Solution of the Fermi--Ulam Model in the Case of Periodic Perturbation
LI Chao1,2, WU Jun-Fang1, XU Wen-Cheng2
1College of Physical Science and Technology, SouthChina University of Technology, Guangzhou 5106402School for Information and Optoelectronic Scienceand Engineering, South China Normal University, Guangzhou 510631
Solution of the Fermi--Ulam Model in the Case of Periodic Perturbation
LI Chao1,2;WU Jun-Fang1;XU Wen-Cheng2
1College of Physical Science and Technology, SouthChina University of Technology, Guangzhou 5106402School for Information and Optoelectronic Scienceand Engineering, South China Normal University, Guangzhou 510631
摘要We discuss the evolution of the state and the average energy of the Fermi--Ulam model in the case of periodic perturbation. By a perturbation technique, the time-dependent Schrodinger equation is solved and it is found that the particle will continuously absorb or radiate energy if the frequency of the oscillating wall meets the resonance condition. Usually, these two states cannot exist together at a certain frequency. However, there is an exception if the frequency is at some special values. We find these values and reveal that the energy for transmission has the minimum equivalent unit, which is in the form of a harmonic oscillator.
Abstract：We discuss the evolution of the state and the average energy of the Fermi--Ulam model in the case of periodic perturbation. By a perturbation technique, the time-dependent Schrodinger equation is solved and it is found that the particle will continuously absorb or radiate energy if the frequency of the oscillating wall meets the resonance condition. Usually, these two states cannot exist together at a certain frequency. However, there is an exception if the frequency is at some special values. We find these values and reveal that the energy for transmission has the minimum equivalent unit, which is in the form of a harmonic oscillator.
LI Chao;WU Jun-Fang;XU Wen-Cheng. Solution of the Fermi--Ulam Model in the Case of Periodic Perturbation[J]. 中国物理快报, 2008, 25(5): 1545-1548.
LI Chao, WU Jun-Fang, XU Wen-Cheng. Solution of the Fermi--Ulam Model in the Case of Periodic Perturbation. Chin. Phys. Lett., 2008, 25(5): 1545-1548.
[1] Fermi E 1949 Phys. Rev. 75 1169 [2] Ulam S M 1961 Proc. 4th Berkeley Symp. Math. Stat. Prob. [3] Blandford R E D 1987 Phys. Rep. 154 1 [4] Leonel E D, McClintock P V E and Silva J K L 2004 Phys.Rev. Lett. 93 029901 [5] Karlis A K, Papachristou P K, Diakonos K, Constantoudis V andSchmelcher P 2007 Phys. Rev. E 76 016214 [6] Leonel E D and Carvalho R E 2007 Phys. Lett. A 364 475 [7] Abal G, Romanelli A, Schifino A C S, Siri R and Donangelo R1999 Physica A 272 87 [8] Ladeira D G and Silva J K L 2006 Phys. Rev. E 73026201 [9]Saif F and Rehman I 2007 Phys. Rev. A 75 (4) [10] Fosco C D, Lombardo F C and Mazzitelli F D 2007 Phys.Rev. D 76 No. 085007 [11] Bose S, Jacobs K and Knight P L 1997 Phys. Rev. A 56 4175 [12] Liu K J, He L and Zhou G L 2001 Chin. Phys. 10 1110 [13] Li L and Li B Z 2002 Chin. Phys. Lett. 19 1061 [14] Chen W Z and Wei R J 1999 Chin. Phys. Lett. 16 767 [15] Li L and Li B Z 2001 Phys. Lett. A 291 190 [16] Doescher S W and Rice M H 1969 Am. J. Phys. 37 1246 [17] Makowski A J 1992 Math. Gen. 25 3419 [18] Makowski A J and Peplowski P 1992 Phys. Lett. A 163 142 [19] Makowski A J and Dembinski S T 1991 Phys. Lett. A 154 172
2008, Vol. 25 
