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Вестник Российского университета дружбы народов. Серия: Математика, информатика, физика

Modeling of the Evolution of the Polaron States

И. В. Амирханов, Амирханов Илькизар Валиевич, Земляная Елена Валериевна, Victor Dmitrievich Lakhno, Лахно Виктор Дмитриевич, D Z Muzafarov, Музафаров Дилшод Зикриёходжаевич, Igor V. Puzynin, Пузынин Игорь Викторович, Т. П. Пузынина, Пузынина Таисия Петровна, З. А. Шарипов, Шарипов Зариф Алимжонович

Published Jun 15, 2010• 0 citations

Abstract

The evolution of polaron in a homogeneous environment is analyzed depending on parameters of the model and initial conditions which are selected in the form of various combinations of stationary polaron states. A computational scheme and results of the numerical modelling are presented. Work supported by RFBR grants 07-07-00313, 08-01-00800, 07-01-00738, 09-01-00770.

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The evolution of polaron in a homogeneous environment is analyzed depending on parameters of the model and initial conditions which are selected in the form of various combinations of stationary polaron states. A computational scheme and results of the numerical modelling are presented. Work supported by RFBR grants 07-07-00313, 08-01-00800, 07-01-00738, 09-01-00770.

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We study the quantum dynamics of small polaron formation and polaron transport through finite quantum structures in the framework of the one-dimensional Holstein model with site-dependent potentials and interactions. Combining Lanczos diagonalization with Chebyshev moment expansion of the time evolution operator, we determine how different initial states, representing stationary ground states or injected wave packets, after an electron-phonon interaction quench, develop in real space and time. Thereby, the full quantum nature and dynamics of electrons and phonons is preserved. We find that the decay out of the initial state sensitively depends on the energy and momentum of the incoming particle, the electron-phonon coupling strength, and the phonon frequency, whereupon bound polaron-phonon excited states may emerge in the strong-coupling regime. The tunneling of a Holstein polaron through a quantum wall or dot is generally accompanied by strong phonon number fluctuations due to phonon emission and reabsorption processes.

We propose a quantum trajectory analysis of a scheme to measure the states of a coupled-dot device (qubit) where there is a fluctuating energy gap Δ between the two states. The system consists of the qubit and a readout dot coupled to source and drain leads. The tunnel rate through the detector is conditioned by the occupation number of the nearer quantum dot (target) of the qubit and therefore probes the states of the qubit. We derive a Lindblad-form master equation to calculate the unconditional evolution of the qubit and a conditional stochastic master equation calculating the conditional evolution for different tunneling rates. The results show the effects of various device parameters and provide the optimum selection and combination of the system structure.