Hydrodynamic Long-Time Tails Achieved Via One-Loop Quantum Fluctuation Corrections

Scientists are increasingly investigating the subtle interplay between quantum mechanics and the macroscopic world of hydrodynamics. Akash Jain, alongside colleagues, now demonstrate how quantum fluctuations fundamentally alter diffusive hydrodynamic behaviour. Their work, conducted without institutional affiliation listed, constructs a theoretical framework revealing intrinsically non-Gaussian noise arising from these fluctuations, challenging conventional understandings of hydrodynamic long-time tails. This research, extending to arbitrarily high orders in the expansion parameter, provides a novel approach to calculating retarded correlation functions and offers a closed-form expression at leading order, potentially impacting fields from condensed matter physics to cosmology.

Quantum Hydrodynamics via KMS Symmetry and Noise offers

Scientists have constructed a quantum Schwinger-Keldysh (SK) Effective field theory to describe the diffusive hydrodynamics of a conserved scalar field, addressing a fundamental need to incorporate quantum fluctuations into hydrodynamic models. This research establishes a framework where quantum corrections are systematically guided by fluctuation-dissipation relations, rigorously enforced through a dynamical Kubo-Martin-Schwinger (KMS) symmetry. The team achieved a quantum-complete SK effective action, revealing that the KMS symmetry intrinsically generates non-Gaussian noise at all orders in the noise field, a significant departure from classical stochastic hydrodynamics. This breakthrough unveils a mechanism to consistently include both thermal and quantum fluctuations, particularly crucial in systems where microscopic and quantum timescales are comparable.

The study employed the SK formalism, an action-based effective field theory, to systematically account for fluctuations, leveraging the KMS symmetry as a guiding principle for introducing these fluctuations consistently with the fluctuation-dissipation theorem. Researchers found that the KMS symmetry, acting non-locally in time, necessitates fluctuation contributions in the SK effective action, leading to the aforementioned non-Gaussian noise. By identifying the average “physical” and difference “noise” field combinations, they simplified the implementation of the KMS symmetry, enabling a systematic derivation of the quantum-complete SK effective action for hydrodynamic models. This approach extends beyond simple models, offering a pathway to incorporate more complex hydrodynamic scenarios.

Experiments show that the resulting framework allows for the computation of one-loop quantum corrections to the two-point density-density retarded correlation function, leading to a generalization of hydrodynamic long-time tails. The one-loop results for these retarded correlation functions have been expressed as a family of polynomials, and a closed-form expression has been derived for the leading order in the wavevector expansion. This work applies at arbitrarily high orders in ħ, demonstrating its robustness and broad applicability. The research establishes a novel approach to understanding hydrodynamic behaviour in regimes where quantum effects are significant, opening avenues for exploring systems like conformal field theories lacking characteristic scales.

The work opens possibilities for investigating systems where the separation between microscopic and quantum timescales is blurred, such as conformal field theories, and provides a foundation for more accurate modelling of complex fluids and other dissipative systems. This quantum-complete SK effective action offers a powerful tool for studying hydrodynamic phenomena in a wider range of physical conditions, potentially impacting fields from condensed matter physics to cosmology. The ability to systematically incorporate quantum fluctuations into hydrodynamic calculations represents a significant advancement, promising a deeper understanding of non-equilibrium dynamics in many-body systems.

Schwinger-Keldysh Theory and Non-Gaussian Fluctuations offer a powerful

Scientists engineered a Schwinger-Keldysh (SK) effective field theory to investigate the diffusive hydrodynamics of a conserved scalar field, addressing the limitations of traditional hydrodynamic frameworks that neglect inherent fluctuations. The research team guided corrections within the SK framework using fluctuation-dissipation relations, rigorously enforcing these through a dynamical Kubo-Martin-Schwinger (KMS) symmetry. This symmetry, crucial for incorporating both thermal and quantum fluctuations, necessitates the generation of fluctuation contributions in the SK effective action at all orders in the noise field, resulting in intrinsically non-Gaussian noise. Consequently, the study pioneered a method for systematically including quantum effects in hydrodynamic models, particularly when intrinsic timescales are comparable to or smaller than ħβ.

Researchers employed a symmetry-based approach to realise the fluctuation-dissipation theorem, utilising the KMS symmetry which acts non-locally in time on fields defined on a closed-time contour. The team defined fields f1(t) and f2(t) on this contour, subjecting them to a KMS transformation involving a relative phase-shift of iħβ in imaginary time, as described by the equation f1(t) →±f1(−t + iθ), f2(t) →±f2(−t −iħβ + iθ). This non-local transformation posed a significant challenge, prompting the identification of average and difference field combinations, fr = (f1 + f2)/2 and fa = (f1 −f2)/ħ, to simplify the symmetry’s implementation. These combinations transform more locally in ħ, facilitating the construction of a quantum-complete SK effective action.

Experiments involved deriving one-loop corrections to the two-point density-density retarded correlation function, leading to a generalization of hydrodynamic long-time tails and applicability at arbitrarily high orders in . The one-loop results for these retarded correlation functions were expressed as a family of polynomials, enabling a closed-form expression at leading order in the wavevector expansion. This innovative approach allows for the computation of quantum corrections to hydrodynamic long-time tails in diffusion theory, offering a significant advancement in understanding systems where quantum and stochastic fluctuations are inseparable. The work demonstrates a systematic mechanism to implement the full quantum version of the KMS symmetry, providing a foundation for deriving quantum-complete SK-EFTs for various hydrodynamic models.