I would love to present to you guys my entire life research in this section. However, readers should notice that this research is one of the most complicated
topics in theoretical physics. The idea has been developed from two completely different physics points of view: i. Quantum Theory is an elegant theory that
describes the nature of the tiny scale of objects, atoms, electrons, protons, etc. ii. General Relativity is a famous Einstein theory that describes the massive
scale of objects like stars, galaxies, and black examples. The two theories perform very well separately. Every GPU, CPU, LED, and millions of electronic
devices were built based on Quantum Physics knowledge.
On the other hand, the prediction of time dilation, which is essential for GPS or space projects, was built based on Einstein's theory.
However, combining these two theories led to some non-logical flows, and it used to develop into one of the most complicated theories humans
so far, has String Theory. Unfortunately, String theory cannot be performed and evidenced by experiments due to the limitation of technology
and at least 100-200 years.
In 1997, an American physicist suggested a crazy idea based on his mathematical proof, which stated that two theories might not be able to be combined
as a unified theory, but they can correspond to each other as Duality. His mathematics proof showed that strong, complex quantum theory could be described
by weakly coupled
Einstein's gravity theory in higher-dimension space. This means that all of the strongly coupled quantum physics in 3+1 dimensions (our universe) can be
described from weakly coupled
general relativity in 3+1 plus one extra-dimensions (extra-dimension universe). People start call this theory gauge-gravity duality since it original
version is used just only
describe strongly gauge theory (Quark-gluon densed). However, after a few years, physicists found that this theory could be applied to condensed matter.
So, we now call them
Holographic Theory, since it seems like physics in our universe is nothing but a Hologram of another bigger universe.
Mean Field Theory for Strongly Coupled Systems by Holographic Principle.
Mean Field Theory is the most useful approximation theory used in condensed matter physics, instead of considering 10^23 degrees of freedom, we consider
an approximation which average out all the effect from the model. One of the most famous application of mean field theory is BCS theory, the theory that describe
the mechanism of superconductivity where the symmetry is broken and cooper pairs are formed. However, in very very strongly coupled system, the mean field theory
loss the precision and cannot be applied eventually.
The problem can be solved by applied Holographic principle! Since the setup of theory is very complicated I suggest everyone see my publication papers which
is published on one of the most famous journal in this field, of course it is free-access.
And it is my pleasure if you guys play around the visualization and simulation by youself. So, I devlope the calculation and visualization on the github :)
Research Results
Spectral Function (SF)
The Holographic principle leads us to get a mathematical object called Green's function . To see the physical interpretation of Green's function we can calculate
spectral function which is define as follow
\[A(\omega,k) = Im[Tr\mathbb{G}(\omega,k)]\]
Raw Analytic Simple Results example
\[G_R = \frac{1}{\sqrt{(b-k_x)^2+k_\perp^2-\omega^2}}
\begin{pmatrix}
\omega+k_x && -k_y+ik_z && -b && 0\\
-k_y-i k_z && \omega -k_x && 0 && b\\
0&&0&&0&&0\\
0&&0&&0&&0
\end{pmatrix}
+\frac{1}{\sqrt{(b+k_x)^2 +k_\perp^2-\omega^2}}
\begin{pmatrix}
0&&0&&0&&0\\
0&&0&&0&&0\\
-b&& 0 && \omega+k_x && -k_y+i k_z\\
0&& b&& -k_y+ ik_z && \omega-k_x
\end{pmatrix}
\]
The results are completely mathematics with complex number in a tensor structure. However, The key to comunicate with other people is visualization!
After visualization technique we have been developing, we get the following stunned results:
Classification
One dream of condensed matter physicist is to see spectral function (SF). SF tell you where the particles in the matter are quantized! Humen speaking in which Energy and momentum
are allow in the matter, this tell us what is the nature of our matter. For example, graphine will have dirac cones spectral function, meaning that the electron in graphene
move very-fast might be 30-40% of speed of light.
In my research, we calculate the spectral function by emplying Holography with 16 types of symmetry breaking and 2 types of quantization. So that we eventually get
32 possible spectral functions. which some of them share the similar features which we developed as a classification. The classification was also developed as a dictionary
for other holography physicist also.
