65 research outputs found
The tolerable windows approach: Theoretical and methodological foundations
The tolerable windows (TW) approach is presented as a novel scheme for integrated assessment of climate change. The TW approach is based on the specification of a set of guardrails for climate evolution which refer to various climate-related attributes. These constraints, which define what we call tolerable windows, can be purely systemic in nature - like critical thresholds for the North Atlantic Deep Water formation - or of a normative type - like minimum standards for per-capita food production worldwide. Starting from this catalogue of knock-out criteria and using appropriate modeling techniques, those policy strategies which are compatible with all the constraints specified are sought to be identified. In addition to the discussion of the basic elements and the general theory of the TW approach, a modeling exercise is carried out, based on simple models and assumptions adopted from the German Advisory Council on Global Change (WBGU). The analysis shows that if the global mean temperature is restricted to 2 degrees C beyond the preindustrial level, the cumulative emissions of CO2 are asymptotically limited to about 1550 Gt C. Yet the temporal distribution of these emissions is also determined by the climate and socio-economic constraints: using, for example, a maximal tolerable rate of temperature change of 0.2 degrees C/ dec and a smoothly varying emissions profile, we obtain the maximal cumulative emissions, amounting to 370 Gt C in 2050 and 585 Gt C in 2100
Manifestation of the Hofstadter butterfly in far-infrared absorption
The far-infrared absorption of a two-dimensional electron gas with a
square-lattice modulation in a perpendicular constant magnetic field is
calculated self-consistently within the Hartree approximation. For strong
modulation and short period we obtain intra- and intersubband magnetoplasmon
modes reflecting the subbands of the Hofstadter butterfly in two or more Landau
bands. The character of the absorption and the correlation of the peaks to the
number of flux quanta through each unit cell of the periodic potential depends
strongly on the location of the chemical potential with respect to the
subbands, or what is the same, on the density of electrons in the system.Comment: RevTeX file + 4 postscript figures, to be published Phys. Rev. B
Rapid Com
The possibility of a metal insulator transition in antidot arrays induced by an external driving
It is shown that a family of models associated with the kicked Harper model
is relevant for cyclotron resonance experiments in an antidot array. For this
purpose a simplified model for electronic motion in a related model system in
presence of a magnetic field and an AC electric field is developed. In the
limit of strong magnetic field it reduces to a model similar to the kicked
Harper model. This model is studied numerically and is found to be extremely
sensitive to the strength of the electric field. In particular, as the strength
of the electric field is varied a metal -- insulator transition may be found.
The experimental conditions required for this transition are discussed.Comment: 6 files: kharp.tex, fig1.ps fig2.ps fi3.ps fig4.ps fig5.p
Butterfly-like spectra and collective modes of antidot superlattices in magnetic fields
We calculate the energy band structure for electrons in an external periodic
potential combined with a perpendicular magnetic field. Electron-electron
interactions are included within a Hartree approximation. The calculated energy
spectra display a considerable degree of self-similarity, just as the
``Hofstadter butterfly.'' However, screening affects the butterfly, most
importantly the bandwidths oscillate with magnetic field in a characteristic
way. We also investigate the dynamic response of the electron system in the
far-infrared (FIR) regime. Some of the peaks in the FIR absorption spectra can
be interpreted mainly in semiclassical terms, while others originate from
inter(sub)band transitions.Comment: 4 pages with 2 embeded eps figures. Uses revtex, multicol and
graphicx styles. Accepted for publication in PRB Brief Report
Bloch Electrons in a Magnetic Field - Why Does Chaos Send Electrons the Hard Way?
We find that a 2D periodic potential with different modulation amplitudes in
x- and y-direction and a perpendicular magnetic field may lead to a transition
to electron transport along the direction of stronger modulation and to
localization in the direction of weaker modulation. In the experimentally
accessible regime we relate this new quantum transport phenomenon to avoided
band crossing due to classical chaos.Comment: 4 pages, 3 figures, minor modifications, PRL to appea
Hall conductance of Bloch electrons in a magnetic field
We study the energy spectrum and the quantized Hall conductance of electrons
in a two-dimensional periodic potential with perpendicular magnetic field
WITHOUT neglecting the coupling of the Landau bands. Remarkably, even for weak
Landau band coupling significant changes in the Hall conductance compared to
the one-band approximation of Hofstadter's butterfly are found. The principal
deviations are the rearrangement of subbands and unexpected subband
contributions to the Hall conductance.Comment: to appear in PRB; Revtex, 9 pages, 5 postscript figures; figures with
better resolution may be obtained from http://www.chaos.gwdg.d
Quantum Interference in Superconducting Wire Networks and Josephson Junction Arrays: Analytical Approach based on Multiple-Loop Aharonov-Bohm Feynman Path-Integrals
We investigate analytically and numerically the mean-field
superconducting-normal phase boundaries of two-dimensional superconducting wire
networks and Josephson junction arrays immersed in a transverse magnetic field.
The geometries we consider include square, honeycomb, triangular, and kagome'
lattices. Our approach is based on an analytical study of multiple-loop
Aharonov-Bohm effects: the quantum interference between different electron
closed paths where each one of them encloses a net magnetic flux. Specifically,
we compute exactly the sums of magnetic phase factors, i.e., the lattice path
integrals, on all closed lattice paths of different lengths. A very large
number, e.g., up to for the square lattice, exact lattice path
integrals are obtained. Analytic results of these lattice path integrals then
enable us to obtain the resistive transition temperature as a continuous
function of the field. In particular, we can analyze measurable effects on the
superconducting transition temperature, , as a function of the magnetic
filed , originating from electron trajectories over loops of various
lengths. In addition to systematically deriving previously observed features,
and understanding the physical origin of the dips in as a result of
multiple-loop quantum interference effects, we also find novel results. In
particular, we explicitly derive the self-similarity in the phase diagram of
square networks. Our approach allows us to analyze the complex structure
present in the phase boundaries from the viewpoint of quantum interference
effects due to the electron motion on the underlying lattices.Comment: 18 PRB-type pages, plus 8 large figure
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