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arXiv:2605.27863

Dark-Soliton Branch Blocking in Transonic Bose--Einstein Condensate Flows

Edilberto Oliveira Silva

Published May 27, 2026• 0 citations

Abstract

Acoustic horizons in Bose--Einstein condensates are usually characterized through long-wavelength Bogoliubov phonons. We study a nonlinear counterpart: whether a one-dimensional dark-soliton branch can sustain upstream laboratory motion in a stationary transonic flow. The mechanism is local at leading order. A regular dark soliton has a bounded fluid-frame velocity, limited by the local sound speed; therefore, in the supersonic region, the background flow exceeds the largest upstream velocity available to the soliton branch. The sonic point is thus the upstream edge of the local dark-soliton branch, rather than a hard wall or a soliton geodesic surface. We construct stationary transonic Gross--Pitaevskii backgrounds and evolve the full order parameter in an open, nonperiodic domain. The simulations show upstream propagation on the subsonic side, finite-depth stalling on the subsonic side, and downstream advection for defects initialized in the supersonic region with upstream velocity relative to the fluid. Convergence, branch-consistency, local-density, phase-jump, and a dense scan of dimensionless upstream attempts support the soliton-like interpretation. The result is a branch-existence constraint, not a rigorous lower bound on arbitrary density minima of the Gross--Pitaevskii field.

DOI: 10.48550/arxiv.2605.27863

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We study solutions of the one-dimensional Gross-Pitaevskii equation to better understand dynamical instabilities occurring in flowing atomic condensates. Whereas transonic stationary flows can be fully described in simple terms, time-dependent flows exhibit a wide variety of behaviors. When the sound speed is crossed once, we observe that flows analogous to black holes obey something similar to the so-called no hair theorem since their late time profile is stationary and uniquely fixed by parameters entering the Hamiltonian and conserved quantities. For flows analogous to white holes, at late time one finds a macroscopic undulation in the supersonic side which has either a fixed amplitude or a widely varying one, signaling a quasiperiodic emission of solitons on the subsonic side. When considering flows which cross the sound speed twice, we observe various scenarios which can be understood from the above behaviors and from the hierarchy of the growth rates of the dynamical instabilities characterizing such flows.

Summary form only given. Bose-Einstein condensates (BEC) of weakly interacting gases allow for the new regime of nonlinear atom optics. Of special interest are macroscopically excited states like dark solitons or vortices. Solitons, as particle like excitations of matter wave fields, provide a link from condensate physics to fluid mechanics, nonlinear optics and fundamental particle physics. Dark solitons in matter waves are characterized by a local density minimum and, a steep phase gradient of the wavefunction at the position of the minimum. We report on experimental and theoretical investigation of dark solitons in BECs of /sup 87/Rb which are produced by the method of phase imprinting. A highly anisotropic confining potential allows us to be close to the (quasi) 1D situation where dark solitons are expected to be dynamically stable. By monitoring the evolution of the density profile we observe the evolution of density minima travelling at a smaller velocity than the speed of sound. By comparison to analytical and numerical solutions of the 3D Gross-Pitaevskii equation for our experimental conditions we identify these density minima to be moving dark solitons. We have studied in detail the creation and the dynamics of dark solitons as a function of evolution time and imprinted phase.

Abstract In this article, we study the dynamics of a Bose–Einstein condensate (BEC) with the idea of finding solutions that could possibly correspond to the so-called acoustic (or Unruh) black/white holes. These are flows with horizons where the speed of the flow changes from sub-sonic to super-sonic. This is because sound cannot return from the supersonic to the subsonic regions. The speed of sound plays the role of the speed of light in a gravitational black hole, with an important difference being that there are excitations that can go faster than the speed of sound and therefore can escape the sonic black hole. Here, the motion of the BEC is described by the Gross–Pitaevskii equation (GPE). More specifically, we discuss singular Stationary solutions of GPE in 2D (with circular symmetry) and 3D (with spherical symmetry). We use these solutions to study the local speed of sound and magnitude of flow velocity of the condensate to determine whether they cross, indicating the potential existence of a sonic analog of a black/white hole. We discuss the numerical techniques used and also study the semi-analytical Laplace–Borel resummation of asymptotic series solutions to see how well they agree with numerical solutions. We also study how the resurgent transseries plays a role in these solutions.

In a previous article, we studied stationary solutions to the dynamics of a Bose-Einstein condensate corresponding to acoustic (or Unruh) black or white holes, namely, configurations where the flow becomes supersonic, creating a horizon for phonons. In this paper, we consider again the Gross-Pitaevskii equation, but looking for stationary numerical solutions in the case where the couplings are position dependent in a prescribed manner. Initially, we consider a two-dimensional quantum gas in a funnel-like spatial metric. We then reinterpret this solution as a solution in a flat metric but with spatially dependent coupling and external potential. In these solutions, the local speed of sound and the magnitude of flow velocity cross, indicating the existence of a supersonic region and therefore of sonic analogs of black and white holes and wormholes. We discuss the numerical techniques used. We also study phase (and density) fluctuations in these solutions and derive approximate acoustic metric tensors. For certain external potentials, we find uniform-density acoustic-black-hole configurations and obtain their Hawking temperature.