Dynamic conductivity of one-dimensional ion conductors. Impedance, Nyquist diagrams

Abstract

Dynamic conductivity of the one-dimensional ion conductor is investigated at different values of the interaction constant between particles and the modulating field. The consideration is based on the hard-core boson lattice model. Calculations are performed for finite one-dimensional cluster using the exact diagonalization method. Frequency dependence of the dynamic conductivity and behaviour of its static component (Drude weight) in the charge-density-wave (CDW) and superfluid (SF) phases are studied. Frequency dispersion of impedance and loss tangent is calculated; the Nyquist diagrams are built and analyzed.

Low-frequency dynamics of 1d quantum lattice gas: the case of local potential with double wells

“…Such splitting of spectrum can be considered as manifestation of appearance of the collective transport of particles along a chain. Such a result correlates in the case of half-filling with the calculation data for dynamical conductivity of linear ionic conductor, where a position of the first low-frequency peak is determined by the short-range interaction constant analogous to V [7]. Besides, the similar behaviour was observed for dynamical susceptibility of the optical lattice with ultra-cold bosonic atoms when the low-frequency modulation of the lattice potential profile is applied [17]; the effect was explained [18] within the Bose-Hubbard model, that is reduced to our one in the limit of hard-core bosons (position of the above mentioned peak is determined here by the repulsion energy of bosons occupying the same potential well).…”

“…In papers [3,4] based on the so-called orientational-tunneling model [5], the phase transitions to the superionic state in the subsystem of protons were described and the coefficients of proton conductivity were calculated for the group of crystals M 3 H(XO 4 ) 2 where M = N H 4 , Rb, Cs and X = S, Se. The mentioned model was taken by us as the basis of calculations of the single-particle spectrum and dynamic conductivity of the one-dimensional (1d) ionic conductors [6,7] by means of exact diagonalization method on finite clusters. Such an approach allowed to establish the existence of different ground-states, to describe the transitions of the crossover type between them at T = 0, and also to investigate the features of collective dynamics that determines the frequency dispersion of conductivity [6,7].…”

“…The mentioned model was taken by us as the basis of calculations of the single-particle spectrum and dynamic conductivity of the one-dimensional (1d) ionic conductors [6,7] by means of exact diagonalization method on finite clusters. Such an approach allowed to establish the existence of different ground-states, to describe the transitions of the crossover type between them at T = 0, and also to investigate the features of collective dynamics that determines the frequency dispersion of conductivity [6,7]. Ideological basis of our calculations was the hard-core boson approach; it was firstly used by Mahan [8] in description of the quantum particle transport in a lattice.…”

Low-frequency dynamics of one-dimensional systems with hydrogen bonds

“…Ґрунтуючись на орiєнтацiйнотунельнiй моделi [11], яку можна вважати узагальненням моделi де Жена, у працях [12,13] були описанi фазовi переходи до суперйонного стану в пiдсистемi протонiв та розрахованi коефiцiєнти протонної провiдностi у кристалах групи M 3 H(XO 4 ) 2 де M = NH 4 , Rb, Cs i X = S, Se. Згадану модель ми поклали в основу розрахункiв одночастинкових спектрiв та динамiчної провiдностi одновимiрних (1d) йонних про-вiдникiв [14,15] у пiдходi точної дiагоналiзацiї на скiнченних кластерах. Такий пiдхiд дозволив установити iснування рiзних основних станiв та описати переходи кросоверного типу мiж ними за T = 0, а також виявити особливостi колективної динамiки, що визначає частотну дисперсiю провiдностi [14,15].…”

“…Згадану модель ми поклали в основу розрахункiв одночастинкових спектрiв та динамiчної провiдностi одновимiрних (1d) йонних про-вiдникiв [14,15] у пiдходi точної дiагоналiзацiї на скiнченних кластерах. Такий пiдхiд дозволив установити iснування рiзних основних станiв та описати переходи кросоверного типу мiж ними за T = 0, а також виявити особливостi колективної динамiки, що визначає частотну дисперсiю провiдностi [14,15]. Iдейну основу наших розрахункiв становив пiдхiд жорстких бозонiв; таку методику вперше сформульював Маган [16], описуючи динамiку квантових частинок на ґратках.…”