_{1}

In this work, we try to build a model to describe the condensation through the couple of bio-solitons in a well based on the BCS theory extended by the nonlinear operator, which can be used to simulate the created process of the internal elixir in the middle of the abdomen of the human body. The goal of this work is to provide a mechanism to explain the effect of stored bio-energy in the bio-systems.

The Davydov soliton is a fundamental nonlinear excitation in the bio-system of human being, which has been discovered by the Davydov in 1973 [

So, in previous works we have presented that the Davydov solitons can condense in two or three potential wells for simulating the oscillation of quasiparticles in the accupoints [

The nonlinear excitations (solitons) are supposed to have a condensation in a well of the belly. This assumption is based on the Chinese medicine theories and Acupuncture theories, and also from the results of the thousands and thousands practicers of Qigong or Yoga over thousands years of the world [

where

Then we can find when

where

Therefore, by adding the terms of the energy part for the soliton, the total Hamiltonian can be expressed as

The Hamiltonian

and supposing the difference of these operators of the couple of solitons is small value; we therefore can replace the above Equations (6) and (7) into

where we have used

Now, by defining

the

where notice

By applying the Heisenberg equation, we get an equation for

For solving these two equations the so-called Bogoliubov transformation is applied,

where denote that

and

For example, for the nonlinear operator

Then all properties of the linear operator can be applicable to the

So, Equations (15) and (16) can be inverted as

by replacing Equations (21) and (22) into the Hamiltonian (11), we get

where notice again that the Slach product has been introduced. So if let the off-diagnal term in

then by use Equations (20) and (24) we can obtain

where

and

Hence, we have

These allow us to obtain the diagnalized Hamiltonian as

where the energy of basic state is expressed by

and the excitation energy is

so

When the system arrives at the lowest condensation temperature

then we get

and

where denote

By considering Equations (28) and (29) replaced into Equation (36) to cancel

finally we can get

and

where

for bio-solitons condensation in our body the temperature

where the bio-system can regulate the

Furthermore if we assume that

then

then since

and

where defining

Then in the situation of no external field condition, which is just a suitable condition for the oscillation inside of the belly, we have the density of the free energy expressed as

then applying the principle of minium of the free energy we get

which allows us to have

This is just a kind of Ginzburg and Landau equation which can describe a soliton. For example in the three dimensional case we can have

where defining

Then the solution of Equation (48) can be gotten by

where notice

This

A couple of bio-solitons condensation has been presented. The two solitons with opposite moments are condensed into a couple of solitons by exchanging imaginary phonons. Then these couple of solitons can form a big soliton with oscillation. The process can be taken place in the room temperature, and the higher temperature makes the realization easier than lower temperature. This model can be used to simulate the bio-energy stored in our body such as the middle of abdomen of the human body, and also provides a kind explanation of mechanism for the internal elixir formation. This means that the so called internal elixir may be formed through the macro-quantum condensation of a couple of solions, and then the condensation plays a sort of oscillation as a big (or macro-) soliton.

Bi, Q. (2017) Bio- Soliton Condensation in Human Body. Journal of Modern Physics, 8, 315-322. https://doi.org/10.4236/jmp.2017.83020