MCTDHB(M) method is based on the following variational ansatz for the many-body wavefunction:
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- time-dependent expansion coefficient |
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- 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