We explore the initial conditions for cosmological N-body simulations suitable for calculating the higher-order cumulants of the density field. In general, the initial conditions based on the perturbation theory (PT) provide incorrect growth in next leading order, which are called transients. Before transients have been completely suppressed compared with the dominant growing mode, we can not r...

The accurate analytical and numerical calculations of the electronic band structure and ground state properties of strongly correlated electrons within the Hubbard model are performed by constructing convergent perturbation theory for general interaction strength and electron concentration. We test the developed perturbation approach about mean field solution in the extreme conditions of one di...

Creation and annihilation operators are used in many-body quantum physics because they provide a less awkward notation than symmetrized or antisymmetrized wave functions, and a convenient language for perturbation theory, etc. These notes are not intended to give anything but an introduction. For a much more extended discussion see books on many-body theory, such as Fetter and Walecka, Quantum ...

Using the second-order Eulerian perturbation theory (SEPT), we study the three-point correlation function in the quasilinear regime for the SCDM, LCDM and MDM models, with the interesting result that these three models have distinctive three-point correlation functions. We test this SEPT prediction using a large set of high-resolution N-body simulations. The N-body results show that the SEPT pr...

Received (received date) Revised (revised date) An algorithm and a computer program in Fortran 95 are presented which enumerate the Hugenholtz diagram representation of the many-body perturbation series for the ground state energy with a two-body interaction. The output is in a form suitable for post-processing such as automatic code generation. The results of a particular application, generati...

1 Definition of the subject and its importance Perturbation Theory: Computation of a quantity depending on a parameter ε starting from the knowledge of is value for ε = 0 by deriving a power series expansion in ε, under the assumption of its existence, and if possible discussing the interpretation of the series. Perturbation theory is very often the only way to get a glimpse of the properties o...