We show that chaos and nonlinear resonances are clearly reflected in the magnetotransport lateral surface superlattices thereby explain a series of magnetoresistance peaks observed recently ``antidot'' arrays on semiconductor heterojunctions. find mechanism cyclotron-orbit pinning an electric field resulting from Kolmogorov-Arnol'd-Moser tori. An experimental verification is suggested terms enhanced cyclotron frequency associated with anomalously reduced radius.

It is shown that conductance fluctuations due to phase coherent ballistic transport through a chaotic cavity generically are fractals. The graph of vs. externally changed parameter, e.g. magnetic field, fractal with dimension D=2-b/2 between 1 and 2. governed by the exponent b (<2) power law distribution P(t) ~ t^{-b} for classically trajectory stay in up time t, which typical systems mixed (chaotic regular) space. phenomenon should be observable semiconductor nanostructures microwave billiards.

We prove that the temporal autocorrelation function C(t) for quantum systems with Cantor spectra has an algebraic decay C(t)\ensuremath{\sim}${\mathit{t}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$, where \ensuremath{\delta} equals generalized dimension ${\mathit{D}}_{2}$ of spectral measure and is bounded by Hausdorff ${\mathit{D}}_{0}$\ensuremath{\ge}\ensuremath{\delta}. study various incommensurate singular continuous absolutely find extremely slow correlation decays in cases...

We point out a new class of level statistics where the level-spacing distribution follows an inverse power law p(s)\ensuremath{\sim}${\mathit{s}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\beta}}}$, with \ensuremath{\beta}=3/2. It is characteristic clustering rather than repulsion and appears to be universal for systems exhibiting unbounded quantum diffusion on 1D lattices. A relaxation this met in model Bloch electorns magnetic field, we find purely diffusive spread wave packets without...

Resonance states in quantum chaotic scattering systems have a multifractal structure that depends on their decay rate. We show how classical dynamics describes this for all rates the semiclassical limit. This result corresponds to well-established ergodicity closed systems. Specifically, we generalize Ulam's matrix approximation of Perron-Frobenius operator, giving rise conditionally invariant measures various rates. There are many approximations leading same rate and conjecture criterion...

We explain the mechanism leading to directed chaotic transport in Hamiltonian systems with spatial and temporal periodicity. show that a mixed phase space comprising both regular motion is required we derive classical sum rule which allows one predict velocity from properties of phase-space components. Transport quantum ratchets arises by same as long uncertainty resolve structure. analogous one, based on relation between band

Conductance fluctuations have been studied in a soft wall stadium and Sinai billiard defined by electrostatic gates on high mobility semiconductor heterojunction. These reproducible magnetoconductance are found to be fractal confirming recent theoretical predictions of quantum signatures classically mixed (regular chaotic) systems. The character the provides direct evidence for hierarchical phase space structure at boundary between regular chaotic motion.

The multifractal dimensions ${D}_{2}^{\ensuremath{\mu}}$ and ${D}_{2}^{\ensuremath{\psi}}$ of the energy spectrum eigenfunctions, respectively, are shown to determine asymptotic scaling width a spreading wave packet. For systems where shape packet is preserved, $k$th moment increases as ${t}^{k\ensuremath{\beta}}$ with $\ensuremath{\beta}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}D}_{2}^{\ensuremath{\mu}}/{D}_{2}^{\ensuremath{\psi}}$, while, in general, an optimal lower bound....

The magnetoresistance ${R}_{\mathrm{xx}}$ was investigated in arrays of abutted square cavities with lengths $L$ ranging from $500\mathrm{nm}$ to $1.2\ensuremath{\mu}\mathrm{m}$ near filling factor $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$. Maxima occur for effective magnetic field values satisfying the focusing condition between cavity spacing and cyclotron radius composite fermions, also direction when fermions are deflected opposite that electrons....

The spectrum of 2D electrons subjected to a weak potential and perpendicular magnetic field is composed Landau bands with fractal internal pattern subbands minigaps referred as Hofstadter's butterfly. Hall conductance may serve spectroscopic tool each filled subband contributes specific quantized value. Advances in sample fabrication now finally offer access the regime away from limiting case very potential. Complex behavior observed assigned band-coupling-induced rearrangements within

The statistical mechanics of periodically driven ("Floquet") systems in contact with a heat bath exhibits some radical differences from the traditional undriven systems. In Floquet all quasienergies can be placed finite frequency interval, and number near degeneracies this interval grows without limit as dimension N Hilbert space increases. This leads to pathologies, including drastic changes states, earlier work these difficulties were put aside by fixing N, while taking coupling smaller...

Bose-Einstein condensation, the macroscopic occupation of a single quantum state, appears in equilibrium statistical mechanics and persists also hydrodynamic regime close to equilibrium. Here we show that even when degenerate Bose gas is driven into steady state far from equilibrium, where notion single-particle ground becomes meaningless, condensation survives generalized form: unambiguous selection an odd number states acquiring large occupations. Within mean-field theory derive criterion...

We study how a Cantor spectrum, its level statistics, and corresponding dynamics are affected by the onset of classical chaos. While spectrum undergoes visible changes, spacing distribution follows an inverse power law p(s)\ensuremath{\sim}${\mathit{s}}^{\mathrm{\ensuremath{-}}3/2}$ on small scales. find crossover which is manifested in time domain two diffusive regimes characterized quantum-mechanical diffusion coefficient. In strong quantum limit we show means transformation that governed...

We present a comprehensive account of directed transport in one-dimensional Hamiltonian systems with spatial and temporal periodicity. They can be considered as ratchets the sense that ensembles particles show ballistic absence an average force. discuss general conditions for such like mixed classical phase space. A sum rule is derived which connects contributions different phase-space components to transport. regular ratchet against external potential gradient while chaotic restricted...

Hamiltonian systems with a mixed phase space typically exhibit an algebraic decay of correlations and Poincar\'e recurrences, numerical experiments over finite times showing system-dependent power-law exponents. We conjecture the existence universal asymptotic based on results for Markov tree model random scaling factors transition probabilities. Numerical simulations different support this permit determination exponent.

We study the fundamental question of dynamical tunneling in generic two-dimensional Hamiltonian systems by considering regular-to-chaotic rates. Experimentally, we use microwave spectra to investigate a mushroom billiard with adjustable foot height. Numerically, obtain rates from high precision eigenvalues using improved method particular solutions. Analytically, prediction is given extending an approach fictitious integrable system billiards. In contrast previous approaches for billiards,...

We derive a prediction of dynamical tunneling rates from regular to chaotic phase-space regions combining the direct regular-to-chaotic mechanism in quantum regime with an improved resonance-assisted theory semiclassical regime. give qualitative recipe for identifying relevance nonlinear resonances given variant Planck's over 2pi For systems one or multiple dominant we find excellent agreement numerics.

For generic 4D symplectic maps we propose the use of 3D phase-space slices, which allow for global visualization geometrical organization and coexistence regular chaotic motion. As an example, consider two coupled standard maps. The advantages slices are presented in comparison to methods, such as projections orbits, frequency analysis, a chaos indicator. Quantum mechanically, Husimi functions eigenstates with classical structures. This confirms semiclassical eigenfunction hypothesis

Partial transport barriers in the chaotic sea of Hamiltonian systems influence classical transport, as they allow for a small flux between phase-space regions only. We find higher-dimensional that quantum through such partial barrier is more restrictive than expected from two-dimensional maps. establish universal transition suppression to mimicking transport. The scaling parameter involves flux, size Planck cell, and localization length due dynamical along resonance channel. This numerically...

Quantum systems subject to time periodic fields of finite amplitude \ensuremath{\lambda} have conventionally been handled either by low-order perturbation theory, for not too large, or exact diagonalization within a basis $N$ states. An adiabatic limit, as is switched on arbitrarily slowly, has assumed. But the validity these procedures seems questionable in view fact that, $N\ensuremath{\rightarrow}\ensuremath{\infty},$ quasienergy spectrum becomes dense, and numerical calculations show an...

We derive a formula predicting dynamical tunneling rates from regular states to the chaotic sea in systems with mixed phase space. Our approach is based on introduction of fictitious integrable system that resembles dynamics within island. For standard map and other kicked we find agreement numerical results for all regime where resonance-assisted not relevant.

We study transport through a two-dimensional billiard attached to two infinite leads by numerically calculating the Landauer conductance and Wigner time delay. In generic case of mixed phase space we find power-law distribution resonance widths dependence increments apparently reflecting classical dwell exponent, in striking difference fully chaotic space. Surprisingly, these power laws appear on energy scales below mean level spacing, contrast semiclassical expectations.

We investigate the asymptotic state of time-periodic quantum systems with regular and chaotic Floquet states weakly coupled to a heat bath. The occupation probabilities these two types follow fundamentally different distributions. Among probability decreases from in center island outermost by orders magnitude, while have almost equal probabilities. derive an analytical expression for occupations kicked systems, which depends on winding numbers tori parameters temperature driving frequency....

The key characteristic of an optical mode in a microcavity is its quality factor describing the losses. numerical computation this quantity can be very demanding for present-day devices. Here we show certain class whispering-gallery cavities that related to dynamical tunneling, phenomenon studied field quantum chaos. We extend recently developed approach determining tunneling rates open cavities. This allows us derive analytical formula which good agreement with full solutions Maxwell's equations.

We investigate non-equilibrium steady states of driven-dissipative ideal quantum gases both bosons and fermions. focus on systems sharp particle number that are driven out equilibrium either by the coupling to several heat baths different temperature or time-periodic driving in combination with a bath. Within framework (Floquet-)Born-Markov theory, analytical numerical methods described detail. This includes mean-field theory terms occupation numbers, an augmented taking into account also...