The concept of «Complexity» in the problems of condensed matter physics: fundamental and applied aspects

Problems of radiation effects of living and inanimate objects are considered within the framework of the concept of complexity. Basic models for the manifestation of the effects of spin chemistry and quantum entanglement in the processes of subthreshold radiation physics have been constructed


Introduction
A historical review of radiation physics development (from the middle of the XIX century up to the present) with a high degree of plausibility points to three reasons for tangible progress in this field: • The emergence of a new type of irradiating installations; • The emergence of new materials and structures -objects of irradiation; • The emergence and formulation of new concepts in radiation physics of condensed matter (RPCM).By the beginning of the XXI century, all these elements combined had changed the outlook of the RPCM fundamentally, and now the code concepts are the following: (1) nonlinearity and disequilibrium caused by exposure to high-intensity radiation with a wide energy spectrum; (2) materials which structure is more important in the radiation response than their physico-chemical properties; (3) the emergence of a general theoretical concept -"COMPLEXITY", which is the brainchild of synergetics.Now it has become the most powerful approach in the study of "complex systems" [1][2][3][4].
Such a metamorphosis has covered most of the areas of the RPCM, including various aspects of radiation degradation of materials and devices based on them, including biological objects (see, for example [1][2][3]).
The purpose of this work is to consider (in brief) a number of new features in the radiation problems that are important for both inanimate and living nature.Naturally, our analysis is carried out within the general framework of "COMPLEXITY", taking into account several new fundamental achievements in physics, chemistry, biology and cybernetics.

A generalized Complexity scheme for studying processes in condensed matter physics
Taking a careful outlook at the dynamics of the development of scientific topics since the end of the XIX century and up to the present moment, it can be noticed that a huge number of phenomena and effects can be naturally reflected in a three-dimensional coordinate system ("Figure 1").If quite familiar "elements" are located on the OX and OY axes (OX -the physical and chemical properties of the object, namely the types of chemical bonds, and the structural features on the OY), a less familiar quantity is located on the OZ axis -the so-called "redundancy" (R), which is the "motivating force of development" complex systems: where () and   mean the amount of entropy at the current moment  and its possible maximum value.
This Complexity scheme allows you to consider an extremely large number of situations from a single position.In particular, at  → 0, equilibrium processes occur in the X-Y plane, where it is easy to trace the interests of the first half of the XX century (lines parallel to the axis OX), or the interests at the end of the XX century (lines parallel to the axis OY), or the interests of the researchers in the XXI century ( > 0).I would especially like to note that such a three-dimensional space diagram easily allows us to find the field of realization of effects/phenomena using three different paradigms: selforganization, dynamic chaos and self-organized criticality.It is also important to note that non-identical elementary acts can be realized in the domain  = .Below, a description of a number of effects from very different areas are presented and they are only a small part of a huge number of effects and phenomena which are already known and described by the concept of Complexity [5].

Figure 1.
Three-cardinate representation of the Complexity concept: on the X-axis -hydrogen bond; Vandervaals bond; metallic bond; ionic bond; covalent bond; on the Y-axis there are various structures: nano; fractality; small dimension; chirality; hierarchy.

The concept of spin catalysis
Spin catalysis (SC) [6], i.e. the use of spin as a catalyst, is a remarkable example of combining crystal chemistry with quantum physics (the so-called "bonds and bands" concept).Its essence is as follows ("Figure 2"). Figure 2 shows that in the flip-flip process leading to the exchange of spins, two different types of electrons can participate as a catalyst: either an electron flying freely past the incident covalent «O-O» bond (attacked by a photon), or an electron localized on a nearby paramagnetic ion.In all cases, the probability of the flip-flip process is estimated within the framework of the second-order perturbation theory and this gives an exponentially strong increase in the probability of the flip-flip process as the distance from the singlet pair to the catalyst electron decreases.In addition, "Figure 2 (d)" demonstrates two possible types of exposure to light: its low intensity and its high intensity.In the case of low intensity, light is absorbed (with a spin reversal) when the "O-O" molecule has a constant bond length  0 -this corresponds to arrow 1-3.In the case of high light intensity, there is a sufficiently high probability that in the local location of this molecule, "O-O" will simultaneously be absorbed, in addition to photon 1-3, also infrared photon 1-4 (since infrared radiation leads to fluctuations in the length of the molecule).Considering the fact that the absorption of a photon with a spin reversal is a second-order effect, the photon absorption energy turns out to be in the denominator under the integral when calculating the probability of the entire process.Therefore, in intense fields of electromagnetic radiation (synchrotron, Large Solar Furnace), the addition of an infrared component dramatically increases the ff process.

Destruction of the oxygen bridge by radiation exposure.
Many lasers functioning today are built on ion-bonded materials, a type of which are glass lasers [7].Glassy oxygen-containing materials often contain so-called "oxygen bridges" O-O as structural elements ("Figure 2").The peculiarity of these bridges is that both oxygen atoms are connected to each other only with a covalent bond.A large number of studies on the radiation effects in such objects (see [8][9][10]) lead to the conclusion that it is the O-O bridges, that is the weakest link and their accumulation during operation leads to degradation of the laser parameters.Taking into account the emergence of ideas of spin catalysis, these general considerations can be concretized.Indeed, according to the scheme presented in "Figure 2", it can be assumed that radiation exposure (e.g., X-ray radiation or UV) can stimulate a flip-flip process, turning a covalent bond singlet into a triplet, naturally, with the participation of a third-party spin belonging either to a nearby paramagnetic ion or to a fast electron, born in the ionization processes of radiation.It is important to note, that the formed triplet, pushing aside oxygen ions, does not always lead to a defect, namely, only in cases when the electronic level of the triplet state, being in the conduction band, becomes resonant.This leads to the possibility of its disruption from the local state and movement through the free zone, so that oxygen ions do not have time to disperse.In this case, the probability of destruction of the O-O bridge is multiplied by the factor  = exp (− + /  ) ≈ exp (−∆  /ħ  ; here ∆  is the width of the resonant level,   is the Debye frequency.If we take into account that there are many constructions of the O-O bridge type, then such a mechanism may be responsible for degradation in a large number of situations.
One of such characteristic and important examples is the bridge structure involving oxygen in a number of first-generation HTS materials, where oxygen located between the planes is responsible for the mechanical stability as well as the electronic properties of the material, so the destruction of the bridge by radiation is an important degradation mechanism [8][9][10].
It should be noted that in many works on the degradation of laser and other materials, various interpretations have been proposed to understand radiation processes.Interesting, for example, is the situation of suppressing the degradation of some lasers by doping scandium garnet crystals with chromium ions [10].At the same time, it is obvious that the universality of the degradation mechanism through spin catalysis is very attractive.As an additional test for its implementation, it would be possible to investigate the situation when an isotope enters the structure of the oxygen bridge, the nucleus of which has an unpaired spin, and such a flip-flip variant with the participation of a nuclear spin is, in principle, quite real [6].

Changes in the local structure of the hydrogen bond under radiation exposure.
The hydrogen bond is one of the most important types of bonds that determines the properties of objects in both living and inanimate nature [8].The impact of radiation has a diverse effect on such objects, sometimes roughly destroying them, but sometimes just subtly modifying the local structure, and so the properties.

Figure 3. Potential function (term)
for a proton (hydrogen bond) in a DNA fragment: 1-tunneling movement to a neighboring metastable state; 2-proton movement as a result of photon absorption during the S→  reaction (compliance with the rules of spin symmetry is due to the participation of the nuclear spin of the proton as a spin catalyst).
Figure 3 shows a fragment of the molecular structure caused by hydrogen bonding, for example, this is exactly the situation realized in DNA [10].It is generally believed that spontaneous mutations are caused by tunneling from a deeper pit to a shallower one ("Figure 3").In the case of induced mutations (for example, when exposed to light), the reorganization of the hydrogen bond occurs differently: when a photon is absorbed, the singlet bond, by flipping one of the spins, turns into a triplet bond, and hydrogen athermically moves to the neighboring potential well (path 2).However, a "simple" reaction  →  is possible only with the participation of a third spin.Nature has also provided for this situation by the fact that the third spin is the spin of a proton, which, turning over, participates in the flip-flip process.Naturally, this process is also intermediate through the virtual state and is described within the framework of the second-order perturbation theory.It is interesting to note that spontaneous hydrogen bond transformations involving proton spin are quite possible, i.e. here spin catalysis can also find application.

The concept of quantum entanglement
The concept of "quantum entanglement" [12], which unexpectedly arose (already on the background of the victorious march of quantum mechanics) in 1935 in the discussion of A.Einstein with co-authors, E. Schrodinger and N. Bohr, only today began to take shape of an in-depth understanding of quantum theory and its new applications (Nobel Prize 2022 -A.Aspe, D. Clauser, A. Zeilinger).As a result, at least three major new directions have emerged, which are intended to become the basic ones in the XXI century: quantum materials science, quantum computer science and quantum teleportation [13].Very briefly, the essence of quantum entanglement can be described as follows.If we analyze the decay of a complex quantum object into some of its components and study the properties of these components -in the sense of their conditioning by the primary complex pattern, it will be found out how much the connectivity these elements in the primary pattern affected their individual properties after separation.As is known [14] in modern synergetics and Complexity there is a property -the so-called emergence, which indicates the magnitude of the "new", which prevails over the simple sum of the original.And what happens if all these objects have a quantum nature?What is the quantum correlation between the initial quantum properties and the quantization of the results?It is believed that it is the degree of entanglement in the original quantum object that determines the level of quantum emergence, i.e. a set of quantum properties of products.It turned out that this process can be described by quantum entropy [12].A deep study of this basic idea, in conjunction with the Niels Bohr complementarity principle, is still sufficient to describe and analyze many of the new phenomena mentioned above.Below we will present an attempt to apply this new ideology, i.e. quantum entanglement, to the process of Auger destruction during the ionization of various materials.In fact, we believe that the difference in the result of this destruction mechanism for different materials can be understood by taking into account the ideas of entanglement.

Destruction of the molecular system in a Coulomb explosion.
The primary product of radiation exposure is often high-energy electronic excitation (for example, plasmon or K-ionization of crystal atoms).These excitations, which are always short-lived and decaying, often lead to a local positive multicharged state (charge Z ≫ 1).In our case, we will have two options in mind: Option 1 -when K-ionization occurs in the volume of the material and is caused by X-radiation ("Figure 4").This Coulomb unstable lattice state is resolved either by local destruction ("Coulomb explosion") or by electronic "flooding" (neutralization) of a local positive charge.It is clear that the choice of these alternatives depends on the ratio of two times: the time of ion expansion ( + ) and the time of "flooding" ( е ).
The analysis showed [2] that the probability of destruction   in this case is proportional to the factor exp (− + /  ). + , which is almost standard ~10 −13 , whereas   is extremely dependent on the nature of the irradiated object.For metals   ≈   ≈ 1   ~10 −16 сек, where  is the permittivity,  is the specific electrical conductivity.For nonmetals   varies in a wide range (10 −14 сек − 10 −12 sec ).It is clear that pouring dominates in metals (no defects are formed), but in nonmetals, in many cases, "pouring" does not prevent the formation of defects.The situation is indicative for Auger destruction of (bio-) polymers, see "Figure 4" [2].Option 2 -the formation of K-ionization consists in the action of a multicharged ion of low energy on the surface of a solid.Here a resonant recharge is possible in which the K-electron of the surface atom is recalibrated to the free state of the irradiating multicharged ion.In this case, an Auger cascade also occurs and causes a Coulomb explosion on the surface of the material with the formation of a cavity on it.Note that this situation is strictly two-dimensional, which additionally affects   (increasing it by 1.2 times), while other considerations of the representation presented are valid.
The small value of   in metals is to neutralization by plasmons, when all electrons participate coherently, but the large value of   is due to incoherent electron neutralization.In modern terms, this can be referred to as quantum entanglement [12] -in metals and quantum non-entanglement -in Anderson-type chains (far right figure).Hence it is clear that with a very large charge (Z), incoherent neutralization becomes coherent, i.e. entangled, since a large charge, tearing electrons from unequal wells, turns them into a drop of metal, but with its small plasmon, which gives a smaller   , and therefore for this case it is still   > 10 −16 .It is important to note that the described Auger destruction effect is quite realistically realized both in all semiconductors [3,4] and in some polymers (for example, RNA viruses, including SARS-2V).Moreover, the last turned out to be an effective method of treating some types of COVID-pneumonia [2,3].
Thus in the case of an Auger cascade involving heavy atoms in a disordered medium, we can observe an amazing situation when unbound states turn into bound ones, providing the manifestation of entanglement.This metamorphosis, apparently, can be adequately described both within the framework of the RPA theory [15] and on the basis of the idea of dephasing individual electrons in an atomic plasmon [16].

Conclusion
The problems of radiation degradation, which is an important aspect of the entire RFCS, and which, in turn, is a part of the modern science of matter, quite clearly reflect all fundamental phenomena, including new ones for general physics, chemistry, biology, mathematics, and which are currently combined in the concept of Complexity [5].Therefore, it is not surprising that such new concepts as spin chemistry, quantum entanglement and the hierarchical structure of objects (especially when exposed to intense radiation with a wide energy spectrum [4]) organically enter into modern ideas about the effects of radiation on matter (since they clearly contain elements of complexity).This ideology (Complexity) is already more than successful, and attempts to plausibly interpret a number of complex radiation effects without taking it into account do not correspond to the ways of progress, but most likely have a chance to become information noise.

Figure 2 .
Figure 2. Diagram f-f of the process leading to the S→  reaction, followed by the decay of the molecule upon photon absorption (the case of irradiation with a wide spectrum and high intensity of electromagnetic radiation).

Figure 4 .
Figure 4. Three-stage scheme for Auger-defect formation in a quasi-one-dimensional polymer chain (from left to right: K-ionization, local Coulomb instability, the reaction of the medium to the charge in periodic and non-periodic chains).