Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/9710173

Amplification and Disorder Effects on the Coherent Backscattering in a Kronig-Penney Chain of Active Potentials

N. Zekri·H. Bahlouli·Asok K. Sen
View original source ↗Read source document ↗Export metadata ↓

Abstract

We report in this paper the analytical and numerical results on the effect of amplification on the transmission and reflection coefficient of a periodic one-dimensional Kronig-Penney lattice. A qualitative agreement is found with the tight-binding model where the transmission and reflection increase for small lengths before strongly oscillating with a maximum at a certain length. For larger lengths the transmission decays exponentially with the same rate as in the growing region while the reflection saturates at a high value. However, the maximum transmission (and reflection) moves to larger lengths and diverges in the limit of vanishing amplification instead of going to unity. In very large samples, it is anticipated that the presence of disorder and the associated length scale will limit this uninhibited growth in amplification. Also, there are other interesting competitive effects between disorder and localization giving rise to some nonmonotonic behavior in the peak of transmission.

Explore related subjects

cond-mat.dis-nncond-mat.mes-hall

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

N. Zekri, H. Bahlouli, Asok K. Sen. 1997-10-17. Amplification and Disorder Effects on the Coherent Backscattering in a Kronig-Penney Chain of Active Potentials. https://doi.org/10.1088/0953-8984%2F10%2F11%2F005

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Transition path sampling in Ising models on heterogeneous graphs

Activated transitions have rates that are often exponentially small in system size. Extracting the associated activation barriers is challenging in practice, especially in the deeply metastable regimes and in the presence of disorder. Here, we use transition path sampling to evaluate transition probabilities between ferromagnetic states in the Ising model on finite sparse random graphs, which are perhaps the simplest example of a disordered system with metastable states. To interpret the transient onset of the transition probability curve, we introduce a minimal three-state kinetic description that highlights the role of intermediate configurations. We validate the method on the heterogeneous Zachary Karate Club network, where distinct dynamical regimes emerge as temperature varies. We then apply the method to random regular graphs and Erdős-Rényi graphs, showing that sample-to-sample fluctuations are weak in the former but that quenched topological disorder induces sizable instance variability in the latter. For Erdős-Rényi graphs, we introduce an instance-dependent temperature rescaling that restores a consistent finite-size scaling of dynamical rates and enables a direct comparison with the corresponding static free-energy barrier.

cond-mat.dis-nn↗
arXiv2026

Estimates of ground state energies for the quantum SK and 2D-EA models, using deGennes-Suzuki-Kubo mean-field annealing dynamics

We perform large scale quantum annealing of the Sherrington-Kirkpatrick (SK) spin glass up to a system size $N=40000$ to estimate its ground state energy using the deGennes-Suzuki-Kubo mean-field quantum Ising dynamics, extending the earlier results (reported in Eur. Phys. J. B {\bf 98}, 226 (2025)). Here we numerically solve the deGennes-Suzuki-Kubo annealing dynamics to obtain the spin configurations and subsequently the ground state energy for a given system size at the end of the annealing, starting from a quantum paramagnetic state. The method shows high efficiency, with an overall algorithmic cost of $O(N^3)$ in estimating the energy of the ground state. We later extend this quantum annealing study to estimate the ground state energies (starting again from the quantum paramagnetic phase, annealing down to any desired low value of the transverse field) for the Edwards-Anderson (EA) spin glass model on a square lattice.

cond-mat.dis-nn↗
arXiv2026

Perfect resonance and fragile localization suppression in correlated disordered chains

Spatial correlations can suppress scattering in disordered chains and produce perfectly transmitting resonances. The practical value of this protection, however, depends not on the resonance peak itself but on the width of the surrounding transmission window and its sensitivity to local ordering errors. We show that a resonance can remain exactly transparent at its center while arbitrarily rare adjacent-swap errors restore an inverse localization length proportional to the square of the energy detuning. For lossless single-channel chains assembled from independent blocks of fixed length and composition, this positive quadratic term is guaranteed by a local scattering invariant and holds for every arrangement and every fixed swap probability between zero and one. With exact tuning and matched contacts, the central transmission remains unity. A microscopic quantum chain exhibits both higher-order suppression of scattering in the ideal recursive arrangement and the predicted response to local exchanges. These results reveal a limitation of spatial ordering that is invisible to a measurement at the resonance alone: spatial ordering protects the resonance peak, not the transport around it. The effect can therefore be tested experimentally by measuring transmission spectra before and after exchanges, without identifying microscopic defects.

cond-mat.dis-nn↗