On the calculation of the energy spectrum of quantum integrable systems

Guang-Liang Li, Junpeng Cao, Yi Qiao +1 more

Zhan Yuan Yan, Zhi Cheng Liu, Pan Zhao

In the framework of regularization process for quantization, the mesoscopic openelectronresonator is quantized using Feynman’s path integral method. With a Gaussian type propagator, the energy spectrum and wave functions are calculated. As an application of the results, the quantum fluctuations and uncertainty relation are discussed. The detailed formulation of energy spectrum and wave functions would be benefit to the further research work of the system.

Михаил Аронович Ольшанецкий

Atefeh Ashouri, S. Mahdavifar, Grégoire Misguich +1 more

Abstract There has been some substantial research about the connections between quantum chaos and quantum correlations in many‐body systems. This paper discusses a specific aspect of correlations in chaotic spin models, through concurrence (CC) and quantum discord (QD). Numerical results obtained in the quantum chaos regime and in the integrable regime of spin‐1/2 chains are compared. The CC and QD between nearest‐neighbor pairs of spins are calculated for all energy eigenstates. The results show that, depending on whether the system is in a chaotic or integrable regime, the distribution of CC and QD are markedly different. On the other hand, in the integrable regime, states with the largest CC and QD are found in the middle of the spectrum, in the chaotic regime, the states with the strongest correlations are found at low and high energies at the edges of spectrum. Finite‐size effects are analyzed, and some of the results are discussed in the light of the eigenstate thermalization hypothesis.

V.M. Yeleonskii, P. S. Zyryanov

Zhan-Yuan Yan, Ma Jin-Ying, XIAO-HONG ZHANG

In the framework of an advanced quantum theory for mesoscopic electric circuits in accord with the discreteness of electric charges, a mesoscopic quartz piezoelectric crystal equivalent circuit is quantized. To resolve the finite difference Schrödinger equation, an improved parameter perturbative method is proposed when WKB and perturbative method are inapplicable. With this method, the energy spectrum and wavefunctions of the system are obtained and used to calculate current quantum fluctuation as an application. The new method would be helpful to the application of the mesoscopic circuits quantum theory. Besides, the detail characters of energy spectrum and wavefunctions in the system would be helpful to the design of integrate circuit.