Abstract
Microscopic one-dimensional noninteracting model for the description of the energy spectrum of the ion subsystem in ionic conductor is considered. The processes of ionic hoppings are described in terms of Pauli operators. Time-dependent correlation functions hb(t)b + (0)ij in Pauli operators are obtained using the exact numerical procedure known for time-dependent spin correlation functions. The frequency dependence of autocorrelation function Jbb+(!) is calculated and analysed at the wide range of temperatures. The frequency and temperature dependences of the one-particle density of states are investigated.
Highlights
An ion transfer in solids has become an active area of research nowadays
One of the most important aspects in this field is the problem of determining the energy spectrum, e. g. the particle density of states, and the ionic conductivity
The simple noninteracting model of ionic hopping in the one-dimensional chain is analysed in the given paper based on the lattice gas model
Summary
An ion transfer in solids has become an active area of research nowadays. Different theoretical models have been developed to perform the necessary investigations in this direction. Taking into account the known exact solutions for Ising model, an explicit expression for the time dependent correlation function was obtained within the framework of lattice gas model [1] using current density operators to determine the ionic conductivity. In a series of papers devoted to ionic conductivity, starting with [1], the particles were described by Pauli creation and annihilation operators This corresponds to an ordinary restriction on the ion occupation number at a certain lattice site and reflects the Bose origin of particles (the approach that corresponds to the picture of hardcore bosons [10]). Our aim is to calculate the correlation functions and analyse the frequency dependences of the one-particle densities of states in the case when ions on the lattice are described using the Pauli statistics.
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