There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Room-temperature ultraviolet lasing in semiconductor nanowire arrays has been demonstrated The self-organized, oriented zinc oxide nanowires grown on sapphire substrates were synthesized with a simple vapor transport and condensation process These wide band-gap semiconductor nanowires form natural laser cavities with diameters varying from 20 to 150 nanometers and lengths up to 10 micrometers Under optical excitation, surface-emitting lasing action was observed at 385 nanometers, with an emission linewidth less than 03 nanometer The chemical flexibility and the one-dimensionality of the nanowires make them ideal miniaturized laser light sources These short-wavelength nanolasers could have myriad applications, including optical computing, information storage, and microanalysis

Room-temperature ultraviolet nanowire nanolasers

The calculation of rate coefficients is a discipline of nonlinear science of importance to much of physics, chemistry, engineering, and biology. Fifty years after Kramers' seminal paper on thermally activated barrier crossing, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry. Theoretical as well as numerical approaches are discussed for single- and many-dimensional metastable systems (including fields) in gases and condensed phases. The role of many-dimensional transition-state theory is contrasted with Kramers' reaction-rate theory for moderate-to-strong friction; the authors emphasize the physical situation and the close connection between unimolecular rate theory and Kramers' work for weakly damped systems. The rate theory accounting for memory friction is presented, together with a unifying theoretical approach which covers the whole regime of weak-to-moderate-to-strong friction on the same basis (turnover theory). The peculiarities of noise-activated escape in a variety of physically different metastable potential configurations is elucidated in terms of the mean-first-passage-time technique. Moreover, the role and the complexity of escape in driven systems exhibiting possibly multiple, metastable stationary nonequilibrium states is identified. At lower temperatures, quantum tunneling effects start to dominate the rate mechanism. The early quantum approaches as well as the latest quantum versions of Kramers' theory are discussed, thereby providing a description of dissipative escape events at all temperatures. In addition, an attempt is made to discuss prominent experimental work as it relates to Kramers' reaction-rate theory and to indicate the most important areas for future research in theory and experiment.

Reaction-rate theory: fifty years after Kramers

The extinction coefficient per mole of nanocrystals at the first exitonic absorption peak, e, for high-quality CdTe, CdSe, and CdS nanocrystals was found to be strongly dependent on the size of the nanocrystals, between a square and a cubic dependence. The measurements were carried out using either nanocrystals purified with monitored purification procedures or nanocrystals prepared through controlled etching methods. The nature of the surface ligands, the refractive index of the solvents, the PL quantum yield of the nanocrystals, the methods used for the synthesis of the nanocrystals, and the temperature for the measurements all did not show detectable influence on the extinction coefficient for a given sized nanocrystal within experimental error.

Experimental Determination of the Extinction Coefficient of CdTe, CdSe, and CdS Nanocrystals

▪ Abstract Solution phase syntheses and size-selective separation methods to prepare semiconductor and metal nanocrystals, tunable in size from ∼1 to 20 nm and monodisperse to ≤5%, are presented. Preparation of monodisperse samples enables systematic characterization of the structural, electronic, and optical properties of materials as they evolve from molecular to bulk in the nanometer size range. Sample uniformity makes it possible to manipulate nanocrystals into close-packed, glassy, and ordered nanocrystal assemblies (superlattices, colloidal crystals, supercrystals). Rigorous structural characterization is critical to understanding the electronic and optical properties of both nanocrystals and their assemblies. At inter-particle separations 5–100 A, dipole-dipole interactions lead to energy transfer between neighboring nanocrystals, and electronic tunneling between proximal nanocrystals gives rise to dark and photoconductivity. At separations <5 A, exchange interactions cause otherwise insulating ass...

Synthesis and Characterization of Monodisperse Nanocrystals and Close-Packed Nanocrystal Assemblies

Quantum-size effects of an electron-hole system confined in microcrystals of semiconductors are studied theoretically with the spherical-dielectric continuum model. An extensive numerical calculation for the eigenvalue problem is carried out by Ritz's variational technique. The motional state of the lowest level is classified into three regimes: the regime of exciton confinement for R/${a}_{B}^{\mathrm{*}}$\ensuremath{\gtrsim}4, the regime of individual particle confinement for R/${a}_{B}^{\mathrm{*}}$\ensuremath{\lesssim}2, and the intermediate regime for 2\ensuremath{\lesssim}R/${a}_{B}^{\mathrm{*}}$\ensuremath{\lesssim}4, where R is the radius of the quantum well and ${a}_{B}^{\mathrm{*}}$ is the exciton Bohr radius. In the region R/${a}_{B}^{\mathrm{*}}$\ensuremath{\gtrsim}4, the high-energy shift of the lowest exciton state is described by the rigid-sphere model of the exciton quite well, which takes into account the spatial extension of the relative motion of the electron and the hole. The oscillator strength of the interband optical transition changes dramatically across the region 2\ensuremath{\lesssim}R/${a}_{B}^{\mathrm{*}}$\ensuremath{\lesssim}4. The metamorphosis of the absorption spectrum is shown as a function of R/${a}_{B}^{\mathrm{*}}$ and compared with the experimental data.

Quantum-size effects of interacting electrons and holes in semiconductor microcrystals with spherical shape

Wannier exciton in microcrystals

Calcul variationnel simple de l'energie de l'etat fondamental d'un systeme electron-trou dans un microcristal a barrieres de potentiel finies. Effet important de la penetration de la fonction d'onde sur le domaine de confinement important, coherent avec le deplacement vers le bleu observe a propos de l'energie d'excitation des microcristaux de CdS

Incomplete confinement of electrons and holes in microcrystals

Some aspects of quantum tunneling of a particle in a double-well potential periodically driven by an external force are studied within the two-level approximation. A closed expression for the temporal evolution of the occupation probability is obtained in the limit of large-amplitude oscillation by the transfer-matrix formalism. The mechanism of coherent destruction of tunneling found by Grossmann et al. [Phys. Rev. Lett. 67, 516 (1991)] is made clear from a viewpoint of interference at periodic level crossings.

Role of phase coherence in the transition dynamics of a periodically driven two-level system

We calculate the exact Landau-Zener transition probabilities for a qubit with an arbitrary linear coupling to a bath at zero temperature. The final quantum state exhibits a peculiar entanglement between the qubit and the bath. In the special case of diagonal coupling, the bath does not influence the transition probability, whatever the speed of the Landau-Zener sweep. It is proposed to use Landau-Zener transitions to determine both the reorganization energy and the integrated spectral density of the bath. Possible applications include circuit QED and molecular nanomagnets.

https://www.physik.uni-augsburg.de/theo1/hanggi/Papers/439.pdf

Yosuke Kayanuma

Papers

Quantum-size effects of interacting electrons and holes in semiconductor microcrystals with spherical shape

Wannier exciton in microcrystals

Incomplete confinement of electrons and holes in microcrystals

Role of phase coherence in the transition dynamics of a periodically driven two-level system

Gauging a quantum heat bath with dissipative Landau-Zener transitions