STUDY OF QUANTUM AND NON-MARKOVIAN EFFECTS IN BROWNIAN MOTION

SUN Zhe-Min; WU Xi-Zhen; ZHUO Yi-Zhong

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2024年10月30日

Chinese Physics C> 1990, Vol. 14> Issue(10) : 952-960

STUDY OF QUANTUM AND NON-MARKOVIAN EFFECTS IN BROWNIAN MOTION

China Institute of Atomic Energy,Beijing

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Abstract：
Based on the new form of the distribution density of the reservoir oscillator frequencies,the analytical expression of the density matrix ρ(x,x,t) for a dissipative quantum system has been obtained.The quantum and Non-Markovian effects on the quantum Brownian motion have been studied quantitatively and the Fokker-Planck equation including the quantum effects has been primarily derived under the Markovian approximation.

References

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I. R. Senirzky, Phys. Rev., 119(1960), 670[2] H. Mori, Prog. Theor. Phys., 33(1965), 423.[3] R. Zwanzig, J.Chem.Phys, 33(1960), 1338.[4] S. Nakajima, Prog. Theor. Phys, 20(1958), 948[5] A. O.Caldeira and A. J. Leggett, Physica, 21A(1983), 587.[6] R. Y.Feynman and A. R. Hibbs, Quantum Machanics and Path Integrals, (New York 1965)[7] F. Smithies, Integral Equation (Cambridge 1962).[8] H. Risken, The Fokker Plank Planck Equation (Springer, Heidelberg, 1984).[9] Xizhen Wu, Zhuxiu Li, J. A. Maruhn, W. Greiner and Yiihong Zhuo, J. Phys. G: Nocl. Phys., 14(1988),1049.

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SUN Zhe-Min, WU Xi-Zhen and ZHUO Yi-Zhong. STUDY OF QUANTUM AND NON-MARKOVIAN EFFECTS IN BROWNIAN MOTION[J]. Chinese Physics C, 1990, 14(10): 952-960.

SUN Zhe-Min, WU Xi-Zhen and ZHUO Yi-Zhong. STUDY OF QUANTUM AND NON-MARKOVIAN EFFECTS IN BROWNIAN MOTION[J]. Chinese Physics C, 1990, 14(10): 952-960. shu

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Received: 1900-01-01
Revised: 1900-01-01

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1.
沈阳化工大学材料科学与工程学院沈阳 110142

STUDY OF QUANTUM AND NON-MARKOVIAN EFFECTS IN BROWNIAN MOTION

Corresponding author: SUN Zhe-Min,

China Institute of Atomic Energy,Beijing

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1990-10-05

Abstract: Based on the new form of the distribution density of the reservoir oscillator frequencies,the analytical expression of the density matrix ρ(x,x,t) for a dissipative quantum system has been obtained.The quantum and Non-Markovian effects on the quantum Brownian motion have been studied quantitatively and the Fokker-Planck equation including the quantum effects has been primarily derived under the Markovian approximation.