Proceedings of the International Conference on Geometry, Integrability and Quantization

From Deformed Surfaces with Prescribed Quantum Properties to New Two-Dimentional Quantum Devices

Victor Atanasov and Rossen Dandoloff

Abstract

We propose a problem in differential geometry, i.e., which dformed surfaces produce prescribed curvature induced quantum potentials. We solve this inverse problem in the case of surfaces of revolution. We also show that there exist rotational surfaces in the form of a circular strip around the axis of symmetry which allow particles with generic angular momentum to bind. The quantum physics of a collection of circular strips of curved surfaces glued together is discussed in the conclusion in view of the possibility to engineer devices based on thin films.

Article information

Source
Proceedings of the Ninth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, ed. (Sofia: Softex, 2008), 135-145

Dates
First available in Project Euclid: 13 July 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1436793142

Digital Object Identifier
doi:10.7546/giq-9-2008-135-145

Mathematical Reviews number (MathSciNet)
MR2436267

Zentralblatt MATH identifier
1197.53121

Citation

Atanasov, Victor; Dandoloff, Rossen. From Deformed Surfaces with Prescribed Quantum Properties to New Two-Dimentional Quantum Devices. Proceedings of the Ninth International Conference on Geometry, Integrability and Quantization, 135--145, Softex, Sofia, Bulgaria, 2008. doi:10.7546/giq-9-2008-135-145. https://projecteuclid.org/euclid.pgiq/1436793142


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