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ɋɈȼɊȿɆȿɇɇɕȿ ɉɊɈȻɅȿɆɕ ɎɂɁɂɄɂ ɌȼȿɊȾɈȽɈ ɌȿɅȺ

_________________________________________________________________________________________________________________________________________________________________________________________________

ɉɥɨɬɧɨɫɬɶ ɪɚɡɪɟɲɟɧɧɵɯ ɫɨɫɬɨɹɧɢɣ ɧɚ ɤɚɠɞɨɦ ɭɪɨɜɧɟ

Ʌɚɧɞɚɭ (ɬ.ɟ. ɤɨɧɰɟɧɬɪɚɰɢɹ ɷɥɟɤɬɪɨɧɨɜ, ɩɪɢɯɨɞɹɳɚɹɫɹ ɧɚ

ɟɞɢɧɢɰɭ ɩɥɨɳɚɞɢ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɧɚɯɨɞɢɬɶɫɹ ɧɚ ɨɞɧɨɦ

ɭɪɨɜɧɟ Ʌɚɧɞɚɭ) (ɫɦ. ɡɚɞɚɱɭ) ɪɚɜɧɚ ɩɥɨɬɧɨɫɬɢ ɤɜɚɧɬɨɜ ɦɚɝ-

ɧɢɬɧɨɝɨ ɩɨɬɨɤɚ

)

, ɩɪɨɧɢɡɵɜɚɸɳɟɝɨ ɞɜɭɦɟɪɧɵɣ ɫɥɨɣ:

2/12// rceHn

)) !

, (2.2)

ɝɞɟ

ec 2/

! )

 ɤɜɚɧɬ ɦɚɝɧɢɬɧɨɝɨ ɩɨɬɨɤɚ. ɂɡ (2.2) ɜɢɞɧɨ,

ɱɬɨ ɤɚɠɞɨɦɭ ɫɨɫɬɨɹɧɢɸ, ɡɚɧɹɬɨɦɭ ɧɚ ɭɪɨɜɧɟ Ʌɚɧɞɚɭ, ɫɨɨɬ-

ɜɟɬɫɬɜɭɟɬ ɩɥɨɳɚɞɶ, ɪɚɜɧɚɹ .

2 r

ɉɥɨɬɧɨɫɬɶ ɫɨɫɬɨɹɧɢɣ N(E) ɞɜɭɦɟɪɧɨɝɨ ɷɥɟɤɬɪɨɧɧɨɝɨ

ɝɚɡɚ ɜ ɩɨɩɟɪɟɱɧɨɦ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɢɦɟɟɬ ɜɢɞ ɧɚɛɨɪɚ ɷɤɜɢ-

ɞɢɫɬɚɧɬɧɵɯ ɞɟɥɶɬɚ-ɮɭɧɤɰɢɨɧɧɵɯ ɩɢɤɨɜ, ɪɚɡɧɟɫɟɧɧɵɯ ɩɨ

ɷɧɟɪɝɢɢ ɧɚ ɜɟɥɢɱɢɧɭ

! '

(ɫɦ. ɡɚɞɚɱɭ).

ɄȼȺɇɌɈȼɕȿ ɗɎɎȿɄɌɕ ɏɈɅɅȺ

_________________________________________________________________________________________________________________________________________________________________________________________________

Ɋɢɫ. .2.2

ɉɥɨɬɧɨɫɬɶ ɫɨɫɬɨɹɧɢɣ g(E) ɢ ɩɨɩɟɪɟɱɧɚɹ ɩɪɨɜɨɞɢɦɨɫɬɶ

ɤɚɤ

ɮɭɧɤɰɢɢ ɤɨɧɰɟɧɬɪɚɰɢɢ ɷɥɟɤɬɪɨɧɨɜ n/n

ɜ ɰɟɥɨɱɢɫɥɟɧɧɨɦ ɤɜɚɧ-

ɬɨɜɨɦ ɷɮɮɟɤɬɟ ɏɨɥɥɚ. Ɉɛɥɚɫɬɢ ɞɟɥɨɤɚɥɢɡɨɜɚɧɧɵɯ ɧɨɫɢɬɟɥɟɣ ɜ

ɩɥɨɬɧɨɫɬɢ ɫɨɫɬɨɹɧɢɣ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɨɛɥɚɫɬɹɦ ɪɟɡɤɨɝɨ ɢɡɦɟɧɟɧɢɹ

ɩɨɩɟɪɟɱɧɨɣ ɩɪɨɜɨɞɢɦɨɫɬɢ.

ɉɪɢ ɧɚɥɢɱɢɢ ɩɪɢɦɟɫɟɣ ɪɚɫɫɟɹɧɢɟ ɷɥɟɤɬɪɨɧɨɜ ɪɚɡɦɚɡɵɜɚɟɬ

ɪɟɡɤɢɟ ɩɢɤɢ ɜ ɷɧɟɪɝɟɬɢɱɟɫɤɢɟ ɪɚɡɪɟɲɟɧɧɵɟ ɡɨɧɵ ɤɨɧɟɱɧɨɣ

ɲɢɪɢɧɵ (ɪɢɫ.2.2). Ʌɟɝɤɨ ɜɢɞɟɬɶ, ɱɬɨ ɭɦɟɧɶɲɚɹ ɢɥɢ ɭɜɟɥɢ-

ɱɢɜɚɹ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɦɵ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɫɛɥɢɠɚɟɦ ɢɥɢ

ɪɚɡɞɜɢɝɚɟɦ ɡɨɧɵ Ʌɚɧɞɚɭ ɩɨ ɷɧɟɪɝɢɢ. ɉɪɢ ɢɡɦɟɧɟɧɢɢ ɤɨɧ-

ɰɟɧɬɪɚɰɢɢ ɧɨɫɢɬɟɥɟɣ (ɢɥɢ ɩɪɢ ɮɢɤɫɢɪɨɜɚɧɧɨɦ ɡɧɚɱɟɧɢɢ

ɤɨɧɰɟɧɬɪɚɰɢɢ, ɧɨ ɫ ɢɡɦɟɧɟɧɢɟɦ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ H) ɦɟɧɹ-

ɟɬɫɹ ɩɨɥɨɠɟɧɢɟ ɭɪɨɜɧɹ Ɏɟɪɦɢ E

- ɦɚɤɫɢɦɚɥɶɧɨɣ ɷɧɟɪɝɢɢ,

ɞɨ ɤɨɬɨɪɨɣ ɡɚɩɨɥɧɟɧɵ ɷɥɟɤɬɪɨɧɚɦɢ ɭɪɨɜɧɢ (ɪɢɫ.2.2). ȿɫɥɢ

ɋɈȼɊȿɆȿɇɇɕȿ ɉɊɈȻɅȿɆɕ ɎɂɁɂɄɂ ɌȼȿɊȾɈȽɈ ɌȿɅȺ

_________________________________________________________________________________________________________________________________________________________________________________________________

ɧɚɯɨɞɢɬɫɹ ɦɟɠɞɭ ɞɜɭɦɹ ɫɨɫɟɞɧɢɦɢ ɡɨɧɚɦɢ Ʌɚɧɞɚɭ j ɢ

j+1, ɬɨ ɜɫɟ ɫɨɫɬɨɹɧɢɹ ɧɚ j- ɭɪɨɜɧɹɯ ɡɚɩɨɥɧɟɧɵ. ɗɬɨ ɫɨɨɬɜɟɬ-

ɫɬɜɭɟɬ, ɫɨɝɥɚɫɧɨ (2.2), ɩɨɥɧɨɣ ɞɜɭɦɟɪɧɨɣ ɤɨɧɰɟɧɬɪɚɰɢɢ

2/2/

ljcjeHjnn

. (2.3)

ɋɨɨɬɧɨɲɟɧɢɟ (2.3) ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɢ ɢɡ ɜɵɪɚɠɟɧɢɹ ɞɥɹ

ɞɜɭɦɟɪɧɨɣ ɩɥɨɬɧɨɫɬɢ ɫɨɫɬɨɹɧɢɣ (ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ 2.7):

() [ ( /)] 

! 

ȿɫɥɢ ɩɨɞɫɬɚɜɢɬɶ ɫɨɨɬɧɨɲɟɧɢɟ (2.3) ɜ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɩɨɩɟ-

ɪɟɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ

(1.3) ɨɛɵɱɧɨɝɨ ɷɮɮɟɤɬɚ ɏɨɥɥɚ,

ɩɨɥɭɱɢɦ

= = 25812,808…Oɦ /

= 1,2,3..... (2.4)

/2 e!

ɗɬɭ ɜɟɥɢɱɢɧɭ ( ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɩɥɚ-

ɬɨ) ɧɚɡɵɜɚɸɬ ɞɚɠɟ “1 Klitzing” ( ~ 25 ɄɈɦ).

! / e

Ɉɰɟɧɢɦ, ɫɤɨɥɶɤɨ ɫɬɭɩɟɧɟɤ IQHE (ɭɪɨɜɧɟɣ Ʌɚɧɞɚɭ i) ɦɵ

ɛɭɞɟɦ ɧɚɛɥɸɞɚɬɶ, ɜ ɩɨɥɹɯ ɞɨ 1 Ɍɥ. ȿɫɥɢ ɬɢɩɢɱɧɚɹ ɞɜɭɦɟɪ-

ɧɚɹ ɤɨɧɰɟɧɬɪɚɰɢɹ n =i/ ɩɨɪɹɞɤɚ 10

2 r

ɫɦ

-2

( ɫɨɨɬɜɟɬɫɬ-

ɜɟɧɧɨ, ɨɛɴɟɦɧɚɹ ~ 10

ɫɦ

-3

), ɩɪɢ ɤɨɬɨɪɨɣ ɧɚɛɥɸɞɚɟɬɫɹ

ɤɜɚɧɬɨɜɵɣ ɏɨɥɥ, ɚ r

~ 100 ɚɧɝɫɬɪɟɦ, ɬɨ i ~ 1-5.

Ⱦɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɨɛɴɹɫɧɢɬɶ ɧɚɛɥɸɞɚɟɦɵɟ ɷɤɫɩɟɪɢɦɟɧ-

ɬɚɥɶɧɨ ɲɢɪɨɤɢɟ ɩɥɚɬɨ

ɢ ɦɢɧɢɦɭɦɵ

, ɜɜɨɞɢɬɫɹ ɩɪɟɞ-

ɩɨɥɨɠɟɧɢɟ ɨ ɫɭɳɟɫɬɜɨɜɚɧɢɢ ɧɚ ɤɪɚɹɯ (“ɤɪɵɥɶɹɯ”) ɡɨɧ Ʌɚɧ-

ɞɚɭ ɫɜɹɡɚɧɧɵɯ ɫɨɫɬɨɹɧɢɣ ɧɨɫɢɬɟɥɟɣ ɡɚɪɹɞɚ, ɧɟ ɫɩɨɫɨɛɧɵɯ

ɭɱɚɫɬɜɨɜɚɬɶ ɜ ɷɥɟɤɬɪɨɩɪɨɜɨɞɧɨɫɬɢ. Ɍɨ ɟɫɬɶ ɜɫɹ ɡɨɧɚ ɫɥɚɝɚ-

ɟɬɫɹ ɤɚɤ ɢɡ ɥɨɤɚɥɢɡɨɜɚɧɧɵɯ (ɡɚ ɫɱɟɬ ɩɪɢɦɟɫɟɣ, ɤɭɥɨɧɨɜɫɤɨ-

ɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɢ ɞɪɭɝɢɯ ɩɪɢɱɢɧ) ɫɨɫɬɨɹɧɢɣ, ɧɟ ɫɩɨɫɨɛ-

ɧɵɯ ɩɪɨɜɨɞɢɬɶ ɬɨɤ ɜ ɩɪɨɞɨɥɶɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ, ɬɚɤɢɢɡɞɟ-

ɄȼȺɇɌɈȼɕȿ ɗɎɎȿɄɌɕ ɏɈɅɅȺ

_________________________________________________________________________________________________________________________________________________________________________________________________

ɥɨɤɚɥɢɡɨɜɚɧɧɵɯ, ɦɨɝɭɳɢɯ ɩɟɪɟɧɨɫɢɬɶ ɬɨɤ. Ɍɟɨɪɟɬɢɱɟɫɤɢɟ

ɪɚɫɱɟɬɵ ɩɨɤɚɡɵɜɚɸɬ (ɜɩɟɪɜɵɟ ɷɬɢ ɜɨɩɪɨɫɵ ɫ ɬɨɱɤɢ ɡɪɟɧɢɹ

ɪɚɫɫɟɹɧɢɹ ɧɚ ɯɚɨɬɢɱɟɫɤɨɦ ɩɪɢɦɟɫɧɨɦ ɩɨɬɟɧɰɢɚɥɟ ɛɵɥɢ ɪɚɫ-

ɫɦɨɬɪɟɧɵ Ɏ.Ⱥɧɞɟɪɫɨɧɨɦ - ɢ ɬɚɤɚɹ ɥɨɤɚɥɢɡɚɰɢɹ ɧɚɡɵɜɚɟɬɫɹ

ɚɧɞɟɪɫɨɧɨɜɫɤɨɣ), ɱɬɨ ɩɪɚɤɬɢɱɟɫɤɢ ɜɫɹ ɡɨɧɚ ɡɚɩɨɥɧɟɧɚ ɥɨɤɚ-

ɥɢɡɨɜɚɧɧɵɦɢ ɧɨɫɢɬɟɥɹɦɢ, ɩɪɢ ɷɬɨɦ ɱɟɦ ɛɨɥɟɟ ɧɢɡɤɨɪɚɡɦɟɪ-

ɧɚɹ ɫɢɫɬɟɦɚ, ɬɟɦ ɦɟɧɶɲɟ ɞɨɥɹ ɞɟɥɨɤɚɥɢɡɨɜɚɧɧɵɯ ɫɨɫɬɨɹɧɢɣ,

ɬɚɤ ɱɬɨ ɜ ɱɢɫɬɨ ɞɜɭɦɟɪɧɨɦ ɫɥɭɱɚɟ ɞɟɥɨɤɚɥɢɡɨɜɚɧɧɚɹ ɨɛ-

ɥɚɫɬɶ ɨɫɬɚɟɬɫɹ ɬɨɥɶɤɨ ɜ ɛɟɫɤɨɧɟɱɧɨ ɭɡɤɨɦ ɩɨɹɫɤɟ ɩɨ ɷɧɟɪɝɢɢ

ɜɛɥɢɡɢ ɫɟɪɟɞɢɧɵ ɡɨɧɵ Ʌɚɧɞɚɭ (ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɞɥɹ ɨɛɪɚɡɰɚ

ɤɨɧɟɱɧɨɣ ɬɨɥɳɢɧɵ ɩɨɹɫɨɤ ɷɧɟɪɝɢɣ ɫ ɞɟɥɨɤɚɥɢɡɨɜɚɧɧɵɦɢ

ɧɨɫɢɬɟɥɹɦɢ ɪɚɫɲɢɪɹɟɬɫɹ).

ɋɟɪɟɞɢɧɚɦ ɧɚɛɥɸɞɚɟɦɵɯ ɫɬɭɩɟɧɟɤ (ɩɥɚɬɨ) ɯɨɥɥɨɜɫɤɨɣ

ɩɪɨɜɨɞɢɦɨɫɬɢ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɪɚɫɩɨɥɨɠɟɧɢɟ ɭɪɨɜɧɹ Ɏɟɪɦɢ

ɩɨɫɟɪɟɞɢɧɟ ɦɟɠɞɭ ɭɪɨɜɧɹɦɢ Ʌɚɧɞɚɭ, ɚ ɩɟɪɟɯɨɞɧɵɣ ɭɱɚɫɬɨɤ

ɦɟɠɞɭ ɞɜɭɦɹ ɩɥɚɬɨ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɧɚɯɨɠɞɟɧɢɸ E

ɜ ɰɟɧɬɪɟ

ɭɪɨɜɧɹ Ʌɚɧɞɚɭ, ɬ.ɟ. ɜ ɨɞɧɨɦ ɢɡ ɦɚɤɫɢɦɭɦɨɜ ɩɥɨɬɧɨɫɬɢ ɫɨ-

ɫɬɨɹɧɢɣ (ɪɢɫ.2.2). ɉɟɪɟɯɨɞ ɨɬ ɨɞɧɨɣ ɫɬɭɩɟɧɶɤɢ ɤ ɞɪɭɝɨɣ ɩɪɢ

ɭɦɟɧɶɲɟɧɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɫɨɩɪɨɜɨɠɞɚɟɬɫɹ “ɡɚɥɢɜɤɨɣ”

ɷɥɟɤɬɪɨɧɚɦɢ ɜɫɟ ɧɨɜɵɯ ɡɨɧ Ʌɚɧɞɚɭ.

Ɋɚɫɫɦɨɬɪɢɦ ɤɚɱɟɫɬɜɟɧɧɨ ɩɨɜɟɞɟɧɢɟ ɦɚɝɧɢɬɨɫɨɩɪɨɬɢɜɥɟ-

ɧɢɹ ɢ ɯɨɥɥɨɜɫɤɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɤɨɧɰɟɧ-

ɬɪɚɰɢɢ ɜ ɞɜɭɦɟɪɧɨɦ ɫɥɨɟ. ɉɭɫɬɶ E

ɜɧɚɱɚɥɟ ɪɚɫɩɨɥɚɝɚɟɬɫɹ ɜ

(ɲɢɪɨɤɨɣ) ɨɛɥɚɫɬɢ ɥɨɤɚɥɢɡɨɜɚɧɧɵɯ ɫɨɫɬɨɹɧɢɣ ɤɚɤɨɝɨ-

ɧɢɛɭɞɶ j-ɝɨ ɭɪɨɜɧɹ (ɧɚɩɪɢɦɟɪ, ɧɚ ɜɟɪɯɧɟɦ, ɛɨɥɶɲɟɦ ɩɨ

ɷɧɟɪɝɢɢ ɤɪɵɥɟ ɡɨɧɵ). Ʌɨɤɚɥɢɡɨɜɚɧɧɵɟ ɧɨɫɢɬɟɥɢ ɧɟ ɭɱɚɫɬ-

ɜɭɸɬ ɜ ɷɥɟɤɬɪɨɩɪɨɜɨɞɧɨɫɬɢ. Ⱦɟɥɨɤɚɥɢɡɨɜɚɧɧɵɟ ɫɨɫɬɨɹɧɢɹ,

ɧɚɩɪɨɬɢɜ, ɦɚɤɫɢɦɚɥɶɧɨ ɡɚɩɨɥɧɟɧɵ, ɢ ɩɪɨɜɨɞɹɬ ɛɟɡɞɢɫɫɢɩɚ-

ɬɢɜɧɨ ɬɨɤ (ɩɨɷɬɨɦɭ

->0), ɬ.ɤ. ɩɪɢɧɰɢɩ ɉɚɭɥɢ ɡɚɩɪɟɳɚɟɬ

ɞɢɫɫɢɩɚɬɢɜɧɵɟ ɩɟɪɟɯɨɞɵ (ɜɫɟ ɫɨɫɟɞɧɢɟ ɩɨ ɷɧɟɪɝɢɢ ɫɨɫɬɨɹ-

ɧɢɹ ɡɚɧɹɬɵ ɥɨɤɚɥɢɡɨɜɚɧɧɵɦɢ ɧɨɫɢɬɟɥɹɦɢ). ɋɥɟɞɭɟɬ ɨɬɦɟ-

ɬɢɬɶ, ɱɬɨ ɩɨɫɥɟɞɧɟɟ ɨɛɫɬɨɹɬɟɥɶɫɬɜɨ ɩɪɢɜɨɞɢɬ ɬɚɤɠɟ ɤ ɭɫɥɨ-

ɜɢɸ

->0, ɬ.ɤ. ɧɟɫɥɨɠɧɨ ɩɨɤɚɡɚɬɶ ɫɜɹɡɶ ɤɨɦɩɨɧɟɧɬ ɬɟɧɡɨ-

ɪɚ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɢ ɩɪɨɜɨɞɢɦɨɫɬɢ:

ɋɈȼɊȿɆȿɇɇɕȿ ɉɊɈȻɅȿɆɕ ɎɂɁɂɄɂ ɌȼȿɊȾɈȽɈ ɌȿɅȺ

_________________________________________________________________________________________________________________________________________________________________________________________________

;

2222

XYXX

XXXY

XYXX







 



Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɧɚɲɟɣ ɞɜɭɦɟɪɧɨɣ ɫɢɬɭɚɰɢɢ ɫ ɢɫɱɟɡɧɨɜɟ-

ɧɢɟɦ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɢɫɱɟɡɚɟɬ ɢ ɩɪɨɜɨɞɢɦɨɫɬɶ (ɢ ɧɚɨɛɨɪɨɬ).

Ɍ.ɤ. ɜɫɟ ɞɟɥɨɤɚɥɢɡɨɜɚɧɧɵɟ ɫɨɫɬɨɹɧɢɹ ɪɚɫɩɨɥɨɠɟɧɵ ɩɨ ɷɧɟɪ-

ɝɢɢ ɧɢɠɟ E

, ɬɨ ɤɨɧɰɟɧɬɪɚɰɢɹ ɧɨɫɢɬɟɥɟɣ n ɜ ɧɢɯ ɦɚɤɫɢ-

ɦɚɥɶɧɚ (ɢ ɪɚɜɧɚ ), ɢ

cjeH !

ɢɦɟɟɬ ɤɜɚɧɬɨɜɚɧɧɨɟ

ɡɧɚɱɟɧɢɟ (2.4). ɉɪɢ ɭɜɟɥɢɱɟɧɢɢ ɤɨɧɰɟɧɬɪɚɰɢɢ ɞɨɛɚɜɥɹɟɦɵɟ

ɜ ɞɜɭɦɟɪɧɵɣ ɫɥɨɣ ɧɨɜɵɟ ɧɨɫɢɬɟɥɢ ɩɨɩɚɞɚɸɬ ɜ ɨɛɥɚɫɬɢ ɥɨ-

ɤɚɥɢɡɨɜɚɧɧɵɯ ɧɨɫɢɬɟɥɟɣ, ɩɨɤɚ ɭɪɨɜɟɧɶ Ɏɟɪɦɢ ɧɟ ɩɨɩɚɥ ɜ

ɞɟɥɨɤɚɥɢɡɨɜɚɧɧɭɸ ɨɛɥɚɫɬɶ. Ʉɨɧɰɟɧɬɪɚɰɢɹ ɞɟɥɨɤɚɥɢɡɨɜɚɧ-

ɧɵɯ ɧɨɫɢɬɟɥɟɣ ɩɪɢ ɷɬɨɦ ɧɟ ɢɡɦɟɧɹɟɬɫɹ ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɧɟ

ɢɡɦɟɧɹɟɬɫɹ ɡɧɚɱɟɧɢɟ

. Ɍɚɤ ɛɭɞɟɬ ɩɪɨɞɨɥɠɚɬɶɫɹ ɞɨ ɬɟɯ

ɩɨɪ, ɩɨɤɚ E

ɧɟ ɜɵɣɞɟɬ ɡɚ ɩɪɟɞɟɥɵ ɨɛɥɚɫɬɢ ɥɨɤɚɥɢɡɨɜɚɧɧɵɯ

ɫɨɫɬɨɹɧɢɣ ɢ ɧɟ ɩɨɩɚɞɟɬ ɜ ɨɛɥɚɫɬɶ ɞɟɥɨɤɚɥɢɡɨɜɚɧɧɵɯ ɫɨ-

ɫɬɨɹɧɢɣ ɧɚ j+1 ɭɪɨɜɟɧɶ. ɉɪɢ ɷɬɨɦ ɤɨɧɰɟɧɬɪɚɰɢɹ ɧɨɫɢɬɟɥɟɣ ɜ

ɨɛɥɚɫɬɹɯ, ɡɚɧɢɦɚɟɦɵɯ ɞɟɥɨɤɚɥɢɡɨɜɚɧɧɵɦɢ ɫɨɫɬɨɹɧɢɹɦɢ,

ɧɚɱɧɟɬ ɢɡɦɟɧɹɬɶɫɹ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɢɡɦɟɧɟɧɢɸ ɭɪɨɜɧɹ Ɏɟɪ-

ɦɢ, ɷɬɨɦɭ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɩɟɪɟɯɨɞɧɵɣ ɭɱɚɫɬɨɤ ɦɟɠɞɭ ɞɜɭɦɹ

ɫɨɫɟɞɧɢɦɢ ɩɥɚɬɨ

(ɪɢɫ.2.2). ȿɫɬɟɫɬɜɟɧɧɨ, ɢɡ-ɡɚ ɢɡɦɟɧɟɧɢɹ

ɤɨɧɰɟɧɬɪɚɰɢɢ ɞɟɥɨɤɚɥɢɡɨɜɚɧɧɵɯ ɧɨɫɢɬɟɥɟɣ ɪɟɡɤɨ ɜɨɡɪɚɫɬɟɬ

(ɢ

). Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫɨɨɬɧɨɲɟɧɢɟ (2.4) ɜɵɩɨɥɧɹɟɬɫɹ

ɜ ɢɧɬɟɪɜɚɥɟ ɷɧɟɪɝɢɣ, ɪɚɜɧɨɦ ɳɟɥɢ ɜ ɫɩɟɤɬɪɟ ɞɟɥɨɤɚɥɢɡɨ-

ɜɚɧɧɵɯ ɫɨɫɬɨɹɧɢɣ. Ʌɨɤɚɥɢɡɨɜɚɧɧɵɟ ɫɨɫɬɨɹɧɢɹ ɢ ɢɝɪɚɸɬ

ɪɨɥɶ ɫɜɨɟɨɛɪɚɡɧɨɝɨ ɛɭɮɟɪɚ (ɷɧɟɪɝɟɬɢɱɟɫɤɨɣ ɳɟɥɢ), ɪɚɡɞɟ-

ɥɹɸɳɟɝɨ ɞɟɥɨɤɚɥɢɡɨɜɚɧɧɵɟ ɫɨɫɬɨɹɧɢɹ ɩɨ ɷɧɟɪɝɢɢ.

Ɍɚɤ ɨɛɴɹɫɧɹɟɬɫɹ ɰɟɥɨɱɢɫɥɟɧɧɵɣ ɤɜɚɧɬɨɜɵɣ ɷɮɮɟɤɬ ɏɨɥ-

ɥɚ (IQHE). Ɂɚɦɟɬɢɦ, ɱɬɨ ɢɡ ɜɵɲɟɢɡɥɨɠɟɧɧɨɝɨ ɫɥɟɞɭɟɬ, ɱɬɨ

ɭɜɟɥɢɱɟɧɢɟ ɤɨɧɰɟɧɬɪɚɰɢɢ ɩɪɢɦɟɫɟɣ ɩɪɢɜɨɞɢɬ ɤ ɭɲɢɪɟɧɢɸ

ɩɥɚɬɨ IQHE (ɞɨ ɢɡɜɟɫɬɧɵɯ ɩɪɟɞɟɥɨɜ).

ɄȼȺɇɌɈȼɕȿ ɗɎɎȿɄɌɕ ɏɈɅɅȺ

_________________________________________________________________________________________________________________________________________________________________________________________________

ɑɬɨ ɤɚɫɚɟɬɫɹ ɭɫɥɨɜɢɣ ɧɚɛɥɸɞɟɧɢɹ ɤɜɚɧɬɨɜɨɝɨ ɷɮɮɟɤɬɚ

ɏɨɥɥɚ, ɬɨ ɷɬɨ:

1) ɞɨɫɬɚɬɨɱɧɨ ɫɢɥɶɧɵɟ ɦɚɝɧɢɬɧɵɟ ɩɨɥɹ ( > 1 Ɍɥ), ɱɬɨɛɵ ɪɚɫ-

ɫɬɨɹɧɢɟ ɦɟɠɞɭ ɫɨɫɟɞɧɢɦɢ ɭɪɨɜɧɹɦɢ Ʌɚɧɞɚɭ ɧɟ ɩɟɪɟɤɪɵ-

ɜɚɥɨɫɶ ɢɯ ɲɢɪɢɧɨɣ, ɨɛɭɫɥɨɜɥɟɧɧɨɣ ɩɪɢɦɟɫɹɦɢ;

2) ɞɨɫɬɚɬɨɱɧɨ ɧɢɡɤɢɟ ɬɟɦɩɟɪɚɬɭɪɵ kT <<

~ 1-5 K, ɱɬɨ-

ɛɵ ɬɟɦɩɟɪɚɬɭɪɧɵɟ ɮɥɭɤɬɭɚɰɢɢ ɷɧɟɪɝɢɢ ɬɚɤɠɟ ɧɟ “ɡɚɦɚ-

ɡɚɥɢ” ɩɨɞɭɪɨɜɧɢ Ʌɚɧɞɚɭ;

3) ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɚɹ ɞɜɭɦɟɪɧɚɹ ɤɨɧɰɟɧɬɪɚɰɢɹ ɧɨɫɢɬɟɥɟɣ

(>10

ɫɦ

-2

), ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɩɪɚɤɬɢɱɟɫɤɢ ɦɟɬɚɥɥɢɱɟ-

ɫɤɨɣ ɩɪɨɜɨɞɢɦɨɫɬɢ ɢɧɜɟɪɫɢɨɧɧɨɝɨ ɫɥɨɹ;

4) ɢ, ɤɨɧɟɱɧɨ, ɫɭɳɟɫɬɜɨɜɚɧɢɟ ɞɜɭɦɟɪɧɨɝɨ ɜ ɮɢɡɢɱɟɫɤɨɦ

ɫɦɵɫɥɟ ɝɚɡɚ ɧɨɫɢɬɟɥɟɣ ɡɚɪɹɞɚ.

ȼ ɩɨɫɥɟɞɧɟɟ ɜɪɟɦɹ ɢɧɬɟɧɫɢɜɧɨ ɨɛɫɭɠɞɚɟɬɫɹ ɜɨɡɦɨɠɧɨɫɬɶ

ɧɚɛɥɸɞɟɧɢɹ IQHE ɜ ɜɢɯɪɟɜɨɣ ɫɬɪɭɤɬɭɪɟ ɜɵɫɨɤɨɬɟɦɩɟɪɚ-

ɬɭɪɧɵɯ ɫɜɟɪɯɩɪɨɜɨɞɧɢɤɨɜ (ȼɌɋɉ). ɉɪɢ ɛɨɥɶɲɢɯ ɩɨɥɹɯ ɦɨ-

ɝɭɬ ɜɵɩɨɥɧɢɬɶɫɹ ɭɫɥɨɜɢɹ ɧɚɛɥɸɞɟɧɢɹ IQHE ɞɥɹ ɞɜɭɦɟɪɧɵɯ

ɜɢɯɪɟɣ (ɮɥɸɤɫɨɢɞɨɜ) ɜ ɤɚɱɟɫɬɜɟ “ɧɨɫɢɬɟɥɟɣ ɡɚɪɹɞɚ”, ɢɦɨ-

ɠɟɬ ɩɪɨɤɜɚɧɬɨɜɚɬɶɫɹ, ɧɚɩɪɢɦɟɪ, ɧɚɦɚɝɧɢɱɟɧɧɨɫɬɶ

(J.Dziarmaga, 1996).

Ɂɚɞɚɱɢ.

Ɂɚɞɚɱɚ 2.1. ɇɚɣɬɢ ɷɧɟɪɝɢɢ ɢ ɜɨɥɧɨɜɵɟ ɮɭɧɤɰɢɢ ɷɥɟɤɬɪɨɧɚ ɜ ɦɚɝɧɢɬɧɨɦ

ɩɨɥɟ (ɡɚɞɚɱɚ ɨɛ ɭɪɨɜɧɹɯ Ʌɚɧɞɚɭ) ɜ ɩɟɪɢɨɞɢɱɟɫɤɨɦ “ɹɳɢɤɟ” L

, L

Ɋɟɲɟɧɢɟ:

ɍɪɚɜɧɟɧɢɟ ɒɪɟɞɢɧɝɟɪɚ:

])/(/)/][(2/1[

;

AcerimHEH

! 

ww\\

ȼɵɛɟɪɟɦ ɤɚɥɢɛɪɨɜɤɭ

AHy H H  (,,); (,,00 00 )

const.

. ȿɫɥɢ ɭɱɟɫɬɶ,

ɱɬɨ ɨɩɟɪɚɬɨɪ Ƚɚɦɢɥɶɬɨɧɚ ɤɨɦɦɭɬɢɪɭɟɬ ɫ p

, p

[



];[



]; ,Hp Hp p p

XZXZ

00const

ɜɨɥɧɨɜɭɸ ɮɭɧɤɰɢɸ ɢɳɟɦ ɜ ɜɢɞɟ:

ɋɈȼɊȿɆȿɇɇɕȿ ɉɊɈȻɅȿɆɕ ɎɂɁɂɄɂ ɌȼȿɊȾɈȽɈ ɌȿɅȺ

_________________________________________________________________________________________________________________________________________________________________________________________________

)()])(/exp[(),,( yzpxpizyx

 ! .

ɉɨɞɫɬɚɜɥɹɹ ɟɟ ɜ ɭɪɚɜɧɟɧɢɟ ɒɪɟɞɢɧɝɟɪɚ, ɩɨɫɥɟ ɧɟɤɨɬɨɪɵɯ ɩɟɪɟɨɛɨɡɧɚ-

ɱɟɧɢɣ ɢɦɟɟɦ ɭɪɚɜɧɟɧɢɟ:

 



yy Ep m

eH mc y p c eH

()( /)

/; /

;

ɗɬɨ ɭɪɚɜɧɟɧɢɟ ɝɚɪɦɨɧɢɱɟɫɤɨɝɨ ɨɫɰɢɥɥɹɬɨɪɚ ɫ ɢɡɜɟɫɬɧɵɦ ɪɟɲɟɧɢɟɦ 

ɩɨɥɢɧɨɦɚɦɢ ɗɪɦɢɬɚ H

, ɢ ɢɡɜɟɫɬɧɵɦ ɫɩɟɤɬɪɨɦ. ȿɫɥɢ ɜɜɟɫɬɢ ɨɛɨɡɧɚɱɟ-

ɧɢɹ:

CZH

mpElyyz

!/]2/[2;/)(

 

ɬɨ ɩɨɥɭɱɚɟɦ ɭɪɚɜɧɟɧɢɟ ɧɚ ɦɨɞɢɮɢɰɢɪɨɜɚɧɧɵɟ ɦɧɨɝɨɱɥɟɧɵ ɗɪɦɢɬɚ:

0)(

MOM

ɢ ɪɟɲɟɧɢɟ:

f

 

 

nnn

ndzzz

xxzHxzHzzHzH

zzHzn

210

!2)()(

;....128)(;24)(;2)(;1)(

];2/exp[)()(;12

GSMM

Ɉɤɨɧɱɚɬɟɥɶɧɨ ɜɵɩɢɫɵɜɚɟɦ:

Ep n p m

yyylHyyllc

nZ C Z

nn Hn HH

() ( /) / ;

() exp([ ]/ ) ([ ]/ ); /



 

12 2

ɇɨɪɦɢɪɨɜɤɚ ɧɚ ɟɞɢɧɢɰɭ ɩɪɢɜɨɞɢɬ ɤ ɫɥɟɞɭɸɳɟɦɭ ɡɧɚɱɟɧɢɸ ɞɥɹ ɩɪɟ-

ɞɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɝɨ ɦɧɨɠɢɬɟɥɹ:

ɄȼȺɇɌɈȼɕȿ ɗɎɎȿɄɌɕ ɏɈɅɅȺ

_________________________________________________________________________________________________________________________________________________________________________________________________

2/14/10



S M nl

Ɂɚɞɚɱɚ 2.2. ɉɨɤɚɡɚɬɶ, ɱɬɨ ɤɜɚɞɪɚɬ ɪɚɞɢɭɫɚ ɩɪɟɰɟɫɫɢɢ ɷɥɟɤɬɪɨɧɚ ɜ

ɩɨɩɟɪɟɱɧɨɦ ɦɚɝɧɢɬɧɨɦɭ ɩɨɥɸ ɧɚɩɪɚɜɥɟɧɢɢ, ɬ.ɟ. ɫɪɟɞɧɟɟ ɜɢɞɚ <x

ɞɥɹ n-ɝɨ ɭɪɨɜɧɹ Ʌɚɧɞɚɭ ɪɚɜɟɧ 2(n+1/2)l

Ɂɚɞɚɱɚ 2.3. ɇɚɣɬɢ ɩɥɨɬɧɨɫɬɶ ɫɨɫɬɨɹɧɢɣ ɢɞɟɚɥɶɧɨɝɨ ɷɥɟɤɬɪɨɧɧɨɝɨ

ɝɚɡɚ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ.

Ɋɟɲɟɧɢɟ.

ɋɨɝɥɚɫɧɨ ɨɩɪɟɞɟɥɟɧɢɸ ɩɥɨɬɧɨɫɬɢ ɫɨɫɬɨɹɧɢɣ ɡɚɩɢɲɟɦ:

NE E E

dp E E p

() ( ) ( ( ))  

³³

Ɍ.ɤ. ɩɨ ɤɨɦɩɨɧɟɧɬɚɦ y, p

ɡɚɞɚɱɚ ɛɵɥɚ ɪɟɲɟɧɚ (ɢ ɩɪɨɤɜɚɧɬɨɜɚɧɚ), ɷɬɢ

ɮɚɡɨɜɵɟ ɩɟɪɟɦɟɧɧɵɟ ɡɚɦɟɧɟɧɵ ɧɨɜɵɦ ɤɜɚɧɬɨɜɵɦ ɱɢɫɥɨɦ n. ɍɱɬɟɦ, ɱɬɨ

ɢɡ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ 1.2.1 ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ

ɢɦɩɭɥɶɫɚ p

: Ip

I<eHL

/c (ɢɡ ɨɩɪɟɞɟɥɟɧɢɹ ɫɞɜɢɝɚ ɤɨɨɪɞɢɧɚɬ y

). Ɍɨɝɞɚ

ɦɨɠɧɨ ɢɧɬɟɝɪɚɥ ɩɨ p

ɜɡɹɬɶ, ɢ ɢɦɟɟɦ ɨɤɨɧɱɚɬɟɥɶɧɨ:

VeH

dp E p m n

ZZC

()

[/ (/ 

f

)] 2

ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɞɚɟɬ

VeH

mE n NE

()

[ ( /)] ; [/ /]





212

!!12

ȼ ɬɨɱɤɚɯ

!

(/12)

ɩɥɨɬɧɨɫɬɶ ɫɨɫɬɨɹɧɢɣ ɢɦɟɟɬ ɨɫɨɛɟɧɧɨɫɬɢ

 ɤɨɪɧɟɜɵɟ ɪɚɫɯɨɞɢɦɨɫɬɢ. ɂɯ ɜɵɫɨɬɚ ɢ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɧɢɦɢ ɨɩɪɟɞɟ-

ɥɹɟɬɫɹ ɜɟɥɢɱɢɧɨɣ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ɉɪɢ ɫɥɚɛɨɦ ɩɨɥɟ ɦɵ ɜɢɞɢɦ ɧɚ “ɩɶɟ-

ɞɟɫɬɚɥɟ”

NE E()~

ɫɥɚɛɵɟ ɩɟɪɢɨɞɢɱɟɫɤɢɟ ɜɫɩɥɟɫɤɢ ɨɫɰɢɥɥɹɰɢɣ (ɞɟ-

Ƚɚɚɡɚ-ɜɚɧ-Ⱥɥɶɮɟɧɚ). ɇɚɪɢɫɨɜɚɬɶ N(E) ɤɚɤ ɮɭɧɤɰɢɹ E, H.

Ɂɚɞɚɱɚ 2.4 ɉɨɥɭɱɢɬɶ ɜ ɩɪɟɞɟɥɟ ɩɨɥɹ H, ɫɬɪɟɦɹɳɟɝɨɫɹ ɤ ɧɭɥɸ,

ɨɛɵɱɧɭɸ ɩɥɨɬɧɨɫɬɶ ɫɨɫɨɹɧɢɣ.

ɋɈȼɊȿɆȿɇɇɕȿ ɉɊɈȻɅȿɆɕ ɎɂɁɂɄɂ ɌȼȿɊȾɈȽɈ ɌȿɅȺ

_________________________________________________________________________________________________________________________________________________________________________________________________

Ɋɟɲɟɧɢɟ:

[ ( /)] ; { ( /)} / ;

() /

En N dxEx E

NE Vm mE

 # 



!!!

ZZZ

12 12 2

Ɂɚɞɚɱɚ 2.5 Ⱦɥɹ ɡɚɞɚɧɧɨɣ ɷɧɟɪɝɢɢ Ɏɟɪɦɢ E

ɧɚɣɬɢ ɩɟɪɢɨɞ ɨɫɰɢɥɥɹ-

ɰɢɣ ɩɥɨɬɧɨɫɬɢ ɫɨɫɬɨɹɧɢɣ ɤɚɤ ɮɭɧɤɰɢɸ ɨɛɪɚɬɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ.

Ɉɬɜɟɬ

1121

cmE H

cmE

nFn



!!(/)

;[ ]'

Ɂɚɞɚɱɚ 2.6 ɉɨɥɭɱɢɬɶ ɩɟɪɢɨɞ ɨɫɰɢɥɥɹɰɢɣ ɞɥɹ ɛɥɨɯɨɜɫɤɢɯ ɷɥɟɤɬɪɨ-

ɧɨɜ.

Ɋɟɲɟɧɢɟ

: ɪɟɡɭɥɶɬɚɬ ɩɨɥɭɱɢɦ ɞɜɭɦɹ ɫɩɨɫɨɛɚɦɢ

ɚ) Ɉɛɨɛɳɢɦ ɩɪɟɞɵɞɭɳɟɟ ɜɵɪɚɠɟɧɢɟ, ɭɱɬɹ, ɱɬɨ ɞɥɹ ɛɥɨɯɨɜɫɤɢɯ ɷɥɟɤɬɪɨ-

ɧɨɜ ɧɚ ɦɟɫɬɟ m ɫɬɨɢɬ ɰɢɤɥɨɬɪɨɧɧɚɹ ɦɚɫɫɚ:

ddScE

)2/1(21

;

1 

ɍɱɢɬɵɜɚɹ, ɱɬɨ ɯɚɪɚɤɬɟɪɧɵɣ ɦɚɫɲɬɚɛ ɢɡɦɟɧɟɧɢɹ ɩɥɨɳɚɞɢ ɨɪɛɢɬɵ - E

ɨɧ ɦɧɨɝɨ ɛɨɥɶɲɟ, ɱɟɦ ɪɚɡɧɢɰɚ ɦɟɠɞɭ ɩɨɞɡɨɧɚɦɢ Ʌɚɧɞɚɭ (E

~ 10 ɷȼ,

~10

-4

ɷȼ), ɫ ɜɵɫɨɤɨɣ ɬɨɱɧɨɫɬɶɸ E

dS/d

~ S. Ɉɤɨɧɱɚɬɟɥɶɧɨ ɩɨɥɭ-

ɱɚɟɦ:

)(/)2/1(2

EcSneH

S



ɛ) ɡɚɦɟɧɢɦ ɦɚɫɫɭ ɰɢɤɥɨɬɪɨɧɧɨɣ ɦɚɫɫɨɣ ɜ ɷɧɟɪɝɢɢ ɷɥɟɤɬɪɨɧɚ, ɢ ɧɚɩɢɲɟɦ

ɪɚɡɧɢɰɭ ɷɧɟɪɝɢɣ n ɢ n+1 ɨɪɛɢɬɵ:

)/(2





HS  dcdSHeEE

, ɨɬɫɸɞɚ , ɭɱɢɬɵɜɚɹ, ɱɬɨ ɩɪɨɢɡɜɨɞ-

ɧɭɸ ɦɨɠɧɨ ɫ ɜɵɫɨɤɨɣ ɬɨɱɧɨɫɬɶɸ ɪɚɫɩɢɫɚɬɶ ɤɚɤ (E

>> !

dS d S E S E E E

nnn

/[()()]/[

]

 

11

ɩɨɥɭɱɚɟɦ:

2)()(





S  HceESES

ɢɥɢ

2)const()(





S HcenES

ɄȼȺɇɌɈȼɕȿ ɗɎɎȿɄɌɕ ɏɈɅɅȺ

_________________________________________________________________________________________________________________________________________________________________________________________________

Ɉɬɫɱɢɬɵɜɚɹɫɶ ɨɬ ɧɭɥɟɜɨɣ (ɩɨ n) ɨɪɛɢɬɵ, ɩɨɥɭɱɚɟɦ ɬɨɬ ɠɟ ɨɬɜɟɬ ɞɥɹ

ɩɟɪɢɨɞɚ ɨɫɰɢɥɥɹɰɢɣ:

' {}

()

cS E

Ɂɚɞɚɱɚ 2.7 ɇɚɣɬɢ ɩɥɨɬɧɨɫɬɶ ɫɨɫɬɨɹɧɢɣ ɜ ɞɜɭɦɟɪɧɨɦ ɫɥɭɱɚɟ, ɟɫɥɢ

ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɧɚɩɪɚɜɥɟɧɨ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɩɥɨɫɤɨɫɬɢ ɫɢɫɬɟɦɵ, ɢ

ɩɨɥɟ ɞɨɫɬɚɬɨɱɧɨ ɫɢɥɶɧɨɟ, ɬɚɤ ɱɬɨ ɮɚɤɬɢɱɟɫɤɢ ɫɩɢɧɵ ɷɥɟɤɬɪɨɧɨɜ ɫɨɧɚ-

ɩɪɚɜɥɟɧɵ ɩɨ ɩɨɥɸ.

Ɋɟɲɟɧɢɟ

: ɋɥɟɞɭɟɬ ɭɛɪɚɬɶ ɢɦɩɭɥɶɫ p

ɢɡ ɡɚɞɚɱɢ, ɢ ɜɫɟ ɢɧɬɟɝɪɢɪɨɜɚ-

ɧɢɹ ɩɨ ɧɟɦɭ, ɬɨɝɞɚ ɩɥɨɬɧɨɫɬɶ ɫɨɫɬɨɹɧɢɣ ɛɭɞɟɬ ɢɦɟɬɶ ɜɢɞ:



)]2/1([

)(

ɉɨɥɭɱɢɥɫɹ ɧɚɛɨɪ ɷɤɜɢɞɢɫɬɚɧɬɧɵɯ ɞɟɥɶɬɚ-ɩɢɤɨɜ. ɇɚ ɩɪɚɤɬɢɤɟ ɩɪɢɦɟɫɢ

ɪɚɡɦɚɡɵɜɚɸɬ ɩɢɤɢ ɜ ɡɨɧɵ (ɧɚɪɢɫɨɜɚɬɶ).

Ɂɚɞɚɱɚ 2.8 ɋɤɨɥɶɤɨ ɷɥɟɤɬɪɨɧɨɜ ɜɦɟɳɚɟɬ ɨɞɢɧ ɭɪɨɜɟɧɶ Ʌɚɧɞɚɭ ɢ

ɤɚɤɨɜɚ ɤɨɧɰɟɧɬɪɚɰɢɹ ɷɥɟɤɬɪɨɧɨɜ ɱɟɪɟɡ ɱɢɫɥɨ ɡɚɧɹɬɵɯ ɭɪɨɜɧɟɣ i.

Ɉɬɜɟɬ

;

SSS

ɉɨɫɥɟɞɧɟɟ ɫɨɨɬɧɨɲɟɧɢɟ ɝɨɜɨɪɢɬ, ɱɬɨ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨ ɧɚ ɤɚɠɞɵɣ ɭɪɨ-

ɜɟɧɶ ɩɪɢɯɨɞɢɬɫɹ ɤɪɭɝ ɪɚɞɢɭɫɨɦ ɨɤɨɥɨ ɦɚɝɧɢɬɧɨɣ ɞɥɢɧɵ.

Ɂɚɞɚɱɚ 2.9 ɇɚɣɬɢ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɏɨɥɥɚ

H ɜ ɫɥɭɱɚɟ, ɟɫɥɢ

ɩɨɥɧɨɫɬɶɸ ɡɚɩɨɥɧɟɧɨ i ɭɪɨɜɧɟɣ Ʌɚɧɞɚɭ.

Ɉɬɜɟɬ

8.25812)/(2/,/1

ienecHnecR

XYH

08 Ɉɦ/i.

ɇɚ ɫɚɦɨɦ ɞɟɥɟ ɤɨɧɰɟɧɬɪɚɰɢɹ n ɡɚɞɚɧɚ, ɢ ɱɢɫɥɨ ɡɚɧɹɬɵɯ ɭɪɨɜɧɟɣ ɟɫɬɶ

ɮɭɧɤɰɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ . ɇɚ ɩɪɚɤɬɢɤɟ ɨɬɤɥɚ-

eHcnHi /2)( !

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