Международная конференция студентов, аспирантов и Ð¼Ð¾Ð»Ð¾Ð´Ñ‹Ñ ...

108
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]_[jZbq_kdbo mjZ\g_gbc k fZljbp_c ( E−ατ∂F ∂u)
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ko_fu gZau\Zxlky y\gh-g_y\gufb Kms_kl\m_l h^gZ ko_fZ CROS ba k_f_ckl\Zk
2
dhfie_dkgufiZjZf_ljhf α= ( 1+ i)
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O( τ ), L2-
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1927 ]Kmlvf_lh^ZaZdexqZ_lky\lhfqlhihj_amevlZlZfjZkqzlh\gZ^\mok_ldZok
N b rN maeZfbih]j_rghklvqbke_ggh]hj_r_gby\kh\iZ^ZxsbomaeZok_lhd\uqbk
ey_lkyihZkbfilhlbq_kdblhqghcijb N →∞nhjfme_
( rN ) ( N )
( rN ) u −u
−p
∆ () t = + o
p ( N )
(5)
r −1
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2
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, ,
lb\gucihjy^hdlhqghklbko_fu
( N) ( rN)
eff ln ∆ −ln
∆
p () t = .
(6)
ln r
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jZkq_lZoko_fhcCROS[Zabjm_lkygZke_^mxsbo^hdZaZgguoZ\lhjZfbml\_j`^_gbyo
Ml\_j`^_gb_ 1. Kms_kl\m_l agZq_gb_ u = ⎡
β
∗ ⎣2 τ ( β+ 1)
⎤ ⎦ , ijbdhlhjhfqbke_ggh_
j_r_gb_ko_fu&526^eyaZ^Zqbg_f_gy_lkyijbi_j_oh^_gZke_^mxsbc\j_f_g
ghckehc û : û = u ∗
.
Ml\_j`^_gb_ k\hckl\h ijbly`_gby. Ijb u > u ∗
ijbjZs_gb_ nmgdpbb
uˆ − u < 0 bgZh[hjhlijb u < u ∗
ijbjZs_gb_nmgdpbb uˆ − u > 0 . L_ijbex[hfagZq_
gbb u gZl_dms_f\j_f_gghfkeh_ke_^mxsbcrZ]ko_fZ&526^_eZ_lihgZijZ\e_
gbxdiheh`_gbxjZ\gh\_kby u = ⎡
β
∗ ⎣2 τ ( β+ 1)
⎤ ⎦ .
Ml\_j`^_gb_ Ijbhkh[_gghklblhqgh]hj_r_gbyH>MlbiZihexkZ β> 0
qbke_ggh_ j_r_gb_ ko_fu CROS klj_fblky dij_^_em u ∗
. Ijbhkh[_gghklblbiZdhjgy
−1≤β< 0 qbke_ggh_j_r_gb_ko_fu&526klZ[bebabjm_lky\ihehk_\hdjm]iheh`_
gbyjZ\gh\_kby u ∗
.
>eyH>Mlhqgh_j_r_gb_dhlhjh]hbf__lhkh[_gghklv\b^Z u ln( t t)
∗− kijZ
\_^eb\uml\_j`^_gby
Ml\_j`^_gb_ Kms_kl\m_liheh`_gb_jZ\gh\_kby u ∗
= ln τ− ln 2 , ijbdhlhjhf
qbke_ggh_j_r_gb_ko_fu&526g_f_gy_lkyijbi_j_oh^_gZke_^mxsbc\j_f_gghc
kehc
Ml\_j`^_gb_ 5. Ijb u > u ∗
ijbjZs_gb_ nmgdpbb uˆ − u < 0 b gZh[hjhl ijb
u< u ∗
ijbjZs_gb_nmgdpbb uˆ − u > 0 .
Ml\_j`^_gb_ 6.