2001/12/20 by Prabasaj Paul, Paul, Prabasaj, Bill Sutherland +1
Engineering · Mathematics · Physics and Astronomy · #Advanced MEMS and NEMS Technologies #FOS: Physical sciences #Mathematical Physics (math-ph) #Particle accelerators and beam dynamics #Plasma Diagnostics and Applications #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0112047
9 pages, 6 figures
arxiv created 2001/12/20 · openalex publication_date 2001/12/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present here a variational method for maximizing the bandgap in a one-dimensional system where the potential is subject to given constraints. Two specific examples are studied in detail. In the first, we show that if the potential is constrained to lie between two values, the largest bandgap is obtained by a mixture of the highest and lowest potential - an exact result valid in any dimension. The second example fixes the first and second moments of the potential and seeks to extremize the bandgap. An exact result is obtained. Finally, we indicate how our techniques may be applied to photonic bandgaps.