## Why energy discreteness occurs in nano materials ?

*Ans**. *The effects of supplementary discreteness of nanostructural process kinetics are caused by the presence in the field plasma systems of temporary lived compound quantum particles-compactons (swarming electron pairs, . electrons together with antielectrons, ternaries, tetrads of them and so on) along with elementary quantum particles. Compactons theory was considered

in one of the first paper about basics of quantum-field chemistry at the beginning of 1990th.

MT’s evolution kinetics has three variants of discrete-by-time, effects of energy exchange. The acts occurring at compound particles decay and formation are – first, the acts if transformers’ unitary transfonnations. with energy emission, second, the acts of transformers’ no unitary transformations with energy emission and entropy production, third the acts of nonequivalent transformations with energy emission and information production.

One can view the complex discrete-algorithmic character of processes’ multikinetics in its falling into sequence of discrete acts of ultra fast emissions,

dissipations, MT reactions and rapid elementary chemical reactions. This is an uniqueness of nano objects’ functional properties, including their potential to adaptability and cybernetic intellectuality.

In the absence of catastrophic nonequivalent transformations in quantum

systems one can consider two principal evolution ways which are differ one from another in dominating energy fluctuations channel, namely, unitary and dissipative ways, using. a general description of algorithmic evolution motion stated below in well-known matrix form of affine transformation from theory of optimization

One has to say that differences in the ways first of all explicitly affects the systems image point translation which is more or less changed parameters. Classical mechanics interpretation of image point’s motion in configuration space gives simple expression for displacement at uniformly accelerated motion without initial velocity

Notice that such an intermittent manner of evolution motion is in agreement with discrete character of energy fluctuation fluxes utilization by the boson component which is a scanning base of multi-structural particle. Using these and some other common considerations, specifically the quantum-field concept of the least upper bound of time of coherence motion, it is not difficult to obtain the expression for time quantum in unitary evolution way

Such a strong enough limitation allows to separate unitary evolution mode from another nonunitary ones which are characterized by a new thermo statistic mechanism of energy dissipation. One can deduce a formula for translation required to keep the evolution unitarily by correlating the expression (iii) with the general law (ii)

In case of homonuclear N-atomic cluster with mass M formula (iv) is simplified to-

In dissipative mode equations of time and spatial displacement quanta include temperature dependence and one can deduce them under certain assumptions of balance between an internal quantum contribution and an external thermal contribution to energy of multi particle’s swarming component fluctuations.

In case of homonuclear cluster with mass M one can simplify the expressions (vi) and\

(vii) as below-