Effective Semiclassical Evolution of Bose Einstein Condensates
Abstract
In this work we analyze the effective evolution of a one dimensional Bose-Einstein Condensate (BEC) within a semiclassical description of quantum systems based on expectation values of quantum dispersions and physical observables, known as momentous quantum mechanics. We show that the most prominent features and physical parameters of the system can be determined from the dynamics of the corresponding semiclassical system, consisting of an extended phase space including original classical observables and quantum dispersions, and we also show that particle trajectories for expectation values of observables are a particular characteristic in this framework. We also demonstrate that interactions with several potentials can be implemented in an intuitive way.
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References
S.N. Bose. ”Plancks gesetz und lichtquantenhypothese.” Zeitschrift f¨ur Physik 26, 178-181 (1924). Einstein. ”Quantentheorie des einatomigen idealen gases, sitzungsberichte kgl.” Preuss. Akad. Wiss 261 (1924). http://dx.doi.org/10.1007/BF01327326
F. Schreck, and K. van Druten, ”Laser cooling for quantum gases,” Nature Phys. 17(12), 1296-1304 (2021). https://doi.org/10.1038/s41567-021-01379-w
B. Rhyno, N. Lundblad, D.C. Aveline, C. Lannert, S. Vishveshwara, ”Thermodynamics in expanding shell-shaped Bose-Einstein condensates,” Physical Review A, 1046, 063310 (2021). https://doi.org/10.1103/PhysRevA.104.063310
R.A. Dunlap, Lasers and Their Application to the Observation of Bose-Einstein Condensates, (Morgan and Claypool Publishers, 2019). https://doi.org/10.1088/2053-2571/ab2f2f
J. Tempere, Bose-Einstein Condensation, Superfluidity and Superconductivity, (Universiteit Antwerpen, 2019).
S. Stringari, ”Collective excitations of a trapped Bose-condensed gas,” Physical Review Letters, 77, 2360 (1996). https://doi.org/10.1103/PhysRevLett.77.2360
F. Dalfovo, S. Giorgini, L. Pitaevskii, and S. Stringari,” Rev. Mod. Phys. 71, 463 (1999). https://doi.org/10.1103/RevModPhys.71.463
M. Bojowald, and A. Skirzewski, ”Effective equations of motion for quantum systems,” Rev. Mathematical Phys. 18(07), 713-745 (2006). https://doi.org/10.1142/S0129055X06002772
B. Bayta¸s, M. Bojowald, and S. Crowe, ”Effective potentials from semiclassical truncations,” Physical Review A, 99(4), 042114 (2019). https://doi.org/10.1103/PhysRevA.99.042114
J.T. Cushing, A. Fine, and S. Goldstein, editors Bohmian mechanics and quantum theory: an appraisal. Vol. 184, (Springer Science Business Media, 2013).
L. Aragon-Mu˜noz, G. Chac´on-Acosta, and H. Hernandez-Hernandez, ”Effective quantum tunneling from a semiclassical momentous approach,” International Journal of Modern Physics B, 34(29), 2050271 (2020). https://doi.org/10.1142/S0217979220502719
L. Pitaevskii, and S. Stringari, Bose-Einstein condensation and superfluidity, Vol. 164. (Oxford University Press, 2016).
J.R. Ensher, et al., ”Bose-Einstein condensation in a dilute gas: Measurement of energy and ground-state occupation,” Physical Review Letters 77, 4984 (1996). https://doi.org/10.1103/PhysRevLett.77.4984
X. Antoine, W. Bao, and C. Besse, ”Computational methods for the dynamics of the nonlinear Schr¨odinger/Gross–Pitaevskii equations,” Computer Physics Communications, 184(12), 2621-2633 (2013). https://doi.org/10.1016/j.cpc.2013.07.012
V.M. P´erez-Garc´ıa, H. Michinel, J.I. Cirac, M. Lewenstein, and P. Zoller, ”Dynamics of Bose-Einstein condensates: Variational solutions of the Gross-Pitaevskii equations,” Physical Review A, 56(2), 1424 (1997). https://doi.org/10.1103/PhysRevA.56.1424
M. Greiner, O. Mandel, T.W. H¨ansch, and I. Bloch, ”Collapse and revival of the matter wave field of a Bose–Einstein condensate.” Nature 419, 6902, 51-54 (2002). https://doi.org/10.1038/nature00968
B. Bayta¸s, M. Bojowald, and S. Crowe, ”Faithful realizations of semiclassical truncations,” Annals of Physics, 420, 168247 (2020). https://doi.org/10.1016/j.aop.2020.168247
L.C. Pereira, and V.A. do Nascimento. ”Dynamics of Bose–Einstein Condensates Subject to the P¨oschl–Teller Potential through Numerical and Variational Solutions of the Gross–Pitaevskii Equation,” Materials, 13(10), 2236 (2020). https://doi.org/10.3390/ma13102236
V.M. P´erez-Garc´ıa, H. Michinel, J.I. Cirac, M. Lewenstein, and P. Zoller, ”Low energy excitations of a Bose-Einstein condensate: A time-dependent variational analysis,” Physical review letters, 77(27), 5320 (1996). https://doi.org/10.1103/PhysRevLett.77.5320
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