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About Double GoodDouble Good is a brand on a mission to raise joy for America's youth. Founded in 1998, Double Good was born out of a love for delicious popcorn and grew into a passion for positively impacting the community. Double Good combines an easy-to-use virtual fundraising platform with award-winning popcorn to help create opportunities for children and teens to realize their dreams. In 2022, Double Good was honored with Inc.'s Best in Business award for its popcorn donation program, which has enabled users to donate millions of dollars worth of popcorn to health care workers and youth advocates across the country. In addition to its fundraising platform and donation program, the company amplifies inspiring stories and social issues facing today's youth through its content production arm, Double Good Studios, and the Double Good Kids Foundation dedicated to providing equitable experiences for children with special needs. To learn more on how Double Good can create joy for you, visit www.doublegood.com.

We decided to participate in the double good popcorn fundraising sale to ensure kids were able to cheer for the following season. There were a lot of parents who were laid off due to COVID-19, and our goal was to ensure every athlete was set up for success.

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We present analytical derivations of the diffusion rates, ratchet currents, and time scales of a new ratchet in a fully chaotic Hamiltonian system, introduced in Phys. Rev. Lett. 89, 194102 (2002)] with a proposed implementation using atoms in pulsed standing waves of light. The origin of this type of ratchet current is in asymmetric momentum diffusion rates which result when a "double-well" lattice is pulsed with unequal "kick" periods. The form of the new short-time correlations which modify the diffusion rates are derived. The resulting formulas for the classical energy diffusion rates are shown to give good agreement with numerical simulations. A closed analytical formula for the ratchet current is also obtained, which predicts correctly the current magnitudes and current reversals. The characteristic "ratchet time," a classical time scale associated with the momentum-diffusion ratchet is derived analytically. The competition between the ratchet time t(r) , and the quantum break time t(*) is investigated further. e24fc04721