Perturbations

‎Louis Marchildon

Gilbert A. Ibitola, Olanrewaju Ajanaku, Abiola Olawale Ilori

There exist several forms of perturbation theory in Quantum Mechanics, namely: non-degenerate perturbation theory, degenerate perturbation theory, time-dependent perturbation theory, time-constant perturbation theory and time-harmonic perturbation theory. This paper presents an extension of the perturbation theory for non-degenerate states. It has been observed that most texts and journal papers treat only the first –order and second-order non-degenerate perturbation theory. Therefore, this paper attempts to treat and present the third order and fourth order non-degenerate perturbation theory in quantum mechanics. It can thus be asserted that the higher the order of perturbations of quantum systems that we know, the more successful will be our efforts in suppressing or eliminating them.

Kwong T. Chung

The previous time-dependent variation-perturbation theory, which is derived from the conventional time-dependent perturbation equations, contains two inconvenient features. When the perturbation becomes static, the wave function so obtained does not satisfy the time-dependent Schr\"odinger equation, and the perturbation equations cannot be reduced to the ordinary time-independent perturbation equations. To remove these difficulties, we introduce a perturbed time-dependent phase factor in deriving a new set of perturbation equations. We then construct the variation-perturbation functionals as in the previous theory; the perturbed wave functions are solved by minimizing these functionals. The same method is also applied to many-electron systems, using the coupled and uncoupled Hartree-Fock scheme.

Zhongjun Yang, Li Chen, Kangjian Qin +2 more

For polar codes, perturbing received information can enhance the error-correction performance of successive cancellation (SC) decoding. This is an effective approach for realizing low-latency yet high decoding performance for long polar codes, since each perturbation-enhanced SC (PSC) decoding can be performed in parallel. This paper provides theoretical insights into the soft information perturbation. It first reveals that the PSC decoding can be equivalently viewed as perturbing the SC decoding a posteriori log-likelihood ratio (LLR) of the information bits. Such a revelation enables us to reduce the perturbation complexity by only targeting the information bits, resulting in an improved PSC (IPSC) decoding. By better utilizing the a posteriori LLRs, a set of possibly erroneous estimations can be formed to be perturbed, further reducing the perturbation complexity. Our simulation results show that, for various codeword lengths, the proposed IPSC decoding can achieve a similar performance as the PSC decoding, while yielding significant perturbation complexity reduction.

Masanori Ohya, Dėnes Petz