skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Dispersion of Ultrarelativistic Tardyonic and Tachyonic Wave Packets on Cosmic Scales
We investigate the time propagation of tachyonic (superluminal) and tardyonic (subluminal, ordinary) massive wave packets on cosmic scales. A normalizable wave packet cannot be monochromatic in momentum space and thus acquires a positional uncertainty (or packet width) that increases with travel distance. We investigate the question of how this positional uncertainty affects the uncertainty in the detection time for cosmic radiation on Earth. In the ultrarelativistic limit, we find a unified result, δx(t)/c3=m2δpt/p03, where δx(t) is the positional uncertainty, m is the mass parameter, δp is the initial momentum spread of the wave function, and p0 is the central momentum of the wave packet, which, in the ultrarelativistic limit, is equal to its energy. This result is valid for tachyons and tardyons; its interpretation is being discussed.  more » « less
Award ID(s):
2110294
PAR ID:
10414580
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Symmetry
Volume:
14
Issue:
12
ISSN:
2073-8994
Page Range / eLocation ID:
2596
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; ; ; (, The Journal of Chemical Physics)
    We show that standard Ehrenfest dynamics does not conserve linear and angular momentum when using a basis of truncated adiabatic states. However, we also show that previously proposed effective Ehrenfest equations of motion [M. Amano and K. Takatsuka, “Quantum fluctuation of electronic wave-packet dynamics coupled with classical nuclear motions,” J. Chem. Phys. 122, 084113 (2005) and V. Krishna, “Path integral formulation for quantum nonadiabatic dynamics and the mixed quantum classical limit,” J. Chem. Phys. 126, 134107 (2007)] involving the non-Abelian Berry force do maintain momentum conservation. As a numerical example, we investigate the Kramers doublet of the methoxy radical using generalized Hartree–Fock with spin–orbit coupling and confirm that angular momentum is conserved with the proper equations of motion. Our work makes clear some of the limitations of the Born–Oppenheimer approximation when using ab initio electronic structure theory to treat systems with unpaired electronic spin degrees of freedom, and we demonstrate that Ehrenfest dynamics can offer much improved, qualitatively correct results. 
    more » « less
  2. ; (, Water Waves)
    Abstract We examine a two-dimensional deep-water surface gravity wave packet generated by a pressure disturbance in the Lagrangian reference frame. The pressure disturbance has the form of a narrow-banded weakly nonlinear deep-water wave packet. During forcing, the vorticity equation implies that the momentum resides entirely in the near-surface Lagrangian-mean flow, which in this context is often called the “Stokes drift”. After the forcing turns off, the wave packet propagates away from the forcing region, carrying with it most of the energy imparted by the forcing. These waves together with their induced long wave response have no momentum in a depth integrated sense, in agreement with the classical results of Longuet-Higgins and Stewart (Deep Sea Research and Oceanographic Abstracts 11, 592−562) and McIntyre (Journal of Fluid Mechanics 106, 331−347). The total flow associated with the propagating packet has no net momentum. In contrast with the finite-depth scenario discussed by McIntyre (Journal of Fluid Mechanics 106, 331−347), however, momentum imparted to the fluid during forcing resides in a dipolar structure that persists in the forcing region—rather than being carried away by shallow-water waves. We conclude by examining waves propagating from deep to shallow water and show that wave packets, which initially have no momentum, may have non-zero momentum in finite-depth water through reflected and trapped long waves. This explains how deep water waves acquire momentum as they approach shore. The artificial form of the parameterized forcing from the wind facilitates the thought experiments considered in this paper, as opposed to striving to model more realistic wind forcing scenarios. 
    more » « less
  3. ; (, Journal of the Atmospheric Sciences)
    The influence of vertical shear on the evolution of mountain-wave momentum fluxes in time-varying cross-mountain flows is investigated by numerical simulation and analyzed using ray tracing and the WKB approximation. The previously documented tendency of momentum fluxes to be strongest during periods of large-scale cross-mountain flow acceleration can be eliminated when the cross-mountain wind increases strongly with height. In particular, the wave packet accumulation mechanism responsible for the enhancement of the momentum flux during periods of cross-mountain flow acceleration is eliminated by the tendency of the vertical group velocity to increase with height in a mean flow with strong forward shear, thereby promoting vertical separation rather than concentration of vertically propagating wave packets. 
    more » « less
  4. ; ; (, Journal of Geophysical Research: Atmospheres)
    Abstract In this paper, we simulate an observed mountain wave event over central Europe and investigate the subsequent generation, propagation, phase speeds and spatial scales, and momentum deposition of secondary waves under three different tidal wind conditions. We find the mountain wave breaks just below the lowest critical level in the mesosphere. As the mountain wave breaks, it extends outwards along the phases and fluid associated with the breaking flows downstream of its original location by 500–1,000 km. The breaking generates a broad range of secondary waves with horizontal scales ranging from the mountain wave instability scales (20–300 km), to multiples of the mountain wave packet scale (420 km+) and phase speeds from 40 to 150 m/s in the lower thermosphere. The secondary wave morphology consists of semi‐concentric patterns with wave propagation generally opposing the local tidal winds in the mesosphere. Shears in the tidal winds cause breaking of the secondary waves and local wave forcing which generates even more secondary waves. The tidal winds also influence the dominant wavelengths and phase speeds of secondary waves that reach the thermosphere. The secondary waves that reach the thermosphere deposit their energy and momentum over a broad area of the thermosphere, mostly eastward of the source and concentrated between 110 and 130 km altitude. The secondary wave forcing is significant and will likely be very important for the dynamics of the thermosphere. A large portion of this forcing comes from nonlinearly generated secondary waves at relatively small‐scales which arise from the wave breaking processes. 
    more » « less
  5. ; ; ; ; ; (, Science)
    The wave function of a Tonks-Girardeau (T-G) gas of strongly interacting bosons in one dimension maps onto the absolute value of the wave function of a noninteracting Fermi gas. Although this fermionization makes many aspects of the two gases identical, their equilibrium momentum distributions are quite different. We observed dynamical fermionization, where the momentum distribution of a T-G gas evolves from bosonic to fermionic after its axial confinement is removed. The asymptotic momentum distribution after expansion in one dimension is the distribution of rapidities, which are the conserved quantities associated with many-body integrable systems. Our measurements agree well with T-G gas theory. We also studied momentum evolution after the trap depth is suddenly changed to a new nonzero value, and we observed the theoretically predicted bosonic-fermionic oscillations. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email