Funct. Mater. 2015; 22 (2): 233-244.

http://dx.doi.org/10.15407/fm22.02.233

Triangular billiard in a constant field

Yu.N.Maslovsky[1], S.V.Slipushenko[1], A.V.Tur[3], V.V.Yanovsky[1,2]

[1] Institute for Single Crystals, STC "Institute for Single Crystals" National Academy of Sciences of Ukraine, Kharkiv 61001, Ukraine
[2] V.Karazin Kharkiv National University 4 Svobody Sq., Kharkiv 61022, Ukraine
[3] Universite de Toulouse [UPS], CNRS, Institut de Recherche en Astrophysique et Planetologie, 9 avenue du Colonel Roche, BP 44346, 31028 Toulouse Cedex 4, France

Abstract: 

The motion of a charged particle in a constant field inside the triangular region with elastically reflecting boundary is considered. The natural phase space is introduced and its properties are clarified. The dynamical map defining a motion of point in the phase space is derived analytically. The typical properties of trajectories and characteristic features of the phase portraits are found.

Keywords: 
triangular billiard, charged particles, constant field, phase space, dynamical map, nonlinear, chaos.
References: 

1. V.V.Yanovsky, A.V.Tur, Yu.N.Maslovsky, Zh. Eksper. Teor. Fiz., 106, 187 (2008).

2. S.V.Slipushenko, A.V.Tur, V.V.Yanovsky, Zh. Eksper. Teor. Fiz., 117, 274 (2013).

3. V.V.Yanovsky, A.V.Tur, Yu.N.Maslovsky, Theor.Math. Phys., 175, 655 (2013). http://dx.doi.org/10.1007/s11232-013-0053-x

4. M.A.Ratner, A.V.Tur, V.V.Yanovsky, J. Comput. Theor. Nanosci., 12, 589 (2015). http://dx.doi.org/10.1166/jctn.2015.3771

5. B.N.Miller, K.Ravishankar, J. Statist. Phys., 53, 1299 (1988). http://dx.doi.org/10.1007/BF01023870

6. H.J.Korsch and J.Lang, J. Phys. A, 24, 45 (1991). http://dx.doi.org/10.1088/0305-4470/24/1/015

7. V.Milner, J.L.Hanssen, W.C.Campbell and M.G.Raizen, Phys. Rev. Lett., 86, 1514 (2001). http://dx.doi.org/10.1103/PhysRevLett.86.1514

8. L.Christensson, H.Linke, P.Omling, Phys. Rev.B, 57, 12306 (1988). http://dx.doi.org/10.1103/PhysRevB.57.12306

9. H.Linke, L.Christensson, P.Omling, Phys. Rev.B, 56, 1440 (1977). http://dx.doi.org/10.1103/PhysRevB.56.1440

10. I.I.Privalov, Analytical Geometry, Phis.- Math. Literature Pub., Moskow, 1966 [in Russian].

11. H.G.Schuster, Deterministic Chaos: An Introduction, John Wiley and Sons, 312, New York (2005).

12. V.G.Baryakhtar, V.V.Yanovsky, S.V.Naydenov, A.V.Kurilo, Zh. Eksper. Teor. Fiz., 103, 292 (2006).

13. A.N.Kolmogorov, Problems of information transmission, 3, 3, (1969).

14. Yu.L.Bolotin, A.V.Tur, V.V.Yanovsky, Chaos: Concepts, Control and Constructive Use, Springer (2009). http://dx.doi.org/10.1007/978-3-642-00937-2

Current number: