Charged excitons at high magnetic fields: the effect of the surrounding electron gas

We study the photoluminescence (PL) spectrum of a two-dimensional electron system at the high magnetic field limit, where all electrons reside at the lowest Landau level (ν<2). Using a gated structure we tune the electron density from the dilute limit to a dense electron gas, and follow the changes in the emission spectrum. We find that the spectrum at the dilute limit consists of two bound triplets, whose behavior is consistent with that of the dark and bright triplets. We show that the spectrum undergoes critical changes at ν=1/3, from an isolated charged exciton-like spectrum at ν<1/3, to a spectrum that reflects the interactions with the surrounding electrons above this filling factor. This behavior is found to be robust, independent of the electron density and magnetic field. We compare our observations with other recent low temperature PL measurements of a two-dimensional electron gas at high magnetic field and find good agreement and consistency.     

Some Examples of Graded C*-Algebras

We apply the theory of C*-algebras graded by a semilattice to crossed products of C*-algebras. We establish a correspondence between the spectrum of commutative graded C*-algebras and the spectrum of their components. This will allow us to compute the spectrum of some commutative examples of graded C*-algebras.     

The spectrum of permutation orbifolds

We study the spectrum of permutation orbifolds of 2d CFTs. We find examples where the light spectrum grows faster than Hagedorn, which is different from known cases such as symmetric orbifolds. We also describe how to compute their partition functions using a generalization of Hecke operators.

     

Spectral Theory of Pseudo-Ergodic Operators

We define a class of pseudo-ergodic non-self-adjoint Schr?dinger operators acting in spaces l ²(X) and prove some general theorems about their spectral properties. We then apply these to study the spectrum of a non-self-adjoint Anderson model acting onl ²(Z), and find the precise condition for 0 to lie in the spectrum of the operator. We also introduce the notion of localized spectrum for such operators. Received: 8 August 2000 / Accepted: 3 October 2000     

Ultraviolet absorption spectrum of molecular fluorine

We have measured the absorption spectrum of molecular fluorine in the spectral range between 200 and 400 nm. We find excellent agreement with the published¹ spectrum above 250 nm, but below that wavelength we observed less absorption than in the earlier measurements.     

Spectral properties of supersymmetric shape invariant potentials

We present the spectral properties of supersymmetric shape invariant potentials (SIPs). Although the folded spectrum is completely random, unfolded spectrum shows that energy levels are highly correlated and absolutely rigid. All the SIPs exhibit harmonic oscillator-type spectral statistics in the unfolded spectrum. We conjecture that this is the reflection of shape invariant symmetry.      

Light-Induced Hofstadter＇s Butterfly Spectrum of Ultracold Atoms on the Two-Dimensional Kagomé Lattice

We investigate the energy spectrum of ultracold atoms on the two-dimensional Kagomé optical lattice under an effective magnetic field, which can be realized with laser beams. We derive the generalized Harper＇s equations from the Schr？dinger equation. The energy spectrum with a fractal band structure is obtained by numerically solving the generalized Harper＇s equations. We analyze the properties of the Hofstadter＇s butterfly spectrum and discuss its observability.     

Energy spectrum of a relativistic two-dimensional hydrogen-like atom in a constant magnetic field of arbitrary strength

We compute, via a variational mixed-base method, the energy spectrum of a two-dimensional relativistic atom in the presence of a constant magnetic field of arbitrary strength. The results are compared to those obtained in the non-relativistic and spinless case. We find that the relativistic spectrum does not present s states.     

Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation

We show that the 1-dimensional Schrödinger equation with a quasiperiodic potential which is analytic on its hull admits a Floquet representation for almost every energyE in the upper part of the spectrum. We prove that the upper part of the spectrum is purely absolutely continuous and that, for a generic potential, it is a Cantor set. We also show that for a small potential these results extend to the whole spectrum.     

Influence of the humidity conditions on the reflectivity spectrum of a porous silicon microcavity

We have designed and fabricated a porous silicon (PS) microcavity that shows a reflectivity resonance around 3 μm in between two spectral regions with high reflectivity values. The microcavity has been simulated following the photonic crystals formalism, which results in good agreement with the measured spectrum. The reflectivity spectrum of the microcavity has been analyzed under different humidity conditions. We demonstrate that the reflectivity resonance shifts to higher wavelengths and that the reflectivity decreases when the humidity increases. In addition, the reflectivity spectrum of the as-prepared device is recovered when the humidity returns to the initial laboratory conditions. Finally, the effect on the reflectivity spectrum of a condensed water layer at the surface of the microcavity is also analyzed.     

Energy spectrum of quasigeostrophic turbulence

We consider the energy spectrum of a quasigeostrophic model of forced, rotating turbulent flow. We provide a rigorous a priori bound E(k)相似文献   

Determination of low concentrations of aromatic hydrocarbons in multicomponent mixtures with iso-octane and n-heptane

We have experimentally studied the absorption spectra of hydrocarbon mixtures based on n-heptane and isooctane with small (1%–2%) additions of aromatic hydrocarbons (benzene, toluene, xylene). The study was conducted in the region of the first overtones of the vibrational spectra for the hydrocarbon groups CH₃, CH₂, CH. We show that four-component modeling of the absorption spectrum of the hydrocarbon mixture and minimization of the deviation of the model spectrum from the experimental spectrum allow us to separately determine the content of the aromatic additives for concentrations from 1%.     

Characterization of the Spectrum of the Landau Hamiltonian with Delta Impurities

We consider a random Schr?dinger operator in an external magnetic field. The random potential consists of delta functions of random strengths situated on the sites of a regular two-dimensional lattice. We characterize the spectrum in the lowest N Landau bands of this random Hamiltonian when the magnetic field is sufficiently strong, depending on N. We show that the spectrum in these bands is entirely pure point, that the energies coinciding with the Landau levels are infinitely degenerate and that the eigenfunctions corresponding to energies in the remainder of the spectrum are localized with a uniformly bounded localization length. By relating the Hamiltonian to a lattice operator we are able to use the Aizenman–Molchanov method to prove localization. Received: 1 June 1998 / Accepted: 29 January 1999     

Radioluminescent mechanism of Li2B4O7:Cu crystal

The structure of the radioluminescent (RL) spectrum of Li₂B₄O₇:Cu crystal is complex, having no normal Gauss peaks. The RL spectrum recorded showed one sharp and strong peak near 365 nm. For the purpose of explaining this phenomenon, we used the self-trapped exciton (STE) model to analyze experimental data of absorption spectrum, emission spectrum, radioluminescence spectrum and decay-time curves. We found a short lifetime component (of the order of ns) from phosphorous signals of Li₂B₄O₇:Cu. We realized that the short lifetime component related to inherent signal of host lattice and the d-p transitions of Cu⁺. This result is applicable in the detector system with high time resolution.     

Formation of Nanoscale Cracks and Fractoluminescence upon Destruction of Carbon Ceramics

Physics of the Solid State - We obtained a Raman spectrum for a surface layer of porous carbon ceramic (porosity ≈5%) of ≈80&nbsp;nm thick. The analysis of the spectrum showed that...     

On the Spectrum¶of Two-Dimensional Schrödinger Operators¶with Spherically Symmetric, Radially Periodic¶Magnetic Fields

We investigate the spectrum of the two-dimensional Schr?dinger operator , where the magnetic field and the electric potential V are spherically symmetric, i.e., , , and b is p-periodic, similarly for V. By considering two different gauges we get the following results: In case the spectrum contains a semi-axis that consists alternately of intervals of absolutely continuous and dense point spectrum. In case the essential spectrum is purely dense point spectrum and possibly there are spectral gaps. Received: 12 March 1997 / Accepted: 2 April 1997     

Optical spectra of organic quantum dots in the strong coupling regime

We analyze the emission spectrum of a single organic quantum dot coupled to a microcavity in the strong coupling regime. We take into account non-linearities arising from both exciton–exciton interactions and the Pauli exclusion principle. We apply the recently developed Pade approximation for regular truncation of Green functions to calculate the emission spectrum. We show that as the number of excitations in the quantum dot increases the Rabi doublet evolves into a more complicated triplet structure.     

Conductance noise spectrum of mesoscopic systems

We investigate the shape as well as the size- and temperature-dependence of the conductance noise spectrum of a small system containing electrons and both fixed and mobile scatterers. If the number of mobile scatterers within a phase-coherent region is sufficiently large, the temporal variation of the conductance can be viewed as a random walk process limited by the universal conductance fluctuations, resulting in a practically Lorentzian power spectrum. We discuss the conditions under which the noise spectrum of a system consisting of many phase-coherent regions is either Lorentzian or 1/f-like. The temperature-dependence of the power spectrum is determined by the hopping mechanism and the variation of the phase breaking length. As a function of temperature the spectrum satisfies power law scaling relations with exponents depending on the dimension and the temperature range; the spectral intensity can both increase and decrease with decreasing temperature.     

Spectral and Scattering Theory¶of Spatially Cut-Off P(ϕ)2 Hamiltonians

We study spatially cut-off P(ϕ)₂ Hamiltonians. We show the local finiteness of the pure point spectrum outside of thresholds, the limiting absorption principle and asymptotic completeness of scattering for such Hamiltonians. Our results imply the absence of singular continuous spectrum. Received: 25 June 1999 / Accepted: 9 February 2000     

Selection of dominant multi-exciton transitions in disordered linear J-aggregates

We show that the third-order optical response of disordered linear J-aggregates can be calculated by considering only a limited number of transitions between (multi-) exciton states. We calculate the pump-probe absorption spectrum resulting from the truncated set of transitions and show that, apart from the blue wing of the induced absorption peak, it agrees well with the exact spectrum.