Abstract
We investigate an infinite array of point interactions of the same strength in \(\mathbb{R}\) d, d = 2, 3, situated at vertices of a polygonal curve with a fixed edge length. We demonstrate that if the curve is not a line, but it is asymptotically straight in a suitable sense, the corresponding Hamiltonian has bound states. An example is given in which the number of these bound states can exceed any positive integer.
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Albeverio, S., Gesztesy, F., Høegh-Krohn, R. and Holden, H.: Solvable Models in Quantum Mechanics, Springer, Heidelberg, 1988.
Duclos, P. and Exner, P.: Curvature-induced bound states in quantum waveguides in two and three dimensions, Rev. Math. Phys. 7 (1995), 73-102.
Exner, P. and Ichinose, T.: Geometrically induced spectrum in curved leaky wires, J. Phys. A 34(7) (2001), 1439-1450.
Exner, P., Joye, A. and Kovařík, H.: Edge currents in the absence of edges, Phys. Lett. A 264 (1999), 124-130.
Exner, P. and Šeba, P.: Bound states in curved quantum waveguides, J. Math. Phys. 30 (1989), 2574-2580.
Hurt, N. E.: Mathematical Physics of Quantum Wires and Devices, Kluwer Acad. Publ., Dordrecht, 2000.
Londergan, J. T., Carini, J. P. and Murdock, D. P.: Binding and Scattering in Two-Dimensional Systems, Lecture Notes in Math. 60, Springer, New York, 1999.
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Exner, P. Bound States of Infinite Curved Polymer Chains. Letters in Mathematical Physics 57, 87–96 (2001). https://doi.org/10.1023/A:1017923426674
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DOI: https://doi.org/10.1023/A:1017923426674