Theoretical solid-state physicists formulate their models usually in the form of a Hamiltonian. In quantum mechanics, the Hamilton operator (Hamiltonian) is of fundamental importance in most formulations of quantum th...Theoretical solid-state physicists formulate their models usually in the form of a Hamiltonian. In quantum mechanics, the Hamilton operator (Hamiltonian) is of fundamental importance in most formulations of quantum theory. Mentioned operator corresponds to the total energy of the system and its spectrum determines the set of possible outcomes when one measures the total energy. Interpretation of results obtained by the applying of models based on the Hamiltonian indicates very specific mechanisms of some observed phenomena that are not fully consistent with the experience. Such approach may occasionally lead to surprises when obtained results are confronted with expectations. The aim of this work is to find Hamilton operator of acoustic phonons in inhomogeneous solids. The transport of energy in the vibrating crystal consisting of ions whose properties differ over long distances is described in the work. We modeled crystal lattice by 1D “inhomogeneous” ionic chain vibrating by acoustic frequencies and found the Hamiltonian of such system in the second quantization. The influence of long-distance inhomogeneities on the acoustic phonons quantum states can be discussed on basis of our results.展开更多
There are a number of experimental methods aimed at the investigation of structural transformations. These methods differ from each other by a spectrum of quantitative indicators and their application is limited by th...There are a number of experimental methods aimed at the investigation of structural transformations. These methods differ from each other by a spectrum of quantitative indicators and their application is limited by the nature of investigated structures and processes. In a sense, it is also possible to consider the silanization of rubber mixtures as a structural transformation. Experimental observation of transformations of disordered rubber mixtures type structures can be quite difficult. The contribution deals with the theoretical principles of experimental methodology oriented on the investigation of silanization of rubber mixtures. We analyze the electrical response of rubber mixtures silanization. Our attention is focused on the modeling of a possible electrical response of a chemical reaction in a system consisting of several components. The results of the model are compared with experimental data measured during the silanization reaction in rubber mixtures.展开更多
文摘Theoretical solid-state physicists formulate their models usually in the form of a Hamiltonian. In quantum mechanics, the Hamilton operator (Hamiltonian) is of fundamental importance in most formulations of quantum theory. Mentioned operator corresponds to the total energy of the system and its spectrum determines the set of possible outcomes when one measures the total energy. Interpretation of results obtained by the applying of models based on the Hamiltonian indicates very specific mechanisms of some observed phenomena that are not fully consistent with the experience. Such approach may occasionally lead to surprises when obtained results are confronted with expectations. The aim of this work is to find Hamilton operator of acoustic phonons in inhomogeneous solids. The transport of energy in the vibrating crystal consisting of ions whose properties differ over long distances is described in the work. We modeled crystal lattice by 1D “inhomogeneous” ionic chain vibrating by acoustic frequencies and found the Hamiltonian of such system in the second quantization. The influence of long-distance inhomogeneities on the acoustic phonons quantum states can be discussed on basis of our results.
基金supported by Slovak Grant Agency APVV under projects VEGA 1/0356/13,APVV-SK-CZ-0168-11 and APVV-SK-CZ-0195-11.
文摘There are a number of experimental methods aimed at the investigation of structural transformations. These methods differ from each other by a spectrum of quantitative indicators and their application is limited by the nature of investigated structures and processes. In a sense, it is also possible to consider the silanization of rubber mixtures as a structural transformation. Experimental observation of transformations of disordered rubber mixtures type structures can be quite difficult. The contribution deals with the theoretical principles of experimental methodology oriented on the investigation of silanization of rubber mixtures. We analyze the electrical response of rubber mixtures silanization. Our attention is focused on the modeling of a possible electrical response of a chemical reaction in a system consisting of several components. The results of the model are compared with experimental data measured during the silanization reaction in rubber mixtures.
