TQFT 2014 @RIKEN

Derivation of the Hydrodynamic Equationfrom the Quantum Transport Equation
Yuta Kikuchi (Kyoto Univ.)
collaborators
Teiji Kunihiro (Kyoto Univ.)
Kyosuke Tsumura (Fujiﬁlm Corp.)
Kazuaki Ohnishi (Shinagawa, Tokyo)

Derivation of the Hydrodynamic Equation from the Quantum Transport Equation

We are interested in the hydrodynamical analyses ofthe following two similar phenomena:Derivation of the Hydrodynamic Equation from the Quantum Transport Equation

We are interested in the hydrodynamical analyses ofthe following two similar phenomena:
Unitary Fermi Gas
Hydrodynamical approach is useful
T. Schafer (2014)

Problems
Two regions: hydrodynamic core and dilute corona
How to describe the transition between these region
Consider a non-zero dissipative relaxation timeDerivation of the Hydrodynamic Equation from the Quantum Transport Equation

We are interested in the hydrodynamical analyses ofthe following two similar phenomena:
Unitary Fermi Gas

Quark-Gluon Plasma

Hydrodynamical approach is useful

Relativistic analysis is needed

T. Schafer (2014)

Problems

Fundamental problems

Two regions: hydrodynamic core and dilute corona

Ambiguity in the deﬁnition of the ﬂow velocity

How to describe the transition between these region

Unphysical instabilities of the equilibrium stateConsider a non-zero dissipative relaxation time

Lack of causality

Derivation of the Hydrodynamic Equation from the Quantum Transport Equation

We are interested in the hydrodynamical analyses ofthe following two similar phenomena:
Unitary Fermi Gas

Quark-Gluon Plasma

Hydrodynamical approach is useful

Relativistic analysis is needed

Second Order (Mesoscopic)
Hydrodynamic Equation isNeeded!!
T. Schafer (2014)

Problems

Fundamental problems

Two regions: hydrodynamic core and dilute corona

Ambiguity in the deﬁnition of the ﬂow velocity

How to describe the transition between these region

Unphysical instabilities of the equilibrium stateConsider a non-zero dissipative relaxation time

Lack of causality

Derivation of the Hydrodynamic Equation from the Quantum Transport Equation

Hierarchy of Transport Equation
Microscopic transport equation(e.g. Kadanoﬀ-Baym equation)coarse graining
Kinetic equation(e.g. Boltzmann equation)coarse graining
Hydrodynamic equation(e.g. Navie-Stokes equation)

Relativistic or Non-Rel.
-systemClassical or Quantum-system

Single or Multi-component

1st or 2nd-order hydro.

We derived 1st order hydrodynamic eq. in quantum multi-component system with the renormalization group method.

Derivation of the Hydrodynamic Equation from the Quantum Transport Equation

Hierarchy of Transport Equation

We want to derive

Microscopic transport equation

Relativistic or Non-Rel.

(e.g. Kadanoﬀ-Baym equation)coarse graining
Kinetic equation(e.g. Boltzmann equation)coarse graining
Hydrodynamic equation(e.g. Navie-Stokes equation)-systemClassical or Quantum-system

Single or Multi-component

1st or 2nd-order hydro.

We derived 1st order hydrodynamic eq. in quantum multi-component system with the renormalization group method.

Derivation of the Hydrodynamic Equation from the Quantum Transport Equation

Hierarchy of Transport Equation

We want to derive

Microscopic transport equation

Relativistic or Non-Rel.

(e.g. Kadanoﬀ-Baym equation)coarse graining
Kinetic equation(e.g. Boltzmann equation)coarse graining
Hydrodynamic equation(e.g. Navie-Stokes equation)-systemClassical or Quantum-system

Single or Multi-component

1st or 2nd-order hydro.

We derived 1st order hydrodynamic eq. in quantum multi-component system with the renormalization group method.