Academic Journal
Mutual distribution of two partial solutions in 1D localisation: new information on the phase transition
| Title: | Mutual distribution of two partial solutions in 1D localisation: new information on the phase transition |
|---|---|
| Authors: | Suslov, I. M. |
| Source: | Philosophical Magazine. :1-32 |
| Publication Status: | Preprint |
| Publisher Information: | Informa UK Limited, 2025. |
| Publication Year: | 2025 |
| Subject Terms: | Condensed Matter - Mesoscale and Nanoscale Physics, Statistical Mechanics (cond-mat.stat-mech), Mesoscale and Nanoscale Physics (cond-mat.mes-hall), FOS: Physical sciences, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Statistical Mechanics, Physics - Optics, Optics (physics.optics) |
| Description: | We consider the mutual distribution of two linearly independent solutions y_1(x) and y_2(x) of the 1D Schroedinger equation with a random potential. Since individual distributions of $y_1$ and $y_2$ are log-normal, it is naturally to suggest that their mutual distribution is also log-normal. Such hypothesis is confirmed in the deep of the allowed and forbidden bands, but failed near the initial band edge. The mechanism of deviations from the log-normal form is elucidated, and the first correction to it is calculated. The latter allows to demonstrate broadening of the spectral lines in the universal conductance fluctuations. A lot of new information is obtained on the phase transition in the distribution P(ψ), where ψis a combined phase entering the evolution equations. According to the previous publications, this transition is related with appearance of the imaginary part of ψat a certain energy E_0, and is not accompanied by singularities in the system resistance. The real sense of this transition consists in the change of configuration of four Lyapunov exponents, which determine the general solution: there are two pairs of complex-conjugated exponents for E>E_0, while for E Latex, 20 pages, 6 figures included |
| Document Type: | Article |
| Language: | English |
| ISSN: | 1478-6443 1478-6435 |
| DOI: | 10.1080/14786435.2025.2541380 |
| DOI: | 10.48550/arxiv.2407.03371 |
| Access URL: | http://arxiv.org/abs/2407.03371 |
| Rights: | arXiv Non-Exclusive Distribution |
| Accession Number: | edsair.doi.dedup.....5f818ff3f974efe84063b92012748a86 |
| Database: | OpenAIRE |
| ISSN: | 14786443 14786435 |
|---|---|
| DOI: | 10.1080/14786435.2025.2541380 |