Collective versus single-particle effects in the optical spectra of finite electronic quantum systems

We study optical spectra of finite electronic quantum systems at frequencies smaller than the plasma frequency using a quasi-classical approach. This approach includes collective effects and enables us to analyze how the nature of the (single-particle) electron dynamics influences the optical spectra in finite electronic quantum systems. We derive an analytical expression for the low-frequency absorption coefficient of electro-magnetic radiation in a finite quantum system with ballistic electron dynamics and specular reflection at the boundaries: a two-dimensional electron gas confined to a strip of width a (the approach can be applied to systems of any shape and electron dynamics -- diffusive or ballistic, regular or irregular motion). By comparing with results of numerical computations using the random-phase approximation we show that our analytical approach provides a qualitative and quantitative understanding of the optical spectrum.Comment: 4 pages, 3 figure

Optical response of two-dimensional electron fluids beyond the Kohn regime: strong non-parabolic confinement and intense laser light

We investigate the linear and non-linear optical response of two-dimensional (2D) interacting electron fluids confined by a strong non-parabolic potential. We show that such fluids may exhibit higher-harmonic spectra under realistic experimental conditions. Higher harmonics arise as the electrons explore anharmonicities of the confinement potential (electron-electron interactions reduce this non-linear effect). This opens the possibility of controlling the optical functionality of such systems by engineering the confinement potential. Our results were obtained within time-dependent density-functional theory, employing the adiabatic local-density approximation. A classical hydrodynamical model is in good agreement with the quantum-mechanical results.Comment: 4 pages, 4 figure

Burrows of the semi-terrestrial crab Ucides cordatus enhance CO2 release in a North Brazilian mangrove forest

Ucides cordatus is an abundant mangrove crab in Brazil constructing burrows of up to 2 m depth. Sediment around burrows may oxidize during low tides. This increase in sediment-air contact area may enhance carbon degradation processes. We hypothesized that 1) the sediment CO2 efflux rate is greater with burrows than without and 2) the reduction potential in radial profiles in the sediment surrounding the burrows decreases gradually, until approximating non-bioturbated conditions. Sampling was conducted during the North Brazilian wet season at neap tides. CO2 efflux rates of inhabited burrows and plain sediment were measured with a CO2/H2O gas analyzer connected to a respiration chamber. Sediment redox potential, pH and temperature were measured in the sediment surrounding the burrows at horizontal distances of 2, 5, 8 and 15 cm at four sediment depths (1, 10, 30 and 50 cm) and rH values were calculated. Sediment cores (50 cm length) were taken to measure the same parameters for plain sediment. CO2 efflux rates of plain sediment and individual crab burrows with entrance diameters of 7 cm were 0.7–1.3 µmol m−2s−1 and 0.2–0.4 µmol burrows−1s−1, respectively. CO2 released from a Rhizophora mangle dominated forest with an average of 1.7 U. cordatus burrows−1m−2 yielded 1.0–1.7 µmol m−2s−1, depending on the month and burrow entrance diameter. Laboratory experiments revealed that 20–60% of the CO2 released by burrows originated from crab respiration. Temporal changes in the reduction potential in the sediment surrounding the burrows did not influence the CO2 release from burrows. More oxidized conditions of plain sediment over time may explain the increase in CO2 release until the end of the wet season. CO2 released by U. cordatus and their burrows may be a significant pathway of CO2 export from mangrove sediments and should be considered in mangrove carbon budget estimates

Universal spectral properties of spatially periodic quantum systems with chaotic classical dynamics

We consider a quasi one-dimensional chain of N chaotic scattering elements with periodic boundary conditions. The classical dynamics of this system is dominated by diffusion. The quantum theory, on the other hand, depends crucially on whether the chain is disordered or invariant under lattice translations. In the disordered case, the spectrum is dominated by Anderson localization whereas in the periodic case, the spectrum is arranged in bands. We investigate the special features in the spectral statistics for a periodic chain. For finite N, we define spectral form factors involving correlations both for identical and non-identical Bloch numbers. The short-time regime is treated within the semiclassical approximation, where the spectral form factor can be expressed in terms of a coarse-grained classical propagator which obeys a diffusion equation with periodic boundary conditions. In the long-time regime, the form factor decays algebraically towards an asymptotic constant. In the limit $N\to\infty$, we derive a universal scaling function for the form factor. The theory is supported by numerical results for quasi one-dimensional periodic chains of coupled Sinai billiards.Comment: 33 pages, REVTeX, 13 figures (eps

Collisions of particles advected in random flows

We consider collisions of particles advected in a fluid. As already pointed out by Smoluchowski [Z. f. physik. Chemie XCII, 129-168, (1917)], macroscopic motion of the fluid can significantly enhance the frequency of collisions between the suspended particles. This effect was invoked by Saffman and Turner [J. Fluid Mech. 1, 16-30, (1956)] to estimate collision rates of small water droplets in turbulent rain clouds, the macroscopic motion being caused by turbulence. Here we show that the Saffman-Turner theory is unsatisfactory because it describes an initial transient only. The reason for this failure is that the local flow in the vicinity of a particle is treated as if it were a steady hyperbolic flow, whereas in reality it must fluctuate. We derive exact expressions for the steady-state collision rate for particles suspended in rapidly fluctuating random flows and compute how this steady state is approached. For incompressible flows, the Saffman-Turner expression is an upper bound.Comment: 24 pages, 3 figure

Spectral correlations in systems undergoing a transition from periodicity to disorder

We study the spectral statistics for extended yet finite quasi 1-d systems which undergo a transition from periodicity to disorder. In particular we compute the spectral two-point form factor, and the resulting expression depends on the degree of disorder. It interpolates smoothly between the two extreme limits -- the approach to Poissonian statistics in the (weakly) disordered case, and the universal expressions derived for the periodic case. The theoretical results agree very well with the spectral statistics obtained numerically for chains of chaotic billiards and graphs.Comment: 16 pages, Late

Spectral Statistics in Chaotic Systems with Two Identical Connected Cells

Chaotic systems that decompose into two cells connected only by a narrow channel exhibit characteristic deviations of their quantum spectral statistics from the canonical random-matrix ensembles. The equilibration between the cells introduces an additional classical time scale that is manifest also in the spectral form factor. If the two cells are related by a spatial symmetry, the spectrum shows doublets, reflected in the form factor as a positive peak around the Heisenberg time. We combine a semiclassical analysis with an independent random-matrix approach to the doublet splittings to obtain the form factor on all time (energy) scales. Its only free parameter is the characteristic time of exchange between the cells in units of the Heisenberg time.Comment: 37 pages, 15 figures, changed content, additional autho

Electron-Electron Interaction in Disordered Mesoscopic Systems: Weak Localization and Mesoscopic Fluctuations of Polarizability and Capacitance

The weak localization correction and the mesoscopic fluctuations of the polarizability and the capacitance of a small disordered sample are studied systematically in 2D and 3D geometries. While the grand canonical ensemble calculation gives the positive magnetopolarizability, in the canonical ensemble (appropriate for isolated samples) the sign of the effect is reversed. The magnitude of mesoscopic fluctuations for a single sample exceeds considerably the value of the weak localization correction.Comment: 13 pages Latex, 3 .eps figures included. To appear in Phys. Rev. B. Minor corrections, in particular in formulae; new references adde

Signature of Chaotic Diffusion in Band Spectra

We investigate the two-point correlations in the band spectra of spatially periodic systems that exhibit chaotic diffusion in the classical limit. By including level pairs pertaining to non-identical quasimomenta, we define form factors with the winding number as a spatial argument. For times smaller than the Heisenberg time, they are related to the full space-time dependence of the classical diffusion propagator. They approach constant asymptotes via a regime, reflecting quantal ballistic motion, where they decay by a factor proportional to the number of unit cells. We derive a universal scaling function for the long-time behaviour. Our results are substantiated by a numerical study of the kicked rotor on a torus and a quasi-one-dimensional billiard chain.Comment: 8 pages, REVTeX, 5 figures (eps

Random Matrices close to Hermitian or unitary: overview of methods and results

The paper discusses progress in understanding statistical properties of complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and non-Hermitian random matrices. Ensembles of this type emerge in various physical contexts, most importantly in random matrix description of quantum chaotic scattering as well as in the context of QCD-inspired random matrix models.Comment: Published version, with a few more misprints correcte