We derive universal relations between thermodynamic quantities and the pair distribution function for bosons interacting via power-law interactions in three and two dimensions. We find beyond mean-field expressions for Tan's contact and establish new connections between the chemical potential and potential energy per particle, characteristic of systems with finite-range interactions. The obtained results are relevant for dipoles, quadrupoles, Rydberg atoms, excitons, van der Waals atoms, and other systems in the dilute limit.We derive universal relations between thermodynamic quantities and the pair distribution function for bosons interacting via power-law interactions in three and two dimensions. We find beyond mean-field expressions for Tan's contact and establish new connections between the chemical potential and potential energy per particle, characteristic of systems with finite-range interactions. The obtained results are relevant for dipoles, quadrupoles, Rydberg atoms, excitons, van der Waals atoms, and other systems in the dilute limit.

arXiv:2407.06419Jul 8, 20241 citation

Universal energy functionals for trapped Fermi gases in low dimensions

Jiansen Zhang, Shina Tan

We study a system of trapped two-component Fermi gases with a zero-range interaction in two dimensions or one dimension. We calculate the one-particle density matrices of these systems at small displacements, from which we show that the $N$ -body energies are linear functionals of the occupation probabilities of single-particle energy eigenstates. A universal energy functional was first derived in 2011 [S. Tan, Phys. Rev. Lett. 107, 145302 (2011)] for trapped zero-range interacting two-component Fermi gases in three dimensions. We also calculate the asymptotic behaviors of the occupation probabilities of single-particle energy eigenstates at high energies.We study a system of trapped two-component Fermi gases with a zero-range interaction in two dimensions or one dimension. We calculate the one-particle density matrices of these systems at small displacements, from which we show that the $N$-body energies are linear functionals of the occupation probabilities of single-particle energy eigenstates. A universal energy functional was first derived in 2011 [S. Tan, Phys. Rev. Lett. 107, 145302 (2011)] for trapped zero-range interacting two-component Fermi gases in three dimensions. We also calculate the asymptotic behaviors of the occupation probabilities of single-particle energy eigenstates at high energies.

arXiv:2312.00325Physical Review AApr 16, 20240 citations

Particles, fields and quantum theory

Peter Bongaarts

Lecture notes in mathematicsJan 1, 19820 citations

General relation between entanglement and fluctuations in one dimension

Hao Song, Stephan Rachel, Karyn Le Hur

In one dimension very general results from conformal field theory and exact calculations for quantum spin chains have established universal scaling properties of the entanglement entropy between two parts of a critical system. Using both analytical and numerical methods, we show that if particle number or spin is conserved, fluctuations in a subsystem obey identical scaling as a function of subsystem size in one dimension. We investigate the effects of boundaries and subleading corrections for critical spin and bosonic chains.In one dimension very general results from conformal field theory and exact calculations for quantum spin chains have established universal scaling properties of the entanglement entropy between two parts of a critical system. Using both analytical and numerical methods, we show that if particle number or spin is conserved, fluctuations in a subsystem obey identical scaling as a function of subsystem size in one dimension. We investigate the effects of boundaries and subleading corrections for critical spin and bosonic chains.

arXiv:1002.0825Physical Review BJul 14, 2010147 citations

Towards a Particle Theory in Two Dimensions

Laurens Vanderstraeten

Springer thesesJan 1, 20171 citation

N

-body energies are linear functionals of the occupation probabilities of single-particle energy eigenstates. A universal energy functional was first derived in 2011 [S. Tan, Phys. Rev. Lett. 107, 145302 (2011)] for trapped zero-range interacting two-component Fermi gases in three dimensions. We also calculate the asymptotic behaviors of the occupation probabilities of single-particle energy eigenstates at high energies.