Thermodynamics at zero temperature: inequalities for the ground state of a quantum many-body system

• URL: http://arxiv.org/abs/2011.00839v3
• Date: Thu, 22 Jul 2021 11:30:24 GMT
• Title: Thermodynamics at zero temperature: inequalities for the ground state of a quantum many-body system
• Authors: N. Il'in, E. Shpagina, O. Lychkovskiy
• Abstract summary: We prove that for a single-component many-body system at zero temperature the inequality $E_rm int leq, P,V$ holds, where $E_rm int$ is the interaction energy, $P$ is pressure and $V$ is volume.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We prove that for a single-component many-body system at zero temperature the inequality $E_{\rm int} \leq\, P\,V$ holds, where $E_{\rm int}$ is the interaction energy, $P$ is pressure and $V$ is volume. This inequality is proven under rather general assumptions with the use of Anderson-type bound relating ground state energies of systems with different numbers of particles. We also consider adding impurity particles to the system and derive inequalities on the chemical potential of the impurity and binding energy of the bound state of two impurities.

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