Research Paper:Time Evolution of Tight-Binding Model in the Presence of Electric Field
Although many theorems exist about the characteristics of equilibrium quantum systems, the dynamical behavior of out-of-equilibrium systems is far less understood. It is demonstrated that dynamical free energy is important in determining the non-equilibrium dynamic signature in dynamical phase trans...
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| Format: | Article |
| Language: | fas |
| Published: |
Alzahra University
2025-06-01
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| Series: | فیزیک کاربردی ایران |
| Subjects: | |
| Online Access: | https://jap.alzahra.ac.ir/article_8565_b005276bbfc2bb96770af70ba3483af1.pdf |
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| Summary: | Although many theorems exist about the characteristics of equilibrium quantum systems, the dynamical behavior of out-of-equilibrium systems is far less understood. It is demonstrated that dynamical free energy is important in determining the non-equilibrium dynamic signature in dynamical phase transitions. The presence of singularities in the time evolution of a physical quantity makes the dynamic behavior of the system interesting. This behavior can occur even in the case of a single-particle system such as the tight-binding model. In this paper, we study non-equilibrium dynamics of the one-dimensional tight-binding lattice with periodic boundary conditions under the influence of DC and AC electric fields, utilizing dynamical quantum phase transitions. Given that such a system has an exact non-perturbative solution, we can analytically predict the conditions for the existence of a dynamical phase transition in the presence of various electrical fields, as well as the corresponding critical times. If the system is placed in a constant electric field, utilizing analytical solutions, firstly, we show that the phase transition only occurs when the field strength is weaker than a certain value. Secondly, the critical times of the system's dynamical phase transition can also be analytically predicted. In the presence of a purely periodic electric field, in addition to numerical methods, some of the critical times can be determined analytically. When constant and periodic fields, both, are present, it is possible to show that the periodicity of the dynamical free energy and its invariance under time-reversal transformations. |
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| ISSN: | 2783-1043 2783-1051 |