Draft: The Emergent Universe and Superconductivity

An Emergent Universe

New states can arise from far from equilibrium, possessing an extraordinary degree of order, whereby trillions of molecules coordinate their actions in space and time.  Prigogine coined the term “dissipative structures” to describe them, since they result from the exchange of matter and energy between system and environment, together with the production of entropy (dissipation) by the system.  

The complex and mutually dependent processes leading to the formation of structures, collectively called “self organisation”…in such a universe, irreversible non-equilibrium thermodynamics allows for the possibility of self organisation leading to structures ranging from planets and galaxies to cells and organisations.  R Highfield and P Coveney 2015.

According to Masser (2006), it would be appropriate to represent the Big Bang not as a single event, but as an on-going process of gradual formation out of chaos.  In other words the evolution of the universe is a continuous self-organisation process that has led to its currently observed structure with a host of galaxies, galaxy clusters and planetary systems.

One indication of such emergence could be seen through patterns known to be generated by self organisation.

Revealing Patterns

The condensed matter physics of quarks has been developed by using methods of superconductivity theory adapted to Quantum Chromo Dynamics (QCD). This analysis results in the identification of condensates in diquark channels, analogous to the Cooper pairs of electrons in ordinary superconductor. This is known as the phenomenon of color superconductivity.

In ordinary superconductors (and semiconductors) various types of patterning (see section below) have been found which can reveal useful information about the nature of the superconductor, it interactions, and phase changes.  Similar patterns are created in reaction -diffusion processes (i.e Turing Patterns).  An understanding of what creates these conditions in superconductors could potential help us better understand emergent universal structures.

Unlike an electrical superconductor, color-superconducting quark matter comes in many varieties, each of which is a separate phase of matter.  There is a 9×9 color-flavor matrix of possible (cooper) pairing patterns. Different patterns break different symmetries of the underlying theory, leading to different excitation spectra and different transport properties.

Color superconductivity might have implications in astrophysics because for some compact stars, e.g. pulsars, the baryon densities necessary for color superconductivity can probably be reached.

Another form of superconductivity that may be of relevance is that of  vacuum superconductivity.  M Chernodub has theorised that superconductivity can appear – provided there is a very strong magnetic field – in the vacuum of empty space.

Self-Organisation and Patterning in Superconductors

Patterns and symmetries have important consequences for superconductivity – they can compete, coexist or possibly even enhance superconductivity.

J Zaanen (2010) found that that the fractal like arrangement of oxygen atoms in a cooper oxide superconductor appeared to influence the quantum behaviors of electrons and support high temperature superconductivity.

Turing type patterns can also be found in semiconductors (V Ardizzone 2015) and superconductors.

Turing Patterns Patterns in Superconductors

In nature, striped arrangements often arise; when they do, they are nearly always the result of an outside external perturbation that induces a directional bias on the actions of the individual. J Tabony – ‎200

Stripes formation occurs in type 1 superconducting film.  In two gap superconductors, superconducting vortices accommodation themselves by forming stripes fluxed patterns. (Y Holovatch 2015)
Hexagons In type II superconductor systems, a magnetic field can penetrate a sample in a tube-like configuration. The magnetic flux (superconducting vortices) arrange in the lattice with hexagonal symmetry. Competition between superconducting and non superconducting phases can result in a formation of a hexagonal pattern. (Y Holovatch 2015)
Grids Cuprate superconductors vortices arrange themselves into a grid resembling a this is actually an interference pattern caused by scattering electrons. At a higher energy, electrons cluster into a thin thread called a nanostripe. The strong magnetic field made this nanostripe more intense, suggesting that greater charge ordering would be accompanied by more of the vortices that stifle superconductivity. This is direct evidence of the competition that exists between superconductivity and charge order. T Machida 2016
Labryinths and Vortices Intertype flux exotic states in thin superconductors can be classified into three typical patterns that are qualitatively different from those in types I and II: superconducting islands separated by vortex chains; stripes/worms/labyrinths patterns; and mixtures of giant vortices and vortex clusters. W. Y. Córdoba-Camacho 2015.

Physicists have also found that the bubble-like arrangement of magnetic domains in superconducting lead exhibits patterns that are very similar to everyday froths.

Vortices and Self-Organisation

Critical superconductivity” may be accessed in a special regime lying at the boundary between type I and type II superconductivity. Inside this regime, small superconducting objects called Abrikosov vortices obey the same laws that participate in shaping the deep structure of the universe. “Vortices control the current carrying ability of all superconductors. And these objects can mimic cosmic strings, elucidating concepts that address fundamental features of the evolution of our universe.

Scientists have already observed self-replication in non-living systems. Vortices in turbulent fluids spontaneously replicate themselves by drawing energy from shear in the surrounding fluid.  Theoretical models and simulations of microstructures that self-replicate have been presented. These clusters of specially coated microspheres dissipate energy by roping nearby spheres into forming identical clusters. Besides self-replication, greater structural organization is another means by which strongly driven systems ramp up their ability to dissipate energy.

In the BZ reaction, vortices in a flow have a significant effect on one dimensional front propagation. In particular, a moving vortex tends to pin and drag a front. If a chain of vortices oscillates periodically mode locking often occurs. Mode locking is often found in oscillating systems that are forced periodically by an external perturbation.  J. R. Boehmer and T. H. Solomon 2008.

Reaction Diffusion and Patterning

Nonequilibrium patterns in open systems are ubiquitous in nature. A theoretical foundation that explains the basic features of a large class of patterns was given by Turing in the context of chemical reactions and the biological process of morphogenesis. These patterns can include stripes, hexagonal arrangement of spots, labyrinths and superlattices (Y Lang 2006).

Overall 7 patterns of reaction diffusion have been evidenced. N Tompkins 2014. Analogs of Turing patterns have also been studied in optical systems where diffusion of matter is replaced by diffraction of light.

The Turing, or reaction-diffusion (RD), model is one of the best-known theoretical models used to explain self-regulated pattern formation – two diffusible substances interacting with each other” to represent patterning mechanisms. Turing structures” can be stationary in time and periodic in space, or periodic in both time and space.

The resemblance between Turing Patterns and patterns found in superconductors raise the issue of whether self-organisation is taking place, but also whether Turing Patterns offer the best topology for superconduction.

The FKPP Equation and Quantum-Classical Correspondence.

One of the fundamental processes involved in nonequilibrium pattern formation is the spatial propagation of interfaces or fronts. Front propagation usually emerges when a local reaction dynamics interplays with diffusion in space of the reacting agents and has been observed in a wide range of physical, chemical, and biological systems. One of the most prominent models which displays propagating fronts is the Fisher-Kolmogorov-PetrovskyPiscounov (FKPP) equation.

Reaction Diffusion, Fronts, Magnetism and QCD

The FKPP equation potentially supports quantum – classical correspondence and could be at the heart of visible matter formation. This equation brings together:

  • The propagation of unstable non-linear wave fronts/population dynamics. Pulled fronts are extremely sensitive to noise in the leading edge. P Bressloff. 2011.
  • Dynamo theory and the azimuthal magnetic field (which can be reduced to the FKPP equation). S Fedotov et al 2003.  An important area of research in dynamo theory is the determination of the speed at which magnetic fronts propagate in a turbulent electrically conducting fluid. This problem is usually studied on the basis of a mean-field dynamo equation for a large scale magnetic field, and has been used to explore the formation of magnetic fields in galactic disks.
  • If the classical treatment of the FKPP equation due to Freidlin is expanded to include the phenomenon of anisotropic diffusion with a finite velocity, in the long-time large-distance asymptotic limit the Hamiltonian dynamical system associated with the anisotropic reaction–diffusion equation has a structure identical to that of general relativity theory. The function determining the position of the reaction front and its speed is nothing else but the action functional for a particle in both gravitational and electromagnetic fields….. It is well known that the macroscale equations for turbulent heat/mass transport involve effective anisotropic transport processes with a finite velocity S Fedotov  et al 2000
  • The same FKPP (reaction diffusion) type of equation appears in various fields of statistical physics and, recently, in the domain of Quantum Chromodynamics (QCD), the interaction theory of quarks and gluons, where it models the evolution of the gluon momenta in the wave-function of a hadron or a nucleus when the energy increases. QCD implies color superconductivity of quark matter at high density.
  • Higher order corrections to the Colour Glass Condensate evolution equations, include the BK and JIMWLK equations (the BK equation lies in the university class of the FKPP equation and correspondences to a spin glass phase of FKPP ). The correspondence between the BK and FKPP equations, clarifies the properties of saturation fronts in QCD in analogy with known properties of reaction–diffusion processes. A crucial property is the emergence of traveling waves. Reaction–diffusion processes exhibit an extreme sensitivity to particle number fluctuations, generated by gluon splittings, which produce correlations among pairs of gluons.  F Gleis 2010
  • In addition the sFKPP equation (which could provide insights into impact parameters dependent fluctuations in high energy QCD beyond the BK equation.  For traveling waves in the diffusive approximation of the QCD evolution equations, the traveling waves go to zero before the transition point of the sFKPP analoguous equation due to a shift of the speed (at least for the leading order kernel in αs)….The dual particle process becomes the diffusion-controlled reaction in the strong noise (or weak growth) limit of the stochastic FKPP equation….Front motion in higher spatial dimensions is of great interest for a variety of growth processes. In higher spatial dimensions even an initially smooth or flat front can develop structure in the transverse direction(s) and fluctuations may play an even more dramatic role in the dynamics.  .  Robi Peschanski 2008Charles R. Doering.
  • It has also been recognised that there is a strong similarity between the FKPP, BK and the Banfi, Marchesini, and Smye (BMS) evolution equation for non-global jet observables that exhibits a remarkable analogy with the BK equation used in the small x context.  It has been suggested that these are essentially identical equations that can be viewed either in terms of the probability, or amplitude, of something not happening or in terms of the nonlinear terms setting unitarity limits Giuseppe Marchesini 2015.   The analogy can be used to generalize the former beyond the leading Nc approximation. The result shows striking analogy with the JIMWLK equation describing the small x evolution of the color glass condensate (CGC).  H Weigert 2004.

The CGC RG equations indicate that – at fixed impact parameter – a proton and heavy nucleus become indistinguishable at high energy.  The physics of saturated gluons is universal and independent of the details of the fragmentation region.  The universal dynamics have a correspondence with the reaction-diffusion processes in statistical physics.  In particular, it may lie in a spin glass universality class.  F Gleis 2010 . The CGC is recognised as having properties similar to Bose Condensates and spin glasses.

The Coupling of Quantum and Classical Chaos

The relationship between reaction diffusion patterning and superconducting may be related to the finding that a map of entanglement entropy of a superconducting qubit that, over time, comes to strongly resemble that of classical dynamics—the regions of entanglement in the quantum map resemble the regions of chaos on the classical map. The islands of low entanglement in the quantum map are located in the places of low chaos on the classical map. “And, it turns out that thermalization is the thing that connects chaos and entanglement. It turns out that they are actually the driving forces behind thermalization’. S Fernandez 2016. 

A Self Organising Universe Using Reaction Diffusion

The following brings together various findings on how the emergence of the universe might resemble reaction-diffusion systems.

Dynamics of quark hadron transition is one of the most important issues in relativistic heavy-ion collisions, as well as in the universe…..lattice results showed that the quark-hadron transition is not first order, rather it is most likely a cross-over for low chemical potential. This cross-over is believed to govern the dynamics of transition in relativistic heavy-ion collisions at high energies…..For the dynamics of the phase transition, the most important difference between a first order transition and a cross-over (or a continuous transition) is the presence of a phase boundary for the former case which separates the two phases. The transition for a first order case is completed by nucleation of bubbles which expand. The moving bubble walls (phase boundaries) lead to physical phenomena, such as non-trivial scattering of quarks, local heating, specific types of fluctuations, etc., which are qualitatively different from the case of cross-over or a continuous transition…It turns out that the presence of moving interfaces more generic, and not necessarily restricted to the case of first order transitions. Such situations routinely arise in the study of so called reaction-diffusion equations.  P Bagchi – ‎2015.

Star and Galaxy Formation

  • It has been suggested that galaxies are dissipative systems, and the spatial and time structure of the interstellar medium and young stars is governed by reaction-diffusion equationsJV Feitzinger – ‎1985, and galactic disks are reaction-diffusion systems.  Lee Smolin 1996 and Nozakura, T. & Ikeuchi, S 1988.
  • The coherent galactic oscillations of star formation self-organized in spiral waves, previously detected by numerical simulations (Seiden, Schulman, Feitzinger, 1982) could analytically described by the concept of a limit cycle. Analytical work on self-propagating stochastic star formation was also done by Kaufman (1979), Shore (1981, 1982) and Cowie and Rybicki (1982). V. Feitzinger
  • Cartin, et al (1999 and 2001), applied the spiral galaxy as a self-regulated system far from equilibrium to look at a reaction-diffusion model for the formation of spiral structures in certain types of galaxies. YF Chang – ‎2009 
  • Evidence suggests that the superficially chaotic process of galaxy formation is underlined by a temporal self-organization up to at least one gigayear. In view of this it is tempting to suggest that, given the known existence of spatial fractals (such as the power-law two-point function of galaxies), there is a joint spatio-temporal self-organization in galaxy formation.. R Cen 2014. 
  • The black-hole-like phenomena might take place in the nonlinear Schrodinger type equation, where black holes of a constant curvature spacetime have been related to the soliton-like solutions for dissipative version of the NLS in the form of the Reaction-Diffusion system. These solutions called dissipatons, characterize completely the black hole horizon, the Hawking temperature and the causal structure. Ok Pashaev – ‎2001

Pattern Stability

One of the basic problems in the theory of pattern formation is, even in the presence of the instability, how do initially disordered structures emerging from small random fluctuations give rise to regular and highly precise structures in the course of development? It is well known that uncontrolled growth of patterns usually produces an array of topological defects that only slowly disappear through mutual repulsion or attraction and annihilation. However, specific feedback control mechanisms can significantly accelerate this process. LS Tsimring – ‎2014.   This could be provided through a number of mechanisms (perhaps interlinked). For example:

  • Cyclic or oscillating models have been suggested for the universe that use infinite or self sustaining cycles.  The idea of an oscillatory universe has been mooted for decades e.gTolmanGraham et al 2011 and 2014   A  Mithani 2015.
  • Periodic orbits play an important role in celestial mechanics. An orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other, usually due to their orbital periods being related by a ratio of two small integers.   Could gravity help stabilise emergent structures?
  • Structural properties of spiral galaxies, such as the distribution of the gaseous components and the luminosity,  have been suggested to arise directly from a feedback mechanism that pins the star formation rate close to the critical point of the phase transition. L S Schulman 2012

Clustering – Cosmic Lattices

When looking at the distribution of galaxies on scales of billions of light-years, astronomers have found that galaxies aren’t evenly distributed: They form a web of filaments and clump around huge galaxy-scarce voids. This arrangement of material is known as the large-scale structure. The large scale organization of the universe comes from different sources: catalogues of galaxy redshifts; absorption lines in quasar spectra; the cosmic background radiation; studies of the distribution of hot ionized gas in clusters of galaxies; measurements of large scale peculiar velocities

Large scale cosmic structures include  superclusters, galaxy filaments and large quasar groups (LQG’s).  It has been found that the rotation axes of the central supermassive black holes in a sample of quasars are parallel to each other over distances of billions of light-years. Findings indicate that the rotation axes of quasars tend to be parallel to the large-scale structures that they inhabit. That means that if the quasars are in a long filament, then the spins of their central black holes will point along the filament.  According estimates, there’s only a one percent probability that these alignments are simply the result of chance.  Also see  New Scientist 21 Nov 2014

Holographic Information

Is the holographic universe based on reaction diffusion memory? i.e memory can be stored in:

  • reaction diffusion like systems (such systems can create chemical memory).
  • Spin based memory systems
  • interference when waves collide. This also offers the potential for the recording of holographic information.
  • Bifurcation
  • Vortices in which the solitons could be stored
  • solitons (as quibits)

2015-2016. This article merely joins up other peoples work into an overall system.  These works have been referenced so it is clear that others have provided the individual pieces of evidence that have been used to shape a specific systems approach.    





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