arXiv:cond-mat/0610828v1 [cond-mat.mtrl-sci] 30 Oct 2006
Adiabatic and Nonadiabatic Electronics of Materials
1Moscow State Institute of Radioengineering,
Electronics and Automation (technical university)
Vernadsky ave. 78, 117454 Moscow, Russia
Physical foundations of adiabatic and nonadiabatic electronics of materials are considered in this
article. It is shown the limitation of adiabatic approach to electronics of materials. It is shown that
nonadiabatic physical properties of solid materials (hyperconductivity, superconductivity, thermal
superconductivity and phonon drag of electrons at Debye’s temperatures of phonons) depend on
oscillations of atomic nuclei in atoms.
PACS numbers: 63.20.Kr, 63.90.+t, 71.00.00, 72.20.Pa
In modern electronics of materials, adiabatic principle mainly is used. According to
this principle, exchanging of energy between electrons and nuclei of atoms are neglected.
Today’s dominating electronics in essence is adiabatic electronics. It allows to consider
materials approximately, in adiabatic approach, and to study limited circle of their physical
properties. Development of nonadiabatic electronics, on the contrary, just begins. It takes
into the account processes of energy exchange by between electrons and nuclei of atoms, has
no basic restrictions, can reduce or remove problems of modern electronics and reveal new
physical properties of materials.
This article is devoted to analysis of physical foundations of adiabatic and nonadiabatic
electronics of materials and properties of boson-fermion fluid, arising under nonadiabatic
conditions in materials.
II. ADIABATIC ELECTRONICS OF MATERIALS
Bases of adiabatic electronics were stated by M. Born and R. Oppenheimer  in the
solution of Shrodinger’s stationary equation for a material HΨ = WΨ, where Hamiltonian
H contains operators of kinetic energies of electrons Te and atomic nuclei Tz , and also
the crystal potential V is dependent on sets of electrons coordinates (r) and atomic nuclei
coordinates (R) in a material. According to M. Born and R. Oppenheimer this equation is
equivalent to the following two equations:
(Te+ V )φ(r,R) = Eφ(r,R), (1)
(Tz+ E + A)Φ(R), (2)
where Te- kinetic energy of electrons’ system, W - energy of a material, φ(r,R) and Φ(R)
- wave functions for electrons system and nuclei system,
A = −
- adiabatic potential, MI- mass of nucleus in I −th atom, dτ - an element of the material’s
volume. Potential A describe exchange of energy between electrons and nuclei. In adiabatic
approach, potential A is small comparing to W, and it is neglected. One believe that if A ≡ 0
then the exchange of energy between electrons and nuclei is impossible, then, one believes
that the problem of a material, stated by the equations (1, 2), is an adiabatic problem, and
electronic properties, described by the equation (1), represent a theoretical basis of adiabatic
electronics of materials. However, one can see from equations (1, 2) that upon exception of
A, a full separation of variables in these equations is not achieved, as r and R are arguments
of V . Hence, the exchange of energy between systems of electrons and nuclei in adiabatic
approach, generally speaking, is not excluded.
So, physical parameters of crystalline silicon were calculated in adiabatic approach by G.
Pastore, E. Smargiassi and F. Buda . It turned out, that kinetic and potential energies
of electrons system and nuclei system deviate from average values in opposite phases to
each other with characteristic frequencies.It means that the energy exchange between
electrons and nuclei system occurs even at adiabatic conditions. Autors  supposed that the
greatest among the frequencies was the result of numerical method of calculation, because
at that time such frequency oscillations in crystals were not known. Later it was found
out, that this frequency coincides with the sum of two frequencies (frequency of inherent
oscillations of nucleus in silicon atom minus frequency of crystal phonon). In other words,
inherent oscillations of atomic nuclei are the fundamental property of manerials. Amplitudes
of nucleus oscillations are close to 10−12meter and consequently processes connected to
them refer to subangstroem electronics of materials. These oscillations in particular can
be an energy source for chemical reactions and for phase transitions even at extremely low
temperatures. The given result allows us to consider the adiabatic principle differently.
Adiabatic condition (A ≡ 0) means impossibility of the systematical, unidirectional stream
of energy from electrons to nuclei or from nuclei to electrons only, but does not exclude the
stream of energy periodically changing its direction.
P. Dirac  investigated the time-dependent Schrodinger’s equation for a crystal and
studied an opportunity of co-ordinates separation for electrons and nuclei that correspond
to adiabatic principle. He has shown that electrons and atomic nuclei move within the
effective self-consisted potential fields and generally their movements cannot be described
by equations, independent from each other. Therefore, the adiabatic principle in materials
is approximate, permitting to use it with some accuracy in certain conditions, and its ap-
plying each time requires substantiation and estimation of possible mistakes arising during
calculation of physical quantity in such an approach.
The regular error of energy calculation for electrons in adiabatic approximation is about
< A >≈ 10−5W. It turns out to be comparable with widths of forbidden energy gapes in
many semiconductors and therefore is not always allowable. In particular, the given error
can be one of the reasons of inexact definition of deep energy levels of the local centers in
semiconductors, calculated under adiabatic approximation.
The amendments to energy of the crystal, that arise as a result of removal of potential
eq. (3) out of equation (2), according to M. Born , are proportional to the integer powers
of small parameter η = (m/MI)1/4<< 1 , where m- electron mass. It has given an occasion
to justify any applying of adiabatic approximation, based on smallness of η, proved to be
wrong, and, as a matter of fact, it is generally wrong in all cases. Nonadiabatic principle
and terms of its applying to materials have other physical sense.
III. CONDITIONS FOR APPLYING ADIABATIC APPROACH
It was shown by C. Herring  (see else: ), that adiabatic approach can be applied, if
where Ekl - energy of the allowed electronic transitions between states k and l , ∆Rµ -
characteristic displacement of nuclei system on frequency ωµ, µ - type of oscillations, φk
and φl- electron wave functions, ¯ h - Dirac’s constant. Adiabatic approach was studied by
A. Davidov  in conditions when oscillations of atomic nuclei are allowed only with one
frequency ωµ. He has come to a conclusion that adiabatic approach can be used if
Ekl>> ¯ hωµ. (5)
In other words, the adiabatic principle can be soundly applied if energy of nuclei oscillations
is less than energy of the allowed electronic transitions, for example if the energy of nuclei
oscillations is less than width of the forbidden energy gape of a semiconductor. The condition
eq. (5) is sufficient, but is not a requirement. Therefore in some cases applying of adiabatic
approximation is justified though condition eq. (5) is not carried out.
Thus, criterion of applicability of adiabatic approach in materials is not so simple, as it
quite often looks. The adiabatic principle dominates in modern physics of materials, but
in some cases it is used unreasonably. Implications of adiabatic theories quite often appear
unproductive because of inaccurate applying of adiabatic approach. On the contrary, using
of nonadiabatic principle allows to reveal and to use new properties of materials. So, con-
ditions for applicability of adiabatic approach stated by C. Herring  and A. Davidov 
contain various types and frequencies of nuclei oscillations. Meanwhile, these nuclei oscilla-
tions (unlike oscillations of atoms or ions) are poorly investigated. It hinders well-founded
applications of adiabatic approach and halts development of nonadiabatic electronics.
IV. TYPES AND FREQUENCIES OF INHERENT OSCILLATIONS IN ATOMS
For determining types and frequencies of nuclei inherent oscillations in atoms, it is ex-
pedient to use model of a crystal in which each atom is represented by an electron shell
and a nucleus connected with each other by quasi-elastic force. Crossection of such a three-
dimensional model by a plane containing centers of some electronic shells is shown on Fig. 1.
Electron shells with masses m” on Fig. 1 are represented as circles, nuclei with masses M′
FIG. 1: Crossection of a three-dimensional crystal model by a plane.
are represented by dark circles in centers of electronic shells. According to analytical me-
chanics the frequency of normal oscillations of a nucleus in j − th atom can be defined if to
suppose absolutely rigid all quasi-elastic connections in considered model except one quasi-
elastic connection acting between a nucleus and shell in a j − th atom. In such conditions
the oscillations of a crystal are represented by oscillations of a nucleus relatively motionless
electronic shell of j − th atom. Physically equivalent situation is established out if mass of
an electronic shell of j−th atom m” = ∞. Hence, the frequencies spectrum of nucleus oscil-
lations is defined by known mass of a nucleus and by the potential (electric) field which hold
a nucleus in neighbourhood of the center of electron shell. This electric field is formed by
coulomb fields of nuclei and electronic shells of all atoms of a crystal. In our case it is enough
to take into account a field created only by shell of j − th atom in a neighborhood of her
center. Thus, frequencies of nucleus oscillations can be defined by considering a movement
of a nucleus in a field of a motionless environment that is in adiabatic conditions.
One can see from equation (2), that in adiabatic approach (A ≡ 0) and the potential
field acting on a nucleus, coincides with full electrons energy which for neutral atom can be
written down so:
E = Te+ EZe+ Eee+ Eex , (6)
were Te - kinetic energy of electrons, EZe - energy of electrons attraction to a nucleus,
energy. Electronic density χ(r) = e?Z
by electron shell in a point r, dτ - differencial of material volume where integration is
?Φ(r)χ(r)dτ - energy of their mutual pushing away from one enother, Eex- exchange
i=1|φi(r)|2, Φ(r) - electrostatic potential, created
carried out, e - electron carge, Z - atomic number, i - elecron number. Cyclic frequency
of harmonious oscillations of a nucleus in field, described by (6) is equal ω = (β/M)1/2,
where β - factor of the qusai-elastic force connecting a nucleus with his environment. This
frequency (ω), as is well known, is equal to a difference of the neighbor oscillations frequencies
in spectrum of quantum harmonious oscillator. We take it into account and begin the
frequencies calculation of nuclei inherent oscillations in various atoms.
In the atom of hydrogen (with atomic number Z = 1) Eee= 0, Eex= 0, Te= −EZe/2
under the virial theorem and E = EZe/2. The normalized wave function in the basic state
of hydrogen atom is Ψ1s= (1/πa3)1/2exp(−r/a), where a - Bohr’s radius. By integrating
twice the Poisson equation
ǫ0|Ψ1s|2at boundary conditions Φ(r = ∞) = 0
and Φ(r = 0) = const we receive Φ(r) = (e/(4πǫ0a3))[(1/a + 1/r)exp(−2r/a) − 1/r] and
E = (eΦ(r))/2, where ǫ0- the electric constant. We expand E in power series, reject all
terms containing r in degrees are higher than two, and determine parabolic potential E”(r)
in which oscillations of a nucleus are harmonious. Then we calculate β = (d2E”(r)/dr2)r=0=
e2/(6πǫ0a3). Further we calculate elementary quantum of nucleus oscillations in the atom
hydrogen ¯ hω1= ¯ h?β/mp∼= 0.519eV , where mpis mass of proton.
Energy of three-dimensional quantum oscillations of a nucleus are described by the for-
E(ν) = ¯ hωZ[(1/2 + ν1) + (1/2 + ν2) + (1/2 + ν3)] ,(7)
where ν1,ν2,ν3- the oscillatory quantum numbers independently accepting values 0, 1, 2,...
In helium atom (Z = 2) two electrons in the basic state have wave functions Ψ =
π(Z∗/a)3exp[(−Z∗/a)(r1+ r2)], where Z∗= 2 − 5/16∼= 1.6875 - the ef-
fective charge of the nucleus not equal to 2 owing to shielding of the nucleus by elec-
trons (see ref.: , p. 338). We simplify the equation (6) using the property of two-
electronic systems for which Eex = −Eee/2.E = Te+ (Ze/4)Φ(r).Under the virial
theorem E = (Ze/8)Φ(r). Similarly to calculations for the hydrogen atom, we in-
tegrate Poisson equation with electronic density e|Ψ|2, determine Φ(r), and determine
β = (Ze2)(24πǫ0)−1(Z∗/a)3. Then we determine quantum of inherent oscillations of nu-
cleus in helium atom ¯ hω2=?(Ze2)(24πǫ0)−1(Z∗/a)3[2(mn+ mp)]−1 ∼= 0.402eV , where mp
and mn- masses of a proton and a neutron.
Potential field in many-electron atoms is spherically symmetric and the normalized ra-
dial wave function (Rnl) of any electronic state can be expressed through hypergeometrical
function F(b,c,d) (see reference: , p. 179):
)lF(l − n + 1,2l + 2,2Zx
where Nnl =
n)3/2, x =
a, n - the principal quantum number, l - the
orbital quantum number. It follows from the (8), that electronic density about a point of
shell center is created mainly by s− electrons but densities of p−,d−,f−,... electrons are
insignificant. The density of s− electrons from L, M, N states (n = 2,3,4...) is supplemented
to density of K - electrons (n = 1). The share of density from these conditions can be
defined as squares of radial wave functions ratios: R20/R2
(R40/R10)2 ∼= 0.0123. Thus, it is visible, that the contribution to electronic density created
10∼= 0.125; (R30/R10)2 ∼= 0.037;
by 2s−, 3s−, 4s− electrons give approximately 17.4 pecent that can cause increase in
frequencies of nucleus oscillations about 5 percent. In the many-electron atoms one take
into account screening of a nucleus charge by electrons, by using an effective charge of a
nucleus Z∗∗= Z − µ, where µ = σZ1/3and values σ differ from unit a little for different
atoms: , vol. 2, p. 153. In view of these data the energy quantum of nucleus inherent
oscillations (quantum α - type of inherent oscillations) in the atom with number Z > 2 is
¯ hωZ= ¯ hω2
(Z − 5/16 − µ)3Λ(Z − µ)/Z ,(9)
where¯ hω2 = 0.402eV - quantum of inherent oscillations of a nucleus in helium atom,
Λ = 1.2 takes into count influence of electronic s− states with quantum numbers n > 1
on value ¯ hωZ at α - type of inherent nuclei oscillations. The same result appears, when
the theorem about ellipsoid’s potentials is applied to the electron shell , according to the
theorem inside regular intervals the potential of a charged ellipsoid is constant. Energy
spectrum of nucleus inherent oscillation in the atom with number Z is described by the
formula (7) where ¯ hωZis calculated under the formula (9).
It is possible to write down the spherically symmetric potential field, in which the atomic
nucleus goes, as power series A[−2+x2
90+...], where A = Z∗∗e2/a, x = 2r
This function differs from parabolic dependence and because of it non-harmonic amendments
to the oscillations’ energy arise. These amendments (∆Eαν) for α - type of one-dimensional
oscillations with oscillatory numbers ν = 0,1,2 and 3 are calculated in accordance with ,
vol. 2, p. 93, in the first and second orders of perturbation theory. As one would expect, the
greatest values of amendments relate to the oscillatory condition with ν = 3. Amendments
to energy of inherent α− type oscillations in conditions with ν = 0,1,2 and 3 for various
atoms are graphically submitted on Fig. 2. On insertion of Fig. 2 these amendments are
FIG. 2: Amendments (∆Eαν) to energy of α− type oscillations in conditions with ν = 0,1,2,3
depending on atoimic number Z.
submitted in the other scale for atoms under Z > 10.
The β− type of inherent oscillations, when the nucleus together with K electrons partic-
ipates in oscillations relatively other parts of the electron shell and the γ− type of inherent
oscillations when the nucleus together with K and L electrons participate in oscillations
relatively other parts of the electron shell are also possible. Calculations have shown, that
the energy spectrum of inherent harmonious oscillations of β− and γ− types are described
by the formula (7) with corresponding value of elementary quantum of oscillations ¯ hωZfor
each of these types that can be defined under the formula (9), supposing Λ = 0.2 for β−
type of inherent oscillations and Λ = 0.05 for γ− type of inherent oscillations. The calcu-
lated and experimental values for energy quanta α−,β−,γ− types of inherent oscillations
depending on nuclear number Z, are submitted on Fig 3.
FIG. 3: Energy quantums of α−,β−,γ− oscillations depending on atomic number Z. Calculated
values are shown by light circles. Experimental values are shown by dark circles.
Experiments show, that inherent oscillations of α−, β− and γ− tipes are one-dimensional
oscillations. Consequently, for calculation of oscillation energy it is expedient to use the
formula linear harmonious oscillator E(ν) = (1/2 + ν)¯ hωZ, where ν = ν1 = 0,1,2... and
ν2= ν3= 0 instead of eq. (7).
It is established experimentaly, that ”zero” energy of inherent oscillations E(ν = 0) =
(1/2)¯ hωZ, and also energies (3/2)¯ hωZ and (5/2)¯ hωZ participate in optical and electrical
processes, that is typical of classical oscillations harmonious oscillators and forbidden for
free quantum oscillators. It gives the basis to consider, that oscillatios of atomic nuclei in
materials are not absolutely free and adiabatic, that meet conclusions of the quantum theory
[1, 3, 5, 6, 9] about impossibility to carry out strictly the adiabatic principle in materials. In
this connection inherent nuclei oscillations in materials show dualism of physical properties,
they manifest classical and quantum properties.
Inherent oscillations of nuclei cause strong electron-phonon interaction and stimulate
corresponding features of physical properties of materials [10, 11, 12]. In adiabatic approach,
as we see the nuclei oscillations are possible, but an electron-phonon interaction is excluded,
though in reality this interaction accompanies inherent oscillations of nuclei. The given
contradiction exists only in adiabatic electronics and absent in nonadiabatic electronics.
V. NONADIABATIC ELECTRONICS OF MATERIALS
Nonadiabatic electronics differs in that it considers an exchange of energy between atomic
nuclei and electrons to be an important feature of materials described by the operator A
in eq. (2). It is known that for the first time researches in non-adiabatic electronics have
been undertaken more than 50 years ago by K. Huang , S. Pekar ,  and by other
researchers who were studying the local color centers in dielectric crystals. In particular, it
has been shown, that optical and thermal properties of these centers are caused by electron-
vibrational transitions in which various oscillations of crystals can participate together with
electrons. In average, S quanta of lattice elastic oscillations of one type participate in each
such transition. According to the estimations, constant S may reach 150, but experimen-
tal values S ≤ 22. In zero-defects crystals, S << 1, that corresponds to the adiabatic
principle, and S > 1 corresponds to nonadiabatic principle. In this connection for nonadi-
abatic electronics any materials with defects of structure such as the color centers, having
the electron-vibrational nature, are important. The opportunity of electron-vibrational pro-
cesses in semiconductors in the beginning caused doubts, but later the electron-vibrational
centers (EVC) have been found in semiconductors too. It appeared that EVC and the
electron-vibrational transitions in semiconductors, associated with EVC, are the cause of
the characteristic phenomena such as phonon drag by electrons at Debye temperatures of
phonons , thermal superconductivity, and also the hyperconductivity representing a ver-
sion of superconductivity, that arises and exists at higher the transition temperatures than
hyperconductivity, nearby the room temperatures and higher . These new properties of
semiconductors, undoubtedly, relate to the nonadiabatic electronics, because they are caused
by exchange of energy between electrons and atomic nuclei by means of electron-vibrational
transitions between stationary vibrational states of nuclei .
It is well known, that thermoelectric power (TEP) or Zeebeck effect in a materials include
contributions from electronic effects (the drift TEP) and electron-phonon effects (”phonon
drag” TEP, or PDE): V = Vd+ Vph. The drift TEP (Vd) is caused by diffusion of electrons
and holes under a gradient of temperature. The PDE (Vph) exist due to dragging of electrons
and holes by phonons stream. Thermoelectric power coefficient is sum of drift thermoelectric
power coefficient and PDE coefficient: α = αd+ αph, according to [19, 20, 21]. PDE was
observed experimentally in Ge monocrystals only, at low temperatures [20, 22, 23].It
forms a band of thermoelectric power and achieves a maximum between 15 K and 30 K.
Calculations by C. Hrrring  predicted the decrease of PDE, observable on experience at
heating of material from 30 K up to 70 K, basically due to decreasing the interaction between
electrons and phonons. It has given the basis to wrongly believe, that PDE may exist only
at low temperatures and to count completed its researches . Really, thermoelectric
power of crystalline ropes of carbon nanotubes at temperatures from 4.2 K up to 300 K in
laboratory of Nobel winner R. Smolli was presumably explained as PDE . It is possible
due to strong electron-phonon interaction on EVC. Moreover, it was shown  that the
PDE exist in semiconductors (containing EVC) as narrow bands of temperature-dependent
thermoelectric power, located at Debye’s temperatures of various phonons of a material.
It is possible to strengthen a connection of electrons with phonons in nonmetallic materials
by introducing into them EVC. Strong interaction of electrons with phonons is provided due
to inherent oscillations of nuclei in atoms of EVC. In such conditions, mobile electrons and
holes are localised on EVC, the drift TEP decreases or disappears in general, and PDE
dominates. The moving of electrical charges in a material under action of temperature
gradient occurs basically as electron-vibrational transitions between EVC or between EVC
groups, and the value Vphdepends on speed of these transitions.
S. Pekar  described the intracenters nonradiative electron-vibrational transitions,
caused by elastic oscillations of a crystal at frequency ω. This theory is important for
description of PDE as it is applicable for transitions between EVC, because in each material
the EVC centers are similar each other and indiscernible. Speed of nonradiative transi-
tions of center υ(ω) from a condition k to a condition l reaches a maximum on frequency
ωm∼= Sωj, where ωj- frequency of phonon such as j, participating in transition, and it may
be expressed by the following function:
υ(ω) = υmexp
−(ω − ωm)2
′′′(ω − ωm)3
) + ...
where υm- the maximal value υ(ω), g”=?
(qjk−qjl) - change of equilibrium coordinates of the center, n∗
j- average value of oscillatory
quantum number. Near to a maximum of function eg. (10) value (ω − ωm) is small, power
row in a parameter exhibitors converges quickly and it is possible to be limited to the first
square-law member of the row.
Then, according to the Debye rule, we having defined a temperature of a material T =
¯ hω/k, a temperature of a material at the maximal speed of transitions Tm= ¯ hωm/k, and
Θ = ¯ h?g”/k. Believing, that the value of PDE is proportional to υ(ω), it is possible to
write down the temperature dependence of PDE as Gauss function
αph(T) = const
(T − Tm)2
where const is independent of temperature. We used this function eq. (11) for approximation
contours of experimental PDE bands in containing EVC materials, by selecting values const
Typical temperature dependence of thermoelectric power in Si monocrystal with con-
centration EVC about 1015sm−3, having rather narrow bands A, B, C, D with complex
contours, is submitted on Fig. 4. Dashed lines 1, 2, 3 on an insertion of Fig. 4 represent
Gauss curves eq. (10), corresponding to longitudinal and transverse acoustic phonons in Si.
Solid line is sum of the dashed lines. It describes a contour of a band C. It is noticed, that
PDE bands exist only in materials containing EVC and in various materials they are located
at Debye temperatures of acoustic and optical phonons of a material. It was observed in thin
epitaxial layers of materials on substrates that the PDE bands located at Debye temper-
atures of a substrate phonons. These bands are caused by electron-vibrational transitions
between EVC or between EVC groups and represent the PDE. Components of PDE bands
are well described by eq. (10) in a vicinity of their extrema. Values Θ are identical to the
contribution from any phonon type in each material and do not depend on temperature.
Values Θ for some of materials are submitted in Tab. I and in Tab. II. They definitely
reflect processes in the materials, independent from external conditions. Undoubtedly, here
there are processes of an exchange by energy between systems of electrons and atomic nuclei
which are characteristic for nonadiabatic electronics.
Contrary to for a long time ratified opinion, the received results convince us that re-
searches of PDE are not completed. The PDE researches are in the beginning of its devel-
opments, as well as nonadiabatic electronics as a whole.
FIG. 4: Temperature dependency of thermoelectric power in Si, showing phonon drag effect as
bands A, B, C, D. On insertion, the dashed curves 1, 2, 3 were calculated under eq. (10). Continuous
curve is sum of the dashed curves. It approximate contour of band C.
TABLE I: Values Θ in some monocrystal materials
MaterialΘ, K MaterialΘ, K
GaAs 3.5InP 3.6
InSb 4.0graphite 5.0
Ge5.8 CdHgTe 14.3
The hyperconductivity phenomenon differs from well-known superconductivity by details
of physical mechanism. The normalized temperature dependences of resistivity of the super-
conductor; hyperconductors are shown on Fig. 5 in the dimensionless units rs= ρ/ρsand
rg= ρ/ρg, on complex planes U and W. Materials resistivity in the beginning of transition
to the state with ρ = 0, at temperatures Tsand Tg, are denoted as ρsand ρg. Normalized
temperatures for semiconductor and superconductor are denoted ξ = T/Tsand η = T/Tg,
correspondingly, where T - Kelvin temperature.
Complex plane W can be projected to the complex plane U, for example, with the help
TABLE II: Values Θ in some single crystal films on substrates
Material Substrate Θ, K
FIG. 5: Normalized temperature dependences of resistivity for a superconductor (rs) and for a
hyperconductor (rg) on complex planes U and W.
U = (1 − W0)/(ReW − W0) (12)
so that the point η = 1 was projected to the point ξ = 1. The real value W0 may be
chosen so that both temperature dependences of ρ have coincided with each other with the
greatest accuracy in plane U. The basic opportunity of such superposing of the temperature
dependences ρ proves the possibility of using of the phenomenological description of super-
conductivity as well as for description of hyperconductivity. Distinctions of these materials
states with zero value ρ consist only in details of physical mechanisms.
It is possible to consider axes ξ and η as lines leaving to positive and negative infinite
large values, closed in infinity and forming the closed contours. Temperatures in terms of ξ
are laying above the axis on Fig. 6. They relate to a superconductor. Temperatures in terms
FIG. 6: Mutual conformity between temperatures are sitting in complex plane U on axis ξ (for a
superconductor) and in complex plane W on axis η (for a hyperconductor).
η are laying below the axis of temperatures on Fig. 5. They relate to a hyperconductor.
Mutual conformity of the temperatures are sitting on the axes ξ and η, shown on Fig 6. It
is received with the help of transformation eq. (12) under W0= 2.
One can see from the Fig. 6 that temperature interval on axis ξ in plane Z, where there is a
superconductivity (0 < ξ < 1), corresponds to the interval (−∞ < η < 1) on the axis η lying
in plane U, where there is a hyperconductivity and there are negative absolute temperatures.
In other words, hyperconductors may be characterized by the negative absolute temperatures
that lie higher than indefinitely high temperatures and may be applied to the description
of physical systems with inverse population of energy levels as was shown in . In our
case negative absolute temperatures should be related to the inverse population of EVC
Inherent oscillations of atomic nuclei influence on thermal, electric, optical and other
physical properties of nonorganic and organic materials, fullerens, carbon nanotubes and
carbon nanotube films. Inherent oscillations of nuclei, apparently, majorly define signals
propagation in nerve fibres, action of some poisons, presence and properties of aura, and also
various physical features of existence of live organisms and life in general. Thus, nonadiabatic
electronics of materials promises to be less expensive, but not less various and useful, than
existing adiabatic electronics.
Fundamental opportunities of nuclei oscillations in atoms of materials are obvious from
Schrodinger equation for a material and from adiabatic theory .Nevertheless, these
oscillations and the properties of materials related to them practically were not under inves-
tigation for decades, and implementations were limited by adiabatic electronics. Researches
of the materials properties related to the transitions between electronic states  that are
accompanied by changes of equilibrium positions or oscillations frequencies of atoms or ions
in a material were related to the nonadiabatic electronics. Thus, displacement and oscil-
lations of atoms or ions as the whole were considered, but one does not take into account
possible oscillations of nucleus in atoms though they correspond in greater degree to the
nonadiabatic principle. Modern nonadiabatic molecular mechanics, as a matter of fact, con-
sider transitions between the basic and excited electron states, and movements of nuclei,
described by classical equations of Newton. They do not take into the account the features
of interaction between moving electric charges, loses nuclei quantum features and miss new
properties of the materials caused by oscillations of atomic nuclei.
Aggregation of classical and quantum-mechanical principles in materials electronics tes-
tifies to inevitability of spreading of the classical mechanics into material microcosm what
was predicted in the beginning of the last century by far-sighted scientists.
Presently, the classical Newton mechanics is successfully applied to calculation of all
electronic quantum states in atoms of any type . It proves to be the most consent with
experiment, uses the simple mathematical tool, and does not require difficult calculations.
Apparently, soon problems related to molecules, fluids and solids will be solved by classical
methods. Then electronics of materials will become classical, not split to adiabatic and
nonadiabatic electronics, because such a division exists only in wave quantum mechanics of
Systems of mutually bound particles and quasi-particles, including fermions and boson,
consisting of electrons, holes, phonons and inherent oscillations of atomic nuclei, may exist
in materials. Presence of the electron-vibration centers (EVC) in materials provokes for-
mation of such fermion-boson systems, so far as, according to the theory and experiments,
significant number of electrons, holes, phonons and inherent nuclei oscillations may have
high concentration on such centers. Though atomic nuclei practically do not migrate within
volume of a material, nevertheless, waves of inherent nuclei oscillations, as a result, cause the
fermion-boson system to be mobile as a whole, giving to it properties of a fluid. Migration
of such a fluid in a homogeneous material apparently doesn’t cause energy consumption, so
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