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Nonclassical ground state for Fröhlich palaron

Luo Zhi-Hua Yu Chao-Fan Lin Qia-Wu

Nonclassical ground state for Fröhlich palaron

Luo Zhi-Hua, Yu Chao-Fan, Lin Qia-Wu
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  • Based on the variational approach proposed by Huybrecht , using the two-mode squeezed coherent state as the second-step canonical transformation, we have investigated the nonclassical ground state for the Fröhlich polaron through considering the dynamical correlation bewteen the phonon wave vectors q and q' . Due to the correlation effect between the phonon coherent state and the phonon squcezed state, caused by the two-mode squeezing effect of the phonon coherent state, the coherent parameter fq and the two-mode squeezing angle φqq' also have a big correction correspondingly. As a result , this effect has greatly enhanced the coherent effect and the squeezing angle effect . The calculation and the analysis based on the ground state energy of the polaron have shown that 1) for the weakly coupled region ,the correction ΔE(1)c due to the effect of the displaced-phonon squcezed state is comparable to the Feynma n' s path integral calculation (ΔEf) and the coherent state correetion by Huybrechts (ΔE0), while the correction (ΔE(2)c) due to the squeezing effect of the phonon coherent state has an essential contribution , i.e. ΔE(2)c«(ΔEf,ΔE0); 2) for the strongly-coupled region ,the contribution from the displaced-phonon squcezed state has a greatly reduction , ΔE(1)c≥(ΔEf,ΔE0) .Althougth, at the same time ,the contribution due to the squeezing effect of the phonon coherent state also has a greatly reduction ,we still have ΔE(2)c«(ΔEf,ΔE0).
    • Funds:
    [1]

    Zhao C L,Gao K Y 2010 Acta Phys. Sin. 59 4857 (in Chinese)[赵翠兰、高宽云 2010 物理学报 59 4857]

    [2]

    Ren X Z,Liao X,Liu T,Wang K L 2006 Acta Phys. Sin. 55 2865 (in Chinese)[任学藻、 廖 旭、刘 涛、汪克林 2006 物 理学报 55 2865] [3] Gao K,Liu X J,Liu D S,Jie S J 2005 Acta Phys. Sin. 54 5324 (in Chinese)[高 琨、刘晓静、刘德胜、解士杰 2005 物理学报 54 5324]

    [3]

    Xie Y L,Chen Z D 2009 Chin. Phys. B 18 5038

    [4]

    Yu Y F ,Xiao J L,Yin J W ,Wang Z W 2008 Chin. Phys. B 17 2236

    [5]

    Xing Yan,Wang Zhi-Ping ,Wang Xu 2009 Chin. Phys. B 18 1935

    [6]

    Larsen D M 1968 Phys. Rev. 174 1046

    [7]

    Röseler J 1968 Phys. Status Solidi 25 311

    [8]

    Miyake S J 1976 J.Phys. Soc.Japan 41 747

    [9]

    Lee T D , Low F, Pines D 1953 Phys. Rev. 90 297

    [10]

    Feynman R P 1955 Phys. Rev. 97 660

    [11]

    Huybrechts W J 1976 J.Phys. C. Solid State Phys. 9 L211

    [12]

    Naoki T 1980 J. Phys. C. Solid State Phys. 13 L851

    [13]

    Tiablikov S V 1962 Sov. Phys. Solid State 3 2500

    [14]

    Mitra T K, Chatterjee A, Mukhopadhyay S 1987 Phys.Rep.153 91

    [15]

    Altanhan T , Kandemir B S 1993 J.Phys. Condens.Matter 5 6729

    [16]

    Kandemir B S , Altan han T 1994 J.Phys. Condens Matter 6 4505

    [17]

    Kervan N, Altanhan T , Chattergee A 2003 Phys. Letters A 315 2003

    [18]

    Lo C F , Sollie R 1993 Phys. Rev. A 47 773

    [19]

    Dodonov V V 2002 J. Opt.B: Quantum S O 4 R1

    [20]

    Bilge S , Altanhan T 2000 J.Phys. Condens Mater 12 1837

    [21]

    Krishna P M, Mukhopadhyay S ,Chatterjee A 2002 Int. J. Mod. Phys. B 16 1489

    [22]

    Yu C F, L G D , Cao X J 2008 Acta. Phys. Sin. 57 4402 (in Chinese)[余超凡、梁国栋、曹锡金 2008 物理学报 57 4402]

  • [1]

    Zhao C L,Gao K Y 2010 Acta Phys. Sin. 59 4857 (in Chinese)[赵翠兰、高宽云 2010 物理学报 59 4857]

    [2]

    Ren X Z,Liao X,Liu T,Wang K L 2006 Acta Phys. Sin. 55 2865 (in Chinese)[任学藻、 廖 旭、刘 涛、汪克林 2006 物 理学报 55 2865] [3] Gao K,Liu X J,Liu D S,Jie S J 2005 Acta Phys. Sin. 54 5324 (in Chinese)[高 琨、刘晓静、刘德胜、解士杰 2005 物理学报 54 5324]

    [3]

    Xie Y L,Chen Z D 2009 Chin. Phys. B 18 5038

    [4]

    Yu Y F ,Xiao J L,Yin J W ,Wang Z W 2008 Chin. Phys. B 17 2236

    [5]

    Xing Yan,Wang Zhi-Ping ,Wang Xu 2009 Chin. Phys. B 18 1935

    [6]

    Larsen D M 1968 Phys. Rev. 174 1046

    [7]

    Röseler J 1968 Phys. Status Solidi 25 311

    [8]

    Miyake S J 1976 J.Phys. Soc.Japan 41 747

    [9]

    Lee T D , Low F, Pines D 1953 Phys. Rev. 90 297

    [10]

    Feynman R P 1955 Phys. Rev. 97 660

    [11]

    Huybrechts W J 1976 J.Phys. C. Solid State Phys. 9 L211

    [12]

    Naoki T 1980 J. Phys. C. Solid State Phys. 13 L851

    [13]

    Tiablikov S V 1962 Sov. Phys. Solid State 3 2500

    [14]

    Mitra T K, Chatterjee A, Mukhopadhyay S 1987 Phys.Rep.153 91

    [15]

    Altanhan T , Kandemir B S 1993 J.Phys. Condens.Matter 5 6729

    [16]

    Kandemir B S , Altan han T 1994 J.Phys. Condens Matter 6 4505

    [17]

    Kervan N, Altanhan T , Chattergee A 2003 Phys. Letters A 315 2003

    [18]

    Lo C F , Sollie R 1993 Phys. Rev. A 47 773

    [19]

    Dodonov V V 2002 J. Opt.B: Quantum S O 4 R1

    [20]

    Bilge S , Altanhan T 2000 J.Phys. Condens Mater 12 1837

    [21]

    Krishna P M, Mukhopadhyay S ,Chatterjee A 2002 Int. J. Mod. Phys. B 16 1489

    [22]

    Yu C F, L G D , Cao X J 2008 Acta. Phys. Sin. 57 4402 (in Chinese)[余超凡、梁国栋、曹锡金 2008 物理学报 57 4402]

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  • Received Date:  21 June 2009
  • Accepted Date:  03 November 2010
  • Published Online:  15 May 2011

Nonclassical ground state for Fröhlich palaron

  • 1. Department of Physics, Guangdong University of Education, Guangzhou 510303, China

Abstract: Based on the variational approach proposed by Huybrecht , using the two-mode squeezed coherent state as the second-step canonical transformation, we have investigated the nonclassical ground state for the Fröhlich polaron through considering the dynamical correlation bewteen the phonon wave vectors q and q' . Due to the correlation effect between the phonon coherent state and the phonon squcezed state, caused by the two-mode squeezing effect of the phonon coherent state, the coherent parameter fq and the two-mode squeezing angle φqq' also have a big correction correspondingly. As a result , this effect has greatly enhanced the coherent effect and the squeezing angle effect . The calculation and the analysis based on the ground state energy of the polaron have shown that 1) for the weakly coupled region ,the correction ΔE(1)c due to the effect of the displaced-phonon squcezed state is comparable to the Feynma n' s path integral calculation (ΔEf) and the coherent state correetion by Huybrechts (ΔE0), while the correction (ΔE(2)c) due to the squeezing effect of the phonon coherent state has an essential contribution , i.e. ΔE(2)c«(ΔEf,ΔE0); 2) for the strongly-coupled region ,the contribution from the displaced-phonon squcezed state has a greatly reduction , ΔE(1)c≥(ΔEf,ΔE0) .Althougth, at the same time ,the contribution due to the squeezing effect of the phonon coherent state also has a greatly reduction ,we still have ΔE(2)c«(ΔEf,ΔE0).

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