80 research outputs found
Resonant-state expansion of the Green's function of open quantum systems
Our series of recent work on the transmission coefficient of open quantum
systems in one dimension will be reviewed. The transmission coefficient is
equivalent to the conductance of a quantum dot connected to leads of quantum
wires. We will show that the transmission coefficient is given by a sum over
all discrete eigenstates without a background integral. An apparent
"background" is in fact not a background but generated by tails of various
resonance peaks. By using the expression, we will show that the Fano asymmetry
of a resonance peak is caused by the interference between various discrete
eigenstates. In particular, an unstable resonance can strongly skew the peak of
a nearby resonance.Comment: 7 pages, 7 figures. Submitted to International Journal of Theoretical
Physics as an article in the Proceedings for PHHQP 2010
(http://www.math.zju.edu.cn/wjd/
The Hyperspherical Four-Fermion Problem
The problem of a few interacting fermions in quantum physics has sparked
intense interest, particularly in recent years owing to connections with the
behavior of superconductors, fermionic superfluids, and finite nuclei. This
review addresses recent developments in the theoretical description of four
fermions having finite-range interactions, stressing insights that have emerged
from a hyperspherical coordinate perspective. The subject is complicated, so we
have included many detailed formulas that will hopefully make these methods
accessible to others interested in using them. The universality regime, where
the dominant length scale in the problem is the two-body scattering length, is
particularly stressed, including its implications for the famous BCS-BEC
crossover problem Derivations and relevant formulas are also included for the
calculation of challenging few-body processes such as recombination.Comment: 66 pages, 33 figure
Nickel and helium evidence for melt above the core–mantle boundary
High ^(3)He/^(4)He ratios in some basalts have generally been interpreted as originating in an incompletely degassed lower-mantle source. This helium source may have been isolated at the core–mantle boundary region since Earth’s accretion. Alternatively, it may have taken part in whole-mantle convection and crust production over the age of the Earth; if so, it is now either a primitive refugium at the core–mantle boundary or is distributed throughout the lower mantle. Here we constrain the problem using lavas from Baffin Island, West Greenland, the Ontong Java Plateau, Isla Gorgona and Fernandina (Galapagos). Olivine phenocryst compositions show that these lavas originated from a peridotite source that was about 20 per cent higher in nickel content than in the modern mid-ocean-ridge basalt source. Where data are available, these lavas also have high ^(3)He/^(4)He. We propose that a less-degassed nickel-rich source formed by core–mantle interaction during the crystallization of a melt-rich layer or basal magma ocean, and that this source continues to be sampled by mantle plumes. The spatial distribution of this source may be constrained by nickel partitioning experiments at the pressures of the core–mantle boundary
Quantum-mechanical and semiclassical study of the collinear three-body Coulomb problem: Inelastic collisions below the three-body disintegration threshold
He-Ar isotope geochemistry of the Yaoling-Meiziwo tungsten deposit, North Guangdong Province: Constraints on Yanshanian crust-mantle interaction and metallogenesis in SE China
Permutational Rademacher Complexity: a New Complexity Measure for Transductive Learning
International audienceTransductive learning considers situations when a learner observes m labelled training points and u unlabelled test points with the final goal of giving correct answers for the test points. This paper introduces a new complexity measure for transductive learning called Permutational Rademacher Complexity (PRC) and studies its properties. A novel symmetrization inequality is proved, which shows that PRC provides a tighter control over expected suprema of empirical processes compared to what happens in the standard i.i.d. setting. A number of comparison results are also provided, which show the relation between PRC and other popular complexity measures used in statistical learning theory, including Rademacher complexity and Transductive Rademacher Complexity (TRC). We argue that PRC is a more suitable complexity measure for transductive learning. Finally, these results are combined with a standard concentration argument to provide novel data-dependent risk bounds for transductive learning
Principles of Geocryology (Permafrost Studies). Part I, General Geocryology. Chapter X, Ground Water in Permafrost Areas. p. 328-364
Peer reviewed: NoNRC publication: Ye
Mobility of Radiogenic Isotopes 4Не and 3Не and Their Retention in a Mineral (by the Example of Amphibole)
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