Modulation instability in the nonlinear Schr\'odinger equation with a synthetic magnetic field: gauge matters
| Autor: | Ozana Čelan, Dario Jukić, David Prelogović, Karlo Lelas, Hrvoje Buljan |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Physics
modulation instability nonlinear Schrödinger equation gauge vector potential synthetic magnetic field FOS: Physical sciences Position and momentum space 01 natural sciences Instability 010305 fluids & plasmas Magnetic field symbols.namesake Classical mechanics Quantum Gases (cond-mat.quant-gas) Electric field 0103 physical sciences symbols Initial value problem Gauge theory 010306 general physics Condensed Matter - Quantum Gases Nonlinear Schrödinger equation Optics (physics.optics) Vector potential Physics - Optics |
| Popis: | We theoretically investigate the phenomenon of modulation instability for systems obeying the nonlinear Schr\"odinger equation, which are under the influence of an external homogeneous synthetic magnetic field. For an initial condition, the instability is detected numerically by comparing dynamics with and without a small initial perturbation; the perturbations are characterized in a standard fashion by wave vectors in momentum space. We demonstrate that the region of (in)stability in momentum space, as well as time evolution in real space, for identical initial conditions, depend on the choice of the gauge (i.e., vector potential) used to describe the homogeneous synthetic magnetic field. This superficially appears as if the gauge invariance is broken, but this is not true. When the system is evolved from an identical initial condition in two different gauges, it is equivalent to suddenly turning on the synthetic magnetic field at $t=0$. This gives rise, via Faraday's law, to an initial instantaneous kick of a synthetic electric field to the wave packet, which can differ for gauges yielding an identical uniform magnetic field for $tg0$. |
| Databáze: | OpenAIRE |
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