A continuum limit for the Kronig–Penney model
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Publication:3302282
DOI10.1088/1742-5468/2015/06/P06006zbMath1456.81228arXiv1409.3453OpenAlexW2963058078MaRDI QIDQ3302282
Sokol Ndreca, Aldo Procacci, Matteo Colangeli
Publication date: 11 August 2020
Published in: Journal of Statistical Mechanics: Theory and Experiment (Search for Journal in Brave)
Abstract: We investigate the transmission properties of a quantum one-dimensional periodic system of fixed length $L$, with $N$ barriers of constant height $V$ and width $lambda$, and $N$ wells of width $delta$. In particular, we study the behaviour of the transmission coefficient in the limit $N o infty$, with $L$ fixed. This is achieved by letting $delta$ and $lambda$ both scale as $1/N$, in such a way that their ratio $gamma= lambda/delta$ is a fixed parameter characterizing the model. In this continuum limit the multi-barrier system behaves as it were constituted by a unique barrier of constant height $E_o=(gamma V)/(1+gamma)$. The analysis of the dispersion relation of the model shows the presence of forbidden energy bands at any finite $N$.
Full work available at URL: https://arxiv.org/abs/1409.3453
Groups and algebras in quantum theory and relations with integrable systems (81R12) Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics (82B21)
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Related Items (2)
Quantum thermostatted disordered systems and sensitivity under compression ⋮ Transport in quantum multi-barrier systems as random walks on a lattice
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