Journal of Thermodynamics & Catalysis
Open Access

Quantum Dots in Semiconductors Nanoelectronics

Christian L^{* *}Correspondence: Christian L, Department of Physics, Institution and Technology (ICTAN)-CSIC, Spain, Email:

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Introduction

For either parameterization Ω is finite for infinitely short perturbations, χ = 0. For very short quench times we notice an abrupt decay which can be explained by the sudden approximation: for very rapid changes, the system cannot respond on the same time scale, and the initial state remains unchanged. For χ > 0 we observe strong oscillatory behavior. Even small perturbations are sufficient to induce transitions away from two states of the harmonic oscillator to the small perturbation. For large switching times, the angle tends to a constant value, since in the adiabatic limit no oscillations are present. The period of the oscillations Ω is inversely proportional to the natural angular frequency of the harmonic oscillator. Every minimum value for the maximal rate of learning occurs for specific switching times, in our case in multiples of 2π given that χ0 was set to the unit. Generally, contains experimentally relevant information. For instance, the global minimum of Ω corresponds to the maximal rate, with which information can be learned about a quantum system evolving in time. We also notice that the two protocols yield qualitatively similar behavior, but that the linear protocol appears to be more effective is larger. Finally, we also compare our results from perturbation theory with the exact solutions. We observe that perturbation theory still gives qualitatively correct behavior, but also that perturbation theory underestimates the magnitude of Ω. As a main result we have established the relation between the accessible information and dynamic response of the system. These results could prove useful to design optimal strategies to maximize the rate with which information can be retrieved from a quantum system given a particular observable. C potential was originally introduced to study vibrational excitations in polyatomic molecules. Since then it has been applied to describe a wide variety of processes ranging from neutron scatteringto many-body systems, and in the description of symmetries of spin-orbit coupling for quantum relativistic systems. On the experimental side, has proven useful in quantum opticsand to describe different refraction indices according to the parameters of the setup . Moreover, Eq. has been used in the laboratory to describe quantum dots in semiconductors nanoelectronics and in the modeling of optoelecetronic devices. In contrast to the time-dependent harmonic oscillator , the dynamics of P¨oschl- Teller potential is not analytically known . Therefore, we have to rely on our results from time-dependent perturbation theory. For the numerical analysis we chose and set as the initial state. Moreover, Ωlin was computed (color online) Comparison of the exact (black, solid line) and approximated result (red, dashed line) for the maximal rate of quantum learning for quantum harmonic oscillator initially in its the ground state. Insets: Change of Holevo information (upper left panel), Δχ, and quantum speed limit χQSL (upper right panel) as a function of the switching time for the parity as observable and the driving protocols. Our results are summarized . Similar to the harmonic oscillator, the short time behavior is fully characterized by the sudden approximation, and by the adiabatic approximation for long quench time’s χ. However, we also observe that the oscillations are smaller, which suggests that the P¨oschl-Teller potential is less susceptible to the specific driving protocol. Overall, however, our findings for the harmonic oscillator and for the P¨oschl-Teller potential are remarkably similar.

Acknowledgment

The authors are grateful to the journal editor and the anonymous reviewers for their helpful comments and suggestions.

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest for the research, authorship, and/or publication of this article.