My interest lies in basic problems and phenomena
in statistical mechanics, superconductivity and superfluidity.
Below are some of the recent achievements.
Superconductivity |
Superfluidity |
Nonequilibrium statistical mechanics
- Field-theoretic approach to non-equilibrium statistical mechanics
[
T. Kita: Prog. Theor. Phys. 123 (2010) 581
]
The universe is full of non-equilibrium phenomena and pattern formations that
accompany flows of mass, momentum and energy,
such as the universe itself with inflation,
the temperature gradient within stars, and formation of clouds and typhoon
on earth. Hence it is not surprising that
quite extensive efforts have been directed towards developing
non-equilibrium statistical mechanics and finding a simple rule/law behind
pattern formation phenomena.
However, statistical mechanics we learn in the undergraduate courses is
limited to equilibrium without any macroscopic flows,
such as ``isolated systems'' or ``canonical ensembles."
Moreover, ``the linear response theory'' and ``Kubo formulas'' can only
handle small deviations from equilibrium.
Thus, some of you may think that we still do not have a well-established theory for non-equilibrium phenomena.
However, there are no fundamental difficulties in studying them based on the field theory with Green's functions.
The above article reviews the topic in full details in a concise and transparent way. First, we introduce the real-time Keldysh Green's function and clarify its symmetry properties.
Second, we present Feynman rules to perform a perturbation expansion in terms of the interaction.
In particular, we focus on the self-consistent
perturbation expansion based on the Luttinger-Ward thermodynamic functional, i.e.,
Baymfs ƒ³-derivable approximation, which has a crucial property to describe non-equilibrium systems
of obeying various conservation laws automatically.
This formalism also embraces the Boltzmann equation and the Navier-Stokes equation; we discuss that they can be derived from Dyson's equation on the Keldysh contour
by successively reducing independent variables
by integration. Finally, we derive an expression of non-equilibrium entropy that evolves with time.
In this context, it should be noted that entropy in thermodynamics is defined only in equilibrium, and we still do not have a widely accepted expression for non-equilibrium entropy that evolves with time.
The expression obtained here is expected to play an important role to establish non-equilibrium entropy.
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