yamagata universityct(1−e −t/τ)!ηγ" 0 t τ =gγ! 0 t σ(t) t/τ σ(t)!gγ(t)! #t
TRANSCRIPT
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σ1(t) = Gγ 1(t)
σ 2 (t) = η γ 2 (t)
G
η
γ 1
γ 2
σ 2
σ1
σ1
σ 2
“ �”
“�����”
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G
η
γ 1
γ 2
γ
σ
σ
σ (t) = σ1(t) = σ 2 (t)
γ (t) = γ 1(t) + γ 2 (t)
σ1(t) = Gγ 1(t)
σ 2 (t) = η γ 2 (t)
γ (t) = γ 1(t) + γ 2 (t)
γ 1(t) =1Gσ1(t) =
1Gσ (t)
γ 2 (t) =
1ησ 2 (t) =
1ησ (t)
γ (t) = γ 1(t) + γ 2 (t)
=1Gσ (t) + 1
ησ (t)
γ 1(t) =
1Gσ (t)
dσ (t)dt
+1τσ (t) = G dγ (t)
dtτ ≡
ηG� ��
�� G���������������
5,=/
4 �%$�����+)�����<�:γ 1(+0) = γ (+0) = γ 0
t
γ(t)
0
γ0
���“:?”0293 t = +0 �5,�7���:?02����;�6?�?��!" '&"#�02������
γ 2 = ∞ σ 2 =η γ 2 = ∞ σ =σ 2 = ∞���(.>B8A1�5,�-�����C�
γ 2 (+0) = 0���0293�!" '&"#�02����D
t
σ(t)
0
Gγ0 ?
σ 1(+0) = Gγ 1(+0) = Gγ 0σ 1(t) = Gγ 1(t)%$�����5,�@*��
σ (t) =σ 1(t) σ (+0) =σ 1(+0) = Gγ 0+)�5, = %$�5,
σ (+0) = Gγ 0∴
!�)�
t > 0 �� γ (t) = γ 0 ����%+������dγ (t)dt
= 0
σ (t) = Gγ 0e− t /τ
��� t > 0 ��
G(t) = σ (t)γ 0
= Ge− t /τ
' t > 0 -���.�!�����* �
dσ (t)dt
+1τσ (t) = 0 dσ (t)
dt= −
1τσ (t)���
σ (t)∝ e− t /τ �� σ(t) �"#,#
�$������(&�� σ (+0) = Gγ 0
G(t)
t0
G
�����
G(t) =Ge− t /τ t > 00 t < 0
⎧⎨⎩
τ ≡ηG
τ
G/e
������
�����
G(t)G(t)
G
t t00
���� �����
�������� γ1(t)
t0
γ0
γ1(t)����
σ1(t) = Gγ 1(t)
σ 2 (t) = η γ 2 (t)
=
σ (t)
=
γ2(t)
t
γ0
0
γ2(t)�����������
γ2(t)γ (t) = γ 1(t)+ γ 2 (t) = γ 0
�������
log t
10−1G
10−2G
10−3G
10−4G
10−5G
10G
G
10τ 102τ 103τ10−1τ10−2τ10−3τ τ
log G
( t)
G(t)
G( t)
t
G(t)
0.2G
0.4G
0.6G
0.8G
G
0τ0 2τ 3τ 4τ 5τ 6τ
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�������
#/1'*
dσ (t)dt
+1τσ (t) = G dγ (t)
dt (1)Maxwell����
���)"�3�
γ (t) = γ 0 cosωt#/1'*.$�4���
�!��2������
σ (t) = acosωt − bsinωt%,��� 2���&�5 �2�
�(������ ��!�� (1) �+�0����a, b�-$�����
$# ��"
dσ *(t)dt
+1τσ *(t) = G dγ *(t)
dt (1*)(1)�$# ��
γ (t) = Re γ *(t)⎡⎣ ⎤⎦γ *(t) ≡ γ 0eiω t
(1*) �%�$# ��� σ*(t) �!�������
dRe σ *(t)⎡⎣ ⎤⎦dt
+1τRe σ *(t)⎡⎣ ⎤⎦ = G
dRe γ *(t)⎡⎣ ⎤⎦dt
(1*)��&�� '����
σ (t) ≡ Re σ *(t)⎡⎣ ⎤⎦
(1*) �% σ*(t) �!����
�(1)�% �����
����$# ��
�(1*)��!�γ *(t) ≡ γ 0eiω t
dσ *(t)dt
+ 1τσ *(t) = Giωγ 0e
iωt
+� (1*) �/����-���
iωσ 0*eiωt
1τσ 0*eiωt
iω + 1τ
⎡⎣⎢
⎤⎦⎥σ 0*eiωt = Giωγ 0e
iωt���
�0�*1�%(�"� eiωt
σ 0* = G iω
iω + 1τ
γ 0 = Giωτ1+ iωτ
γ 0
�#� )�$ ���.���
���,��/����
eiωt
��/�
σ *(t) = σ 0*eiω t
�' ����&��!����
σ *(t) = σ 0*eiω t = G iωτ
1+ iωτγ 0e
iω t
= Giωτ 1− iωτ( )1+ iωτ( ) 1− iωτ( ) = G
iωτ +ω 2τ 2
1+ω 2τ 2
(1*)���
= G*(ω )γ *(t)
= ′G (ω ) + i ′′G (ω )
′G (ω ) = Gω 2τ 2
1+ω 2τ 2′′G (ω ) = G ωτ
1+ω 2τ 2
���� ���
G*(ω ) = G iωτ1+ iωτ
������
′G (ω ) = G ω 2τ 2
1+ω 2τ 2′′G (ω ) = G ωτ
1+ω 2τ 2
ωτ 1
ωτ 1
1+ω 2τ 2 ≈1
1+ω 2τ 2 ≈ω 2τ 2
′G (ω ) ≈Gω 2τ 2 ′′G (ω ) ≈Gωτ
′′G (ω ) ≈ Gωτ
′G (ω ) ≈G
′G (ω )∝ω 2 ′′G (ω )∝ωMaxwell /
�������
G'( ω
) , G
''(ω
)
ω
G''(ω)
G'(ω)
1τ
2τ
3τ
4τ
5τ
6τ
7τ
8τ
0
G
0.8G
0
0.6G
0.4G
0.2G
0
0.2
0.4
0.6
0.8
1
-3 -2 -1 0 1 2 3
log ωτ
G'( ω
)/G, G
''(ω
)/G
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����� ��
�������
����������
������
log G
'(ω) ,
log G
"(ω
)
log ω
1τ
10τ
G
10G
10−2G
10−3G
10−4G102
τ103
τ10−3
τ10−2
τ10−1
τ
10−1G
G'(ω)
G''(ω)
�� �
��2
��1
/%8'��()/%�
γ (t) =0 (t < 0)γ 0 (t ≥ 0)
⎧⎨⎪
⎩⎪.# t = 0 �!(���6* /%�8'��9
t→∞ �()0-�7�����9 dσdt
→ 0 (t→∞)
σ →Gτ γ 0 =η γ 0
σ (t = 0) = 0/%8'3+���,$�21�����9
dσ (t)dt
+ 1τσ (t) = G γ 0
---(1) ���5��
dσ (t)dt
+ 1τσ (t) = G γ 0t > 0 �
4*�� ��/"�&�,$
σ (t) ≡η !γ 0 − Δσ (t)
dσ (t)dt
+ 1τσ (t) = G !γ 0 ---(1)
dΔσ (t)dt
+ 1τΔσ (t) = 0
Δσ (t)∝ e− t /τdΔσ (t)dt
= − 1τΔσ (t)
t=0 ( σ(t=0)=0 Δσ (t = 0) =η !γ 0 Δσ (t) =η !γ 0e− t /τ
σ (t) =η !γ 0 1− e− t /τ( )
2 )
( ) (
σ (t)η !γ 0
t / τ
σ (t) =η !γ 0 1− e− t /τ( )
3 t >> τη
σ (t) !η "γ 0
4
e− t /τ ! 1− tτ+ ...t << τ )
γ (t) = !γ 0tt (
σ (t) ! Gγ (t)
σ (t) =η !γ 0 1− e− t /τ( ) !η "γ 0 tτ = G !γ 0t
σ(t)
t/τ
σ (t) ! Gγ (t)
t << τ)
G(