Quantum Primordial Soup
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WHAT IS IT?
This is a model of quantum dissipative structures' emergence in a quantum chaotic medium. The model is part of the quantum complex systems science and risk mathematics research project, under development by the author at ISCSP  Technical University of Lisbon.
The model combines quantum statistical mechanics and chaos theory, and it leads to the emergence of a fluctuating complex millieu. After a few steps of the simulation, there emerge organized structures akin to unicellular organisms that have a pulsating body (pulsating either in dark grey and light grey RGB scheme (see the description below for the details), a colored nucleous, and a border (usually pulsating inversely to the body in the RGB scheme), these structures survive for a while feeding upon the environment and assimilating other organisms whenever their borders touch.
Complex quantum structures' individuation takes place in this model with a struggle for growth territory, for survival against dissolution and against assimilation from other structures.
This lifelike quantum game emergence is not preprogrammed in the model, we did not preprogram the large cellular structures, they just happen to emerge.
The model has been used both for research in risk science as well as an example used in the author's MsC Classes on Decision Making Techniques, for a basic understanding of the problem of risk in complex systems science.
The model implements an example of a computational structure resulting from the article:
 Gon_ves (2012) "Quantum Chaos and Quantum Computing Structures" arXiv:1208.2610v1 [nlin.CD], http://arxiv.org/abs/1208.2610
Each patch contains a threeentry quantum register machine, each entry is assigned a color, and each entry is in a coherent state. The quantum computation implements a local unitary transition at each patch from coherent state to coherent state (by the general scheme explained in arXiv:1208.2610v1 [nlin.CD])) according to a nonlinear map rule.
The coherent state sequence is such that each coherent state leads to an occupation number quantum average that coincides with a definite energy eigenstate (even though the quantum state is NOT in a definite energy state, but in a superposition of energy eigenstates as per the coherent state notion).
Each patch is colored in accordance with an RGB scheme represenation of its mean quantum energy.
THE MODEL (FORMAL EXPLANATION):

Each patch contains a bosonic quantum register machine, with three entries corresponding to three colors Red, Green and Blue, in a coherent state for each color:
 psi(j,t)> = CRed(j,t),CGreen(j,t),CBlue(j,t)>
At each round, a local quantum logical gate of the product coherent state category Coh^3 (see the article for details) is implemented such that a coherent state transition takes place:
 psi(j,t1)> > psi(j,t)>
The relation between the coherent states is such that:
 CRed(j,t),CGreen(j,t),CBlue(j,t)> = F(CRed(j,t1)),F(CGreen(j,t1)), F(CBlue(j,t1))>
Where F is a complexvalued nonlinear map that transforms the phase of each coherent state (in the polar coordinate representation of a complex number) as follows:
 PhiRed(j,t) = (1  epsilon  delta) * Mred(j,t1) + epsilon * meanfield(PhiRed) + meanfield(h)
 PhiGreen(j,t) = (1  epsilon  delta) * Mred(j,t1) + epsilon * meanfield(PhiRed) + meanfield(h)
 PhiBlue(j,t) = (1  epsilon  delta) * Mred(j,t1) + epsilon * meanfield(PhiRed) + meanfield(h)
With the updates:
 Mred(j,t) = b * PhiRed(j,t1) * (1  PhiRed(j,t1))
 Mgreen(j,t) = b * PhiGreen(j,t1) * (1  PhiGreen(j,t1))
 Mblue(j,t) = b * PhiBlue(j,t1) * (1  PhiBlue(j,t1))
 h(j,t) = [Mred(j,t) + Mgreen(j,t) + Mblue(j,t)] / 3
and where the meanfield(PhiColor) is the mean of the coherent state phases of the patches in radius r of the j'th patch for the corresponding "Color", the same holding for meanfield(h).
In turn, the amplitude of each coherent state for a patch is transformed by the complexvalued nonlinear map as:
 AmplitudeRed(j,t) = sqrt{int(PhiRed(j,t) * 255)}
 AmplitudeGreen(j,t) = sqrt{int(PhiGreen(j,t) * 255)}
 AmplitudeBlue(j,t) = sqrt{int(PhiBlue(j,t) * 255)}
Thus, the expected energy for each register at each patch is given by:



Each patch is colored in RGB scheme by the occupation numbers, therefore each patch Red, Green Blue color in the model is in proportion to the combination of the expected energy eigenstates for each quantum register.
HOW TO USE IT
The user can control the logistic map's parameters, as well as the couplings (epsilon and delta) and the radius r for the local mean field coupling.
The slider noplottransient allows the user to control a the moment upon which the mean color value for the entire system of patches is plotted.
THINGS TO NOTICE
One should address the model in terms of the spatial and temporal patterns that emerge, the different behaviors of the model for different couplings, try to look and identify emerging individuated structures and look at how they interact with the environment and with each other.
You can also watch the video below which shows several examples of relevant points to notice in the model.
http://www.youtube.com/watch?v=zc61oy5R9hQ
CREDITS AND REFERENCES
 Gon_ves, (2012) "Quantum Chaos and Quantum Computing Structures" arXiv:1208.2610v1 [nlin.CD], http://arxiv.org/abs/1208.2610
 Gon_ves, (2012) "Risk Governance  A Framework for Risk ScienceBased Decision Support Systems" http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2085482
Comments and Questions
patchesown [ PhiRed_t1 PhiRed_t PhiGreen_t1 PhiGreen_t PhiBlue_t1 PhiBlue_t M0 M1 M2 h c2red ; cred^2 corresponds to the expected number of red quanta in the register c2green ; cgreen^2 corresponds to the expected number of green quanta in the register c2blue ; cblue^2 corresponds to the expected number of blue quanta in the register indicator ] globals [ mred mgreen mblue ] to setup ca ask patches [ set PhiRed_t randomfloat 1.000 set PhiGreen_t randomfloat 1.000 set PhiBlue_t randomfloat 1.000 ] ask oneof patches [ set indicator 1 ] end to go nodisplay tick ask patches [ previousstatephase ] ask patches [ nmap ] ask patches [ updatequantumphases ] ask patches [ setcolor ] set mred mean[c2red] of patches set mgreen mean [c2green] of patches set mblue mean [c2blue] of patches if ticks >= noplottransient [ doplot ] display end to previousstatephase set PhiRed_t1 PhiRed_t set PhiGreen_t1 PhiGreen_t set PhiBlue_t1 PhiBlue_t end to nmap set M0 PhiRed_t1 * b * (1  PhiRed_t1) set M1 PhiGreen_t1 * b * (1  PhiGreen_t1) set M2 PhiBlue_t1 * b * (1  PhiBlue_t1) set h ( M0 + M1 + M2 ) / 3 end to updatequantumphases set PhiRed_t (1  epsilon  delta) * M0 + epsilon * mean [ M0 ] of patches inradius r + delta * mean [ h ] of patches inradius r set PhiGreen_t (1  epsilon  delta) * M1 + epsilon * mean [ M1 ] of patches inradius r + delta * mean [ h ] of patches inradius r set PhiBlue_t (1  epsilon  delta) * M2 + epsilon * mean [ M2 ] of patches inradius r + delta * mean [ h ] of patches inradius r end to setcolor set c2red int (PhiRed_t * 255) set c2green int (PhiGreen_t * 255) set c2blue int (PhiBlue_t * 255) set pcolor (list c2red c2green c2blue ) end to doplot setcurrentplot "Mean Red" plot mred setcurrentplot "Mean Green" plot mgreen setcurrentplot "Mean Blue" plot mblue end
There is only one version of this model, created almost 12 years ago by Carlos Pedro S. Gonçalves.
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