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arXiv:2607.07203

Wall tension of a Bose-Einstein condensate: Effects of quantum fluctuations and finite-range interactions

Pham Duy Thanh, Nguyen Van Thu

Published Jul 8, 2026• 0 citations
arXivHTMLPDF

Abstract

We investigate the effects of quantum fluctuations (QFs) and finite-range interatomic interactions on the ground state and wall tension of a Bose-Einstein condensate (BEC) at zero temperature by means of modified Gross-Pitaevskii equations. The QFs are shown to stiffen the condensate near the hard wall, narrowing the density profile and raising the wall tension above its mean-field value by an amount proportional to square-root of the gas parameter. Finite-range corrections always reduces the wall tension relative to the QFs correction value regardless of the effective range. We find the ordering $γ_0 < γ_{\rm II} < γ_{\rm I}$ in the dilute regime and identify a crossover condition under which the two beyond-mean-field contributions mutually cancel. These results provide an experimentally accessible way for probing beyond-LHY physics through precision measurements of the wall tension in ultracold Bose gases.

DOI
10.48550/arxiv.2607.07203

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We investigate the effects of quantum fluctuations (QFs) and finite-range interatomic interactions on the ground state and wall tension of a Bose-Einstein condensate (BEC) at zero temperature by means of modified Gross-Pitaevskii equations. The QFs are shown to stiffen the condensate near the hard wall, narrowing the density profile and raising the wall tension above its mean-field value by an amount proportional to square-root of the gas parameter. Finite-range corrections always reduces the wall tension relative to the QFs correction value regardless of the effective range. We find the ordering γ0<γII<γIγ_0 < γ_{\rm II} < γ_{\rm I}γ0​<γII​<γI​ in the dilute regime and identify a crossover condition under which the two beyond-mean-field contributions mutually cancel. These results provide an experimentally accessible way for probing beyond-LHY physics through precision measurements of the wall tension in ultracold Bose gases.
We examine the influence of nonzero temperature on a bounded surface of a dilute Bose gas confined by a hard wall, utilizing the Gross-Pitaevskii theory and the Bogoliubov-de Gennes equation to describe surface excitations. The theoretical calculations are compared with experimental data for liquid helium II, demonstrating excellent agreement. An empirical relation is found for the temperature-dependence of the surface tension. Furthermore, our findings indicate that the contribution of surface excitations remains below 0.7\% in the most of recent experiments on Bose-Einstein condensate.
We study a dilute and ultracold Bose gas of interacting atoms by using an effective field theory which takes into account the finite-range effects of the interatomic potential. Within the formalism of functional integration from the grand canonical partition function, we derive beyond-mean-field analytical results which depend on both the scattering length and the effective range of the interaction. In particular, we calculate the equation of state of the bosonic system as a function of these interaction parameters both at zero and finite temperature including one-loop Gaussian fluctuation. In the case of zero-range effective interaction, we explicitly show that, due to quantum fluctuations, the bosonic system is thermodynamically stable only for very small values of the gas parameter. We find that a positive effective range above a critical threshold is necessary to remove the thermodynamical instability of the uniform configuration. Remarkably, also for relatively large values of the gas parameter, our finite-range results are in quite good agreement with recent zero-temperature Monte Carlo calculations obtained with hard-sphere bosons.
Abstract We discuss the effects of quenched disorder in a dilute Bose–Einstein condensate confined in a hard walls trap. Starting from the disordered Gross–Pitaevskii functional, we obtain a representation for the quenched free energy as a series of integer moments of the partition function. Positive and negative disorder-dependent effective coupling constants appear in the integer moments. Going beyond the mean-field approximation, we compute the static two-point correlation functions at first-order in the positive effective coupling constants. We obtain the combined contributions of effects due to boundary conditions and disorder in this weakly disordered condensate. The ground state renormalized density profile of the condensate is presented. We also discuss the appearance of metastable and true ground states for strong disorder, when the effective coupling constants become negative.
Quantum fluctuations play a pivotal role in determining the ground state properties and phase transitions of ultra-cold bosonic systems. This study presents a comprehensive theoretical investigation of fluctuation effects beyond mean-field theory in dilute Bose gases, examining their impact on the superfluid–Mott insulator transition, quantum droplet formation, and critical phenomena. Beginning with the Gross–Pitaevskii mean-field framework , we systematically incorporate quantum corrections through Bogoliubov theory, yielding the Lee–Huang–Yang (LHY) energy correction scaling as . The quantum depletion quantifies the fraction of atoms driven from the condensate by zero-point fluctuations. For the Bose–Hubbard model , quantum Monte Carlo simulations establish the superfluid–Mott insulator critical point at , shifted 15% from the mean-field prediction. Critical exponents and confirm 3D XY universality. Quantum droplets in binary mixtures are stabilized by the repulsive LHY correction against mean-field collapse, with equilibrium densities matching experimental observations in K mixtures. Finite-size scaling analysis and the Ginzburg criterion delineate regimes where fluctuation effects dominate. All theoretical predictions are validated against precision measurements in ultracold atomic gases.
In this thesis we present a detailed investigation of the role played by quantum and thermal fluctuations in ultracold Bose gases. We begin with a review of several important concepts and analytical tools within a functional integration formalism. We first focus on the so-called zero-range approximation for the interaction potential, by recovering the Bogoliubov results and the Landau two-fluid model from a field-theory perspective. In deriving the beyond-mean-field equation of state, we are going to show that a crucial point concerns the proper regularization of the divergent zero-point energy. Among the alternative approaches to investigate finite-temperatures Bose gases, we apply the kinetic theory to explain some recent results on the sound propagation in two-dimensional Bose gases. We then move to consider the eventual corrections to the thermodynamics of Bose gases due to the finite-range character of the interaction potential. The coupling constants of the finite-range model are related to measurable scattering parameters through an effective-field-theory approach. The role of finite-range corrections is considered not only in three spatial dimensions but also in systems with lower dimensionalities. Our analytical predictions are in good agreement with available Monte Carlo simulations and consistent with other theoretical frames, as the Lieb-Lininger theory for one-dimensional systems. In the third chapter, the relevance of fluctuations is investigated from an alternative point of view. Indeed, for a single-component Bose gas we have actually considered their effect as deviations of thermodynamic quantities from the mean-field and zero-range picture. In the case of collapsing Bose mixtures, we are going to show that zero-temperature fluctuations play a crucial stabilizing role against the collapse instability. Because of this peculiar mechanism, ultracold mixtures can display finite-density configurations also in free space. Inspired by recent experiments, we characterize this novel self-bound state by comparison with bright solitons, following a variational scheme. We also consider the case of binary mixtures where a coherent internal coupling is turned on. In the last chapter, we move to deal with dipolar condensates. In particular, we are interested in beyond-mean-field effects leading to the formation of inhomogeneous ground states. In order to provide a reliable answer to the open issue of superfluid properties of these structures, we present our recent numerical investigation on the phase diagram of dipolar bosons.
We investigate an ultracold and dilute Bose gas by taking into account a finite-range two-body interaction. The coupling constants of the resulting Lagrangian density are related to measurable scattering parameters by following the effective-field-theory approach. A perturbative scheme is then developed up to the Gaussian level, where both quantum and thermal fluctuations are crucially affected by finite-range corrections. In particular, the relation between spontaneous symmetry breaking and the onset of superfluidity is emphasized by recovering the renowned Landau’s equation for the superfluid density in terms of the condensate one.