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We study the modulational dynamics of striped patterns formed in the wake of a planar directional quench. Such quenches, which move across a medium and nucleate pattern-forming instabilities in their wake, have been shown in numerous applications to control and select the wavenumber and orientation of striped phases. In the context of the prototypical complex Ginzburg–Landau and Swift–Hohenberg equations, we use a multiple-scale analysis to derive a one-dimensional viscous Burgers’ equation, which describes the long-wavelength modulational and defect dynamics in the direction transverse to the quenching motion, that is, along the quenching line. We show that the wavenumber selecting properties of the quench determine the nonlinear flux parameter in the Burgers’ modulation equation, while the viscosity parameter of the Burgers’ equation is naturally determined by the transverse diffusivity of the pure stripe state. We use this approximation to accurately characterize the transverse dynamics of several types of defects formed in the wake, including grain boundaries and phase-slips.
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Dynamics for the Haldane phase in the Bilinear-Biquadratic Model
The BBM is a promising candidate to study spin-one systems and to design quantum simulators based on its underlying Hamiltonian. The variety of different phases contains amongst other valuable and exotic phases the Haldane phase. We study the Kibble-Zurek physics of linear quenches into the Haldane phase. We outline ideal quench protocols to minimize defects in the final state while exploiting different linear quench protocols via the uniaxial or interaction term. Furthermore, we look at the fate of the string order when quenching from a topologically non-trivial phase to a trivial phase. Our studies show this depends significantly on the path chosen for quenching; for example, we discover quenches from \Neel{} to Haldane phase which reach a string order greater than their ground state counterparts for the initial or final state at intermediate quench times.
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- Award ID(s):
- 1839232
- PAR ID:
- 10297295
- Date Published:
- Journal Name:
- ArXivorg
- ISSN:
- 2331-8422
- Page Range / eLocation ID:
- 2012.11479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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