�4E�j khfdlf bgefic�� (�4E�A ()&�] ���� ��4E�J�
�. �4E��\mT��:P (A>)
�/11m�/18m�/25m�/2
�. T3�:Pm�4w1�s$L (�n))
�/9m�/16m�/23 ��/�7 <8 �����C
�. �4�� (������ut) (`/)
5/30m6/6m6/13m(6/20x7&OH)
�. �4E�sY��� (Z��w^�mT��mT3�) (,6)
� /2�m7/�m7/11 � �/18 �_�M�
�4E�B (Z&5] 201� (9vT��sqw"={�!v)��8RwB#sT��
(��^�G�W1^�G�%poT��8Rzr) (�*)2�8RwT���'0T��� ( X)3�T��"=I (T��BA�-B2aMRIyw"=) (FI)4�T��"=II (}��~�QKm^�UVm?^yw"=) (@�)5�T��"=III (T��Y�B+Nw�;8<�yw"=) (D>) 6. B#I ��B�s�48#� (.>)7. B#II ([w�B#wS5sB#�w��|�"=� (�*)
#�
2F#�+/G2. 6 =E8D45C7?95C��-#�2. 7 ���>;A-#��"2. 8 $��
����� ������ ������� �&� ! (telH075-753-3755)[email protected]
�.�',8@5<0http://www.ltm.kyoto-u.ac.jp/lecturenote23:6CBE<��1*%��.(��)'%
2[) /.0 RXNWIJVMTOJV�'=)
!�\"(H��8E��A&�Y��1��?>Z5CDCD@�:*KQULXA���
�%?Y+��A�,H�6;3?3Z&�A�$
KQULX ε
&����
f
-!
�!
KQULX ε
&��
n-!
�!
KQULXεH�:&�A��BRUPSV��<�4DFE
�7KQULX@2E#�A�H�6�G9E=
�
f ∝ exp −εkBT
⎛
⎝ ⎜
⎞
⎠ ⎟
�
kBTexp $ = &', e=2.718,,,�:
2M �'&( EJBI=>HAFC>H��3 �
"��6��N#��4��K!")!?DG@JL68-*:
"��6�$<�.1+:EJB��6��
?DG@J ε
���
n
?DG@Jε<�0��6��7EJB��2�,9;:
?DG@J ε
���
n
%�
��
↓ /!��
�
n = expε − µkBT
⎛
⎝ ⎜
⎞
⎠ ⎟ −1
⎡
⎣ ⎢
⎤
⎦ ⎥ −1
EJBI=>HAFC>H������27�"6��-��?DG@J6 /!��54:
2X���&%' NUITDESHOKES��8��� ;��V��)?W8����V��9/W
;��7<MPMP:"�1@���;!�;�,
��;"�;-:�C�5(
���,��C�?�1#:!�;�<JR:9@(19B4�*6*@��<*2A$�1@(V��W
NUITDESHOKES��C+./3����7<���,
��FLQGU;�0"���:)@(*5=7>�0"�C1@(V��;��W
�
v ≠ 0, v = v0
2L���"!# BI>H9:G=D?:G��-���
V
J���.(/�76K
��/�$��
��/�$�8�36
J>I@IHEI<K
�,1)2*+$6%T<2.17K,1��/�7�6
��AE;C
� 0�M'.�4>F>F-�5�&6
��/�76
021 =−=Δ PPP
1P 2P
26����� -3)2$&1(/*&1� ���
+%0.7���������30nm�+%0.�#��� ���"!
+%0.�#������"!
4'&,1���530nm�(2π�1cm)�10m/s=20mm3/s
�
Δp = ρgh
22���
��� ���.-/#�����
V
Tλ42.17KT
Tλ42.17KT
Vc
,���%)+�"&��&���##'%(! *��
���%)+�"&��&Tλ"��$*��
?
0���Vc��"&ΔP431
�
ΔP = P1 − P2
�
ΔP ∝ v
�
ΔP = 0
1P 2P
�
ΔI
�
ω ∝k
I + ΔI
2F ��&%' ���A=B1 ����
���05 ����.+*�9-�9���05����4"*��,9-
��42) ���� ρs 1��4(8���� ρn4���
TλH2.17KT
����G��;?B<E� 3)8;D>C@E:�-2)!��#�05100%328
����G
67$);?B<E� 3)8;D>C@E:�/!��#�05��
V
�
ρ = ρs + ρn
�
ρs
�
ρn
�
ρ
1P 2P
����C �#+��%1���:=5;,�������)����$
4�0*$/�2 31�����,��4�3*"�,�2
2B���
�! ���<7>)�����
�����C6@8?9A4�&*"D�4�-*"
����C6@8?9A4�'D�4�.
T<2.17K(��#/��%1��:=5;��
�
�
ρv = ρsvs + ρnvn = 0
�
ρs
�
ρn
�
ρs
�
ρn
�
˙ Q
�
vs
�
vn
����R�����SURSUBOGNIPS
��� ΔT 7)>4.@+� 65>1;68 �� Δp +�! ��+�-=?5-?9�,�0
2T$�'&( ���JFL4$��#
DPHPKPC
��%��NPMOE�6�/2��7�3$�A"2:<*Q
�
Δp = ρS ΔT
�
T + ΔT
�
ρs
�
T
2I'��/.0 *��
��� #@�J�-
'���A*���?�2��,�<%)7DC
��,�@G 57H2A:@��@*F$9⇒��ρ�!ΦA�=8;@�&F$81��@B3>��*?A�;�>24�!4"+��9C=6E?A�&@�Dv4�9C
x
x
y
�
C
C
v
�G(9C�DHA�8>2
�
Ψ = ρ exp iφ( )
�
Ψ 2 = ρ , exp(iφ) = e iφ = cos(φ) + isin(φ)
�
j = −i!2m
Ψ*∇Ψ−Ψ∇Ψ*( ) = ρ!m∇φ = ρv
�
Γ = v⋅ dℓC∫ =
"m
∇φ⋅ dℓC∫ =
"m
φ fin −φini( ) = 0�
φ �
φ
�
v
2F���(') #��
�D� 3>�?E.+>6��:AB57/7>
���7�G %
���7�5:��9�@?>.*#���9�"@�0>����:��$�9���@�>4<8*&;&;9�2-?7,
�9�1D��E.#�1?4#��C
r v�?9!1=&;&;9�2-�1?7,
C
v
�
Γ = v⋅ dℓC∫ =
"m
∇φ⋅ dℓC∫ =
"m
φ fin −φini( )
�
Γ =!m
φ fin −φini( ) =!m
× 2πN =hm
× N (N = 0,±1,±2,,,)
�
exp iφ( ) = exp i φ + 2πN( )( )
�
Γ = v⋅ dℓC∫ = v × 2πr
v ="mN ×
1r
29������ ���
r v
���.��-�)#+��46758!���-� '1: �.�� 0.��
��
���+/�����.�*��'1$+/*",�
���%2(�/��&,�.
�3&���
�
Γ = v⋅ dℓC∫ = v × 2πr
v ="mN ×
1r
�
v
�
r
2I���'&( !�
!�:��
r v
!�:��9�4.7��BEFCH-�#�9��1?J ⇒ NO
�:��,>:�$
��
!�0@2�9<�%:�:=+8�-*?
��"�:
����6��"�: ADG91?/76��BEFCH:��A�
�:�3��BEFCH;
N=2,3,,:�;N�:N=1:�9�,@5)���A7?
�
Ψ = ρ exp iφ( )
�
E ∝ v 2 ∝ N 2
�
v
�
ρ
�
r