=P/Q$.Comment: 4 pages RevTex, 4 eps figures; the final version to appear in Phys.Rev.

Relaxation process in a regime of quantum chaos

We show that the quantum relaxation process in a classically chaotic open dynamical system is characterized by a quantum relaxation time scale t_q. This scale is much shorter than the Heisenberg time and much larger than the Ehrenfest time: t_q ~ g^alpha where g is the conductance of the system and the exponent alpha is close to 1/2. As a result, quantum and classical decay probabilities remain close up to values P ~ exp(-sqrt(g)) similarly to the case of open disordered systems.Comment: revtex, 5 pages, 4 figures discussion of the relations between time scale t_q and weak localization correction and between dynamical and disordered systems is adde

Multifractality of Hamiltonians with power-law transfer terms

Finite-size effects in the generalized fractal dimensions $d_q$ are investigated numerically. We concentrate on a one-dimensional disordered model with long-range random hopping amplitudes in both the strong- and the weak-coupling regime. At the macroscopic limit, a linear dependence of $d_q$ on $q$ is found in both regimes for values of q \alt 4g^{-1}, where $g$ is the coupling constant of the model.Comment: RevTex4, 5 two-column pages, 5 .eps figures, to be published in Phys. Rev.

Andreev conductance of a domain wall

At low temperatures, the transport through a superconductor-ferromagnet tunnel interface is due to tunneling of electrons in pairs. Exchange field of a monodomain ferromagnet aligns electron spins and suppresses the two electron tunneling. The presence of the domain walls at the SF interface strongly enhances the subgap current. The Andreev conductance is proven to be proportional to the total length of domain walls at the SF interface.Comment: 4 pages and 1 figur

Quantum Hall ferromagnets, cooperative transport anisotropy, and the random field Ising model

We discuss the behaviour of a quantum Hall system when two Landau levels with opposite spin and combined filling factor near unity are brought into energetic coincidence using an in-plane component of magnetic field. We focus on the interpretation of recent experiments under these conditions [Zeitler et al, Phys. Rev. Lett. 86, 866 (2001); Pan et al, Phys. Rev. B 64, 121305 (2001)], in which a large resistance anisotropy develops at low temperatures. Modelling the systems involved as Ising quantum Hall ferromagnets, we suggest that this transport anisotropy reflects domain formation induced by a random field arising from isotropic sample surface roughness.Comment: 4 pages, submitted to Physical Review

f(α)f(\alpha) Multifractal spectrum at strong and weak disorder

The system size dependence of the multifractal spectrum $f(\alpha)$ and its singularity strength $\alpha$ is investigated numerically. We focus on one-dimensional (1D) and 2D disordered systems with long-range random hopping amplitudes in both the strong and the weak disorder regime. At the macroscopic limit, it is shown that $f(\alpha)$ is parabolic in the weak disorder regime. In the case of strong disorder, on the other hand, $f(\alpha)$ strongly deviates from parabolicity. Within our numerical uncertainties it has been found that all corrections to the parabolic form vanish at some finite value of the coupling strength.Comment: RevTex4, 6 two-column pages, 4 .eps figures, new results added, updated references, to be published in Phys. Rev.