Theoretical Concepts and Numerical Methods

Part of the Springer Theses book series (Springer Theses)


The scope of this chapter is to equip the reader with the necessary conventions and tools from the second quantization formalism. Quantities of interest like reduced density matrices and normalized correlation functions are defined. The theoretical framework of the methods used throughout the remainder of the book is outlined. In detail, the derivation of the time-dependent Gross–Pitaevskii equation, the time-dependent multi-orbital mean-field equations of motion as well as the multiconfigurational time-dependent Hartree method for bosons are given. Furthermore, the time-evolved block decimation for the Bose–Hubbard Hamiltonian and the discrete non-linear Schrödinger equation are introduced, as they are the subject of a later comparison.


Krylov Subspace Wannier Function Pitaevskii Equation Normalize Correlation Function Backwards Differentiation Formula 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Condensed Matter Theory and Quantum Computing GroupUniversity of BaselBaselSwitzerland

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