A master equation with a Lindblad structure is derived, which describes the interaction of a test particle with a macroscopic system and is expressed in terms of the operator valued dynamic structure factor of the system. In the case of a free Fermi or Bose gas the result is evaluated in the Brownian limit, thus obtaining a single generator master equation for the description of quantum Brownia...

A Fokker-Planck type equation for interacting particles with exclusion principle is analysed. The nonlinear drift gives rise to mathematical difficulties in controlling moments of the distribution function. Assuming enough initial moments are finite, we can show the global existence of weak solutions for this problem. The natural associated entropy of the equation is the main tool to derive uni...

The naive perturbation expansion for many-fermion systems is infrared divergent. One can remove these divergences by introducing counterterms. To do this without changing the model, one has to solve an inversion equation. We call this procedure Fermi surface renormalization (FSR). Whether or not FSR is possible depends on the regularity properties of the fermion self{energy. When the Fermi surf...

The rearrangement of the Fermi surface of a homogeneous Fermi system upon approach to a second-order phase transition is studied at zero temperature. The analysis begins with an investigation of solutions of the equation ǫ(p) = μ, a condition that ordinarily has the Fermi momentum pF as a single root. The emergence of a bifurcation point in this equation is found to trigger a qualitative altera...

We study non-linear ground states of the Gross–Pitaevskii equation in the space of one, two and three dimensions with a radially symmetric harmonic potential. The Thomas–Fermi approximation of ground states on various spatial scales was recently justified using variational methods. We justify here the Thomas–Fermi approximation on an uniform spatial scale using the Painlevé-II equation. In the ...

I derive a Wick ordered continuous renormalization group equation for fermion systems and show that a determinant bound applies directly to this equation. This removes factorials in the recursive equation for the Green functions, and thus improves the combinatorial behaviour. The form of the equation is also ideal for the investigation of manyfermion systems, where the propagator is singular on...

A previous calculation of the leading corrections from quantum field fluctuations to the ground state of a trapped Bose-Einstein condensate at zero temperature is extended to general time-independent states, including vortex states. The calculation is streamlined by using dimensional regularization to regularize both ultraviolet and infrared divergences. We calculate the leading quantum correct...

The foundations of weak turbulence theory is explored through its application to the (alpha) Fermi-Pasta-Ulam (FPU) model, a simple weakly nonlinear dispersive system. A direct application of the standard kinetic equations would miss interesting dynamics of the energy transfer process starting from a large-scale excitation. This failure is traced to an enforcement of the exact resonance conditi...