Energy evolution in time-dependent harmonic oscillator

The theory of adiabatic invariants has a long history, and very important implications and applications in many different branches of physics, classically and quantally, but is rarely founded on rigorous results. Here we treat the general time-dependent one-dimensional harmonic oscillator, whose Newton equation $\ddot{q} + \omega^2(t) q=0$ cannot be solved in general. We follow the time-evolution of an initial ensemble of phase points with sharply defined energy $E_0$ at time $t=0$ and calculate rigorously the distribution of energy $E_1$ after time $t=T$, which is fully (all moments, including the variance $\mu^2$) determined by the first moment $\bar{E_1}$. For example, $\mu^2 = E_0^2 [(\bar{E_1}/E_0)^2 - (\omega (T)/\omega (0))^2]/2$, and all higher even moments are powers of $\mu^2$, whilst the odd ones vanish identically. This distribution function does not depend on any further details of the function $\omega (t)$ and is in this sense universal. In ideal adiabaticity $\bar{E_1} = \omega(T) E_0/\omega(0)$, and the variance $\mu^2$ is zero, whilst for finite $T$ we calculate $\bar{E_1}$, and $\mu^2$ for the general case using exact WKB-theory to all orders. We prove that if $\omega (t)$ is of class ${\cal C}^{m}$ (all derivatives up to and including the order $m$ are continuous) $\mu \propto T^{-(m+1)}$, whilst for class ${\cal C}^{\infty}$ it is known to be exponential $\mu \propto \exp (-\alpha T)$.Comment: 26 pages, 5 figure

Decay dynamics of excitonic polarons in InAs/GaAs quantum dots

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Journal of Applied Physics 110, 074303 (2011) and may be found at https://doi.org/10.1063/1.3639310.We present time-resolved studies of the exciton-phonon interaction in self-assembled InAs/GaAs quantum dots. Different scattering and luminescence processes were investigated by time-resolved spectroscopy exciting resonantly into the quantum dot’s electronic structure. By studying the characteristic decay times of the ground state and of several phonon-assisted recombinations we were able to distinguish a resonant Raman process from a phonon-assisted photoluminescence process which are always simultaneously present and can interfere with each other. While lifetimes under 30 ps were observed for the coherent Raman process, the incoherent phonon-assisted recombination exhibited typical lifetimes of around 1 ns independently of the excitation energy. We conclude that under resonant excitation the dominant radiative recombination process in this system always involves an electronic state of the ground state of the quantum dot’s electronic structure. Combining temperature-dependent and time-resolved measurements we show that a weak phonon-bottleneck is present in the low temperature regime (< 130 K), while it disappears for higher temperatures.DFG, 43659573, SFB 787: Halbleiter - Nanophotonik: Materialien, Modelle, BauelementeDFG, 53182490, EXC 314: Unifying Concepts in Catalysi

Conductance of a tunnel point-contact of noble metals in the presence of a single defect

In paper [1] (Avotina et al. Phys. Rev. B,74, 085411 (2006)) the effect of Fermi surface anisotropy to the conductance of a tunnel point contact, in the vicinity of which a single point-like defect is situated, has been investigated theoretically. The oscillatory dependence of the conductance on the distance between the contact and the defect has been found for a general Fermi surface geometry. In this paper we apply the method developed in [1] to the calculation of the conductance of noble metal contacts. An original algorithm, which enables the computation of the conductance for any parametrically given Fermi surface, is proposed. On this basis a pattern of the conductance oscillations, which can be observed by the method of scanning tunneling microscopy, is obtained for different orientations of the surface for the noble metals.Comment: 8 pages, 5 figure

Scraping the Social? Issues in live social research

What makes scraping methodologically interesting for social and cultural research? This paper seeks to contribute to debates about digital social research by exploring how a ‘medium-specific’ technique for online data capture may be rendered analytically productive for social research. As a device that is currently being imported into social research, scraping has the capacity to re-structure social research, and this in at least two ways. Firstly, as a technique that is not native to social research, scraping risks to introduce ‘alien’ methodological assumptions into social research (such as an pre-occupation with freshness). Secondly, to scrape is to risk importing into our inquiry categories that are prevalent in the social practices enabled by the media: scraping makes available already formatted data for social research. Scraped data, and online social data more generally, tend to come with ‘external’ analytics already built-in. This circumstance is often approached as a ‘problem’ with online data capture, but we propose it may be turned into virtue, insofar as data formats that have currency in the areas under scrutiny may serve as a source of social data themselves. Scraping, we propose, makes it possible to render traffic between the object and process of social research analytically productive. It enables a form of ‘real-time’ social research, in which the formats and life cycles of online data may lend structure to the analytic objects and findings of social research. By way of a conclusion, we demonstrate this point in an exercise of online issue profiling, and more particularly, by relying on Twitter to profile the issue of ‘austerity’. Here we distinguish between two forms of real-time research, those dedicated to monitoring live content (which terms are current?) and those concerned with analysing the liveliness of issues (which topics are happening?)

Inhomogeneity-induced second-order phase transitions in Potts model on hierarchical lattices

The thermodynamics of the $q$-state Potts model with arbitrary $q$ on a class of hierarchical lattices is considered. Contrary to the case of the crystal lattices, it has always the second-order phase transitions. The analytical expressions fo the critical indexes are obtained, their dependencies on the structural lattice pararmeters are studied and the scailing relations among them are establised. The structural criterion of the inhomogeneity-induced transformation of the transition order is suggested. The application of the results to a description of critical phenomena in the dilute crystals and substances confined in porous media is discussed.Comment: 9 pages, 2 figure

An analytical stability theory for Faraday waves and the observation of the harmonic surface response

We present an analytical stability theory for the onset of the Faraday instability, applying over a wide frequency range between shallow water gravity and deep water capillary waves. For sufficiently thin fluid layers the surface is predicted to occur in harmonic rather than subharmonic resonance with the forcing. An experimental confirmation of this result is given. PACS: 47.20.Ma, 47.20.Gv, 47.15.CbComment: 10 pages (LaTeX-file), 3 figures (Postscript) Submitted for publicatio

Simple model for scanning tunneling spectroscopy of noble metal surfaces with adsorbed Kondo impurities

A simple model is introduced to describe conductance measurements between a scanning tunneling microscope (STM) tip and a noble metal surface with adsorbed transition metal atoms which display the Kondo effect. The model assumes a realistic parameterization of the potential created by the surface and a d3z2-r2 orbital for the description of the adsorbate. Fano lineshapes associated with the Kondo resonance are found to be sensitive to details of the adsorbate-substrate interaction. For instance, bringing the adsorbate closer to the surface leads to more asymmetric lineshapes while their dependence on the tip distance is weak. We find that it is important to use a realistic surface potential, to properly include the tunnelling matrix elements to the tip and to use substrate states which are orthogonal to the adsorbate and tip states. An application of our model to Co adsorbed on Cu explains the difference in the lineshapes observed between Cu(100) and Cu(111) surfaces.Comment: 11 pages, 8 eps figure

STM conductance of Kondo impurities on open and structured surfaces

We study the scanning tunneling microscopy response for magnetic atoms on open and structured surfaces using Wilson's renormalization group. We observe Fano resonances associated with Kondo resonances and interference effects. For a magnetic atom in a quantum corral coupled to the confined surface states, and experimentally relevant parameters, we observe a large confinement induced effect not present in the experiments. These results suggest that the Kondo screening is dominated by the bulk electrons rather than the surface ones.Comment: 6 pages, 6 figure

ac Josephson effect in the resonant tunneling through mesoscopic superconducting junctions

We investigate ac Josephson effect in the resonant tunneling through mesoscopic superconducting junctions. In the presence of microwave irradiation, we show that the trajectory of multiple Andreev reflections can be closed by emitting or absorbing photons. Consequently, photon-assisted Andreev states are formed and play the role of carrying supercurrent. On the Shapiro steps, dc component appears when the resonant level is near a series of positions with spacing of half of the microwave frequency. Analytical result is derived in the limit of infinite superconducting gap, based on which new features of ac Josephson effect are revealed.Comment: 11 pages, 3 figure