scholarly journals Characteristic Length Scale during the Time Evolution of a Turbulent Bose-Einstein Condensate

2021 ◽  
Author(s):  
Lucas Madeira ◽  
Arnol D. García-Orozco ◽  
Michelle A. Moreno-Armijos ◽  
Francisco Ednilson Alves dos Santos ◽  
Vanderlei S. Bagnato
Keyword(s):  
Time Evolution ◽  
Quantum Turbulence ◽  
Characteristic Length ◽  
Three Dimensional ◽  
Einstein Condensate ◽  
Length Scale ◽  
Turbulent Regime ◽  
Characteristic Length Scale ◽  
Momentum Distributions ◽  
Bose Einstein

Quantum turbulence is characterized by many degrees of freedom interacting non-linearly to produce disordered states, both in space and time. The advances in trapping, cooling, and tuning the interparticle interactions in atomic Bose-Einstein condensates (BECs) make them excellent candidates for studying quantum turbulence. In this work, we investigate the decaying regime of quantum turbulence in a trapped BEC. Although much progress has been made in understanding quantum turbulence, other strategies are needed to overcome some intrinsic difficulties. We present an alternative way of investigating this phenomenon by defining and computing a characteristic length scale, which possesses relevant characteristics to study the establishment of the quantum turbulent regime. One intrinsic difficulty related to these systems is that absorption images of BECs are projected to a plane, thus eliminating some of the information present in the original momentum distribution. We overcome this difficulty by exploring the symmetry of the cloud, which allows us to reconstruct the three-dimensional momentum distributions with the inverse Abel transform. We present our analysis with both the two- and three-dimensional momentum distributions, discussing their similarities and differences. We argue that the characteristic length allows us to visualize the time evolution of the turbulent state intuitively.

scholarly journals Characteristic Length Scale during the Time Evolution of a Turbulent Bose–Einstein Condensate

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1865
Author(s):  
Lucas Madeira ◽  
Arnol D. García-Orozco ◽  
Michelle A. Moreno-Armijos ◽  
Francisco Ednilson Alves dos dos Santos ◽  
Vanderlei S. Bagnato
Keyword(s):  
Time Evolution ◽  
Quantum Turbulence ◽  
Characteristic Length ◽  
Three Dimensional ◽  
Einstein Condensate ◽  
Length Scale ◽  
Characteristic Length Scale ◽  
Bose Einstein Condensate ◽  
Momentum Distributions ◽  
Bose Einstein

Quantum turbulence is characterized by many degrees of freedom interacting non-linearly to produce disordered states, both in space and in time. In this work, we investigate the decaying regime of quantum turbulence in a trapped Bose–Einstein condensate. We present an alternative way of exploring this phenomenon by defining and computing a characteristic length scale, which possesses relevant characteristics to study the establishment of the quantum turbulent regime. We reconstruct the three-dimensional momentum distributions with the inverse Abel transform, as we have done successfully in other works. We present our analysis with both the two- and three-dimensional momentum distributions, discussing their similarities and differences. We argue that the characteristic length allows us to intuitively visualize the time evolution of the turbulent state.

scholarly journals Tethered fleximags as artificial cilia

2011 ◽  
Vol 678 ◽  
pp. 5-13 ◽  
Author(s):  
AVIN BABATAHERI ◽  
MARCUS ROPER ◽  
MARC FERMIGIER ◽  
OLIVIA DU ROURE
Keyword(s):  
Characteristic Length ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Length Scale ◽  
Driving Frequency ◽  
Characteristic Length Scale ◽  
Filament Dynamics ◽  
Elastic Filaments ◽  
Artificial Cilia ◽  
Net Fluxes

Flexible superparamagnetic filaments (‘fleximags’) are very slender elastic filaments, which can be driven by distributed magnetic torques to mimic closely the behaviour of biological flagella. Previously, fleximags have been used as a basis for artificial micro-swimmers capable of transporting small cargos Dreyfus et al. (Nature, vol. 437, 2005, p. 862). Here, we demonstrate how these filaments can be anchored to a wall to make carpets of artificial micro-magnetic cilia with tunable densities. We analyse the dynamics of an artificial cilium under both planar and three-dimensional beating patterns. We show that the dynamics are controlled by a single characteristic length scale varying with the inverse square root of the driving frequency, providing a mechanism to break the fore and aft symmetry and to generate net fluxes and forces. However, we show that an effective geometrical reciprocity in the filament dynamics creates intrinsic limitations upon the ability of the artificial flagellum to pump fluid when driven in two dimensions.

Identification of the characteristic length scale for fatigue cracking in fretting contacts

1998 ◽  
Vol 08 (PR8) ◽  
pp. Pr8-159-Pr8-166 ◽  
Author(s):  
S. Fouvry ◽  
Ph. Kapsa ◽  
F. Sidoroff ◽  
L. Vincent
Keyword(s):  
Characteristic Length ◽  
Fatigue Cracking ◽  
Length Scale ◽  
Characteristic Length Scale

scholarly journals Lettau’s Contribution to the Obukhov Length Scale: A Scientific Historical Study

2021 ◽  
Author(s):  
Thomas Foken ◽  
Michael Börngen
Keyword(s):  
Characteristic Length ◽  
Stability Parameter ◽  
Historical Study ◽  
Length Scale ◽  
Characteristic Length Scale ◽  
Obukhov Length ◽  
The Future

AbstractIt has been repeatedly assumed that Heinz Lettau found the Obukhov length in 1949 independently of Obukhov in 1946. However, it was not the characteristic length scale, the Obukhov length L, but the ratio of height and the Obukhov length (z/L), the Obukhov stability parameter, that he analyzed. Whether Lettau described the parameter z/L independently of Obukhov is investigated herein. Regardless of speculation about this, the significant contributions made by Lettau in the application of z/L merit this term being called the Obukhov–Lettau stability parameter in the future.

λ-Transition to the Bose-Einstein Condensate

1995 ◽  
Vol 50 (10) ◽  
pp. 921-930 ◽  
Author(s):  
Siegfried Grossmann ◽  
Martin Holthaus
Keyword(s):  
Heat Capacity ◽  
Three Dimensional ◽  
Einstein Condensate ◽  
Einstein Condensation ◽  
Condensation Temperature ◽  
Harmonic Oscillator Potential ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Analytical Expressions ◽  
Grand Canonical

Abstract We study Bose-Einstein condensation of comparatively small numbers of atoms trapped by a three-dimensional harmonic oscillator potential. Under the assumption that grand canonical statis­tics applies, we derive analytical expressions for the condensation temperature, the ground state occupation, and the specific heat capacity. For a gas of TV atoms the condensation temperature is proportional to N1/3, apart from a downward shift of order N-1/3. A signature of the condensation is a pronounced peak of the heat capacity. For not too small N the heat capacity is nearly discon­tinuous at the onset of condensation; the magnitude of the jump is about 6.6 N k. Our continuum approximations are derived with the help of the proper density of states which allows us to calculate finite-AT-corrections, and checked against numerical computations.

scholarly journals Three-Dimensional Skyrmions with Arbitrary Topological Number in a Ferromagnetic Spin-1 Bose-Einstein Condensate

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Huan-Bo Luo ◽  
Lu Li ◽  
Wu-Ming Liu
Keyword(s):  
Magnetic Field ◽  
Vortex Ring ◽  
Three Dimensional ◽  
Einstein Condensate ◽  
Laser Beams ◽  
Quantization Axis ◽  
Density Distributions ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Topological Number

AbstractWe propose a new scheme for creating three-dimensional Skyrmions in a ferromagnetic spin-1 Bose-Einstein condensate by manipulating a multipole magnetic field and a pair of counter-propagating laser beams. The result shows that a three-dimensional Skyrmion with topological number Q = 2 can be created by a sextupole magnetic field and the laser beams. Meanwhile, the vortex ring and knot structure in the Skyrmion are found. The topological number can be calculated analytically in our model, which implies that the method can be extended to create Skyrmions with arbitrary topological number. As the examples, three-dimensional Skyrmions with Q = 3, 4 are also demonstrated and are distinguishable by the density distributions with a specific quantization axis. These topological objects have the potential to be realized in ferromagnetic spin-1 Bose-Einstein condensates experimentally.

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