Kinetic theory of non-thermal fixed points in a Bose gas
We outline a kinetic theory of non-thermal fixed points for the example of a dilute Bose gas, partially reviewing results obtained earlier, thereby extending, complementing, generalizing and straightening them out. We study universal dynamics after a cooling quench, focusing on situations where the...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
19 April 2019
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| In: |
Physical review
Year: 2019, Volume: 99, Issue: 4 |
| ISSN: | 2469-9934 |
| DOI: | 10.1103/PhysRevA.99.043620 |
| Online Access: | Resolving-System, Volltext: https://doi.org/10.1103/PhysRevA.99.043620
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| Author Notes: | Isara Chantesana, Asier Piñeiro Orioli, and Thomas Gasenzer |
MARC
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| 520 | |a We outline a kinetic theory of non-thermal fixed points for the example of a dilute Bose gas, partially reviewing results obtained earlier, thereby extending, complementing, generalizing and straightening them out. We study universal dynamics after a cooling quench, focusing on situations where the time evolution represents a pure rescaling of spatial correlations, with time defining the scale parameter. The non-equilibrium initial condition set by the quench induces a redistribution of particles in momentum space. Depending on conservation laws, this can take the form of a wave-turbulent flux or of a more general self-similar evolution, signaling the critically slowed approach to a non-thermal fixed point. We identify such fixed points using a non-perturbative kinetic theory of collective scattering between highly occupied long-wavelength modes. In contrast, a wave-turbulent flux, possible in the perturbative Boltzmann regime, builds up in a critically accelerated self-similar manner. A key result is the simple analytical universal scaling form of the non-perturbative many-body scattering matrix, for which we lay out the concrete conditions under which it applies. We derive the scaling exponents for the time evolution as well as for the power-law tail of the momentum distribution function, for a general dynamical critical exponent $z$ and an anomalous scaling dimension $\eta$. The approach of the non-thermal fixed point is, in particular, found to involve a rescaling of momenta in time $t$ by $t^{\beta}$, with $\beta=1/z$, within our kinetic approach independent of $\eta$. We confirm our analytical predictions by numerically evaluating the kinetic scattering integral as well as the non-perturbative many-body coupling function. As a side result we obtain a possible finite-size interpretation of wave-turbulent scaling recently measured by Navon et al. | ||
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