arXiv subjects

Florian Haberberger

Publications and source records attributed to Florian Haberberger.

3 recordsLinked to original sources

arXiv2026

A second order upper bound to the free energy of the two dimensional Bose gas

We consider a two-dimensional Bose gas in the dilute regime where $ρa^2$ is small. For temperatures below the Berezinskii-Kosterlitz-Thouless critical temperature, we derive an explicit upper bound for the free energy density using Bogoliubov theory. Our result captures the contribution of quasiparticle modes with dispersion relation $\sqrt{p^4 + 8πρ\, δ\, p^2}$ and where $δ= 2 / (|\log(ρa^2)| + \log |\log(ρa^2)|)$.

math-ph↗

arXiv2024

Upper Bound for the Free Energy of Dilute Bose Gases at Low Temperature

We consider a Bose gas at density $ρ> 0$, interacting through a repulsive potential $V \in L^2 (\mathbb{R}^3)$ with scattering length $\mathfrak{a} > 0$. We prove an upper bound for the free energy of the system, valid at low temperature $T \lesssim ρ\mathfrak{a}$. Combined with the recent lower bound obtained in \cite{HabHaiNamSeiTri-23}, our estimate resolves the free energy per unit volume up to and including the Lee--Huang--Yang order $\mathfrak{a} ρ^2 (ρ\mathfrak{a}^3)^{1/2}$.

math-ph↗

arXiv2024

The free energy of dilute Bose gases at low temperatures

We consider a low density Bose gas interacting through a repulsive potential in the thermodynamic limit. We justify, as a rigorous lower bound, a Lee--Huang--Yang type formula for the free energy at suitably low temperatures, where the modified excitation spectrum leads to a second order correction of the same order as the Lee--Huang--Yang correction to the ground state energy.

math-ph↗