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We suggest a quantum procedure, based on our recent statistical theory offlow stress in polycrystalline materials under quasi-static plasticdeformations, with the intention to approach a theoretical description of theChernov-L\"uders shear macroband of localized deformation, exhibited by someFe-containing materials with a second phase beyond the yield-strength point onthe stress-strain curve {\sigma}={\sigma}({\epsilon}). The procedure makessubstantial use of a quasi-particle interpretation for the minimal portion ofmechanical energy in a given single-mode polycrystalline aggregate that isnecessary for the thermal-fluctuation mechanism to create a 0D-defect nanoporeas the initial zone of a localized deformation under external loading. Using aquasi-particle description, we obtain analytic expressions both for the scalardensity of dislocations, given the size of grains, the temperature, the mostprobable sliding system, and for the dependence {\sigma} ={\sigma}({\epsilon})itself. A two-level system, which characterizes the mechanism of absorption andemission of such quasi-particles (dislocons) by the crystal lattice of anygrain under quasi-static loading provides an effective physical description forthe emergence and propagation of the Chernov-L\"uders shear macroband. Anenhancement of acoustic emission observed in experiments and accompanied by themacroband phenomenon justifies the interpretation of a dislocon as a compositeshort-lived particle consisting of acoustic phonons. A more realisticthree-level system within a two-phase model with third (with dispersionparticles) phase presence for actual polycrystalline samples is also produced.

On a joint quantized and mechanical description for the Chernov-L\"uders macroband of localized deformation