By Axel U. J. Lode
This thesis addresses the exciting subject of the quantum tunnelling of many-body platforms similar to Bose-Einstein condensates. regardless of the large quantity of labor at the tunneling of a unmarried particle via a barrier, we all know little or no approximately how a procedure made up of a number of or of many debris tunnels via a barrier to open house. the current paintings makes use of numerically certain strategies of the time-dependent many-boson Schrödinger equation to discover the wealthy physics of the tunneling to open area technique in ultracold bosonic debris which are before everything ready as a Bose-Einstein condensate and to that end allowed to tunnel via a barrier to open house. The many-body procedure is outfitted up from at the same time taking place unmarried particle approaches which are characterised through assorted momenta. those momenta correspond to the chemical potentials of structures with lowering particle quantity. The many-boson method indicates fascinating collective phenomena: the escaping debris fragment and lose their coherence with the resource and between one another, when correlations increase in the procedure. The specified knowing of the many-body approach is used to plan and attempt a scheme to manage the ultimate nation, momentum distributions or even the correlation dynamics of the tunneling process.
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Extra info for Tunneling Dynamics in Open Ultracold Bosonic Systems: Numerically Exact Dynamics – Analytical Models – Control Schemes
R p . If g ( p) = 1 then the measurement of the p coordinates is statistically independent and, consequently, the positions of the particles are not correlated. In this case it is said that the system is p-th order coherent. Full coherence can only be reached for p = 1. In the case of big particle numbers and p N, the maximally achievable p-th order coherence is 1 + O(N −1 ) [20, 24]. In the case of g ( p) > 1 the measurement of the p positions is correlated and in the case of g ( p) < 1 it is anticorrelated.
S. I. E. Alon, Fragmented Metastable States Exist in an Attractive Bose–Einstein Condensate for Atom Numbers Well Above the Critical Number of the Gross– Pitaevskii Theory. Phys. Rev. Lett. 100, 040402 (2008) References 33 13. I. E. S. Cederbaum, Role of Excited States in the Splitting of a Trapped Interacting Bose–Einstein Condensate by a Time-Dependent Barrier. Phys. Rev. Lett. 99, 030402 (2007) 14. E. I. S. Cederbaum, Zoo of Quantum Phases and Excitations of Cold Bosonic Atoms in Optical Lattices.
3 Best Mean-Field The straightforward generalization of the GP ansatz for the many-boson wave function is simply to allow the bosons to occupy M, instead of one, single particle states. This permits the description of single-configurational condensed or fragmented quantum states, given that one uses an appropriate number M of single-particle states. Here, single-configurational means that a single permanent, cf. Eq. 8), is used in the description. This section will sketch the derivation of the equations of motion of the time-dependent multi-orbital mean-field or, in short, best mean-field (BMF) as given in .
Tunneling Dynamics in Open Ultracold Bosonic Systems: Numerically Exact Dynamics – Analytical Models – Control Schemes by Axel U. J. Lode