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Dec 10, 2023 38 likes •451 views

The Reasonable and Unreasonable Effectiveness of Hydrodynamics in Exotic Quantum Matter Hong Liu Theoretical Physics colloquium, Nov. 3 rd 2020, Arizona State Univerity Fluid phenomena are ubiquitous in our life: Hydrodynamics Long history,

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The Reasonable and Unreasonable Effectiveness of Hydrodynamics in Exotic Quantum Matter Hong Liu

Theoretical Physics colloquium, Nov. 3rd 2020, Arizona State Univerity

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Fluid phenomena are ubiquitous in our life:

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Hydrodynamics

Long history, dating back to Archimedes (~200 BC), Da Vinci, Newton, Euler, Bernoulli, Navier, Stokes,…... Fluid approximation: Equations: Energy + momentum conservation, continuity equation Express energy, momentum in terms

  • f these variables

a continuum of fluid elements each of which is considered to be a macroscopic object in local equilibrium: (Eulerian) ,

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Hydrodynamics has also made unexpected entries in 21st century physics.

I will quickly describe three examples.

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Quark-Gluon Plasma

At room temperature, quarks and gluons are always confined inside colorless

  • bjects (hadrons):

protons, neutrons, pions, ….. à Quark-gluon plasma (QGP) Hadrons melt at sufficient high temperatures à quarks and gluons deconfined

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Relativistic Heavy ion collisions

Size: 10-14 m Lifetime: 10-23 sec Temperature: ~ 1012 K

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To explain correlations of detected particles: The QGP behaves like a fluid evolution of QGP after its creation should follow hydrodynamics

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Graphene

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Electrons in a metal

Taken from: J. Zaanen Science 351 (2016)

Impurities

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Electrons in Graphene

  • J. Trinastic,

GotScience Magazine, 2016 Graphene can made very pure and one can assume impurities do not exists.

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From Levitov and Falkovich, Nature Physics, Feb. 2016

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Science 315 March 2016

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Ultracold Fermi gases

A confined cigar-shaped cloud of fermionic 6Li atoms, strongly interacting

Courtesy of John Thomas’s group

T: 10-9 K

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Exhibit collective flows governed by hydrodynamics, indicating a viscous fluid.

O’Hara et al Science, 298, (2002)

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Why is hydrodynamics so effective in describing these exotic quantum matter?

Strong interactions Coulomb interactions Atomic interactions at unitarity limit There is in fact a simple reason behind it.

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Universality of hydrodynamics

Consider a long wavelength disturbance of a system in thermal equilibrium conserved quantities: cannot relax locally, only via transports non-conserved quantities: relax locally, If we are interested in physics at scales: Only dynamics of conserved quantities are relevant, all other details are washed out by interactions !

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Hydrodynamics is a theory of conserved quantities.

Strongly interacting quantum liquids !

Their mean free paths have to be sufficiently short, i.e. strongly interacting Key: Thus a universal theory for non-equilibrium dynamics of generic many-body systems at sufficiently long distances and times!

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Despite the long and glorious history of hydrodynamics There is an important defect: formulated as equations of motion, cannot capture fluctuations

(There exist phenomenological fixes, but not applicable to far-from-equilibrium situations. )

There are always statistical fluctuations ….. Important in many physical contexts. Thermal noises are everywhere …... At low temperatures, quantum fluctuations can also be important.

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Non-equilibrium phase transitions: Rayleigh-Benard problem

Hydrodynamic fluctuations hot cold

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Searching for QCD critical point

Large fluctuations

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Thermal fluctuations in turbulence

….........

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Need a formulation of fluctuating hydrodynamics in far-from-equilibrium situations Need a formulation based on action principles.

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Searching for an action principle for dissipative hydrodynamics has been a long standing problem, dating back at least to the ideal fluid action of G. Herglotz in 1911.

Grozdanov and Polonyi, arXiv:1305.3670 Kovtun, Moore and Romatschke, arXiv:1405.3967 Dubovsky, Gregoire, Nicolis and Rattazzi hep-th/0512260

The last decade has seen a renewed interest:

Dubovsky, Hui, Nicolis and Son, arXiv:1107.0731

Haehl, Loganayagam and Rangamani, arXiv:1502.00636, 1511.07809

Harder, Kovtun, and Ritz, arXiv:1502.03076 …....

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Michael Crossley Paolo Glorioso arXiv: 1511.03646, 1612.07705, 1701.07817, 1701.07445 Recently we were able to have a complete formulation of fluctuating hydrodynamics from first principles (i.e. based on symmetries and action principle). Used techniques and insights from quantum field theories, gravity, and string theories. A review: 1805.09331

Paolo Glorioso, HL

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Framework: Effective field theory

Full path integral of a quantum many- body system Direct computation: rarely possible : low energy effective action

: Low energy degrees

  • f freedom

Identify Integrate out the rest Identify symmetries and constraints of Write down the most general theory consistent with the symmetries Should be able to formulate hydrodynamics this way

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Challenges

  • 1. Dissipation
  • 2. Dynamical variables

Standard lore: Dissipative systems don't have an action formulation Standard variables: Unsuitable!

  • 3. Symmetries

What symmetries define a fluid? Need analogue of potentials for Electromagnetism

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Dissipations

This issue is naturally resolved by quantum mechanics. interested in dynamics of a non-equilibrium state. Closed time path (CTP) or Schwinger-Keldysh contour Example: Brownian motion Quantum Classical Key: develop effective field theories for systems

  • n a closed time path (double d.o.f.)

(action principle for Langevin equation)

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Dynamical variables

Key: identify universal variables associated with energy- momentum conservation. Trick: put the system in a curved spacetime: because of energy- momentum conservation, the system should be diffeomorphism invariant Promote spacetime coordinates into dynamical variables Need a new auxiliary spacetime with coordinates That is, invariant under any coordinate transformations Equations of equivalent to energy-momentum conservation.

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This is just a generalization of the Lagrange description! Dynamical variables: : label fluid elements

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label individual fluid elements, internal time

Dynamical variables:

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Symmetries

  • 1. Symmetries defining a fluid:
  • 2. Constraints from quantum unitarity (survive in the classical limit)
  • 3. A Z2 symmetry: dynamical KMS symmetry, which

imposes micro-time-reversibility and local equilibrium A “statistical” field theory which fully recovers the standard hydrodynamic as equations of motion, but also treats statistical and quantum hydrodynamic fluctuations systematically.

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Emergent entropy as a Noether charge

Combination of unitarity constraints and dynamical KMS symmetry leads to a remarkable consequence: ∆S ≡ Z

t=tf

dd−1x s0 − Z

t=ti

dd−1x s0 = R ≥ 0

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Universal expression for entropy production. One can construct a local current , the “charge” of which never decreases. sµ

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R

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can be found explicitly using the action

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Emergent supersymmetry

Consequence of unitarity and dynamical KMS, independent of details of any specific system. The action is such that it can always be supersymmetrized: an emergent supersymmetry.

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This framework is very general and can be generalized to other continuous media such as solids, liquid crystals, quasicrystals, systems undergoing chemical reactions, MHD, …….

  • M. Landry: arXiv: 1912.12301, arXiv: 2006.13220,

Baggioli and Landry: arXiv: 2008.05339,

  • A. Jain: arXiv: 2008.03004,

…….

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Application to quantum scrambling and quantum chaos

Mike Blake Hyunseok Lee

arXiv: 1801.00010

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Chaotic phenomena are ubiquitous in nature. Much has been learned about chaos in classical systems But much to be understood in quantum many-body systems.

(strange attractor of the Lorenz model)

There have been intense recent studies of out-of-time-ordered correlation functions.

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  • 1. Chaotic behavior can be described by the propagation an

effective chaos mode Our proposals (for maximally chaotic systems) :

  • 2. Chaos mode can be identified with the hydrodynamic

mode associated with Energy conservation. Effective field theory of chaos

=

Quantum hydro theory

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  • 1. Explain connection between energy diffusion constant and

quantum chaos observed in the literature.

Implications and predictions:

  • 2. Predict a new manifestation of quantum chaos: pole-skipping

phenomenon, which has been checked in a large number of systems.

  • 3. The surprising connection between quantum chaos and

hydrodynamics remains mysterious (very different regime from turbulence).

(See also Grozdanov, Schalm, and Scopelliti, arXiv:1710.00921)

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Summary

  • Hydrodynamics plays important role in characterizing

various exotic quantum matter.

  • We now have a first principle formulation of hydrodynamics

which incorporates statistical and quantum fluctuations.

  • Unreasonable effectiveness: maximal quantum chaos.

a universal definition of strongly coupled quantum liquids

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Thank you!