Atomic Structure and Lifetimes

Curtis, L. J.

doi:10.1017/cbo9780511755552

Cited by 75 publications

(94 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this paper, however, the arguments are not in this interval since 1+t 2 1−t 2 ≥ 1. Legendre polynomials with arguments greater than unity have been used in the literature, for instance in [13,Chapter 2]. We now establish a connection between the density f d (t) and the Legendre polynomials.…”

Section: Lemma 3 It Holds Thatmentioning

confidence: 89%

Analysis of the expected density of internal equilibria in random evolutionary multi-player multi-strategy games

Duong

2016

J. Math. Biol.

View full text Add to dashboard Cite

In this paper, we study the distribution and behaviour of internal equilibria in a d-player n-strategy random evolutionary game where the game payoff matrix is generated from normal distributions. The study of this paper reveals and exploits interesting connections between evolutionary game theory and random polynomial theory. The main contributions of the paper are some qualitative and quantitative results on the expected density, f n,d , and the expected number, E(n, d), of (stable) internal equilibria. Firstly, we show that in multi-player two-strategy games, they behave asymptotically as √ d − 1 as d is sufficiently large. Secondly, we prove that they are monotone functions of d. We also make a conjecture for games with more than two strategies. Thirdly, we provide numerical simulations for our analytical results and to support the conjecture. As consequences of our analysis, some qualitative and quantitative results on the distribution of zeros of a random Bernstein polynomial are also obtained.

show abstract

Section: Lemma 3 It Holds Thatmentioning

confidence: 89%

Analysis of the expected density of internal equilibria in random evolutionary multi-player multi-strategy games

Duong

2016

J. Math. Biol.

View full text Add to dashboard Cite

show abstract

“…The effective polarizabilities consist of the DC polarizability and a non-adiabatic correction. The polarization potential is given by [27] V pol = −e 2 16π 2 2 0 1 2…”

Section: Quantum Defectsmentioning

confidence: 99%

Measuring the Rydberg constant using circular Rydberg atoms in an intensity-modulated optical lattice

2017

View full text Add to dashboard Cite

A method for performing a precision measurement of the Rydberg constant, R∞, using cold circular Rydberg atoms is proposed. These states have long lifetimes, as well as negligible quantumelectrodynamics (QED) and no nuclear-overlap corrections. Due to these advantages, the measurement can help solve the "proton radius puzzle" [Bernauer, Pohl, Sci. Am. 310, 32 (2014)]. The atoms are trapped using a Rydberg-atom optical lattice, and transitions are driven using a recentlydemonstrated lattice-modulation technique to perform Doppler-free spectroscopy. The circular-state transition frequency yields R∞. Laser wavelengths and beam geometries are selected such that the lattice-induced transition shift is minimized. The selected transitions have no first-order Zeeman and Stark corrections, leaving only manageable second-order Zeeman and Stark shifts. For Rb, the projected relative uncertainty of R∞ in a measurement under the presence of the Earth's gravity is 10 −11 , with the main contribution coming from the residual lattice shift. This could be reduced in a future micro-gravity implementation. The next-important systematic arises from the Rb + polarizability (relative-uncertainty contribution of ≈ 3 × 10 −12 ).

show abstract

“…Collisions are treated as a loss channel with a rate proportional to the interrogation length,l = 2ω 0 , and the mean free path of the particles, (ρσ) −1 , where ρ is the number density of the atoms [m −3 ] and σ is the Van der Waals radius [m 2 ]. The number density, ρ, exponentially increases with temperature (14). The risk of collision increases with interrogation length and cell temperature.…”

Section: E Experimental Detection Of 3 P 0 Atomsmentioning

confidence: 99%

Two-photonE1-M1optical clock

2014

View full text Add to dashboard Cite

An allowed E1-M1 excitation scheme creates optical access to the 1 S 0 → 3 P 0 clock transition in group II type atoms. This method does not require the hyperfine mixing or application of an external magnetic field of other optical clock systems. The advantages of this technique include a Doppler-free excitation scheme and increased portability with the use of vapor cells. We will discuss technical mechanisms of a monochromatic excitation scheme for a hot E1-M1 clock and briefly discuss a bichromatic scheme to eliminate light shifts. We determine the optimal experimental parameters for Hg, Yb, Ra, Sr, Ba, Ca, Mg, and Be and calculate that neutral Hg has ideal properties for a hot, portable frequency standard.

show abstract

Atomic Structure and Lifetimes

Cited by 75 publications

References 0 publications

Analysis of the expected density of internal equilibria in random evolutionary multi-player multi-strategy games

Analysis of the expected density of internal equilibria in random evolutionary multi-player multi-strategy games

Measuring the Rydberg constant using circular Rydberg atoms in an intensity-modulated optical lattice

Two-photonE1-M1optical clock

Contact Info

Product

Resources

About