The BBGKY hierarchy for ultracold bosonic systems: II. Applications

Abstract

In this work, which is based on our previously derived theoretical framework [1], we apply the truncated Born-Bogoliubov-Green-Kirkwood-Yvon (BBGKY) hierarchy for ultracold bosonic systems with a fixed number of particles to two out-of-equilibrium scenarios, namely tunneling in a double-well potential and an interaction quench in a harmonic trap. The efficient formulation of the theory provided in [1] allows for going to large truncation orders such that the impact of the truncation order on the accuracy of the results can be systematically explored. While the short-time dynamics is found to be excellently described with controllable accuracy, significant deviations occur on a longer time-scale for a sufficiently strong interaction quench or the tunneling scenario. Theses deviations are accompanied by exponential-like instabilities leading to unphysical results. The phenomenology of these instabilities is investigated in detail and we show that the minimal-invasive correction algorithm of the equation of motion as proposed in [1] can indeed stabilize the BBGKY hierarchy truncated at the second order.

References in corpus (23)

• Many-Body Physics with Ultracold Gases
• The multi-configurational time-dependent Hartree method for bosons: Many-body dynamics of bosonic systems
• Fragmentation of Bose-Einstein Condensates
• Reduced density matrices and coherence of trapped interacting bosons
• A unified ab-initio approach to the correlated quantum dynamics of ultracold fermionic and bosonic mixtures
• Exact quantum dynamics of bosons with finite-range time-dependent interactions of harmonic type
• Beyond mean-field dynamics in open Bose-Hubbard chains
• Best mean-field for condensates
• Propagating two-particle reduced density matrices without wavefunctions
• Challenges in Truncating the Hierarchy of Time-Dependent Reduced Density Matrices Equations: Open Problems
• Accurate high-harmonic spectra from time-dependent two-particle reduced density matrix theory
• Time-dependent multi-orbital mean-field for fragmented Bose-Einstein condensates
• Revealing single-trap condensate fragmentation by measuring density-density correlations after time of flight
• Hyperbolic Bloch equations: atom-cluster kinetics of an interacting Bose gas
• Spectral properties and breathing dynamics of a few-body Bose-Bose mixture in a 1D harmonic trap
• Equations of motion for natural orbitals of strongly driven two-electron systems
• Solvable Model of a Mixture of Bose-Einstein Condensates
• Solvable Model of a Generic Trapped Mixture of Interacting Bosons: Reduced Density Matrices and Proof of Bose-Einstein Condensation
• Excitation picture of an interacting Bose gas
• Effect of fluctuations on the superfluid-supersolid phase transition on the lattice
• Truncation scheme of time-dependent density-matrix approach II
• Single-photon double ionization: renormalized-natural-orbital theory vs multi-configurational Hartree-Fock
• On the reduced dynamics of a subset of interacting bosonic particles

Cited by in corpus (8)

• Achieving the Ultimate Scaling Limit for Nonequilibrium Green Functions Simulations
• The G1--G2 Scheme: Dramatic Acceleration of Nonequilibrium Green Functions Simulations Within the Hartree--Fock-GKBA
• Ultrafast Dynamics of Strongly Correlated Fermions -- Nonequilibrium Green Functions and Selfenergy Approximations
• The dynamically screened ladder approximation: Simultaneous treatment of strong electronic correlations and dynamical screening out of equilibrium
• One-body reduced density-matrix functional theory in finite basis sets at elevated temperatures
• Boltzmann relaxation dynamics in the strongly interacting Fermi-Hubbard model
• Benchmarking the multiconfigurational Hartree method by the exact wavefunction of two harmonically trapped bosons with contact interaction
• Symmetries & Correlations in Continous Time Crystals