An Equation of State for Turbulence in the Gross-Pitaevskii model

Abstract

We report the numerical observation of a far-from-equilibrium equation of state (EOS) in the Gross-Pitaevskii model. We first show that the momentum distribution of the turbulent cascade is well described by wave-turbulent kinetic theory in the appropriate limits. Calculating the energy and particle fluxes ${\Pi }_{\epsilon }(k)$ and ${\Pi }_N(k)$, we show that the turbulent state possesses the hallmarks of a direct energy cascade. Building on this, we show that the GP model encodes a universal EOS in the form of a relationship between the turbulent cascade's momentum distribution amplitude $n_0$ and the energy flux $\epsilon$ in the steady state. We find that in our regime of `mixed' turbulence - where both vortices and waves play a significant role - $n_0\propto {\epsilon }^{0.67(2)}$, a result that is not captured by any existing theory of turbulence but that agrees with a recent experimental measurement for large energy fluxes. Finally, we find that the concept of quasi-static thermodynamic processes between equilibrium states extends to far-from-equilibrium steady states.

arXiv commentMain text: 4 pages, 4 figures; End Matter: 2 pages, 3 figures; Supplementary information: 4 pages, 4 figures

References in corpus (27)

• Non-thermal fixed points: effective weak-coupling for strongly correlated systems far from equilibrium
• Emergence of a Turbulent Cascade in a Quantum Gas
• Towards a 'Thermodynamics' of Active Matter
• Observation of universal dynamics in a spinor Bose gas far from equilibrium
• Kolmogorov spectrum of superfluid turbulence: numerical analysis of the Gross-Pitaevskii equation with the small scale dissipation
• Observation of universal dynamics in an isolated one-dimensional Bose gas far from equilibrium
• Nonequilibrium equation of state in suspensions of active colloids
• Quantum Gases in Optical Boxes
• A classical field method for time dependent Bose condensed gases
• Simulations of thermal Bose fields in the classical limit
• Numerical Studies of Quantum Turbulence
• Synthetic dissipation and cascade fluxes in a turbulent quantum gas
• Bidirectional dynamic scaling in an isolated Bose gas far from equilibrium
• Kinetic theory of non-thermal fixed points in a Bose gas
• Direct and inverse cascades in turbulent Bose-Einstein condensate
• Emergence of isotropy and dynamic scaling in 2D wave turbulence in a homogeneous Bose gas
• Vinen turbulence via the decay of multicharged vortices in trapped atomic Bose-Einstein condensates
• From single-particle excitations to sound waves in a box-trapped atomic Bose-Einstein condensate
• Universal equation of state for wave turbulence in a quantum gas
• Universality class of a spinor Bose-Einstein condensate far from equilibrium
• Quantum turbulence simulations using the Gross-Pitaevskii equation: high-performance computing and new numerical benchmarks
• Theoretical analysis of quantum turbulence using the Onsager "ideal turbulence" theory
• Universal Coarsening in a Homogeneous Two-Dimensional Bose Gas
• Observation of Relaxation Stages in a Nonequilibrium Closed Quantum System: Decaying Turbulence in a Trapped Superfluid
• Kolmogorov turbulence in atomic Bose-Einstein condensates
• Regimes of Steady-State Turbulence in a Quantum Fluid
• A universal speed limit for spreading of coherence

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