MCTDHB(M) method is based on the following variational ansatz for the many-body wavefunction:

  - time-dependent expansion coefficient 
 - time-adaptive (self-consistent) orbitals used to build permanents

Each permanent is a symmetrized Hartree-product:

The time-dependent expansion coefficients and shapes of the time-adaptive orbitals are the variational parameters of the MCTDHB method, determined by the Dirac-Frenkel time-dependent variational principle.  We find them by solving a corresponding coupled system of integro-differential equations...

M- number of the orbitals, it defines the level of the MCTDHB(M). For M=1 the  MCTDHB(1) is fully equivalent to the famous Gross-Pitaevskii theory. 

For a general N-boson system the total number of the expansion coefficients is 

Nconf = (N + M − 1N),

where M is the number of one-particle functions (orbitals) used to build the symmetrized Hartree products. In the MCTDHB method all possible permutations of N bosons over M orbitals are taken into account.

MCTDHB  is the acronym of  Multi-Configurational Time-Dependent Hartree for Bosons


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