Abstract
We derive a semiclassical secular equation which applies for quantized (compact) billiards of any shape. Our approach is based on the fact that the billiard boundary defines two dual problems: the `inside problem` of the bounded dynamics, and the `outside problem` which can be looked upon as a scattering from a boundary as an obstacle. This duality exists both on the classical and quantum mechanical levels, and is therfore very useful in deriving a semiclassical quantization rule. We obtain a semiclassical secular equation which is based on classical input from a finite number of classical periodic orbits. We compare our results to secular equations which were recently derived by other means, and provide some numerical data which illustrates our method when applied to the quantization of the Sinai billiard. (author).
Doron, E;
[1]
Smilansky, U
[2]
- Weizmann Inst. of Science, Rehovoth (Israel). Dept. of Physics
- Bristol Univ. (United Kingdom). H.H. Wills Physics Lab.
Citation Formats
Doron, E, and Smilansky, U.
Semiclassical quantization of chaotic billiards. A scattering theory approach.
Israel: N. p.,
1991.
Web.
Doron, E, & Smilansky, U.
Semiclassical quantization of chaotic billiards. A scattering theory approach.
Israel.
Doron, E, and Smilansky, U.
1991.
"Semiclassical quantization of chaotic billiards. A scattering theory approach."
Israel.
@misc{etde_10157344,
title = {Semiclassical quantization of chaotic billiards. A scattering theory approach}
author = {Doron, E, and Smilansky, U}
abstractNote = {We derive a semiclassical secular equation which applies for quantized (compact) billiards of any shape. Our approach is based on the fact that the billiard boundary defines two dual problems: the `inside problem` of the bounded dynamics, and the `outside problem` which can be looked upon as a scattering from a boundary as an obstacle. This duality exists both on the classical and quantum mechanical levels, and is therfore very useful in deriving a semiclassical quantization rule. We obtain a semiclassical secular equation which is based on classical input from a finite number of classical periodic orbits. We compare our results to secular equations which were recently derived by other means, and provide some numerical data which illustrates our method when applied to the quantization of the Sinai billiard. (author).}
place = {Israel}
year = {1991}
month = {Sep}
}
title = {Semiclassical quantization of chaotic billiards. A scattering theory approach}
author = {Doron, E, and Smilansky, U}
abstractNote = {We derive a semiclassical secular equation which applies for quantized (compact) billiards of any shape. Our approach is based on the fact that the billiard boundary defines two dual problems: the `inside problem` of the bounded dynamics, and the `outside problem` which can be looked upon as a scattering from a boundary as an obstacle. This duality exists both on the classical and quantum mechanical levels, and is therfore very useful in deriving a semiclassical quantization rule. We obtain a semiclassical secular equation which is based on classical input from a finite number of classical periodic orbits. We compare our results to secular equations which were recently derived by other means, and provide some numerical data which illustrates our method when applied to the quantization of the Sinai billiard. (author).}
place = {Israel}
year = {1991}
month = {Sep}
}