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ϕ =
πδ _ ε
, (1)
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6 f_jy_fucgZhiul_^a_lZ-ihl_gpbZe^he`_g[ulvjZ \_giheghfmihl_gpbZemqZklbpuϕhF_`^ml_fdZd ihdZaZehiul \k_]^Z ξ<ϕh Djhf_ lh]h kh]eZkgh ]b^jh^bgZfbq_kdbf bkke_^h\Zgbyf ]jZgbpZ kdhev`_gbygZoh^blky\`b^dhcnZa_gZjZkklhygbbij_\urZxs_ffhe_dmeyjgu_ jZaf_jul_aZij_^_eZfbkehy=_evf]hevpZ LZdbfh[jZahfwe_dljhdbg_lbq_kdb_y\e_gby\hh[s_hdZau\Zxlkyg_\hafh` gufb\kemqZ_iehkdh]h>WK Wlbijhlb\hj_qbymkljZg_gu\l_hjbb=mb-Qwif_gZ ] Ih=mbbQwif_ gm kljmdlmjZ \g_rg_c h[deZ^db >WK hij_^_ey_lky ^\mfy l_g^_gpbyfb we_dljh klZlbq_kdbf ijbly`_gb_f m^_j`b\Zxsbf ijhlb\hbhgu m ih\_joghklb b l_ieh \uf ^\b`_gb_f ^bnnmab_c wlbo bhgh\ dhlhjh_ bf__l klj_fe_gb_ \ujZ\gylv bo dhgp_gljZpbb\[ebabih\_joghklbb\h[t_f_ MklZgZ\eb\Z_lky jZ\gh\_kgh_ jZkij_^_e_gb_ ijhlb\hbhgh\ \ ihe_ we_dljbq_ kdbokbe\\b^_³h[eZdZ´we_dljbq_kdboaZjy^h\km[u\Zxs_ciehlghklvxijbm^Z e_gbbhlih\_joghklb:gZeh]bqgufby\eyxlkygZijbf_jjZkij_^_e_gb_iehlgh klb]ZaZ\ihe_kbe]jZ\blZpbb\Zlfhkn_j_K^jm]hcklhjhgudhbhguhllZedb\Z xlkyhlih\_joghklbdhgp_gljZpbybo\hajZklZ_lkm^Ze_gb_fhlih\_joghklb LZdbf h[jZahf \g_rgyy h[d^Z^dZ >WK ijbh[j_lZ_l jZafulh_ ^bnnmagh_ kljh_gb_LhesbgZ^bnnmagh]hkehy\aZ\bkbfhklbhlmkeh\bc dhgp_gljZpbbl_f i_jZlmju baf_gy_lkyhl^_kyldh\Zg]klj_fh\^hfbdjhg JZ\gh\_kgu_dhgp_gljZpbbdZlbhgh\k+bZgbhgh\k-\^bnnmaghf>WKih^qb gyxlkyaZdhgmjZkij_^_e_gby;hevpfZgZ k + = k ∞ H[S −
]) ϕ ]) ϕ ; F− = F∞ H[S , (2) 57 57
]^_ K∞-dhgp_gljZpby bhgh\ \ h[t_f_ jZkl\hjZ ϕ-ihl_gpbZe >WK gZ jZkklhygbb o ^haZjy`_gghcih\_joghklbz-\Ze_glghklvbhgZ)-qbkehNZjZ^_y <khhl\_lkl\bbkmjZ\g_gbyfb dhgp_gljZpbyijhlb\hbhgh\iZ^Z_lZdhbh gh\-\hajZklZ_lijbm^Ze_gbbhlih\_joghklb jbkZ GZjZkklhygbbo ∞wlbdhg
7 p_gljZpbbklZgh\ylkyh^bgZdh\ufbbjZ\gufbdhgp_gljZpbbwe_dljheblZ\h[t_f_ jZkl\hjZ K+ K- K∞Wlhmkeh\b_hij_^_ey_liheh`_gb_\g_rg_c]jZgbpu^bnnm abhgghcqZklb>WK
Bajbk[ykghqlhijbo ∞,ϕ Zijbo ϕ=ϕhl_gZ[_kdhg_qgh[hevrhf jZkklhygbbhl]jZgbpujZa^_eZnZaihl_gpbZeZjZ\_ggmexZgZ]jZgbp_jZa^_eZiheghfm kdZqdm ihl_gpbZeZ ih\_joghklb =jZgbpZ kdhev`_gby e_`bl \ ij_^_eZo ^bnnmabhgghc qZklb >WK jbk[ ]^_ ihl_gpbZe g_ miZe _s_ ^h gmey WlZ qZklv ihl_gpbZeZ b h[gZjm`b\Z_lky \ we_dljhdbg_lbq_kdbo y\e_gbyo ξ-ihl_gpbZe Ba jbk[ ykgh qlh ξ-ihl_gpbZe \k_]^Z f_gvr_ ihegh]h ihl_gpbZeZ qZklbpu ϕh b g_ fh`_l[ulvjZ\_g_fm Djb\ZyiZ^_gbyihl_gpbZeZϕ o \^bnnmaghcqZklb>WK ijbfZeuoagZq_gb yoϕ0 hibku\Z_lkymjZ\g_gb_f ϕ = ϕ0 ⋅ e -χx ,
(3)
]^_[-jZkklhygb_hl]jZgbpukehyRl_jgZ^h^Zgghclhqdb χ =λ - wnn_dlb\ gZy lhesbgZ ^bnnmaghc qZklb >WK Nbabq_kdbc kfuke λ ke_^m_l ba mjZ\g_gby ijbo λ ϕ = ϕ0_l_λ -wlhjZkklhygb_gZdhlhjhfihl_gpbZe>WKmf_gvrZ _lky\_jZaIjbfZehcbhgghckbe_Fj_^uλkhklZ\ey_lkhlgbgZghf_ljh\L_hjby >WK^Z_lke_^mxs__\ujZ`_gb_^eyjZkq_lZλ : λ=1/χ=√εε0RT/2F2J ,
(4)
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ξ =
ηX εε + , (12)
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15 =jZ^b_glihl_gpbZeZhij_^_ey_lky\ujZ`_gb_fG ?/ ?-ijbeh`_ggh_gZijy`_ gb_< Kh]eZkghaZdhgmhfZ? ,.R=IL/χ.6lh]^ZG ,χ.S.
(14)
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