The ultimate goal of our current
project is
to construct a phase diagram for
quantum chromodynamics (QCD).
Right now, as we speak, we are 
all living on a world that owes
the existence of its very 
substance to the dynamics of 
QCD.
However, if we imagine rewinding
the history of the cosmos
and traveling further and 
further back in time
toward the very beginning of the
universe, we find that the 
"temperature" of the universe
grows hotter and hotter the 
further back we go.
When the temperature of the 
universe rises above certain 
threshold values,
it becomes possible for various 
unusual things to occur.
Among the various possibilities,
the one that is "most likely" to
occur is
something known as the "QCD 
phase transition".
Of course, phase transitions are
phenomena
that we are all familiar with in
our daily lives.
For example, think of water,
a substance with which we are 
all intimately acquainted.
When water is cooled below zero 
degrees Celsius, it becomes ice.
On the other hand, if you put 
water in a pan
and heat it above 100 degrees,
it becomes a gas.
The points at which these sorts 
of major transformations take 
place,
as well as the phenomena  
themselves, are called phase 
transitions.
Now, these things may happen at 
the Earth's surface
- that is, under standard 
atmospheric pressure -
but we might also consider 
performing experiments on top of
a mountain,
in which case the air pressure 
drops
and water boils at a lower 
temperature.
This means we can make a graph 
with pressure
on the vertical axis and 
temperature on the horizontal 
axis,
and then draw lines delineating 
the regions of the graph
in which water is a gas and the 
regions in which it is a solid.
These are called "phase-
transition curves".
A plot of this sort
- in which regions corresponding
to different states are
separated by phase-transition 
curves -
is called a "phase diagram".
Thus, this research hopes
to generate new knowledge
and insight that may prove 
essential for understanding
how the cosmos evolved from its 
inception
into the universe we observe 
today
- and how the matter we 
observein the universe today was
created.
The most fundamental particles.
If we start with tiny subatomic 
particles
like protons and neutrons and 
try to decompose them "even 
further",
we arrive at the level of 
particles known as "quarks".
One combination of three quarks 
forms a proton,
whereas a different combination 
of three quarks forms a neutron.
The phase transition that we are
considering here is
a process in which particles  
such as protons and neutrons
- which are composite states 
consisting of multiple quarks 
bound tightly together -
disintegrate at higher 
temperatures to yield individual
quarks
that behave essentially 
independently of each other.
The key point here is that we 
have two totally different 
states of matter
- one state in which quarks are 
bound tightly together into 
protons and neutrons,
and another state in which 
quarks behave nearly 
independently of each other -
which is precisely the situation
we describe in terms of distinct
"phases".
The question we are  
investigating is
whether the distinct states are 
separated by a phase transition
whether the distinct states are 
separated by a phase transition 
or similar phenomenon.
Our technique for addressing 
these questions is
to conduct numerical 
simulations.
Today, we are able to conduct 
simulations involving two 
quarks.
When this work is complete
- in the post-K era -
we are hoping to map out the 
entire QCD phase diagram.
Actually, the typical 
calculations that have been done
to date
- the state of the art, in terms
of what we are currently able to
calculate -
use computational cells (boxes)
that are barely large enough to 
accommodate a few particles
such as protons or neutrons.
However, since these conditions 
are little too cramped for 
protons and neutrons
- we are constantly needing to 
consider larger and larger 
boxes.
One thing that can be said about
lattice QCD simulations is that,
for a long time, they proceeded 
on the basis of two possible 
approaches:
Wilson fermions and staggered 
fermions.
Of these two possibilities,
the use of Wilson fermions 
completely breaks chiral 
symmetry,
whereas staggered fermions 
"preserve" a portion of the 
chiral symmetry exactly.
Later, a method known as 
"domain-wall fermions"
was developed to address the 
shortcomings of these types of 
fermions.
This is a formulation in which 
"all" chiral symmetry is
preserved almost exactly
- but at the expense of 
extremely high computational 
costs.
During the course of our 
research using domain-wall 
fermions,
we ultimately decided that we 
would prefer to use an 
alternative approach
known as "overlap" fermions, 
which offer exact symmetry.
However, the computational cost 
of overlap fermions is
extremely high even compared to 
that of domain-wall fermions,
and computations using them 
remain impractical
even using the highest-
performance supercomputers 
available today.
In the approach that we have 
adopted,
we begin by using domain-wall 
fermions
and constructing statistical 
ensembles for Monte Carlo 
simulations.
These simulations have almost 
exact chiral symmetry.
An advantage of our method is 
that,
even though the starting point  
is
a simulation using domain-
wall fermions,
the final results are equivalent
to
what we would obtain from 
simulations using overlap 
fermions.
At present, we are right on top 
of this line
- we are using simulations with 
just two quarks
to investigate the situation on 
this line.
Once we have solved this 
problem,
we will also need to understand 
what is happening in the 
surrounding vicinity.
Which is to say that we want to 
understand exactly
where this phase-transition 
curve passes.
Therefore,
right now we are working right 
here,
but we are hoping to continue 
these simulations
to determine where this curve 
will go.
The undergraduate research that 
I was doing in my fourth year of
university
had nothing to do with computers
whatsoever.
It was around that time that I 
discovered,
“Hey, there's a branch of 
elementary-particle physics that
uses computers!”
That was when I realized
that computer-based elementary-
particle physics was being done 
there,
and that it was an opportunity
to get close to some of the 
world's leading research in this
field.
And I thought, “This looks 
interesting!”
and pretty much jumped into it 
right there.
In our construction of a phase 
diagram,
we are in some sense drawing a 
"map".
But obtaining every single point
on this phase diagram
requires computer simulations 
that take an extremely long 
time.
Therefore, once we have obtained
one point,
we then determine the next 
point, and then the next point.
As we proceed, our overall 
knowledge expands
and we wind up drawing a map.
Doesn't that strike you as 
rather romantic?
