arXiv subjects

Lukas Junge

Publications and source records attributed to Lukas Junge.

6 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 $\rho a^2$ 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 $\sqrt{p^4 + 8\pi \rho\, \delta\, p^2}$ and where $\delta = 2 / (|\log(\rho a^2)| + \log |\log(\rho a^2)|)$.

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arXiv2026

Propagation of Condensation via Neumann Localization in the Dilute Bose Gas

We prove a Neumann localization inequality for the Laplacian that includes a spectral gap. This result is obtained by partitioning a cube into overlapping families of subcubes and analysing the associated projection operators. The resulting operator inequality goes through a discrete Neumann Laplacian on the lattice of boxes and yields a quantitative spectral gap estimate. As an application, we consider the dilute Bose gas with Neumann boundary conditions. Combining the localization method with recently established free-energy lower bounds, we propagate strong condensation estimates from the Gross Pitaevskii scale to larger boxes of side length $R\sim a(\rho a^3)^{-\frac{3}{4}-\eta}$.

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arXiv2025

Derivation of Hartree theory for two-dimensional attractive Bose gases in almost Gross-Pitaevskii regime

We study the ground state energy of trapped two-dimensional Bose gases with mean-field type interactions that can be attractive. We prove the stability of second kind of the many-body system and the convergence of the ground state energy per particle to that of a non-linear Schrödinger (NLS) energy functional. Notably, we can take any polynomial scaling of the interaction, and even exponential scalings arbitrarily close to the Gross--Pitaevskii regime, which is a drastic improvement on the best-known result for systems with attractive interactions. As a consequence of the stability of second kind we also obtain Bose-Einstein condensation for the many-body ground states for a much improved range of the diluteness parameter.

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arXiv2024

Ground state energy of a dilute Bose gas with three-body hard-core interactions

We consider a gas of bosons interacting through a three-body hard-core potential in the thermodynamic limit. We derive an upper bound on the ground state energy of the system at the leading order using a Jastrow factor. Our result matches the lower bound proven by Nam-Ricaud-Triay and therefore resolves the leading order. Moreover, a straightforward adaptation of our proof can be used for systems interacting via combined two-body and three-body interactions to generalise Theorem 1.2. from arXiv:2402.05646 to hard-core potentials.

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arXiv2023

Lower bounds on the energy of the Bose gas

We present an overview of the approach to establish a lower bound to the ground state energy for the dilute, interacting Bose gas in a periodic box. In this paper the size of the box is larger than the Gross-Pitaevski length scale. The presentation includes both the 2 and 3 dimensional cases, and catches the second order correction, i.e. the Lee-Huang-Yang term. The calculation on a box of this length scale is the main step to calculate the energy in the thermodynamic limit. However, the periodic boundary condition simplifies many steps of the argument considerably compared to the localized problem coming from the thermodynamic case.

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arXiv2023

Quantitative Magnetic Isoperimetric Inequality

In 1996 Erdoes showed that among planar domains of fixed area, the smallest principal eigenvalue of the Dirichlet Laplacian with a constant magnetic field is uniquely achieved on the disk. We establish a quantitative version of this inequality, with an explicit remainder term depending on the field strength that measures how much the domain deviates from the disk.

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