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Via a system of two kicked particles that are coupled in an infinite square well, we numerically show that the interaction with a particle of very small mass is able to lead to a quantum-to-classical transition on condition that the corresponding classical dynamics is almost unaffected. With the decrease of the mass of one of the particles, its effect on the classical dynamics of the other one decreases. Such an effect is even negligible if the mass of the particle is small enough. The classically chaotic dynamics of this small particle is effective for promoting the decoherence of the heavy particle. Therefore its quantum behavior exhibits the transition from the dynamical localization to the classically chaotic diffusion with the decrease of the effective Planck's constant ħ. Under the perturbation from the small particle, the linear entropy is rapidly saturated as time passes by. With the decrease of ħ, the time-averaged linear entropy exponentially increases from zero to almost unity.
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Keywords:
- decoherence /
- quantum-classical transition /
- quantum chaos
[1] Joos 2003 Decoherence and the Appearance of a Classical World in Quantum Theory (Springer, Berlin)
[2] Zurek W H 2003 Rev. Mod. Phys. 75 715
[3] Schlosshauer M 2004 Rev. Mod. Phys. 76 1267Schlosshauer M 2008 Found. Phys. 38 796
[4] Pattanayak A K, Sundaram B, Greenbaum B D 2003 Phys. Rev. Lett. 90 014103
[5] Feynman R P, Vernon F L 1963 Ann. Phys. (Leipzig) 24 118
[6] Caldeira A O, Leggett A J 1983 Physica (Amsterdam) 121A 587
[7] Wisniacki D, Toscano F 2009 Phys. Rev. E 79 025203(R)
[8] Toscano F, De Matos Filho R L, Davidovich L 2005 Phys. Rev. A 71 010101(R)
[9] Toscano F, Wisniacki D A 2006 Phys. Rev. E 74 056208
[10] Rossini D, Benenti G, Casati G 2006 Phys. Rev. E 74 036209
[11] Bandyopadhyay J N 2009 EPL 85 50006
[12] Adachi S, Toda M, Ikeda K 1988 Phys. Rev. Lett. 61 659
[13] Graham R, Kolovsky A R 1996 Phys. Lett. A 222 47
[14] Park H K, Kim S W 2003 Phys. Rev. A 67 060102(R)
[15] Petitjean C, Jacquod Ph 2006 Phys. Rev. Lett. 97 194103
[16] Jie Q L, Hu B, Dong G 2006 arXiv:quantph/ 0601025
[17] Liu J, Cheng W T, Cheng C G 2000 Commun. Theor. Phys. 33 15Liu J, Hu B, Li B 1998 Phys. Rev. Lett. 81 1749
[18] Hu B, Li B, Liu J, Gu Y 1999 Phys. Rev. Lett. 82 4224
[19] Izrailev F M 1990 Phys. Rep. 196 299Fishman S, Grempel D R, Prange R E 1982 Phys. Rev. Lett. 49 509
[20] Shepelyansky D L 1986 Phys. Rev. Lett. 56 677Shepelyansky D L 1987 Physica D 28 103
[21] Casati G, Chirikov B V, Izraelev F M, Ford J 1979 Stochastic Behavior in Classical and Quantum Hamiltonian Systems, edited by Casati G and Ford J, Lecture Notes in Physics (Vol. 93) (Springer, Berlin)
[22] Lakshminarayan A 2001 Phys. Rev. E 64 036207Bandyopadhyay J N, Lakshminarayan A 2002 Phys. Rev. Lett. 89 060402
[23] Cohen D, Heller E J 2000 Phys. Rev. Lett. 84 2841
[24] Wisniacki D A, Cohen D 2002 Phys. Rev. E 66 046209
[25] Wisniacki D A, Ares N, Vergini E G 2010 Phys. Rev. Lett. 104 254101
-
[1] Joos 2003 Decoherence and the Appearance of a Classical World in Quantum Theory (Springer, Berlin)
[2] Zurek W H 2003 Rev. Mod. Phys. 75 715
[3] Schlosshauer M 2004 Rev. Mod. Phys. 76 1267Schlosshauer M 2008 Found. Phys. 38 796
[4] Pattanayak A K, Sundaram B, Greenbaum B D 2003 Phys. Rev. Lett. 90 014103
[5] Feynman R P, Vernon F L 1963 Ann. Phys. (Leipzig) 24 118
[6] Caldeira A O, Leggett A J 1983 Physica (Amsterdam) 121A 587
[7] Wisniacki D, Toscano F 2009 Phys. Rev. E 79 025203(R)
[8] Toscano F, De Matos Filho R L, Davidovich L 2005 Phys. Rev. A 71 010101(R)
[9] Toscano F, Wisniacki D A 2006 Phys. Rev. E 74 056208
[10] Rossini D, Benenti G, Casati G 2006 Phys. Rev. E 74 036209
[11] Bandyopadhyay J N 2009 EPL 85 50006
[12] Adachi S, Toda M, Ikeda K 1988 Phys. Rev. Lett. 61 659
[13] Graham R, Kolovsky A R 1996 Phys. Lett. A 222 47
[14] Park H K, Kim S W 2003 Phys. Rev. A 67 060102(R)
[15] Petitjean C, Jacquod Ph 2006 Phys. Rev. Lett. 97 194103
[16] Jie Q L, Hu B, Dong G 2006 arXiv:quantph/ 0601025
[17] Liu J, Cheng W T, Cheng C G 2000 Commun. Theor. Phys. 33 15Liu J, Hu B, Li B 1998 Phys. Rev. Lett. 81 1749
[18] Hu B, Li B, Liu J, Gu Y 1999 Phys. Rev. Lett. 82 4224
[19] Izrailev F M 1990 Phys. Rep. 196 299Fishman S, Grempel D R, Prange R E 1982 Phys. Rev. Lett. 49 509
[20] Shepelyansky D L 1986 Phys. Rev. Lett. 56 677Shepelyansky D L 1987 Physica D 28 103
[21] Casati G, Chirikov B V, Izraelev F M, Ford J 1979 Stochastic Behavior in Classical and Quantum Hamiltonian Systems, edited by Casati G and Ford J, Lecture Notes in Physics (Vol. 93) (Springer, Berlin)
[22] Lakshminarayan A 2001 Phys. Rev. E 64 036207Bandyopadhyay J N, Lakshminarayan A 2002 Phys. Rev. Lett. 89 060402
[23] Cohen D, Heller E J 2000 Phys. Rev. Lett. 84 2841
[24] Wisniacki D A, Cohen D 2002 Phys. Rev. E 66 046209
[25] Wisniacki D A, Ares N, Vergini E G 2010 Phys. Rev. Lett. 104 254101
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