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Bounds on Transport from Univalence and Pole-Skipping
1Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Physical Review Letters
|February 19, 2021
Summary
Researchers developed new methods to derive exact bounds on hydrodynamic transport coefficients, like diffusivity and sound speed. These techniques combine hydrodynamics with complex function theory, offering rigorous insights into quantum and classical dynamics.
Area of Science:
- Theoretical Physics
- Quantum Dynamics
- Hydrodynamics
Background:
- Understanding transport phenomena in quantum and classical dynamics is crucial.
- Existing bounds on transport coefficients are often not exact or universally applicable.
- Hydrodynamic dispersion relations govern transport properties.
Purpose of the Study:
- To derive exact, rigorous, and sharp bounds on all coefficients of hydrodynamic dispersion relations.
- To introduce novel methods combining analytic properties of hydrodynamics and univalent function theory.
- To explore connections between transport bounds, quantum chaos, and holographic theories.
Main Methods:
- Utilizing analytic properties of hydrodynamics.
- Applying the theory of univalent (complex holomorphic and injective) functions.
- Investigating pole-skipping phenomena in theories with holographic duals.
Main Results:
- A new set of methods and sufficient conditions for deriving exact bounds on hydrodynamic transport coefficients.
- Demonstration of bounds relating transport to quantum chaos via pole-skipping.
- Examples of bounds and holographic theories validating the derived conditions.
Conclusions:
- The developed methods provide exact and sharp bounds on hydrodynamic transport coefficients.
- Univalence methods offer a powerful tool for bounding transport phenomena, including those related to quantum chaos.
- Potential applications extend to bounds not directly related to chaos, such as conformal bounds on sound speed.
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