Existence and absence of Bose-Einstein condensation in the interacting random Kac-Luttinger model

• URL: http://arxiv.org/abs/2606.30277v1
• Date: Mon, 29 Jun 2026 13:22:22 GMT
• Title: Existence and absence of Bose-Einstein condensation in the interacting random Kac-Luttinger model
• Abstract summary: We study interacting bosons at zero temperature in a random and higher-dimensional continuum model introduced by Kac and Luttinger.<n>For weak interactions we prove that there is condensation in the lowest eigenstate of the one-particle Hamiltonian (type-I BEC).<n>For strong interactions, however, we show that condensation in a localized state cannot occur.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we study interacting bosons at zero temperature in a random and higher-dimensional continuum model introduced by Kac and Luttinger. For weak interactions we prove that there is condensation in the lowest eigenstate of the one-particle Hamiltonian (type-I BEC). For strong interactions, however, we show that condensation in a localized state cannot occur. We also prove generalized condensation, where a family of eigenstates of the one-particle Hamiltonian is macroscopically occupied as a whole. Combining these results yields a scenario where there is generalized condensation into a family of eigenstates of the one-particle Hamiltonian, but none of them is macroscopically occupied itself (type-III BEC). This proves a transition in the type of condensation. To the best of our knowledge, this is the first rigorous result in this direction for a random continuum model in higher dimensions.

Related papers

• Hamiltonian for a Bose gas with Contact Interactions [49.1574468325115]
  We study the Hamiltonian for a three-dimensional Bose gas of $N geq 3$ spinless particles interacting via zero-range (also known as contact) interactions.<n>Such interactions are encoded by (singular) boundary conditions imposed on the coincidence hyperplanes, i.e., when the coordinates of two particles coincide.<n>We construct a class of Hamiltonians characterized by such modified boundary conditions, that are self-adjoint and bounded from below.
  arXiv  Detail & Related papers  (2024-03-19T10:00:12Z)
• Higher-order topological Peierls insulator in a two-dimensional atom-cavity system [58.720142291102135]
  We show how photon-mediated interactions give rise to a plaquette-ordered bond pattern in the atomic ground state. The pattern opens a non-trivial topological gap in 2D, resulting in a higher-order topological phase hosting corner states. Our work shows how atomic quantum simulators can be harnessed to investigate novel strongly-correlated topological phenomena.
  arXiv  Detail & Related papers  (2023-05-05T10:25:14Z)
• Simultaneous fermion and exciton condensations from a model Hamiltonian [0.0]
  We capture fermion-exciton condensation through a model Hamiltonian. Fermion-pair and exciton condensation occur simultaneously in a single coherent quantum state. The results confirm that the dual-condensate wave function arises from the entanglement of fermion-pair and exciton wave functions.
  arXiv  Detail & Related papers  (2022-12-29T18:30:46Z)
• Large Cumulant Eigenvalue as a Signature of Exciton Condensation [0.0]
  We show that exciton condensates can be predicted from a combination of reduced density matrix theory and cumulant theory. The computational signature has applications to the prediction of exciton condensation in both molecules and materials.
  arXiv  Detail & Related papers  (2022-12-29T17:50:49Z)
• Full counting statistics of interacting lattice gases after an expansion: The role of the condensate depletion in the many-body coherence [55.41644538483948]
  We study the full counting statistics (FCS) of quantum gases in samples of thousands of interacting bosons. FCS reveals the many-body coherence from which we characterize iconic states of interacting lattice bosons.
  arXiv  Detail & Related papers  (2022-07-28T13:21:57Z)
• Regularized Zero-Range Hamiltonian for a Bose Gas with an Impurity [77.34726150561087]
  We study the Hamiltonian for a system of N identical bosons interacting with an impurity. We introduce a three-body force acting at short distances. The effect of this force is to reduce to zero the strength of the zero-range interaction between two particles.
  arXiv  Detail & Related papers  (2022-02-25T15:34:06Z)
• Classical analog of qubit logic based on a magnon Bose-Einstein condensate [52.77024349608834]
  We present a classical version of several quantum bit (qubit) functionalities using a two-component magnon Bose-Einstein condensate. The macroscopic wavefunctions of these two condensates serve as orthonormal basis states that form a system being a classical counterpart of a single qubit.
  arXiv  Detail & Related papers  (2021-11-12T16:14:46Z)
• Bose--Einstein condensation for particles with repulsive short-range pair interactions in a Poisson random external potential in $\mathbb R^d$ [0.0]
  We study Bose gases in $d$ dimensions, $d ge 2$, with short-range repulsive pair interactions, at positive temperature, in the canonical ensemble and in the thermodynamic limit. For sufficiently strong interparticle interactions, we show that almost surely there cannot be Bose-Einstein condensation into a sufficiently localized, normalized one-particle state.
  arXiv  Detail & Related papers  (2021-10-09T14:52:14Z)
• On the effect of repulsive interactions on Bose-Einstein condensation in the Luttinger-Sy model [0.0]
  We investigate the effect of repulsive pair interactions on Bose-Einstein condensation in a random one-dimensional system known as the Luttinger-Sy model at positive temperature. We prove in both cases that for sufficiently strong interactions all eigenstates of the non-interacting one-particle Luttinger-Sy Hamiltonian as well as any sufficiently localized one-particle state are almost surely not macroscopically occupied.
  arXiv  Detail & Related papers  (2020-07-13T15:36:23Z)
• On the complex behaviour of the density in composite quantum systems [62.997667081978825]
  We study how the probability of presence of a particle is distributed between the two parts of a composite fermionic system. We prove that it is a non-perturbative property and we find out a large/small coupling constant duality. Inspired by the proof of KAM theorem, we are able to deal with this problem by introducing a cut-off in energies that eliminates these small denominators.
  arXiv  Detail & Related papers  (2020-04-14T21:41:15Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.