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The multiconfigurational time-dependent Hartree method (MCTDH) [Chem. Phys.Lett. {\bf 165}, 73 (1990); J. Chem. Phys. {\bf 97}, 3199 (1992)] iscelebrating nowadays entering its third decade of tackling numerically-exactlya broad range of correlated multi-dimensional non-equilibrium quantum dynamicalsystems. Taking in recent years particles' statistics explicitly into account,within the MCTDH for fermions (MCTDHF) and for bosons (MCTDHB), has opened upfurther opportunities to treat larger systems of interacting identicalparticles, primarily in laser-atom and cold-atom physics. With the increase ofexperimental capabilities to simultaneously trap mixtures of two, three, andpossibly even multiple kinds of interacting composite identical particlestogether, we set up the stage in the present work and specify the MCTDH methodfor such cases. Explicitly, the MCTDH method for systems with three kinds ofidentical particles interacting via all combinations of two- and three-bodyforces is presented, and the resulting equations-of-motion are brieflydiscussed. All four possible mixtures of fermions and bosons are presented in aunified manner. Particular attention is paid to represent the coefficients'part of the equations-of-motion in a compact recursive form in terms ofone-body density operators only. The recursion utilizes the recently proposedCombinadic-based mapping for fermionic and bosonic operators in Fock space[Phys. Rev. A {\bf 81}, 022124 (2010)] and successfully applied and implementedwithin MCTDHB. Our work sheds new light on the representation of thecoefficients' part in MCTDHF and MCTDHB without resorting to the matrixelements of the many-body Hamiltonian with respect to the time-dependentconfigurations. It suggests a recipe for efficient implementation of theschemes derived here for mixtures which is suitable for parallelization.

chemical physics

Recursive formulation of the multiconfigurational time-dependent Hartree  method for fermions, bosons and mixtures thereof in terms of one-body density  operators