Elliptic Ding-Iohara Algebra and the Free Field Realization of the Elliptic Macdonald Operator

The Ding-Iohara algebra is a quantum algebra arising from the free field realization of the Macdonald operator. Starting from the elliptic kernel function introduced by Komori, Noumi and Shiraishi, we can define an elliptic analog of the Ding-Iohara algebra. The free field realization of the elliptic Macdonald operator is also constructed.Comment: 42 page

楕円 Ding-Iohara-Miki 代数とその自由場表示

Tohoku University長谷川 浩司課

Commutative Families of the Elliptic Macdonald Operator

In the paper [J. Math. Phys. 50 (2009), 095215, 42 pages, arXiv:0904.2291], Feigin, Hashizume, Hoshino, Shiraishi, and Yanagida constructed two families of commuting operators which contain the Macdonald operator (commutative families of the Macdonald operator). They used the Ding-Iohara-Miki algebra and the trigonometric Feigin-Odesskii algebra. In the previous paper [arXiv:1301.4912], the present author constructed the elliptic Ding-Iohara-Miki algebra and the free field realization of the elliptic Macdonald operator. In this paper, we show that by using the elliptic Ding-Iohara-Miki algebra and the elliptic Feigin-Odesskii algebra, we can construct commutative families of the elliptic Macdonald operator. In Appendix, we will show a relation between the elliptic Macdonald operator and its kernel function by the free field realization

Probabilistic risk assessment of solar particle events considering the cost of countermeasures to reduce the aviation radiation dose

太陽フレアによる被ばくの脅威から航空機搭乗者を「合理的」に護る --経済的損失リスクの定量化により最適な航空機運用指針の策定が可能に--. 京都大学プレスリリース. 2021-09-03.Cosmic-ray exposure to flight crews and passengers, which is called aviation radiation exposure, is an important topic in radiological protection, particularly for solar energetic particles (SEP). We therefore assessed the risks associated with the countermeasure costs to reduce SEP doses and dose rates for eight flight routes during five ground level enhancements (GLE). A four-dimensional dose-rate database developed by the Warning System for Aviation Exposure to Solar Energetic Particles, WASAVIES, was employed in the SEP dose evaluation. As for the cost estimation, we considered two countermeasures; one is the cancellation of the flight, and the other is the reduction of flight altitudes. Then, we estimated the annual occurrence frequency of significant GLE events that would bring the maximum flight route dose and dose rate over 1.0 mSv and 80 μSv/h, respectively, based on past records of GLE as well as historically large events observed by the cosmogenic nuclide concentrations in tree rings and ice cores. Our calculations suggest that GLE events of a magnitude sufficient to exceed the above dose and dose rate thresholds, requiring a change in flight conditions, occur once every 47 and 17 years, respectively, and their conservatively-estimated annual risks associated with the countermeasure costs are up to around 1.5 thousand USD in the cases of daily-operated long-distance flights

EVALUATION OF SPEED CHANGE IN 100 M SPRINT RUNNING

The purpose of this study was to propose a method to evaluate speed in 100m running with modified exponential equations. The speed changes in 100m sprint race of ninetysix sprinters (62 men and 34 women) were measured with a LAVEG system. The 100m race was divided into the acceleration and deceleration phases based on the maximum speed, and speed were estimated. 1) The exponential equations proposed in this study well estimated the speed change pattern of the 100m on the different record groups. The average errors between the official time and the time estimated were 0.024±0.040s in men and 0.04±0.039 in women. 2) The maximum speed was the most important factor for both men and women sprinters to achieve best performance the race. 3) The men world class sprinters accelerated quickly (large k), but reached the maximum speed later than the other sprinters, which resulted in shorter deceleration phase and smaller decreases in speed after reaching the maximum speed

Controlled Production of Sub-Radiant States of a Diatomic Molecule in an Optical Lattice

We report successful production of sub-radiant states of a two-atom system in a three-dimensional optical lattice starting from doubly occupied sites in a Mott insulator phase of a quantum gas of atomic ytterbium. We can selectively produce either sub-radiant 1g state or super-radiant 0u state by choosing the excitation laser frequency. The inherent weak excitation rate for the sub-radiant 1g state is overcome by the increased atomic density due to the tight-confinement in a three-dimensional optical lattice. Our experimental measurements of binding energies, linewidth, and Zeeman shift confirm observation of sub-radiant levels of the 1g state of the Yb_2 molecule.Comment: To be published in Phys. Rev. Let

Coherent destruction of tunneling, dynamic localization and the Landau-Zener formula

We clarify the internal relationship between the coherent destruction of tunneling (CDT) for a two-state model and the dynamic localization (DL) for a one-dimensional tight-binding model, under the periodical driving field. The time-evolution of the tight-binding model is reproduced from that of the two-state model by a mapping of equation of motion onto a set of ${\rm SU}(2)$ operators. It is shown that DL is effectively an infinitely large dimensional representation of the CDT in the ${\rm SU}(2)$ operators. We also show that both of the CDT and the DL can be interpreted as a result of destructive interference in repeated Landau-Zener level-crossings.Comment: 5 pages, no figur

Gauging a quantum heat bath with dissipative Landau-Zener transitions

We calculate the exact Landau-Zener transitions probabilities for a qubit with 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 a 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.Comment: 4 pages, 1 figur