arXiv subjects

Marcin Napiorkowski

Publications and source records attributed to Marcin Napiorkowski.

2 recordsLinked to original sources

arXiv2025

A note on spontaneous symmetry breaking in the mean-field Bose gas

We consider the homogeneous Bose gas in the three-dimensional unit torus, where $N$ particles interact via a two-body potential of the form $N^{-1} v(x)$. The system is studied at inverse temperatures of order $N^{-2/3}$, which corresponds to the temperature scale of the Bose--Einstein condensation phase transition. We show that spontaneous $U(1)$ symmetry breaking occurs if and only if the system exhibits Bose--Einstein condensation in the sense that the one-particle density matrix of the Gibbs state has a macroscopic eigenvalue.

math-ph↗

arXiv2019

Free energy asymptotics of the quantum Heisenberg spin chain

We consider the ferromagnetic quantum Heisenberg model in one dimension, for any spin $S\geq 1/2$. We give upper and lower bounds on the free energy, proving that at low temperature it is asymptotically equal to the one of an ideal Bose gas of magnons, as predicted by the spin-wave approximation. The trial state used in the upper bound yields an analogous estimate also in the case of two spatial dimensions, which is believed to be sharp at low temperature.

math-ph↗