Vibrating soap films: An analog for quantum chaos on billiards

American Journal of Physics

Volumn 66, Issue 7, 1998, Pages 601-607

  Arcos, E ^a   Baez G ^a   Cuatlayol P A ^a   Prian, M L H ^a   Mendez Sanchez R A ^a   Hernandez Saldana H ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040714213     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.18913     Document Type: Article

References (34)

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10. Both the Schrödinger equation for a billiard and the wave equation for a membrane are reduced to the Helmholtz equation when the time-independent part is taken. Nevertheless, to deduce the wave equation for the membrane air, gravity, and damping in the high frequency regime are usually neglected.
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18. These authors developed a formula according to which a solution to quantum problems may be written as a sum over all periodic orbits of its classically chaotic counterpart. This formula is exceedingly complicated due to the exponential increase of the number of such orbits as a function of their length. On the other hand, the shortest orbits are few and display some typical features of the problem. There are textbooks on classical and quantum chaos containing discussions of the Selberg-Gutzwiller-Balian periodic orbits sum expression. See, for example, L. E. Reichl, The Transition to Chaos (Springer-Verlag, New York, 1992), pp. 318-381. See also M. C. Gutzwiller, Ref. 5, pp. 282-321.
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26. The possibility to introduce a billiard of any shape easily is the great advantage of the experimental setup which we present. Domains with different shape but the same spectrum may be studied. See, for instance, H. Weidenmüller, "Why different drums can sound the same," Phys. World (22-23 August 1994). Other billiards associated with classically chaotic or integrable billiards may be studied. This is the case of the ellipse billiard, the oval billiard, the triangle billiard (all kinds of triangles), polygonal billiards, etc., and in general, billiards constructed in order to obtain some special feature of classically chaotic systems such as special discrete symmetries.
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