Onset of a Fold Cascade in a Hopf Texture Driven by a Navier--Stokes Blow-Up Analog

Antti J. Niemi

Home/Archive/arXiv

arXiv · 2609.24490

Onset of a Fold Cascade in a Hopf Texture Driven by a Navier--Stokes Blow-Up Analog

Antti J. Niemi

View original source ↗Read source document ↗Export metadata ↓

Abstract

A two-component Bose--Einstein condensate can host a pseudospin Hopf texture while its thermal cloud obeys viscous Navier--Stokes dynamics. Motivated by OpenAI's reported finite-time singular solution, we drive such a texture with a surrogate of the collapsing core, using an effective Madelung--Schrödinger theory with a Faxén-like advective correction. The texture undergoes fold-mediated creation and annihilation of preimage pairs at conserved Hopf charge with the first one-to-three transition confirmed to obey the square-root opening of a Thom $A_2$

Explore related subjects

cond-mat.quant-gas math-ph math.MP nlin.PS

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Antti J. Niemi. 2026-09-21. Onset of a Fold Cascade in a Hopf Texture Driven by a Navier--Stokes Blow-Up Analog. https://arxiv.org/abs/2609.24490

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Limit of Spin Squeezing in Finite Temperature Bose-Einstein Condensates

We show that, at finite temperature, the maximum spin squeezing achievable using interactions in Bose-Einstein condensates has a finite limit when the atom number $N\to \infty$ at fixed density and interaction strength. We calculate the limit of the squeezing parameter for a spatially homogeneous system and show that it is bounded from above by the initial non-condensed fraction.

cond-mat.quant-gas↗

arXiv2026

Quantum fields in a cold atomic simulator: relaxation and phase locking in tunnel-coupled 1D bosonic quasi-condensates

We consider a prime example of simulating interacting relativistic QFT with cold atoms: the realisation of the sine-Gordon model by tunnel-coupled quasi-1D Bose gases. While experiments have shown that it can realise the sine-Gordon model in equilibrium, studies of non-equilibrium dynamics have revealed phase-locking behaviour that contrasts with predictions from sine-Gordon field theory. Here, we examine a one-dimensional field-theoretic model of the system and find that the phase-locking behaviour can be understood in terms of the longitudinal harmonic trap, and that the additional degrees of freedom observed in the experiment do not appear to play a significant role. Therefore, the experimental setup provides a good simulator of the sine-Gordon quantum field theory, even out of equilibrium, if the inhomogeneous background induced by the trap is taken into account. Furthermore, our results support the idea that modifying the longitudinal trap to a box shape should result in agreement with standard sine-Gordon dynamics. The main remaining open issues are accounting for 3D corrections and modelling the effect of the boundaries.

cond-mat.quant-gas↗

arXiv2026

Supersolid crystals of dipolar excitons in a lattice

In condensed-matter physics, long-range correlations introduce quantum states of matter that challenge intuition. For example, supersolids combine density order that manifests as symmetry-breaking spatial arrangement, and frictionless superfluid flow. However, supersolids have proven to only exist under very stringent conditions, with evidence limited to a few spontaneously fragmented superfluids observed in the weakly-interacting regime. Here, we demonstrate a framework to realize crystalline supersolids in the strong interaction regime, by confining dipolar bosons in a lattice with long-range hopping. We show that dipolar excitons realize this lattice model. At fractional lattice fillings of one quarter, one third and one half we observe mesoscopic quantum crystals across around 100 sites that spontaneously break the lattice translational symmetry. At the same time, coherent long-range hopping induces off-diagonal long-range order such that the exciton solids are superfluids. Our numerical methods quantitatively confirm that supersolidity builds up in the ground-state of the lattice Hamiltonian.

cond-mat.quant-gas↗