15 research outputs found
Fluctuations and correlations in rotating Bose-Einstein condensates
We investigate the effects of correlations on the properties of the ground
state of the rotating harmonically-trapped Bose gas by adding Bogoliubov
fluctuations to the mean-field ground state of an -particle single-vortex
system. We demonstrate that the fluctuation-induced correlations lower the
energy compared to that of the mean-field ground state, that the vortex core is
pushed slightly away from the center of the trap, and that an unstable mode
with negative energy (for rotations slower than a critical frequency) emerges
in the energy spectrum, thus, pointing to a better state for slow rotation. We
construct mean-field ground states of 0-, 1-, and 2-vortex states as a function
of rotation rate and determine the critical frequencies for transitions between
these states, as well as the critical frequency for appearance of a metastable
state with an off-center vortex and its image vortex in the evanescent tail of
the cloud.Comment: Added a paragraph to Section III; Revised arguments in Section III.A,
results unchanged; Added reference
Properties of rotating ultracold bosonic quantum gases
In this dissertation, we study rotational properties of ultracold bosonic quantum gases in two trapped configurations, a quasi-two-dimensional gas in a harmonic trap and a quasi-one-dimensional gas in a toroidal trap.
First, we investigate the effects of correlations on the properties of the ground state of the rotating harmonically-trapped Bose gas by adding Bogoliubov fluctuations to the mean-field ground state of an N-particle single-vortex system. We demonstrate that the fluctuation-induced correlations lower the energy compared to that of the mean-field ground state, that the vortex core is pushed slightly away from the center of the trap, and that an unstable mode with negative energy (for rotations slower than a critical frequency) emerges in the energy spectrum, thus, pointing to a better state for slow rotation. We construct mean-field ground states of 0-, 1-, and 2-vortex states as a function of rotation rate and determine the critical frequencies for transitions between these states, as well as the critical frequency for appearance of a metastable state with an off-center vortex and its image vortex in the evanescent tail of the cloud.
Then, we show how the configuration-space form of the above-mentioned Bogoliubov ground-state wave function of a bosonic condensate with a single vortex in a harmonic trap can be described in terms of bosonic Jastrow correlations. We then generalize this result to study the effects of such correlations on a mean-field vortex lattice state and show that the included correlations lower the energy below that of the mean-field state. Although the reduction is relatively small, it is a precursor of the more general expected effect of correlations in describing the melting of the vortex lattice at a high angular momentum per particle.
Finally, we study the stability and dynamics of an ultracold bosonic gas trapped in a toroidal geometry and driven by rotation in the absence of dissipation. We first delineate, via the Bogoliubov mode expansion, the regions of stability and the nature of instabilities of the system for both repulsive and attractive interaction strengths. To study the response of the system to variations in the rotation rate, we introduce a “disorder” potential, breaking the rotational symmetry. We demonstrate the breakdown of adiabaticity as the rotation rate is slowly varied and find forced tunneling between the eigenstates of the system. The nonadiabaticity is signaled by the appearance of a swallow-tail loop in the lowest-energy level, a general sign of hysteresis. Then, we show that this system is in one-to-one correspondence with a trapped gas in a double-well potential and thus exhibits macroscopic quantum self-trapping. Finally, we show that self-trapping is a direct manifestation of the behavior of the lowest-energy level
Business closures and (re)openings in real-time using Google Places: Proof of concept
We present a new estimation of business opening and closure rates using data from Google Places-the data set behind the Google Maps service. Our algorithm, through a bisection routine, counts the appearance and disappearance of "pins" that represent unique businesses. As a proof of concept, we compute business opening and closure rates for the city of Ottawa during the reopening phase of the COVID-19 pandemic in mid-2021. The lifting of restrictions coincides with a wave of re-entry of temporarily closed businesses, suggesting that government support may have facilitated the survival of hibernating businesses. Our entry estimates are validated by a survey of new businesses. This methodology allows policymakers to monitor business dynamics in quasi-real-time during rapidly unfolding crises
Business closures and (re)openings in real time using Google Places
We present a new method to measure business opening and closure rates using real-time information from Google Places, the dataset behind the Google Maps service. Our Canadian application confirms the importance of temporary closures and reopenings during the COVID-19 pandemic. Over 50% of the temporarily closed food and retail businesses during the April 2021 lockdown reopened by the end of September. Our estimates align well with the timing of COVID-19 restrictions and are validated by a survey of recently opened businesses. Our framework provides policy-makers with a tool for the timely monitoring of business dynamics
Business Closures and (Re)Openings in Real-Time Using Google Places: Proof of Concept
We present a new estimation of business opening and closure rates using data from Google Places—the data set behind the Google Maps service. Our algorithm, through a bisection routine, counts the appearance and disappearance of “pins” that represent unique businesses. As a proof of concept, we compute business opening and closure rates for the city of Ottawa during the reopening phase of the COVID-19 pandemic in mid-2021. The lifting of restrictions coincides with a wave of re-entry of temporarily closed businesses, suggesting that government support may have facilitated the survival of hibernating businesses. Our entry estimates are validated by a survey of new businesses. This methodology allows policymakers to monitor business dynamics in quasi-real-time during rapidly unfolding crises
The Great Migration and African-American Genomic Diversity
We present a comprehensive assessment of genomic diversity in the African-American population by studying three genotyped cohorts comprising 3,726 African-Americans from across the United States that provide a representative description of the population across all US states and socioeconomic status. An estimated 82.1% of ancestors to African-Americans lived in Africa prior to the advent of transatlantic travel, 16.7% in Europe, and 1.2% in the Americas, with increased African ancestry in the southern United States compared to the North and West. Combining demographic models of ancestry and those of relatedness suggests that admixture occurred predominantly in the South prior to the Civil War and that ancestry-biased migration is responsible for regional differences in ancestry. We find that recent migrations also caused a strong increase in genetic relatedness among geographically distant African-Americans. Long-range relatedness among African-Americans and between African-Americans and European-Americans thus track north-and west-bound migration routes followed during the Great Migration of the twentieth century. By contrast, short-range relatedness patterns suggest comparable mobility of similar to 15-16km per generation for African-Americans and European-Americans, as estimated using a novel analytical model of isolation-by-distance