Marcin Napiórkowski

Excitation Spectrum of Interacting Bosons in the Mean-Field Infinite-Volume Limit

We consider homogeneous Bose gas in a large cubic box with periodic boundary conditions, at zero temperature. We analyze its excitation spectrum in a certain kind of a mean-field infinite-volume limit. We prove that under appropriate conditions the excitation spectrum has the form predicted by the Bogoliubov approximation. Our result can be viewed as an extension of the result of Seiringer (Commun. Math. Phys. 306:565–578, 2011) to large volumes.

Bogoliubov correction to the mean-field dynamics of interacting bosons

We consider the dynamics of a large quantum system of

The Bogoliubov Free Energy Functional I: Existence of Minimizers and Phase Diagram

N

Calculation of the critical temperature of a dilute Bose gas in the Bogoliubov approximation

identical bosons in 3D interacting via a two-body potential of the form

THE BOGOLIUBOV FREE ENERGY FUNCTIONAL II. THE DILUTE LIMIT

N^{3\beta-1} w(N^\beta(x-y))

Norm Approximation for Many-Body Quantum Dynamics and Bogoliubov Theory

. For fixed

Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations

0\leq \beta <1/3

A note on the validity of Bogoliubov correction to mean-field dynamics

and large

Norm approximation for many-body quantum dynamics: focusing case in low dimensions

N

On the Energy-Momentum Spectrum of a Homogeneous Fermi Gas

, we obtain a norm approximation to the many-body evolution in the