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1.
We examine the validity of the application of the Factorization Approximation to derive the Master Equation for a microscopic system coupled to a reservoir. We developed a formal perturbation expansion for the time evolution of the system reduced density matrix. We employed a diagrammatic schemes to produce each term of the perturbation series. The diagrams in the time domain provide a distinct criteria to distinguish the diagrams which survive the Factorization Approximation. The Feynmann-like diagrams in the energy domain, originated from the Resolvent method, are used for execution of diagram summations to estimate their overall contributions. We demonstrated that for a two level atomic system, interacting with a thermal reservoir, the summation over the diagrams which survived the Factorization Approximation, yields the proper time evolution of the system, in agreement with the solution of the Master Equation. The summation of the diagrams which are excluded by applying the Factorization Approximation are characterized by a dimensionless parameter: Γ/ω0, where ω0 is the frequency of the transition line, and Γ is the line width. The Factorization Approximation is thus rigorously justified when this expansion parameter is very small. 相似文献
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The outer-distance of a nodeu in a rooted treeT
n
is the height of the subtree determined byu and all nodesv such thatu is on the path joiningv and the root ofT. We show that the expected outer-distance of nodes of treesT
n
in certain families is asymptotic toB logn where the constantB depends on . 相似文献
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— , B
n
, B p1., , p=1 , - . , , , p. 相似文献
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Thomas Ihn Susanne Dröscher Stephan Schnez Helena Knowles Johannes Güttinger Magdalena Huefner Christoph Stampfer Yigal Meir Klaus Ensslin 《Solid State Communications》2012,152(15):1306-1310
We report two experiments on graphene nanostructures. The first was performed on a graphene nanoribbon, where the nature of electronic transport was investigated in detail. Electrons or holes are found to localize in pockets of the potential along the ribbon. Transport is governed by the joint action of localization and Coulomb interaction. The temperature-dependence of the conductance shows activated behavior at temperatures above a few Kelvin. The activation energy retraces the edges of Coulomb blockade diamonds found in nonlinear transport. In the second experiment the metallic tip of a low-temperature scanning force microscope was scanned above a graphene quantum dot. In addition to the familiar Coulomb blockade fringes, localized states are detected forming in the constrictions connecting the dot to source and drain. 相似文献
9.
Lüscher S Moore LS Rejec T Meir Y Shtrikman H Goldhaber-Gordon D 《Physical review letters》2007,98(19):196805
Compressibility measurements are performed on a quantum point contact (QPC). Screening due to mobile charges in the QPC is measured quantitatively, using a second point contact. These measurements are performed from pinch-off through the opening of the first few modes in the QPC. While the measured signal closely matches a Thomas-Fermi-Poisson prediction, deviations from the classical behavior are apparent near the openings of the different modes. Density functional calculations attribute the deviations to a combination of a diverging density of states at the opening of each one-dimensional mode and exchange interaction, which is strongest for the first mode. 相似文献
10.
We studied the characteristics of a circular metallic grating illuminated by broadband radial and azimuthal polarizations. We demonstrated that this scenario is the cylindrical analogue of a one-dimensional Cartesian grating illuminated by TM and TE polarizations. We measured the transmission spectra of this structure and observed strong polarization selectivity and, specifically, a resonance for radial polarization excitation, indicating a strong coupling to surface plasmons. The structure may be attractive for applications where pure radial polarization is needed, such as tight focusing, material processing, and particle trapping. 相似文献