Quantum turbulence, superfluidity, non-Markovian dynamics, and wave function thermalization

Abstract: While quantum turbulence has been addressed both experimentally (predominantly for superfluid $^4$He and $^3$He) and theoretically, the dynamics of various ensembles of quantized vortices was followed in time only until the vortices decay into phonons. How this ``thermalization'' is achieved is still an unaddressed and thus an unelucidated question. The Unitary Fermi Gas (UFG) is a unique quantum system, which has no classical counterpart and of relevance to neutron stars, cold atoms, condensed matter and nuclear many-body systems. The non-Markovian evolution of an isolated UFG is put in evidence and its entire non-equilibrium evolution can be studied theoretically within a unified theoretical framework. The initial lattice of quantum vortices and anti-vortices evolves through a couple of vortex tangles and excitation of Kelvin waves, where vortices cross and reconnect, until very slowly thermalization sets in.

• The paper demonstrates quantum turbulence by simulating vortex reconnections in a superfluid Unitary Fermi Gas using an extended TDSLDA framework.
• The paper reveals non-Markovian thermalization through time-dependent occupation probabilities and coherent quantum interference effects.
• The paper shows that vortex dynamics evolve into a quasi-homogeneous state with effective temperature fluctuations below the critical pairing threshold.

Quantum Turbulence and Non-Markovian Dynamics in Unitary Fermi Gases

The paper "Quantum turbulence, superfluidity, non-Markovian dynamics, and wave function thermalization" presents a comprehensive study on quantum turbulence (QT) in superfluid systems, specifically focusing on the Unitary Fermi Gas (UFG). The research provides valuable insights into the non-Markovian evolution and thermalization dynamics of quantum vortices. The authors employ a robust theoretical framework that extends the Time-Dependent Density Functional Theory (TDDFT), incorporating the Superfluid Local Density Approximation (SLDA) to study these phenomena.

Summary of Key Findings

1. Initial Conditions and Vortex Dynamics: The study initiates with an ensemble of quantum vortices and anti-vortices in an unpolarized UFG system. Through numerical simulations, the authors observe the evolution of these vortices into a tangled state, characterized by interactions such as crossings and reconnections. The vortex dynamics align qualitatively with Feynman's conjecture regarding turbulence in superfluids, effectively demonstrating quantum vortex behavior.
2. Non-Markovian Evolution: A significant contribution of the work is the evidence of non-Markovian dynamics during the thermalization process. Unlike classical Markovian processes, the redistribution of occupation probabilities in the UFG demonstrates a non-linear time dependence, reflecting the complex quantum nature of interactions within the UFG. The study emphasizes that the instantaneous occupation probabilities change significantly over time, indicative of entanglement and coherent interference effects in the system.
3. Thermalization and Effective Temperature: The thermalization process, described as "wave function thermalization," occurs over a much extended timescale compared to traditional ETH predictions. Thermalization results in a quasi-homogeneous state with small fluctuations in particle densities and pairing gaps, implying an effective temperature below the critical pairing temperature. The work provides a direct comparison of the initial and final states, illustrating minimal changes in canonical occupation probabilities, which underlines the stability and resilience of the superfluid phase.
4. Use of TDSLDA Framework: The authors leverage a specialized toolkit, W-SLDA, to implement the TDSLDA framework, simulating the system's evolution on high-performance supercomputers. This approach provides a detailed, accurate description of the UFG's non-equilibrium behavior, showing comprehensive results in a large phase space with controlled numerical errors.

Implications and Future Directions

The findings from this paper have significant implications for understanding QT in different superfluid systems, notably neutron stars, nuclear systems, and cold atom systems. The demonstration of non-Markovian behavior and extended thermalization times may influence the development of theoretical models for other strongly interacting quantum systems, where classical physics fails to capture the inherent quantum coherence and entanglement.

Future research could potentially explore:

• Incorporation of $p$-wave interactions: Extending the current framework to include $p$-wave interaction effects might provide deeper insights into the complex energetic and dynamic properties of UFGs.
• Cross-system comparisons: Investigating other systems, such as helium 3 and 4 or more exotic states of matter, could enhance our understanding of QT and superfluidity across different physical conditions.
• Advanced computational models: Further refinement of computational methods and algorithms to reduce complexity and enhance the simulation of quantum phases at varying scales.

This body of work expands the theoretical understanding and provides a comprehensive platform for future explorations of QT and its applications in both theoretical and practical realms of quantum physics.