# Constraints on hydrodynamics from many-body quantum chaos

@article{Lucas2017ConstraintsOH, title={Constraints on hydrodynamics from many-body quantum chaos}, author={Andrew Lucas}, journal={arXiv: High Energy Physics - Theory}, year={2017} }

Is the hydrodynamics of an interacting many-body system fundamentally limited by basic principles of quantum mechanics? Starting with the conjecture that viscosity is at least as large as entropy density (as measured in fundamental units), there has been a long search for a precise answer to this question. In this work, we identify a simple relationship between hydrodynamics and many-body quantum chaos in a broad class of experimentally realizable systems. Consistency with the quantum butterfly…

## 29 Citations

### Hydrodynamics and the quantum butterfly effect in black holes and large N quantum field theories

- Physics
- 2019

Why do black holes emit thermal radiation? And how does a
closed quantum system thermalize? These apparently unrelated questions might be both connected to an essential feature of quantum techanics:…

### Many-Body Chaos in Thermalized Fluids.

- PhysicsPhysical review letters
- 2021

Using nonlinear fluid equations in one and three dimensions, it is shown that in thermalized flows λ∝sqrt[T], in agreement with results from frustrated spin systems, suggests an underlying universality and provides evidence for recent conjectures on the thermal scaling of λ.

### Quantum butterfly effect in polarized Floquet systems

- PhysicsPhysical Review B
- 2020

We explore quantum dynamics in Floquet many-body systems with local conservation laws in one spatial dimension, focusing on sectors of the Hilbert space which are highly polarized. We numerically…

### Hydrodynamics of electrons in graphene

- PhysicsJournal of physics. Condensed matter : an Institute of Physics journal
- 2018

A review of recent progress in understanding the hydrodynamic limit of electronic motion in graphene is presented, written for physicists from diverse communities with no prior knowledge of hydrodynamics.

### A quantum hydrodynamical description for scrambling and many-body chaos

- PhysicsJournal of High Energy Physics
- 2018

A bstractRecent studies of out-of-time ordered thermal correlation functions (OTOC) in holographic systems and in solvable models such as the Sachdev-Ye-Kitaev (SYK) model have yielded new insights…

### Operator Size at Finite Temperature and Planckian Bounds on Quantum Dynamics.

- PhysicsPhysical review letters
- 2019

This proposed bound explains why previously conjectured Planckian bounds do not always apply to weakly coupled theories, and how Planckerian timescales can be relevant to both transport and chaos.

### Many-body chaos and energy dynamics in holography

- PhysicsJournal of High Energy Physics
- 2018

A bstractRecent developments have indicated that in addition to out-of-time ordered correlation functions (OTOCs), quantum chaos also has a sharp manifestation in the thermal energy density two-point…

### Asymmetric butterfly velocities in 2-local Hamiltonians

- PhysicsSciPost Physics
- 2020

The speed of information propagation is finite in quantum systems with local interactions. In many such systems, local operators spread ballistically in time and can be characterized by a ``butterfly…

### Hydrodynamic Diffusion and Its Breakdown near AdS2 Quantum Critical Points

- Physics
- 2020

Hydrodynamics provides a universal description of interacting quantum field theories at sufficiently long times and wavelengths, but breaks down at scales dependent on microscopic details of the…

### Slow Relaxation and Diffusion in Holographic Quantum Critical Phases.

- PhysicsPhysical review letters
- 2019

This work underlines the connection between dangerously irrelevant deformations and slow equilibration and conjecture that there exists a long-lived, propagating collective mode with velocity v_{s}, and in this case the relation D=v_{s}^{2}τ_{eq} holds exactly in the limit Tτℏ/(k_{B}T).

## References

SHOWING 1-10 OF 77 REFERENCES

### Holographic Quantum Matter

- Physics
- 2018

We present a review of theories of states of quantum matter without quasiparticle excitations. Solvable examples of such states are provided through a holographic duality with gravitational theories…

### Thermal diffusivity and chaos in metals without quasiparticles

- Physics
- 2017

We study the thermal diffusivity DT in models of metals without quasiparticle excitations (“strange metals”). The many-body quantum chaos and transport properties of such metals can be efficiently…

### Quantum chaos on a critical Fermi surface

- PhysicsProceedings of the National Academy of Sciences
- 2017

The results establish a connection between quantum dephasing and energy transport in states of quantum matter without quasiparticles, and characterize the quantum chaos in a model of fermions at nonzero density coupled to an emergent gauge field.

### Quantum thermalization dynamics with Matrix-Product States

- Physics
- 2017

We study the dynamics of thermalization following a quantum quench using tensor-network methods. Contrary to the common belief that the rapid growth of entanglement and the resulting exponential…

### On entanglement spreading in chaotic systems

- Physics
- 2016

A bstractWe discuss the time dependence of subsystem entropies in interacting quantum systems. As a model for the time dependence, we suggest that the entropy is as large as possible given two…

### Viscosity in strongly interacting quantum field theories from black hole physics.

- PhysicsPhysical review letters
- 2005

It is provided evidence that this value of shear viscosity to volume density of entropy may serve as a lower bound for a wide class of systems, thus suggesting that black hole horizons are dual to the most ideal fluids.

### Upper Bound on Diffusivity.

- PhysicsPhysical review letters
- 2017

The bound relates transport data-including the electrical resistivity and the shear viscosity-to the local equilibration time, even in the absence of a quasiparticle description, and establishes a relation between the hydrodynamic and leading nonhydrodynamic quasinormal modes of planar black holes.

### Quantum Butterfly Effect in Weakly Interacting Diffusive Metals

- Physics
- 2017

We study scrambling, an avatar of chaos, in a weakly interacting metal in the presence of random potential disorder. It is well known that charge and heat spread via diffusion in such an interacting…

### Hydrodynamic transport in strongly coupled disordered quantum field theories

- Physics
- 2015

We compute direct current thermoelectric transport coefficients in strongly coupled quantum field theories without long lived quasiparticles, at finite temperature and charge density, and disordered…