Logarithmic catastrophes and Stokes's phenomenon in waves at horizons

• URL: http://arxiv.org/abs/2209.11148v1
• Date: Thu, 22 Sep 2022 16:49:28 GMT
• Title: Logarithmic catastrophes and Stokes's phenomenon in waves at horizons
• Authors: L. M. Farrell and C. J. Howls and D. H. J. O'Dell
• Abstract summary: waves propagating near an event horizon display interesting features including logarithmic phase singularities and caustics. We consider an acoustic horizon in a flowing Bose-Einstein condensate where the elementary excitations obey the Bogoliubov dispersion relation. We find that the horizon is a physical manifestation of a Stokes surface, marking the place where a wave is born.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Waves propagating near an event horizon display interesting features including logarithmic phase singularities and caustics. We consider an acoustic horizon in a flowing Bose-Einstein condensate where the elementary excitations obey the Bogoliubov dispersion relation. In the hamiltonian ray theory the solutions undergo a broken pitchfork bifurcation near the horizon and one might therefore expect the associated wave structure to be given by a Pearcey function, this being the universal wave function that dresses catastrophes with two control parameters. However, the wave function is in fact an Airy-type function supplemented by a logarithmic phase term, a novel type of wave catastrophe. Similar wave functions arise in aeroacoustic flows from jet engines and also gravitational horizons if dispersion which violates Lorentz symmetry in the UV is included. The approach we take differs from previous authors in that we analyze the behaviour of the integral representation of the wave function using exponential coordinates. This allows for a different treatment of the branches that gives rise to an analysis based purely on saddlepoint expansions, which resolve the multiple real and complex waves that interact at the horizon and its companion caustic. We find that the horizon is a physical manifestation of a Stokes surface, marking the place where a wave is born, and that the horizon and the caustic do not in general coincide: the finite spatial region between them delineates a broadened horizon.

Related papers

• Dispersive shock waves in a one-dimensional droplet-bearing environment [7.370081795303041]
  We demonstrate the controllable generation of distinct types of dispersive shock-waves emerging in a quantum droplet bearing environment. Surprisingly, dispersive shock waves persist across the hyperbolic-to-elliptic threshold. A plethora of additional wave patterns arise, such as rarefaction waves, traveling dispersive shock waves, (anti)kinks and droplet wavetrains.
  arXiv  Detail & Related papers  (2024-04-03T18:39:57Z)
• Lattice-induced wavefunction effects on trapped superfluids [0.0]
  We propose gauge-independent tensors describing Bloch wavefunction effects on local interaction between correlated particles. We derive an effective hydrodynamic theory for ultracold bosons in optical lattices. Our discovery advances the connections between the modern band theory and quantum many-body physics.
  arXiv  Detail & Related papers  (2024-01-25T08:04:47Z)
• Investigation of a non-Hermitian edge burst with time-dependent perturbation theory [0.6617341769966992]
  Edge burst is a phenomenon in non-Hermitian quantum dynamics. We investigate the evolution of real-space wave functions for this lattice system.
  arXiv  Detail & Related papers  (2023-03-30T08:27:20Z)
• In-Gap Band Formation in a Periodically Driven Charge Density Wave Insulator [68.8204255655161]
  Periodically driven quantum many-body systems host unconventional behavior not realized at equilibrium. We investigate such a setup for strongly interacting spinless fermions on a chain, which at zero temperature and strong interactions form a charge density wave insulator.
  arXiv  Detail & Related papers  (2022-05-19T13:28:47Z)
• Clarifying nonstatic-quantum-wave behavior through extending its analysis to the p-quadrature space: Interrelation between the q- and p-space wave-nonstaticities [0.0]
  Nonstatic waves can appear even when the parameters of the medium do not vary. In this work, the properties of nonstatic waves in a static environment are investigated from their $p$-space analysis.
  arXiv  Detail & Related papers  (2021-11-26T12:36:24Z)
• Green's functions of and emission into discrete anisotropic and hyperbolic baths [0.0]
  We study wave propagation in generic Hermitian local baths. We investigate the effects of anisotropy and quasi-breaking of periodicity on resonant emission into the band of the bath.
  arXiv  Detail & Related papers  (2021-05-29T07:21:04Z)
• Fano interference in quantum resonances from angle-resolved elastic scattering [62.997667081978825]
  We show that probing the angular dependence of the cross section allows us to unveil asymmetric Fano profiles in a single channel shape resonance. We observe a shift in the peak of the resonance profile in the elastic collisions between metastable helium and deuterium molecules.
  arXiv  Detail & Related papers  (2021-05-12T20:41:25Z)
• Collective radiation from distant emitters [63.391402501241195]
  We show that the spectrum of the radiated field exhibits non-Markovian features such as linewidth broadening beyond standard superradiance. We discuss a proof-of-concept implementation of our results in a superconducting circuit platform.
  arXiv  Detail & Related papers  (2020-06-22T19:03:52Z)
• Dynamical solitons and boson fractionalization in cold-atom topological insulators [110.83289076967895]
  We study the $mathbbZ$ Bose-Hubbard model at incommensurate densities. We show how defects in the $mathbbZ$ field can appear in the ground state, connecting different sectors. Using a pumping argument, we show that it survives also for finite interactions.
  arXiv  Detail & Related papers  (2020-03-24T17:31:34Z)
• Zitterbewegung and Klein-tunneling phenomena for transient quantum waves [77.34726150561087]
  We show that the Zitterbewegung effect manifests itself as a series of quantum beats of the particle density in the long-time limit. We also find a time-domain where the particle density of the point source is governed by the propagation of a main wavefront. The relative positions of these wavefronts are used to investigate the time-delay of quantum waves in the Klein-tunneling regime.
  arXiv  Detail & Related papers  (2020-03-09T21:27:02Z)
• External and internal wave functions: de Broglie's double-solution theory? [77.34726150561087]
  We propose an interpretative framework for quantum mechanics corresponding to the specifications of Louis de Broglie's double-solution theory. The principle is to decompose the evolution of a quantum system into two wave functions. For Schr"odinger, the particles are extended and the square of the module of the (internal) wave function of an electron corresponds to the density of its charge in space.
  arXiv  Detail & Related papers  (2020-01-13T13:41:24Z)

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.