Dynamics of formation of soliton conductivity in a 2D-array of linear chains containing commensurate charge density wave near the contact with a normal metal
We make a numerical study of the conversion of conduction electrons into charge density wave (CDW) topological solitons at the interface between a normal metal and a 2D-array of the CDW-carrying linear chains. The interplay of commensurability potential, interchain interaction, and electric field on...
Збережено в:
| Дата: | 1999 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
1999
|
| Назва видання: | Физика низких температур |
| Теми: | |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/137869 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Dynamics of formation of soliton conductivity in a 2D-array of linear chains containing commensurate charge density wave near the contact with a normal metal / Y.V. Pershin, A.S. Rozhavsky // Физика низких температур. — 1999. — Т. 25, № 6. — С. 609-615. — Бібліогр.: 12 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-137869 |
|---|---|
| record_format |
dspace |
| spelling |
nasplib_isofts_kiev_ua-123456789-1378692025-02-23T18:54:14Z Dynamics of formation of soliton conductivity in a 2D-array of linear chains containing commensurate charge density wave near the contact with a normal metal Pershin, Y.V. Rozhavsky, A.S. Низкоразмерные и неупорядоченные системы We make a numerical study of the conversion of conduction electrons into charge density wave (CDW) topological solitons at the interface between a normal metal and a 2D-array of the CDW-carrying linear chains. The interplay of commensurability potential, interchain interaction, and electric field on the dynamics of soliton formation is studied. When the interchain interaction exceeds the commensurability energy, the dynamic mechanism of creation of fractionally charged solitons near the contact is suppressed and specific contact nonlinearity in transport current is not observed. 1999 Article Dynamics of formation of soliton conductivity in a 2D-array of linear chains containing commensurate charge density wave near the contact with a normal metal / Y.V. Pershin, A.S. Rozhavsky // Физика низких температур. — 1999. — Т. 25, № 6. — С. 609-615. — Бібліогр.: 12 назв. — англ. 0132-6414 https://nasplib.isofts.kiev.ua/handle/123456789/137869 en Физика низких температур application/pdf Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Низкоразмерные и неупорядоченные системы Низкоразмерные и неупорядоченные системы |
| spellingShingle |
Низкоразмерные и неупорядоченные системы Низкоразмерные и неупорядоченные системы Pershin, Y.V. Rozhavsky, A.S. Dynamics of formation of soliton conductivity in a 2D-array of linear chains containing commensurate charge density wave near the contact with a normal metal Физика низких температур |
| description |
We make a numerical study of the conversion of conduction electrons into charge density wave (CDW) topological solitons at the interface between a normal metal and a 2D-array of the CDW-carrying linear chains. The interplay of commensurability potential, interchain interaction, and electric field on the dynamics of soliton formation is studied. When the interchain interaction exceeds the commensurability energy, the dynamic mechanism of creation of fractionally charged solitons near the contact is suppressed and specific contact nonlinearity in transport current is not observed. |
| format |
Article |
| author |
Pershin, Y.V. Rozhavsky, A.S. |
| author_facet |
Pershin, Y.V. Rozhavsky, A.S. |
| author_sort |
Pershin, Y.V. |
| title |
Dynamics of formation of soliton conductivity in a 2D-array of linear chains containing commensurate charge density wave near the contact with a normal metal |
| title_short |
Dynamics of formation of soliton conductivity in a 2D-array of linear chains containing commensurate charge density wave near the contact with a normal metal |
| title_full |
Dynamics of formation of soliton conductivity in a 2D-array of linear chains containing commensurate charge density wave near the contact with a normal metal |
| title_fullStr |
Dynamics of formation of soliton conductivity in a 2D-array of linear chains containing commensurate charge density wave near the contact with a normal metal |
| title_full_unstemmed |
Dynamics of formation of soliton conductivity in a 2D-array of linear chains containing commensurate charge density wave near the contact with a normal metal |
| title_sort |
dynamics of formation of soliton conductivity in a 2d-array of linear chains containing commensurate charge density wave near the contact with a normal metal |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
1999 |
| topic_facet |
Низкоразмерные и неупорядоченные системы |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/137869 |
| citation_txt |
Dynamics of formation of soliton conductivity in a 2D-array of linear chains containing commensurate charge density wave near the contact with a normal metal / Y.V. Pershin, A.S. Rozhavsky // Физика низких температур. — 1999. — Т. 25, № 6. — С. 609-615. — Бібліогр.: 12 назв. — англ. |
| series |
Физика низких температур |
| work_keys_str_mv |
AT pershinyv dynamicsofformationofsolitonconductivityina2darrayoflinearchainscontainingcommensuratechargedensitywavenearthecontactwithanormalmetal AT rozhavskyas dynamicsofformationofsolitonconductivityina2darrayoflinearchainscontainingcommensuratechargedensitywavenearthecontactwithanormalmetal |
| first_indexed |
2025-11-24T12:43:51Z |
| last_indexed |
2025-11-24T12:43:51Z |
| _version_ |
1849675724112265216 |
| fulltext |
��� �������
�� ��������
������
����������������� ���!�"��#!$&%!'(�) �*,+"�-�.$/+�0���1!+.��' 2�3�4 5 6�7 8:9<; =<; > 8 ?A@CB D 6 > E 5 F GIH<; J�; K�G 8 > L�7 M 5NB�O O B�4 LN>�P 7 B�8NB�O 5 B�Q 7 P B�8NM B�8 ?�R M P 7 E 7 P GN7 8I>�S TNU > 4 4 > GNB�O Q 7 8�3 > 4�M 6 > 7 8 5VM B�8 P > 7 8�7 8�WM B�LXLA3�8 5 R�4 > P 3NM 6 >�4 W�3N?�3 8 5 7 P G<YI> E 3N8�3 > 4�P 6�3:M B�8 P > M P YV7 P 6:>V8�B�4 LN>�Q L�3�P > Q 2�3�4 5 6 7 8I9�R�4 7 Z =<; >�8 ?A@CB D 6 > E 5 F G<HN; J<; KCG 8 >�L�7 M 5NB�O O B�4 LN>�P 7 B�8:B�O 5 B�Q 7 P B 8�M B 8�?�R M P 7 E 7 P GV7 8I>AS TNU > 4 4 > GVB�O Q 7 8�3 >�4�M 6 >�7 8 5NM B 8�P >�7 8 7 8�WNM B�LXLA3�8 5 R�4 >�P 3NM 6 > 4 W�3N?�3 8 5 7 P GIYI> E 3N8�3 > 4�P 6�3NM B�8 P > M P YN7 P 6N>N8�B�4 LN>�Q L�3�P > Q
[]\
^`_badcAegfih
jkj-hml an_
o c�hp^qhrjsfghptucIo�hp^vewhb^yxmzwe{o�cI|
cNo�\
cX^v_~}�����_ml�l-_`\vhyj�tXc�^
�`_ml�e`�y_bcX^`fieghb^,o-_bcX^kcX^
�
ewh�a�av�p^`f
z�l�_ro���ey�`_ml��
��xp��^`fycIo�\���_r|`��f�^
��_�lko��`��eghb^,o-_ke�o
��cIo��v_�^,hml an_bt,av�`o-_bt
�y�.��� ���`�"�����X �¡��£¢ ¤¥¢�¦ §y¨ �.©�¤"¢ª¦«�¬�®w�®¯±°.²�¡ª¤ª³ª .´�µ
¶!·!¸�¹»º�¼¾½�¿"À»¿ÂÁuÃ<½VÃ�Ä�ÃC¹�ÅNƾº�Ç�ƾÈ
Éʹ»Ë�Ì�¹uºNÍ-ÃCÄκ:¹�ÏÑÐ�Ò�ÁÓ½�Ô�Á�;¿�Õ�Ö!¿�×&½C¿¾¹X¹�ºA½C¿�×-ØÙ�Ú.Ç�¹u¿¾½I¿�Û�Ü�¹u¿�Ä/¹XØ)Ý ÞXß-ÞXàuÙ�Ø�á�Ð�Í�ºA¼�ƾÜ�Ø(â�¼¾º:;½I¿�¹ã)ä�å.æ»çCèNé�ê/ëXì�íNî/ç£ï�ð�î�ñ»ò:åªæ�ç�èNó ôuñ�å
õ�ë�ôXëuç ö¾ëu÷®ø�æ�ï¾ù/æ�ìNú{û�ü�ý�û�þ¾þ�þ�ý�ì�ëXö/ç íNëX÷ ÿ&ë � ì�ù¾æ�ìIú���ý�ûXþ�þ¾þ
�
ëwå"æ��-ëgæ,ï-ù-å«ë�ìÓçCôuæ¾è®í�òAù-÷�ú
ñ��¬òNî-ëgô»ñ�ï-ö/ë�ìAíXç�ñ�ï
ñ��¬ôuñ¾ï-÷-ù�ô�òAçCñ¾ï
ëÂèCë�ôuò�ìAñ�ï/í{ç£ï-òAñyôuî-æ�ì
�ëg÷-ëuï-íXç�ò:ú��.æ¾ö�ë
���� ���ªòNñ�ê�ñÎèCñ� -ç�ô�æ/è�í�ñ/èIç�ò�ñ¾ï-í�æ»ò�òNî-ë�ç£ï-òAë�ì��Iæ�ôuë � ë�ò
�.ëuë�ï�æ�ï�ñ/ì�嫿¾è å«ëuò�æ¾è�æ¾ï�÷�æ�����ä<æ�ì�ìXæ�ú ñ���ò�î/ë ��� ��äIô�æ¾ìAì:ú-ä
ç£ï� èIç�ï-ë�æ�ìªô�î-æ¾ç�ï-í�ó���î-ë®ç�ï-ò�ëuì�ê�è�æÂú ñ���ô�ñ/å«å"ëuï-í�ù/ìXæ � ç�èIç£òNú�ê-ñ¾òAë�ï-òÓç£æ¾èAý�ç£ï-òAë�ìAô�î-æ¾ç�ï{ç£ï-òNë�ìAæ�ôuòXç�ñ�ï�ý�æ»ï-÷�ë¾èCëuô�òAìXçCô��NçCë»èC÷
ñ�ïwò�î/ë ÷�ú/ï-æ�å�çCôuí«ñ��.íAñ�è<ç£òAñ�ï �Iñ�ì�嫿�òÓç£ñ¾ï çCí«í�ò�ù/÷�ç£ë»÷�ó!�
î-ë�ïwò�î-ë�ç�ï-ò�ëuì�ôuî-æ¾çCïwçCï/ò�ëuìXæ�ô�òÓç£ñ¾ïwë�"-ôuë�ëu÷-í"òNî-ë�ô�ñ¾å«å«ë�ï-ä
í�ù�ìXæ � çCèIç�ò:ú�ë»ï�ë�ì
�ú ýÊòAî-ë.÷�ú-ï-æ�å�ç�ô«å"ëuôuî-æ�ï�ç£íAåbñ�� ô�ìAë�æ�òÓç£ñ/ï ñ����VìAæ¾ô�òÓç£ñ¾ï-æ¾èIèCú�ôuî-æ�ì# /ë�÷�í�ñ/èNç�ò�ñ¾ï-í!ï-ë�æ»ì�òNî-ë«ô�ñ¾ï-òAæ�ô�òªç�í
í�ù�ê-ê-ìAë�íAí�ë�÷ æ�ï-÷�í�ê-ëuô»ç$�Nç£ô�ô�ñ¾ï-ò�æ»ô�ò�ï-ñ¾ï�èIçCï�ë»æ�ìXç�ò:ú±çCï�òAì�æ�ï-íAê-ñ�ìAò�ô»ù�ìXì�ëuï-òªç£í.ï-ñ¾ò�ñ � í�ëuìXö�ëu÷�ó
%'& ��( é*)���óIû�+�ó ,�-�ý!)�.�ó ��/-ó102�
3547698;:!< =?>A@CBDB @7E1:!8;F < @#6G@
B�>H@7I < F @76G=$@76�J7K�=?F < L7< F 4�< 6M8*N;O�P 8
E1E 8;4
Q�R!S9T�U*VXW�YZS�[;U*R
\�]!^`_baXc�d�eDf$g;]!h*_�g#i�f;^j_�hMe9f$]!h!dZk2^l_�m�dZk#knf$obdZk#k$]qp!ercMh!g
iX_�s�t�]2u!vMd�e�_wmDs9d�hMe9f$mDf$]qhxm9]ymDv!_lz{_�fH_�s5kne|iMfH_�k$_�o�mDs�fno`}�z|~��
e�m�d�m�_�d�m�k�]Z��m9_�^�u*_�sDd�m�c�s�_�e�}�e7_�_!�y_X� t��#�������M�G�D�Z��z|~
f;e�o�vMd�sDd�o�m�_�s�f$��_�i��!p�d�o�]q^�uMk$_���]!s9iX_�s�u!d�sDd�^y_�m9_�s
∆
_���u
( � ϕ)
����v*_�s�_
∆
f;e�m�vX_rt�d�u�f;h�d�e�f;h't�k$_�g;_Zk�_�o�m�s7]!h
eDu*_�o�mDs�c�^�d�h!i�u!v�d�eC_�t�s9d�iMf$_�h*m�e�i*_� 7f;h*_rmDv!_ro�]!k#k�_�o�mDf$¡*_
o�v�d�sCt!_¢mDs9d�hXe� #_�s�£¥¤w~`¦ o�]!h!i!cXo�mDf$¡!f$m9p§�©¨§]!u*]!k$]Zt�f$o�dZk#k$p
e�m�d��ªk�_«h*]!hMknf?h*_�dZs�u!v�d�e�_¬_��!o�f$m�d�mDf$]qhMe���f;huXd�s9mDfHo�c§knd�s��
e�]!k;f$m�]'hXe�d�hMi¬d�h*mDf;e7]Mk;f$m9]*h�e��je�_�s7¡!_�d�e¢mDv*_b_Zk�_�^l_�h*mDd�sCp
¤¥~y¦ o�vMd�sCt'_®o�d�s9sDfH_�s�e���¨�v*_¯e7]Mk;f°m�]!h±i*_�e�o�s�f;u*mDf$]qh²f;e
^l]!s7_�]qsrk$_�e�e�e7c!o�o�_�eDe9 #c§k³f;h´_���u�kndZh!d�m�f$]!h�]! ymDv!_�h*]!h!g
k;f;hX_�d�s��!cªknµ�m�sDd�h!eDu*]!sCmr}�e�_�_!�|_X� t��#��m�v*_�¶|_�¡�fn_��ye·�*�¹¸M�Z�
º�]��y_�¡*_�sA��]!h*_¯uMs9f;h*o�f;u!d'k�d�e9uX_�o�m�]q ´¤w~`¦»g#u!v*p�e�f$o�e��
¡�fn���Mm�vX_2u!s�]��Gk$_�^«]! �f$hXm9_�s9d�o�m�fH]!h�]! |mDv*_yo�c�sDs7_�h!mDg;o�d�sDs7p!g
f;h't¢¤w~`¦¯g#u�v!d�e�_yi*_� #]!s9^�d�m�f$]!h!e¼�2f$mDv�o�]'hXi!c!o�m�fn]qh�_Zk$_�o�g
mDs9]*h�e��½f;huMd�s7mDf$o�cGkndZs��rm�v*_«h�d�m�c�s�_¬]' ¾¤�~y¦�¿y^l_�mDdZk
_Zk�_�o�m�s�]qiX_Àf?h!m�_�s� 7d�o�_bu!vX_�h*]!^`_�hMdX�³f$erh!]Zm�p*_�m�_�h!mDf;s7_Zk$p
cGh!iX_�s�e9m�]�]!iÁd�h!iÁo�]qhXm�sC]q¡*_�sDe9f;dZk�_���u�knd�hMd�m�f$]*h�e�e�m�f?k#k
dZs9f;eC_�eA�
¨§]�iX_�eCo�sDf$�!_�m�vX_�u!s7]*o�_�e�ew]* Âo�vMd�sCt!_2mDs9d�hXe� #]*sD^yd�mDf°]!h
dAm³mDv!_·¤�~y¦�¿yh!]*sD^2dZk�^`_�mDd*k�f;h'm9_�s� 7d�o�_X��m�v'_�f$i!_�]!k$]Zt!p
]! �u!vMd�e7_»e5k;f;u²o�_�h*m�_�sDe®}�z¼¤³\M�Ã��v!f$o�v_���uMk$]'fnm�e�mDv*_
dZh!dZk�]Zt!p��!_�m9�y_�_�h�m�vX_yzÂ\M¤Äd�h�i�i!f;e�k�]*o�d�m�f$]*h�eÂv!d�ix�!_�_�h
uXc!m2 #]*s9��d�s9i�}�eC_�_X��_X� t��#�©�#Å!�GÆM�D�Z��¨�vX_�uMv*p!e�fno�e`�X_�vMf$h�i
mDv!_Çz�\M¤�f?ebmDv*_¯e7mDs�]qh't�k$p±u!s�]*h!]Zc�h!o�_�i±u*]XkndZs7]!h«_� 7g
#_�o�m��
�G�5£�fC� _X�#�{o�]*h�i*cXo�mDf$]!h¢_Zk�_�o�m�s7]!h!e`f;^l�!_�i!iX_�i�f;h·m�v*_
o�]!h!iXc!o�m�f$]*h®��d�h!i®]! �dÄa'c�d�e�f;g;]*h!_�g#i!f;^l_�h!eDf$]*h�dZk2e�_�^yf;g
o�]!h!iXc!o�m9]qs®d�s7_Çc�hMe7m�d��§k$_¯d5t�d�f;h!e�m�e�_�k; 7g;mDs9d�uMu!f;hZtÈd�hMi
e9cX��e�_�a*cX_�hXm�d��Ge7]!s9u'm�f$]!h¾�!p�m�vX_�¡�dZk$_�h*o�_É�Md�h�i���v!_�s7_
m�vX_�p¯d�sC_´ 7f?h!d*k#k�p¬o�]qhX¡*_�s�m�_�iÇf;h*m9]Ǥw~y¦ uMv!d�e�_Äe�]!k;f;g
m9]!h!e���ÊM�5��Ë�hXm9_�s7o�v�d�f?h¯f$h!m�_�s�d�o�m�fH]!h¯u!sC]*¡'f?i!_�e¢d�t*t�s�_�t�d�g
m�f$]*h®]' �e�]!k;f$m9]!h!e¢f?h*m9]ÃiMf;e�k�]*o�d�m�f$]*h�gCknf$µX_�k�]Z]!u!eA£yz�\!¤�e��
¤©v!dZs#t!_�m�sDd�h!eD #]qsD^�d�m�f$]*h¢mDd�µ*_�e`uMk;d�o�_ hX_�d�s¥mDv*_�o�]*h!mDd�o�m
�2f$m�v�d`h*]!s�^2dZkG^y_�m�dZk���Ë7h�m�vX_wo�f°m�_�i�uXc!�Gk;f$o�d�m�f$]*h�eÌ�
Å!�GÆM�
}�e7_�_2dZkne�]�sC_� #_�s�_�h*o�_�eÂm�vX_�sC_�f;hª�Z��m�v*_�z�\M¤�e|�l_�s�_`m�sC_�dAm9_�i
d�e�m�vX_2e�m�d�mDf$oy]*�*Í9_�o�mDeA�
~yp!h�d�^�fHo�e¼]! {o�]qhX¡*_�sDe�f$]!h��2d�e�e�m�c�i!f$_�i�f;h�d`e�_�s9f$_�e|]*
u!f$]!h*_�_�s�u!dZu*_�s9er�9ÎZ�Â��ÏM�5��Ë7m2�2d�e�e�v!]Z�2h�m�v!dAm uXs�fH]!s�m9]
#]'s�^2d�mDf$]qhÐ]q Ñz�\M¤Òo�]qhMi*c!o�m�fn]'h�e�]Xknf$m�]qhMe�^�d�h�f; #_�e7m
v�f¹t�vMk$pÓh!]*h!mDs9f$¡!f;dZk�f;h!iMf$¡!f;i*cGdZk«�!_�vXd�¡!f$]qsA�¯d�h!iÔm�v*_
u!s�]quX_�s�vMf$_�s9d�s�o�v'pÄ]* �m�f$^l_�e�o�dZk$_�ex�2v!f$o�v�t!]�¡X_�s�h�exm�v*_
o�vMd�s#t�_¬mDs9dZh!eD #]qsD^yd�mDfH]'h²�ydZeb_�e�m�d��Gk;f;eDv*_�i���\Z_Zkn 7g?m�sDd�u!g
u!f;h'tÕf;e½o�]*h�h*_�o�m9_�i¬�yf$m�vÇk$]*o�dZklt�d�u¬i!_� #]qsD^�d�m�f$]*h�e¢f?h
o�]!h!iXc!o�m�f;hZto�v!d�f;hMe���¨�v!_¯u']qm�_�h'm�f;dZk¢�Gd�s9sDf$_�s� #]'s´m�v*_
e9_Zk; 7g;mDs9d�uMu!f;hZt¢f;e ∼ ∆
��d�h!i·i*c�sDf;hZtrm�vX_ym�f;^j_ ∼ Ö−× ∆
m�v*_
a*c�d�e�f;u!dZs7m�fno�k$_�ele9u*_�o�mDs�c�^f;ey^ydAm9o�v*_�i�m9]¢drk$]*o�dZk|¡�dZk$c!_
∆(
TZ�{Ø
) Ù m�v*_�m�f$^y_�]q ¥m�v'_�t�d�uÉi*_� #]'s�^2d�mDf$]!hÉf$e`]! �]!s9iX_�s]'
ω
__
− û } ω__ f$elm�v*_r 7s9_�a*c!_�hXo�p�]! wmDv*_¢z§_�f$_�sDk;e�u!v!]*h!]*h�e
�2v!f$o�v�f;e¼]q Úm�v*_¥]'s�i!_�s¼]q §m�vX_y~y_��!p*_³ 7s�_�a*c!_�h!o�p���¸M�1���D�Z�
m�vX_½f?h!m�_�sCo�vMd�f;h�f;h*m�_�sDd�o�m�f$]*hb�M_�f�h'tÄ]* y]!s�i!_�s�Û Ô }�Û Ô f;em�vX_³m�_�^lu!_�s9d�m�c�sC_³]! �mDv*_�z{_�f$_�s�kneÂmDs9d�hMe9f$mDf$]qh§�Z�'fnm©i*_� 7f;hX_�e
m�vX_ÄmDf;^l_ Ö−× Û Ô ]* ¢mDv!_�f;hXm9_�s7o�v�d�f?h»uXv�d�eC_�o�]!v*_�s�_�h'o�_
Ü Ý'Þ�ß;à á�â�ã5ä�å�ß$æ�ç�à è�é�è�ê¼ë'ì å5í�é�è5ê�å�ß�îMã5ï�ð�ñ�ç�é�ò�æ�óCô�õ�ö9÷�÷�÷
]!h!e�_�m��GË9h�dj�y_�d�µªk$p�o�]*c�uMk$_�i�dZs9sDd�p�]! |vMf1tGvMk�p�o�]*h�i'c!o�mDg
f;h't�o�vMd�f;h!eA���2v*_�h¢Û Ô���� Ö−ω
__ ��� ∆
��m�vX_2e�_�k; 7g?m�s9d�uMu!f;hqt
]! ²_Zk�_�o�mDs�]qhMeÈ]Zo�o�cGs9e�f;hÁf;h!iMf°¡Mf;i*c�d'k»o�v!d�f$hMe�f�hMi*_�g
uX_�hXi!_�h*m�k$p¢�#�§� ÅG�|d�hMi�m�v'_³o�v!d�sCt!_`m�s9d�hMe9 #]!s�^2d�mDf$]!h!e�uXs9]*g
o�_�_�iMe�f$h¾m9�y]�eCm9_�u!eA�©_�d�o�v¾o�v!d�s�d�o�m�_�sDf$�D_�i��!p�f$mDe�]��2h
mDf;^y_X£|m�sDd�hMe9 #_�s�]' lo�]qhMi*c!o�m�f$]!h�_�k$_�o�mDs7]!h!e�f;hXm9]ÉmDv*_¢¡!d�g
k$_�hXo�_³�Md�h�i�f;hrdye9f;h'tGk�_`o�v!d�f$hrd�m
τ∆ ∼ ω
__
− � ��d�hMi� #]!s9^�d�gmDf$]!h�]q �d·o�]Mk#k�_�o�m�f$¡*_�o�v!d�sCt!_�o�d�s�s�fn_�s�f;h´m�v!f;exo�vXd�f$h�d�m
τϕ
��� τ∆
��¨�v'_�mDf$^y_
τϕ
f;elm�v*_¢f$hXm�s9f?h�e�f$o�e�o�dZk�_�]' ¥mDv*_
¤¥~y¦¯g
u!vMd�e7_�º�d�^2f?k$m9]!h!f;d�h®�7¸*�MÅ��5��d�m�Ø � τϕ
f?h!i�fn¡'f?i!g
cGdZk¢o�vMd�s#tM_¬o�d�s�s�fn_�s�e�]��!_�p²m�v*_��{d�t�s�d�hZt!_¬_�a!c�d�mDf$]qhMe
e�c�u!uªk$_�^`_�hXm9_�i¢�!p·m�v*_��!]*c�hXi�d�s�pro�]!h!iMf$mDf°]!h!eA�{¨�v!_�knd�mDg
m�_�sDe®d�s9_« #]!s9^l_�i�i*c�s�f;hZtÈmDv*_«m�f$^y_ÑØ � τ∆
�7Æ�� Ù mDv*_f;hMfHm�f;dZk{u!vMd�e7_yu*_�s�m9c�sC��d�mDf$]qh�f;eÂk$]*o�dZk;f$��_�i�h!_�d�s¼m�v*_yf$h!m�_�s�g
7dAo�_ ]�¡X_�s mDv*_ i�f;eCm�d�hXo�_ ]! mDv*_ ]qsDi*_�s ]q
�
τ∆ ∼ ξ / = Ö− �
� ∆ Ù �2v!_�s7_ ξ / f;e�m�vX_ d�^�uMk;f$m9cMi*_o�]!v*_�s�_�h*o�_�k$_�h't!m�v�f$hÉz|~��{¨�vX_lÍ9c�^2u
δϕ
]' ÂmDv*_�f;h�fHmDf;dZk
uMv!d�e�_�u!s�]q 7f#k$_
ϕ( � =
Ï
)
f;eli*_� 7f?h*_�i��Xp¢m�vX_�o�vXd�s#t!_�o�]!h!g
e�_�s7¡�d�mDf$]qhÑk;d�� f;hÕm�vX_ÄuMs7]*o�_�e9e·]! ¢e7_Zk; 7g;mDs�d�uXu!f;h't���Ë9h!g
iX_�_�i§�2mDv*_�o�]Mk#k�_�o�m�f$¡*_®¤w~y¦ o�vMd�s#t�_�i*_�h�e�f$m9p
ρ
f;h¯d
eDf;hZtGk$_�o�v�d�f;h«f;e�s7_Zknd�m�_�i�m9]¯u!vMd�e7_�t�sDd�iMf°_�hXmÉ¡'f?d�mDv*_
�{s�].. vªknfno�v¢sC_�k;d�m�fn]'h�£
ρ = �
π
∂ϕ
∂�
� }*���
¦¯v*_�h���_Zk�_�o�mDs7]!h!eydZs7_�o�]*h!¡*_�s9m�_�iÉf?h*m9]�m�v*_·¤w~`¦¯g
o�]!h!i!_�h!eDd�m9_X��mDv!_ru!vMd�e9_rd�o�a'c�f$s�_�e�d·k�]*o�dZk©iX_� #]*sD^yd�mDf°]!h
�2fnm�vrmDv*_ h'_�m`u!v�d�eC_ e�v�f? #m�£
δϕ = ϕ(� = ∞) − ϕ(� = − ∞) =
�
π
� }�¸M�
Ë
m��yd�eyeDv*]*�2hÉf;h¾�7Ê��¥m�vMd�m2iXc�sDf$h*tÉm�vX_�_Zk�_�^l_�h*mDd�sCp
dAo�my]* ye7_Zk; 7g;mDs�d�uXu!f;h't�d�m�m�v*_r^y_�m�dZk7¿�z|~Èf;h*m�_�sD 7d�o�_�mDv*_
o�v�d�sCt!_ɸ
�
f$e�m�sDd�h!eD #]*s�^l_�i�f;hXm9]Äd�¤¥~y¦ f;h�dÉeDf;hZtGk$_
o�v�d�f?h§��f�� _X�!m9�`]�_Zk�_�o�mDs7]!h!eÂ�2fHmDv�]*u�u']qeDf$m9_ye�u!f;hMe�d�s�_ye7_Zkn
k$]*o�dZk;f$��_�i�i*c�s�f;hZt�m�vX_¢m�f$^l_
ω
__
−
û ��¨�vXf;e�u!s�]�o�_�eDe�sC_�e�_�^yg
�§k�_�eÇm�v*_��whXi�sC_�_�¡ s�_� �k$_�o�mDf$]qh�f;h�e7cGu*_�sCo�]!h!iXc!o�m9]!s9eA�
¨�vXc�eA�'mDv*_yf;h!f$mDf;dZkGo�]!h!iMfHm�f$]!hxm9]�m�v'_juXv�d�eC_³_�a*cGd�m�f$]*h�e¼]q
^l]*m�fH]!h�k�_�d�i�ejm9]��
= −
¸¢f;h��Úa§�|}�¸X�Z���we¥m�vX_�e7o�dZk�_
ξ /f;el^yc!o�v�k$_�e9e`mDv�d�hÉdZh*pÀf?h*m�sDf;h!eDfHo¢k$_�h*t!m�vÉf?h�m�v*_ru!v�d�eC_
º�d�^2f?k$m9]!h!f;d�h��7¸q�MÅG�5���³_®o�d�h± #]*s�^jc{k;d�m9_�mDv!_®f;h�fHmDf;dZk
o�]!h!i�fnm�fH]!h±d�e�dÇu*]qf?h!mDg7k;f$µ!_¬e�m9_�u� #c�h'o�mDf$]qhÑ�2f$mDv�mDv*_
vX_�f�tXv'mw_�a*c�d*k§m9]
− � π �9ÆX���Ë�h�]*c�sÇu!s�_�¡!f$]Zc�eÇu*c!�Gk;f$o�d�m�f$]!h!eÑ�7ÎG�#��ÏM���y_±vMd�¡*_
e�m9cMi�fH_�i¬m�vX_b_�¡!]Xk�cMm�fH]!h¬]* rm�v*_�f;hMf°mDf;dZkr¤�~y¦ u�sC]' 7f?k$_
�M]�mDv¬d�h!d*k$p*m�f$o�dZk
k$pÃd�hMiÃhXc�^l_�s�f$o�dZk
k$p f$h®m��y]�^y]*i!_Zkne��
�2vX_�h¢e7_Zkn 7g?m�sDd�u!uXf;h*tr]*o�o�c�sDe�£
����f;hÉd�o�_�hXm�s�dZk�o�v�d�f;h���v!f$o�v��!_�k$]!hZt�e`m�]�d�o�k$c�e�m9_�s
]! ®h*_�d�s�_�e7m¬o�v�d�f?h!e®o�]!h*mDd�f$hMf;hZt d�h�f;h'o�]!^�^`_�hMe7cGs9d�m�_
¤¥~y¦²� ¨�v*_�_Zk�_�o�mDs9f$o® 7f$_�k;iÇ�2d�eÉhX]�mÉm�d�µ'_�h�f$hXm9]¯d�o�g
o�]*c�h!my�7ÎM� Ù¸!�yf;h·d�h�f$e�]!k;d�m�_�iro�v!dZf�h·o�]qhXm�d�f;h!f?hZt¢o�]!^�^`_�hMe7cGs9d�m�_
¤¥~y¦ f;h½m�vX_2u!s�_�eC_�hXo�_y]! �d�iXo�g?_Zk�_�o�mDs9f$o� 7f$_�k;iÉ�5��ÏM���
Ë
mr�2d�ere9vX]���h�mDv�d�m�m�vX_Àf;hMfHm�f;dZkyo�]qhMi!f$mDf$]qh®d*k$�yd�p!e
mDs�d�hMe9 #]!s�^2e f$hXm9] eCm�d��§k�_�m�]quX]!k$]ZtXfno�dZkÈ\*f;hX_�g��w]qsDi*]!h
}�\�����e�]!k;f$m�]qhMe���Ë7h�m�vX_w^y]!i*_Zk�]* �h*_�d�s�_�e7m|o�v!dZf�hMe�oZk�cMe9m�_�s
_�d�o�v¢e�]!k;f$m9]*h¢vMd�e�o�v!d�sCt'_�¸
�
�Gd�h�irmDv*_�s7]Mk�_l]' ¼m�vX_y�McGk;µ
m9_�s�^�f$h�m�vX_É\��²_�aXc�d�m�fn]qh�uMk;d�p�eymDv!_¢sC]�k$_r]q yf?h*m9_�sDd�o�g
m�f$]*h��X_�m��y_�_�h�o�v!dZf�hMe¼]' §mDv!_`m9p!u*_ye�f;h
(ϕ / − ϕ û ) �'��v!_�s7_
ϕ / d�h!i ϕ û d�s7_�m�vX_�u�v!d�e�_�e`f;h¢mDv*_�o�_�h*mDsDdZk�d�h!i�hX_�d�s9_�e7mo�vMd�f;h!eA�{Ë9h¢d�o�]q^�^y_�h!e�c�sDd�m9_x¤w~y¦Á�y_ vXd�¡!_y]*��e�_�sC¡!_�i
m�vX_Ó_� 7 #_�o�m ]! �dÓo�v!d�sCt!_ 7s9dAo�mDf°]!h!d'knfH��d�mDf$]!h }�e7_�_!�
_!� t��
�w�5�*�¹¸X�����2v*_�hÉm�vX_�f?h!f$m�f?dZkÌuXs7]! 7f#k$_�iX_�o�d�p!e2f;h'm9] �
7s�d�o�m�fn]qhMdZk
k$p�o�v!d�sCt!_�i�e�]!k;f$m9]*h�e½}�d�h�f;h*m�_�t!_�s!� � ¸bf;e
d�h f$hMi*_�� ]q �o�]q^�^l_�h!e�c�s�d���f�knfHm9p§��_�d�o�v o�d�sDs7pMf�h't
o�vMd�s#t�_X£
� Á =
¸
� ×
� � }��M�
Ë�mÉ��d�ebeDv*]*�yh�f;h²¶Â_� 5�¢��ÏÕm�vMd�mbe9]Xknfnm9]qhMg#d�h!mDf�e�]Xknf$m�]!h
u!d�f$sDe��2fnm�vro�v!d�sCt!_�e
± "$# }��G�`d�s�_yo�s�_�d�m9_�i¢f;h¢d�i'o�g?_�k$_�o�gm�sDfHo� 7f$_Zkni� 7s�]q^dZh�f;hMfHm�f;dZk¥¤�~y¦ uMs7]! 7f?k�_X��mDv*c�e¥t�f$¡Mf�h't
s�f$e�_�m9]¬d�h«d�i!i�fnm�fH]!h!d*k�o�]!h*mDd�o�m�h!]*h�gCk;f;h*_�d�s�fnm9p¯f$hÇm�v*_
¤w~`¦»g?o�]*h�i*cXo�mDf$¡�fHm9p��
Ë7mjf?e`o�_�s�m�d�f;h�k�pÉf;h*m�_�s�_�e7m�f?hZtÀm�]�e�m9c�i'p�mDv!_�_�¡!]!k$c!mDf$]!h
]' �f?h!f$m�f?dZk�¤¥~y¦Òu!s�]q 7f#k$_ dZh!i�f;h*m9_�sDd�o�mDf$]qh·]q ¥u!v!dZe7_�e³f?h
i�f$ 7 #_�s9_�h*m�o�v�d�f?h!ewf;hrd�^y]*s�_wtM_�h*_�sDdZk�¸&% ^l]qiX_Zk9���yvMf$o�v
m�d�µX_�e`f;h*m�]�d�o�o�]*c�h*m`mDv!_�_� 7 #_�o�m�e¥]* �o�]'^l^y_�h�eCc�sDd���f#k;f$m9p§�
f;h*m9_�sDg;o�v!dZf�h·f;h*m9_�sDd�o�mDf$]qhrdZh!i�_�k$_�o�m�sDf$oy 7f$_Zk;i���¨�v�f$e¥u!s7]*��g
k�_�^¯f;e¼h!]Zm�f;h*m�_�t�s�d��{k$_ Ù fHm�f;eÂe7]Mk$¡q_�i�hXc�^y_�s9fno�dZk#k�p�f;h�mDv�f;eu!d�u*_�s��
'ÉU*V)(+*
¤�]!h!eDf$i!_�srmDv*_b¸,%½g#d�s9sDd�pÃ]* �mDv!_�¤�~y¦¯g?o�]!h*mDd�f;hMf�h't
o�vMd�f;h!e��yv�fno�v�]*o�o�cMu*p�m�vX_�e�_�^�f$g
dA��f;e � ≥
Ϫ�©¨�vX_��{d�g
tXsDd�h't!_�d�hr]! ¼m�vX_2e�p!e7m9_�^²f�ej}�e�_�_X��_X� t��#�{¶�_� 5��¸M�Z£
-
=
�
π Ö− .
∑½
∆ /
ω
__ �
∂ϕ ½
∂ �
�
−
Ö−�
�Å
∂ϕ ½
∂�
�
+
+ ∆
�
ω
__�
¸
� � ω 0� o�]*e�1 ϕ ½ +
¸qÛ Ô�32&465 (ϕ ½ − ϕ ½ − û ) +
+ �
π
7− �
8 (ϕ ½ − ϕ9 )
� }�ÅM�
�2v*_�s9_
ϕ ½ i!_�h*]*m9_�e`m�v'_�u!vMd�e7_rf;h�m�v*_ � g?m�v�o�vMd�f;h§� ω / f;em�vX_yo�]*^2^l_�h!e�c�sDd���f#k;f$m9pr 7s9_�a*c!_�hXo�p§��d�hMi
ϕ9 f;eÌm�v*_�u!v!dZe7_d�m � → + ∞
��\*c!o�vÉ #]'s�^]* wmDv*_¢k;d�e�m`m9_�s�^f?h:��a��|}�ÅM�
m�d�µX_�e¥f;h!m�]�dAo�o�]�c�hXmwmDv!_�s7_�hX]qsD^2dZk;f$��d�mDfH]'h·]q ÂmDv!_�u!v!dZe7_
f;hr_�d�o�vro�vMd�f;h¢f$hrm�vX_2uMs7_�e�_�h*o�_�]q �d�hr_Zk�_�o�m�s9fno 7fH_ZkniÚ�
¨�v!_¢_�a*cGd�m�f$]*h�]q �^j]qmDf$]qh¾ #]qs�mDv*_;�{d�t�s�d�hZt�f;d�h®}�ÅM�
v�d�eÌm�v*_� #]qsD^½£
∂
�
χ ½
∂
Ø � −
∂
�
χ ½
∂ < � + = 5?>A@ � (χ ½ + ϕB ) +
+ C e�f
h (χ ½ − χ ½ − � ) + D 5?>E@ (χ ½ − χ ½ + � ) = ε
� }GFX�
HJILK �NM 3O)P �
K�Q Ö �SRUTVR�W =YX � � TVR�W �
KJZ.O\[^]`_ Ö TLa Qcb <
dMöfe g�à ñ9à ó�éih'à ñ9ó5à óDç\j�ålk�m�å�ßHé?n;Þ�ß#õ�ö7÷�÷�÷qõ#ò�ãfo&p�õ?h!ðqd
�2vX_�s7_
< =
¸
∆
Ö− ��� ω
__ � � ε = �¸
π
7− � ω
__ �
∆
� � �
= =
ω /�� � D = ω
__ /
∆
� Û Ô� �ÑdZh!i χ ½ = ϕ ½ − ϕ9 �
}��M�
Ë9h¢d�h*]!h*�5_�sC]� 7f$_Zkni � mDv!_`t�s�]�cGh!i¢e�mDd�m9_2f;eA£
ϕ9 =
d�s7o�eDf;h
(ε)
� }�ÆM�
�|a*c�dAm�fH]!h�}�ÆM�2f?^2uMk;f$_�e¥m�vX_�s9_�e7mDsDf°o�m�fn]'h·]!h�m�v*_�_Zk$_�o�m�sDfHo
7f$_Zk;ir�2v*_�s�_��!prmDv*_ eCm�dA�Gk�_�u�v!d�e�_yo�]!h! 7fHt!cGs9d�m�fn]'h�_���f?e7m�eA£
ε
=
��� � }�Î!�
�2hªk°p¬m�vX_� 9f?_!k�iMe�m�vMd�m·]!�!_�p¬mDv!_�oZ]�h�iXf;mDf;]�hÇ}�ÎM��dZs7_
o*]�h!e�f#i*_qs�_qi* �c�sCm�vX_qsA�
��a*c�dZmDf;]�h½}GFM�©f#e`e�cMu!uGkH_q^l_qh*m�_qi��!p�mDv!_�f#h!f;mDf
d'k�d*h!i
�M]!c�h!iMd�sCpro�]�hMi!f?m�f?]�h!e¥�yv�f?oqvri*_*e�o*s�f?�!_�o�]�hX¡*_qsDe�f$]�hx]�
m�v*_�u�dZf
sX]� X_!k°_Zo*m�s7]Gh!e§f
h*mD]`d�¤�~y¦�g7u!s�]� �f7k°_�f#hwd¼o�_qh'm�sDd*k
o!v!d*f;h
( � =
Ï
)
}�e9_�_`m�v*_�d��!]*¡q_yiMf;e7o�c�eDe9fn]'hx]! �m�vX_yv!f$_�s�d�s�g
o�v!pr]* Âm�f$^y_�ewf?hrm�v!f?ewu!s�]��§k$_�^��Z£
∂χ ½
∂
Ø
à =
/ =
�� }��dX�
χ ½ ( Ø =
Ï
) = −
¸
π θ (ξ
_/ − < ) δ ½$/ � }�Ê����
χ ½ (< =
Ï
) = −
¸
π δ ½ / � }�ÊZo*�
�2vX_�s7_
δ ½ � =
�Z� � = M d�h!i δ ½ � =
Ϫ� � ≠ M Ù ξ
_ / f$e�mDv*_o�]�v*_�sC_�h*o�_`k°_�hAt!m9v
ξ / = Ö− �
× ∆
f$hyc�hXf°m9e©} �X���
ξ
_ / ��� � ÙdZh!i
θ(< )
f;e�mDv*_�ºy_�d�¡!p!e�f;i!_�e9m�_�ur #cGh*o�m�f$]*h��
Ë�h²�2vMd�mà #]Xk
k$]*�jeA���y_«e7]Mk$¡q_ ��a§��} FM����f$m�v²mDv*_
o�]!h!i�fnm�fH]!h!el}�ÊM�yh*c�^l_�s�fHo�d*k#k�pr�!p¢^`_�d�hXe�]! |mDv!_�^y_�m�v*]!i
]! w 7f?h!f$m9_�iMf; 7 #_�s7_�h!o�_�e���¨�v!_�iXf; 7 #_�s�_�h*o�_�_�aXc�d�m�fn]qh�o�]qsDs7_�g
eDu*]!h!iMf$h*t¢m9] ��a§��} FM�`v�d�eÌm�vX_2 #]!s9^
χ ½ ý ¼ +
û»ý�
+ χ ½ ý ¼ − �
�
− ¸ χ ½ ý ¼ ý �
(∆
Ø
) / −
χ ½ ý ¼ ý
+ û + χ ½ ý ¼ ý�
− û −
¸
χ ½ ý ¼ ý��
(∆ < )
� +
+ = 5 >E@ � (χ ½ ý ¼ ý
+ ϕ / ) + D eDf;h (χ ½ ý ¼ ý
− χ � + ��� ��� � ) +
+ D 5f> @ (χ ½ ý ¼ ý
− χ ½ − û�ý ¼ ý�
) = ε
� }*��ÏM�
�2vX_�s7_
∆
ØÚf$e¼m�vX_wmDf;^y_`e�m9_�u§�
∆< f;e¼o�]Z]!s9iMf;h!d�m9_yeCm9_�u��!d�h�i
χ ½�ý � � � = χ� (∆ Øfb � ∆<qX ) �;�Úa*cMd�m�f$]!h�}*��ÏM�¯f$e¬e7]Mk�¡*_�iÈ #]!s
iMf; 7 #_�s7_�h!m|¡MdZk�c!_�eÂ]q ¼u!d�sDd�^y_�m9_�s9eÂd�h�i�d�m©iXf; 7 #_�sC_�hXm|_�h!¡*_�g
k$]!u*_� #c�h*o�m�f$]!h!e�f;h«}�ÊA���A�j¨�vX_Äs�_�e7cGk$m�e�u!s�_�eC_�hXm9_�i¯d�sC_
]*�!mDd�f;h!_�i� #]qs�^�d��
(
b
) =
� Ï*Ï*Ï�}�^yd��
(
b
)
f;e�m�v'_�h*cG^yg
�M_�sl]! ye9fnm9_�e��Z��Ë
m�f;e� #]�cMh�i�f;hbu!dZs7mDf$o�cªknd�s�mDv!d�m hX_�f°mDv!_�s
o�v�d�h't�f;hZt�mDv!_�e�v�d�u'_�]' Ìm�v*_�f?h�fHm�f?dZk�u!_�s7m�c�s���d�m�f$]!h�}�Ê����
}�s�_�o�mDd�hZt�cGk;d�s�]qs�mDs�f$dZhZt!c{k;d�s�e7m�_�uG��h!]*s�f;h*o�s9_�d�e9f?h*tbmDv*_
h!c�^l�!_�s�]q �e�f$m9_�eru!s�]�¡�f?i*_�erd�hXp�e�f�tXhXf; 7f$o�d�h!m�_� 7 #_�o�m�]!h
m�vX_2e�]!k$c!m�f$]!hr]* ��a§��}���ÏM�Z�
� U*R�� (AT��A[nU'RÉ[�R�����[$R�� *E(�Y����![$R
~yp!h�d�^�fHo�e�]* `o�]!h*¡X_�s�e�fn]qh�]q `o�]qhMi*cMo�mDfH]'h�_�k$_�o�mDs9]*h�e
f;h*m9]bd·]qhX_�g
i!f?^y_�h!eDfH]'hXd*k`¤w~`¦ �ydZe2e�m9cMi�fH_�iÄf?h�����Ï��5�
¨�vX_Èe�p!e7m9_�^ f$e�iX_�e7o�s�fn�!_�i��Xp mDv*_Ès�_�i*cMo�_�i _�aXc�d�g
m�f$]*h�}GFM�Z£
∂
�
χ
∂
Ø � − ∂
�
χ
∂< � + = eDf�h � (χ + ϕ9 ) = ε
� }*�q���
Ë9h��`_�dZµ�i*_�o�_Zk�_�sDd�m�f;hqt d�h!i�d�o�o�_Zk$_�sDd�m�f?hZtÐ 7fn_�k;i�e
}��
ε × = � � ÏM�#���`m�v*_�i'p'hMd�^�f$o�eÌ]! �u!v�d�eC_ iX_�¡q_Zk$]'uXe³dZk$]qh'to�]!h*¡!_�h*mDf$]qhMdZkyk;f�hX_�e��wË7hÄd�h�d�o�o�_Zk$_�sDd�m�f?hZt´ 7fH_Zkni�m�vX_¢f;h!g
f$m�f;dZk{uMs7]! 7f?k�_�u!s�]qu!d�tXd�m�_�e�dZk$]!hZt�mDv!_`o�v!d�f$hrµ*_�_�uMf$h*t�eDd� #_
f$m�e��qe�m9_�u!gCknf?µ*_! � #]qsD^�}�ÊZ�{��}&�{fHt��2�*� T �Z�³Ë9h®db�`_�d�µMk$pi!_�o�_Zk$_�s�d�m�f;h't� 7f$_Zkni½}c�ªf¹t|�§�*�#"M�Z�qmDv*_yf$h�f$mDf$d*k�uXs7]! 7f#k$_yk$]qe�_�e
f$m�eÂe�m�d���f#k;f$m�p�d� #m9_�s�eC]'^l_wmDf;^l_³d�hMi�e9uªk;f°mDe�f?h!m�]2o�]q^�^y_�h!g
e9cMs9d��Mf#knfHm�p�e9]Xknfnm9]!h!eÌ}����A�!�2v!f$o�v�sC_�¡X_�s�e9_¥m�vX_�f?s�i!f?s7_�o�mDf$]!h
]' �^l]�mDf$]qhÚ�wd�h�i¾_�¡*_�h!m�c�dZk#k�p�o�]�k#k$_�o�m�h*_�d�s � =
Ϫ�̨�v*_
s�d�iXf;d�m�f$]!h�uMs7]!u!d5t�d�mDf$h*t��2f$mDv�m�v'_³^�d���f;^jc�^Õ¡q_Zk$]qo�fHm9p�f;e
o�k$_�d�s5k$pr]���e�_�s7¡!_�i§�
¨�v!_�u!f$o�m9c�sC_bo�v!d�hZt!_�e¢iMs9d�eCm�f$o�dZk#k�p®�2v*_�h$�
ε× = ��_���go�_�_�iMe�d�mDv�sC_�eDv*]Mk;ib 7f$_Zk;i
ε É ��Ë�h�m�vMf$eyo�d�eC_�mDv*_ro�vXd�s7t!_o�s�_�d�m�f$]*h�iXc�sDf�h't�m�v'_³_�¡!]Xk�c!mDf$]!h�]* �m�vX_³f;hMfHm�f;dZk{u!s�]* 7f#k�_yf;e
]q�Me7_�s9¡*_�i��!]*m�vÉf$hÉd�o�o�_Zk�_�sDd�m�f;hqtb}c�{fHt����q�&%Z�2d�hMiÉi*_�o�_Zkng
_�sDd�m�f?hZt½ 7f$_Zk;i!e`}&�{fHt��|��� W �Z��¨�v*_2sC_�¡!_�s9eDdZk{]* |mDv*_yeDfHt�h�]* o�s�_�d�m9_�iÉo�v!d�sCt'_�el�2fHm�vÉmDv!_�o�vXd�hZt!_r]q ¥m�vX_� 7fn_�k;iÉi�f?s7_�o�g
m�f$]*h�c�hMd�^y�MfHt!c!]*c�e5k�p�f;h!iMf$o�d�m9_�e|mDv!d�m�mDv*_³^l_�o�vMd�h!f;eD^¬]*
m�vX_�o�v!dZs#t!_� #]!s9^�d�m�f$]!h�f;e¥m�vX_�u*]Mknd�s�f$��d�mDf$]qh�]* wd·¤�~y¦
¡�d�o�cXc�^r£�d�m
ε � Ϫ�2m�v'_Ãe7]Mk;f°m�]!h (
Q
)
d�hMi«d�h!mDf�e�]Xknf$m�]!h
(
Q_
)
^l]�¡!_bu!sC]!g�d�h�i¾o�]!h*mDsDdÉm�v'_É_�k$_�o�m�sDf$ob 7fH_Zkni®o�]qsDsC_�g
e�u']qhMi!f;h't�k$p Ù d�m ε � Ï¢eC]�k;fHm9]!h�d�h!i�d�hXm�f?e7]MknfHm�]'h·o�v!d�h*t!_m�vX_�f$sbu']'e�f$m�fn]qhMe���\*c!o�v�d®^y_�o�v�d�h!f?e�^ ]q ·m�vX_�o�vXd�s7t!_
o�s�_�d�m�f$]*hbf;e�s�_�e�u*]!h!eDf$�Gk$_� #]!symDv*_¢e9uX_�o�f$ 7f$o¢h*]!hMk;f;h*_�d�s9fnm9p
]' ¼m�vX_yo�]!h*m�d�o�mwo�]qhMi*cMo�mDf°¡Mf$m9p�����ÏM�5£
M ∼ � √
8
− � É
D + √� − � É
� }*�5¸X�
'©]*m9_`mDv!d�mÂm�v*_lm�v!s�_�e9vX]!k;i� 7fn_�k;i � É ����v!f$o�v�i'_� 7f;hX_�eÂm�v*_]'hXe9_�mw]* Âm�v*_�hX]qhªknf$hX_�d�sÌo�]!h*mDd�o�m�o�]!h!iXc!o�m�f$¡!f$m�p�}*��¸X�Z�ªf;e
i�f$ 7 #_�s9_�h*m¢ 7s�]q^�mDv!_É]*h!_Éh!]*sD^2dZk#k�p¾]��Ge7_�s9¡*_�iÃf?h��McGk;µ
m�sDd�h!eDu*]!s7m��5�*�°¸!����¨�v*_·knd�m�m9_�syf;e`]* w_Zk$_�o�m�sC]'eCm�dAm�fHo�]*s�f�tXf?h
d�h�ix]q §o�]*c�sDeC_wo�d�h!hX]�m�d�uMu*_�d�s�f$h�h*c�^j_�sDf$o�dZk�e�f;^ycªknd�mDf$]!h
]' i�|a§�G}��*���Z�'¨�vX_³^�f$o�s7]!e7o�]!u!f$ow]!s�fHt�f;h�]! §m�vX_wmDv�sC_�eDv*]Mk;i
}*�q���»f?e®m�vX_�o�]*h!o�c�sDs7_�hXo�_��X_�m��y_�_�h�m�vX_«_�hX_�s�t�pÈ]*
e9]Xknfnm9]qhMg#d�h!mDf�e�]Xknf$m�]!h�o�]qhM 7f;h*_�^y_�h*m¢f;h®db^l]�¡�f$h't u!v!dZe7_
u!s�]q 7f#k$_bd�h�i¾m�vX_É_Zk�_�o�mDs9f$ob 7fn_�k;i§�w�2vMfHo�v®m�_�h!iMe�m9]�iMf;e9g
e9]Xk�¡X_ym�vX_3QfQ_g?�!]�cGh!i¢e�mDd�m9_�����ÏM���
% < R�T)(y� %?Q ]
*+* ] K ( T Ø � ] R ],* Q ] X � Ø ] R %&] RVW I�%�Ø � aq� Ø < �SR
T.- % / T K K T <
g�à ñ9à ó�é h!à ñ9ó�à óDç\j�åck�m�å�ßHé?n;Þ�ß#õ�ö7÷�÷�÷*õ#ò�ãfoGpZõ?h!ðqd dMö�ö
� U*R�� (AT��A[nU*R�[�R���� %��7YV*$W �5S (AT³U��ÌR ( �ZT (��5SwY!� ��[HR �
Ë�h®mDv�f;e·^y]*i!_Zky�y_bo�]qhMe9f?i!_�srm�v'_bo�]'h'¡!_�s�eDf°]!h¬f;h¬d
o�_�hXm�s�d*kÂo�vMd�f;hÉ��v!f$o�vbf;e�e7c�sDsC]qcMh�i*_�iÉ�Xp���e7p�^l^y_�m�sDf$g
o�d*k#k�p¢dZs9sDd�hZt�_�i�h'_�d�s�_�e7m`o�vXd�f;h�e��ª¨�vX_ eCp�^y^l_�mDs�p�]! ÂmDv*_
uMs7]*�Gk$_�^ dZk#k�]*�2e®cMe®m9]Èi*_�e�o�s�f$�!_�mDv*_±i*p�hXd�^2f$o�e®]q
o�]!h*¡!_�s9eDf$]qh½�!prm�vX_2 #]Mk
k$]��2f?hZt¢m9�y]�_�a*cMd�m�f$]!h!eA£
∂
�
χ /
∂ � / −
∂
�
χ /
∂ < / +
+ � e�f#h � (χ / + ϕ9 ) +
� D e�f
h (χ / − χ û ) = ε
� }*���qdX�
∂
�
χ û
∂ � / −
∂
�
χ û
∂ < � +
+ � e�f?hY� (χ û + ϕ9 ) + D e�f;h (χ û − χ / ) = ε
� }*�������
�2vX_�s7_
χ / f$e�mDv!_�u!v�d�eC_ f$hrmDv!_lo�_�h*m�sDdZk{o�vMd�f;hrd�h!i χ û f;hhX_�f�tXv'��]*s�f$h't�]!h*_�eA� �|a*c�dAm�fH]!h!e`}*�D�G�³d�s�_ye�c�u!uªk�_�^`_�h!m�_�i
�!p�m�vX_¢o�]!h!iMfHm�f$]!h!e½}�ÊM���3��a*cGd�m�f$]*h�e½}����G�ri�f$ 7 #_�s� 7s�]q^
�Úa§��}*�q��� �!p m�vX_ f;hXm9_�s7o�v�d�f?h f$h!m�_�s�d�o�m�fH]!h m9_�s9^
D 5f>E@ (χ / − χ û ) �¨�v!_`]*¡*_�sDe9f?^2uMk;f; 7f$_�iru!s7]*�Gk$_�^�}���f$m�v*]*c!mÂm�vX_`_�k$_�o�mDs9f$o
7f$_�k;i¯d�hXi¬o�]'^l^y_�h�eCc�sDd���f#k;f$m9p¬uX]�m9_�hXm�f$d*k7���jdZe¢e�]!k$¡!_�i
d�h�dZk$p*m�f$o�dZk
k$pÉf;hɶÂ_� 5��Ϊ�|Ë#my�yd�e`eDv*]*�2h�f?h�¶�_� 5��Î�mDv�d�m
u!d�f$s�]* �e�_Zkn 7g?m�s�d�u�u'_�i�o�]'hXi!c!o�m�fn]qh�_�k$_�o�mDs9]*h�eÂmDsDd�h!eD #]qsD^2e
f;h*m9]Édro�v!d�s�t!_�i�¸
π
g
µ!f?h!µ�k$]�o�dZknfn��_�i�f$hbdro�_�h'm�sDdZk�o�v�d�f?h
d�h�i¬eCc�sDs7]*c�hMi*_�i®�XpÃi�f?u*]!k$_�e·f;hÃhX_�f1tGv*�!]!s9f;h'tÃo�v!d�f$hMe��
¨�vX_�s9_�e7c§k$mw]! wd�h*c�^l_�sDfHo�d'kÚe�m�c�i!p·]q we�d�^`_�uXs9]Z�{k$_�^±f;e
uMk�]*m�m9_�ibf;h:�{fHt��Ú¸ª� T �©¨�v*_�s�_¢d�s�_rm9�y]biMf$e9mDf;h*o�m�f$]*h�e��X_�gm9�y_�_�h�mDv!_�sC_�e�cGk$m�ex]��!mDd�f$hX_�i�d�hXdZk�p!mDfHo�d'k
k$pÄd�h!i¾h*c�^l_�g
s�fHo�d*k#k�p§� �ªf$sDe7m²f;e�mDv*_È_��Gf�e�m�_�h*o�_È]! Çm�v'_ sDd�i!f;d�mDf$]!h
}c�ªf�t��G¸G� T ���jvMf$o�vÉv!d�ej�!_�_�hÉiMs7]!u!u*_�ibf$h��7ÎM�5��\*_�o�]qhMi§�i!_�o�sC_�d�e�_¢]* ymDv*_¢¡!_Zk$]�o�f$m9p�]q lm�v*_�¸
π
g#µ!f;hMµÉ}c�{fHt���¸ª� T �Z��2v!f$o�vÈf;e¾m�v'_»m�p!u!f$o�dZk� #_�d�m9cMs9_Ç]! bmDv!_«e7]Mk;f$m9]*h�g?m9p!u*_
e9]Xk�cXm�f$]!h!e f;h m�v*_ iXf;e�o�sC_�m�_ \qf;h'_�g��³]*sDi*]!h _�aXc�d�g
m�f$]*h¯�5�*���#��¸��5�w¨�v*_Àf?h*o�k$c�eDf$]*h�]! ymDv!_¢o�]!^y^l_�hMe7c�sDd���f�kng
½£×η(Þ ó � ú/ï�æuå«ç ôXí�ñ�� ôXñ¾ï¾ö�ëuìNíAç ñ�ï ñ���ò:î¾ë«ëuè�ë�ôXòNìNñ�ï�í!òNñ�ò:î/ë.ôuñ�å.å.ëXï/í:ù/ìNæ�òNë.ñ¾ï¾ë�ä�÷/ç£åªëXï�íAç ñ�ï�æ»è �'� �pó Û
=
û¾é Í æuôXôXë�è�ëXìNæ�òNç�ï� w�Iç ë�è�÷�é
ε =
/-ó /�+�
� ÷�ëXôXë»è£ëXìNæ�òNç�ï� `�<ç ëuè£÷ é
ε = −
/�ó /D+
Ô æuôXô�ëuè�ëXì�æuòAç ï� w�Iç ëuè�÷Êé
ε =
//ó ��ó���î¾ë«å.ëXô�î¾æ�ï/ç�íNåpñ���òNî¾ë«ê�æ»ç ì�ôXìAëXæ�òAç ñ�ï{ç í!ñ � íNëXì�ö¾ëX÷�
Õ ÷/ëXôXë�è�ëXìNæ�òNç�ï5
�Iç�ëuè£÷ é
ε = −
/-ó �-ó���î�ë.åªëXôXî�æuï-ç íNåpñ���òIî�ëªê�æ»ç ì!ôXì:ëuæuò�ç ñ»ï�ç£í�ñ � íNëXì�ö¾ëX÷ ó
HJILK �NM 3O)P �
K�Q Ö �SRUTVR�W =YX � � TVR�W �
KJZ.O\[^]`_ Ö TLa Qcb <
dMöfo g�à ñ9à ó�éih'à ñ9ó5à óDç\j�ålk�m�å�ßHé?n;Þ�ß#õ�ö7÷�÷�÷qõ#ò�ãfo&p�õ?h!ðqd
f$m�pÉ� = ≠
Ï�f;h �Úa��{}����G����sC_�e�cGk$m�e�f?h�e�c�uXu�sC_�eDe9fn]qhr]* |mDv*_
o�v�d�sCt!_�i¢i!f;u*]Mk$_�e��
¨�d�µ!f;hZt�f;hXm9]2d�o�o�]*c�h'm|m�vX_�_�k$_�o�mDs�fnow 7f$_�k;i�f;h�mDv!_`s��°v§�¹eA�
]!
�|a!e��y}*���G��k�_�d�i!erm�]�¡!d�s9fn]�cGe�uXf$o�m�c�s�_�e��w�2vMf°o�v¬i*_�g
uX_�hXi�]qhxm�v*_¥_�a'c�d�mDf$]qh�u!d�sDd�^y_�m9_�s9eA�+�we|f;h�mDv!_w^l]!i*_Zk�]q
d²eDf;hZtGk�_Ño�vMd�f;h§��mDv*_�mDv!s�_�e�v!]Xkni� 7f$_Zkni�f;e®]Z��e�_�sC¡!_�i§�
�2vMfHo�v�f$e�v!fHt�vX_�slm�vXd�m2f;h�m�vX_�]!h*_�g
iMf$^y_�hMe9f$]*h�dZkw^`]!i*_Zk
dZh!i��2v!fno�v�iX_�u*_�hXi�ex]qh�mDv!_�hXc�^l�!_�s�]q �h'_�fHt�vX�!]qsDf;hqt
o�v�d�f?h!e �É��mDv*_�uMd�s9d�^j_�m�_�sDe = d�h�i D ��d�hMi�e�f�tXh·]! �mDv*_ 7f$_Zk;i���ËCh'o�s�_�d�e�f$h'tÈm�vX_»hXc�^l�!_�s¾]! �o�v!d�f;hMe¬k$_�d�iMe¾m9]
f;hXo�s7_�d�e�f?hZt¢m�vX_2mDv!s�_�e�v!]Xkni� 7f$_Zkni§��Ë�h·�y_�d�µ¢d�o�o�_Zk�_�sDd�m�f;hqt
7f$_Zk;i�e�}
ε× = � Ϫ� �G�Éo�v�d�s�t�_�iǸ π g
µXf;h!µ«^y]Z¡!_�e�f;hÇmDv*_o�_�hXm�s�d*kÂo�v!d�f?hbd�h!i�]qhªk�p�m�v*_rs9dZi!f;d�m�fn]qhbf$el]���e�_�s7¡!_�iÉf;h
mDv!_`h!_�fHt�v*�M]qsDf$h*t�o�v!d�f;hMe��MËCh�v!fHt�vX_�sÂd�o�o�_Zk�_�sDd�m�f;hZt� 7fH_ZkniMe
}
ε× = � Ϫ� �G�r 7s9dAo�mDf°]!h!d'kwo�v!d�sCt'_·o�s�_�d�m�f$]*h�f$e�]��Me9_�s7¡X_�i}c�{fHt���¸ª�&"�� Ù f$m�]*o�o�c�sDe�f;hrmDv*_2o�_�h*m�sDdZk�d�hMi¢f$h¢hX_�f¹t�v*�X]'s�gf;h't�o�vXd�f$h�e�eDf;^`c§k�mDd�h*_�]*c�e5k$p§�©�2vXf$o�v´_��GuMk;d�f;h!e�m�v*_�_�h!g
vMd�h!o�_�^`_�hXm�]! |mDv!_lm�vMs7_�e�v']�k;i¢ 7f$_Zk;i§�
�{f1tMc�s7_�e¸ª�#% d�hXi ¸ª� W eDv*]*� m�v*_ eC]Mk�c!mDf$]qhMe²]q
�|a!eA�³}*���M��f;h®i*_�o�_Zk�_�sDd�m�f;hqt 7f$_ZkniMe��³¨�v*_bi*pMh!d�^2fno�erf;h
�y_�d�µri*_�o�_Zk�_�sDd�m�f;hqt½ 7fH_�k;iMe�}��
ε× = � � ÏG�?�`FM�wf?e�dZh!dZk�]Zt!]*c�em�]�mDv!_�o�]!s9s�_�e9uX]qhMi!f;hZtÄs�_�e7cGk$m� #]qs�d¢e9f;hqt{k�_�o�vXd�f$h��|¨�v*_
f;h!f$mDf;dZk{u�sC]' 7f?k$_!�M�jvMf$o�v�^l]*¡q_�eÂ]quMu*]*e�fnm9_`m�v*_y 7f$_Zk;i��Gk$]qe�_�e
f$m�e¼¡*_�k$]*o�f$m�p dZ #m9_�s�eC]!^`_`m�f;^`_yd�hMirk$]�o�dZknfn��_�eÂh*_�d�s � =
ÏM�
ËCh�vMf¹t�v*_�s� 7fH_ZkniMeÂ}��
ε × = � � ÏM�#�`FM�¼m�vX_wo�v!d�s�t'_¥o�s�_�d�m�f$]*h�f;e]q�Me7_�s9¡*_�i�}c�{fHt�e��|¸ª�#%'�̸�� W �Z�©¨�v!_·o�vMd�sCt'_�o�s7_�d�m�f$]!h�]Zo�go�c�sDe¥f;hrm�vX_2hX_�f�tXv'��]*s�f$h't¢o�v!d�f?h�eÌ]qhªk�p·}c�ªf�t��G¸G�&%Z�w]!swf?h
m�vX_wo�_�h*mDsDdZk�d�hXi�f;h�mDv!_`h*_�f�tXvX�!]!s9f?hZt�o�vXd�f;h�e¼e�f$^lcGk$m�d�h'_�g
]qcMeDk$pb}c�{fHt���¸ª� W ���Â�!c!m�dZk$�2d�p!e�e9]Xknfnm9]!h!e�d�hMiÄd�hXm�f$e�]!k;f;gm9]!h!e¢f;h¾m�vX_bhX_�f¹t�v*�X]'s�f;h'tÃo�vMd�f;h!e· #]qsD^��!]*c�h!i¬eCm�d�m�_�e
�2f$m�vÉe�]Xknf$m�]qhMeyd�hXibd�h*mDf;e�]!k;f$m9]*h�eyf?h�m�vX_�o�_�h!mDs9d'k|o�vMd�f;h§�
Ë�mw^lc�e�mw�X_2_�^yuMv!d�eDf$�D_�i·m�v!d�m¥m�vX_y¡�dZk$c!_�]' ¼m�vX_ymDv�sC_�eDv!g
]�k;i� 7fH_Zkni�i!_�u*_�h�iXe|]!h�mDv*_ye9fHt�hx]' §mDv*_yd�u!uMk;f$_�i� 7f$_Zkni§�MË9h
]qcMs`]quMf$h�f$]*h��{mDv�f$eyf?eyd�s�m�f; 7d�o�m`]' Ìm�vX_�^y]*i!_Zk Ù d�o�m�c�dZk#k�p§�f;hrs7_�d*kG_��Gu*_�s9f;^l_�h*m�]qhX_yv�d�e�d�e7p�^l^y_�m�sDfHo2e7pMe7m9_�^Ç�2f$mDv
m9�y]�^y_�m�dZk7¿�¤�~y¦Áf;h*m9_�sD 7d�o�_�eA��d�h!i � É f;e�f$hMi*_�u!_�h!iX_�h*m]'h½m�v*_�e9fHt�hr]!
ε
�
��(���U*RXV¢S�� (�Y *$W �5S (�T �����!T�U��G[
�ZS�[;U*R
¤�]!h!eDf$i!_�s·m�vX_Ä 7f;h!fnm9_�h*c�^l�!_�s¢]! �o�vMd�f;h!e�d�s�sDd�hZt�_�i
e9p!^�^`_�m�sDf$o�dZk
k$p s�_Zknd�mDf$¡*_¯m�]±mDv*_¯o�_�hXm�s�dZk�o�v�d�f?h§��¦¬_
e9mDd�s7mà 7s�]*^ m�vX_»^j]'i'_�k��2f$m�v']qcXm�_�k$_�o�mDs9f$o« 7f$_�k;id�hMi
o�]!^y^l_�hMe7cMs�d��Mf#knfnm9p�m9_�s�^�}c�{fHt����G� T ����¨�vX_½uXf$o�m�c�s7_r]*��gm�d�f;hX_�irf;e¥f;hrf$m�eÌo�]*^2^l]qh· #_�d�m�c�sC_�e¥e9f;^�f?kndZsÂm9] �{f¹t|��¸ª� T �
½£×η��/· � ú¾ï�æuå«ç�ôXí�ñ���ôXñ¾ï¾ö�ëuìNíAç ñ�ï{ñ���òNî�ë®ëuè�ëXôuòIì�ñ�ï/í�òNñ�òIî�ë�òNî�ë�ôuèCù¾íNò:ëXìªñ���òNî¾ë®ï/ëXæ�ìAëXíNò�ôXî/æ�ç�ï¾í�ó
=
��ý ¶
=
û�é Í ç ï/ôXñ�å.å.ëuï¾í:ù/ìNæ�òIë®ôXî/æ�ç ï/íué
ε =
/-ý Û
=
/ ó§��î�ë{ç�ï/ç£òNç�æ»è(ôuñ�ï/÷�ç�òNç�ñ�ï`ò:ìNæuï�í
�Cñ�ìNå.í�òIñ,æ �
π
äH�Îç ï��`í:ù/ìNì:ñ»ù�ï�÷/ëX÷ � ú,÷Îç ê�ñ¾èCëXí
� ôXñ�åªå.ë�ï¾íNù�ìNæ�ò<ë�ôXî/æ�ç ï/íuý�æuôuôXëuè£ëuìNæ�òAç ï� ��<ç ëuè£÷ é
ε =
/-ó �-ý Û
=
û�ó!�Êî/ë�å.ëXôXî�æuï-ç íNå ñ���òNî¾ë�ê�æ»ç ì«ôXì:ëXæ»òNç£ñ»ïgç íªñ � íNëuì:ö¾ëX÷
Ô ôXñ�å.åªë�ï¾íNù�ìNæ�òIë�ôXî/æ�ç ï/íuý ÷¾ëuôXëuè£ëuìNæ�òAç ï� j�Iç ëuèC÷�é
ε = −
//ó ��ý Û
=
û»óX��î�ë
å.ëuôXî�æuï-ç íNå ñ���òNî�ë�ê/æ�ç ì�ôXì:ëuæuò�ç ñ»ï,ç í®ñ � íNëXìNö�ëX÷
Õ ôXñ�å.å.ëXï/í:ù/ìNæ�òNë�ôXî�æ»ç ï�íuý ÷/ëXô�ëuè�ëXì�æuòAç ï� 2�Iç ëuè�÷�é
ε = −
/-ó .-ý Û
=
û�ó!��î�ë�åªëXô�î¾æ�ï/ç�í:å�ñ���òNî�ë
ê�æ»ç£ì�ô�ìNëXæuòAç ñ�ï�ç í!ñ � íNëXìNö�ëX÷ ó
% < R�T)(y� %?Q ]
*+* ] K ( T Ø � ] R ],* Q ] X � Ø ] R %&] RVW I�%�Ø � aq� Ø < �SR
T.- % / T K K T <
g�à ñ9à ó�é h!à ñ9ó�à óDç\j�åck�m�å�ßHé?n;Þ�ß#õ�ö7÷�÷�÷*õ#ò�ãfoGpZõ?h!ðqd dMö��
¨�vX_³o�vMd�s#t�_�i�¸
π
g#µ!f;h!µr^`]*¡*_�e�f;h�m�v*_`o�_�hXm�s�d*kGo�vXd�f$hrd�h�i
f;e`e�c�sDs7]*c�hXi!_�i¢�Xp�i�f?u*]!k$_�eld�h!iÉs9d�iMf;d�m�fn]qh�f;h¢mDv!_�d�s�sDd�p
]! �o�v!dZf�hMe��w¦¯fnm�v¬f$h!o�s7_�d�eC_bf;h¾m�vX_ÀeDf$�D_É]! �d�s�s�d�p§�wmDv*_
iMf;u*]Xk�_�e|��f#k
kM�!_³eDu!s�_�d�i�f;h�mDv*_³iMf$s�_�o�m�f$]*h�u*_�s9uX_�h!i�fHo�c{k;d�s
m�] � �©¨�vX_�d�^�uMknfnm9c�iX_¢]! 2s�d�i!f?d�m�f$]*h�f;e�d�uMu!s7]*��f;^�d�m9_Zk$pmDv!_2eDd�^l_2f;h¢dZk#k�m�v*_�o�vXd�f$h�e��
�{f1tMc�s7_Ç�G�&"»e�v!]Z�2eÉmDv!_®e9]Xk�cXm�f$]!h!e�]' ���aÚ��} F���d�m
ε =
Ϫ��¨�v!_`o�]'^�^`_�h�eCc�s�d���f?k;f$m9pre7cGu!u!s�_�e9e�_�eÂmDv*_`o�vMd�sCt!_�i
iMf;u*]Xk�_�eA�j¨�v!_�¸
π
g
µXf;h�µÇ^`]*¡*_�eÉf$hÇm�v*_�o�_�h'm�sDdZk2o�v�d�f?h§�
k$]!e9f;h't½f$mDe�¡!_Zk$]�o�f$m9p§�
Ë�hÕm�v*_�u!s�_�eC_�hXo�_�]q rd�h®_Zk$_�o�m�s�f$oÄ 7f$_Zk;iÇ}c�ªf¹t�e��³�ª�#%'�
�§� W �A�'_� 7 #_�o�mDeÂ]q �mDv!_ye7]Mk;f$m9]*h�g#d�h*mDf;e�]!k;f$m9]*h�uXd�f;sDe|o�s7_�d�mDf°]!hdZh!i¢ 7sDd�o�mDf$]qhMdZk{o�v�d�sCt!_2e�]!k;f$m�]'hXe`}��G�³d�sC_ h']qm�]Z��eC_�s�¡*_�i��
Ë9hÑm�vX_ iX_�o�_Zk�_�s9dAm�f$h*t 7f$_�k;i }c�ªf¹t|���§�#%Z�¬mDv!_�¸
π
g#µ!f;h!µ
k$]*]qe�_�e®¡*_Zk�]*o�fHm9p d�hMi�k$]*o�dZk;f$��_�e®h!_�d�s � =
Ϫ�ÉË�h�mDv*_
d�o�o�_�k$_�s�d�mDf;hZtÀ 7fn_�k;iÉ}c�{fHt��{�ª� W �Z�{m�v*_r¸ π g#µ!f;hMµ�d�o�o�]'^�u!d�gh�fH_�ir��prsDd�i�f$d�mDfH]'h·^y]Z¡!_�e¥f$h!m�]�m�v'_2�!cªknµÚ�
Ë9h �{fHt���ÅbmDv!_�e�]Xknf$m�]!h!g
e�]Xknf$m�]qh�f?h!m�_�s�d�o�mDf$]!hÄ #]!sxm�v*_
e9]Xknfnm9]qhMerk$]�o�d�m9_�i�f;h´m�v*_�hX_�fHt�v*��]*sDf�h'tÄo�vMd�f;h!e�f$e�e7m9cGi!g
f$_�i��'¨�v�f$eÂu!s�]��Gk$_�^¯f;e|f?h!m�_�sC_�e�m�f$h'txf?h�m�vX_wo�]qhXm9_��!m|]! §m�v*_
u!s�]��§k�_�^«]q ÂmDv*_�e7]Mknfnm9]qhMewd5t*t�s�_�t�d�mDf$]!h�f?h!m�]�m�vX_2^2d�o�s�]qg
e9o�]quXf$oÀuXv!d�eC_�g#e5knf$u�o�_�hXm9_�s9eA�©¨�v*_�¸
π
g
µ!f?h!µ®k$]�o�d*k;f°�5_�i�f?h
m�vX_¬o�_�h*m9_�s�]! ÉmDv*_» 7f$sDe7m¾o�v!d�f?hf;e�u!s�_�u!d�s�_�i±f?h²m�v*_
#]�k#k$]��2f;hqt��2d�p�£qmDv!_`f;hMf°mDf;dZkGo�]!h!iMfHm�f$]!h� #]qsÂm�vXf;e|o�vMd�f;h�f;e
o�vX]qe�_�h¢f$hrm�vX_2 #]!s9^½£
ϕ û ( Ø =
Ï
) = −
¸
π θ
X¸ − <
� }*��ÅM�
�2v*_�s9_ X f$e�m�vX_�k$_�hqt'mDvr]q ¼m�vX_yo�v!d�f$hÚ��¨�v*_�h���d� #m�_�s�e�]*^y_m�f;^l_!�rm�v*_«o�]qhMi!f$mDf$]qh }*��ÅG�¬i!_�o�d�p!e®f;h*m�]±mDv*_»e�m�d��ªk�_
½£×η�Ýη � ú/ï�æuå«ç ôXí®ñ��(ôXñ¾ï¾ö¾ë�ìNíAç ñ�ï,ñ��.òNî¾ë ë»è�ëXôXò:ìNñ¾ï¾í®òNñ{òNî�ëw� � äCæuì�ìNæXúgñ���ôXî/æ�ç�ï¾íuó ¶
=
û¾é Í ç ï�ôXñ�å.åªë�ï¾íNù�ìNæ�òIë�ôXî�æ»ç�ï�íué
ε =
/ ý Û
=
/ óM��î�ë
ç£ï/ç�òNç�æ�è�ôXñ�ï/÷-ç òAç ñ�ï�òNìNæ�ï¾í
�Cñ¾ìNå.í�òNñ�æ �
π
äH�Îç ï���íNù/ì:ìNñ¾ù¾ï�÷/ëX÷ � ú ÷-ç ê/ñ¾è£ëXí
� ôXñ�åªå.ëXï�íNù¾ì�æuòNë"ôXî/æ�ç�ï¾íué
ε =
/&ý Û
=
û¾ó � ñ»å.å.ëXï�íNù/ì:æ � ç�è�ç�òCú{è�ëXæ�÷/í�òNñ
òNî�ë�íNù¾ê�ê�ìNëXíNíAç£ñ»ï�ñ���òNî�ë�÷-ç ê/ñ¾èCëXí
Ô ôXñ�åªå.ë�ï¾íNù�ìNæ�ò<ë�ôXî�æ»ç ï�íuý ÷¾ëuôXëuè£ëuìNæ�òAç ï� y�Iç ëuèC÷�é
ε = −
/�ó +�ý Û
=
û�óX��î�ë¥ç£ï/ç�òNç�æ�è�ôuñ�ï�÷/ç�òNç�ñ�ï{ò:ìNæuï�í
�Cñ�ìNå.í«òIñ æ
�
π
ä°�-ç ï���÷�ëXôXëuè�ëXì:æuòAç ï� � ú òNî�ë©�Iç ëuèC÷�
Õ ôXñ�åªå.ë�ï¾íNù�ìNæ�ò<ë®ôXî�æ»ç ï�íuý�æuôXôXë�è�ëXìNæ�òNç�ï� `�Iç ë»è�÷�é
ε =
/-ó +-ý Û
=
û¾óZ��î�ë�ç£ï/ç�òNç�æ�è�ôXñ�ï¾÷Îç ò�ç ñ¾ï�òNì:æ»ï�í
�Cñ¾ìNå.í�òNñ�æ
�
π
ä°�-ç ï���æ�ôuôXëuè�ë�ìNæuò�ç ï� � ú�òNî�ë��Iç�ëuè£÷ ó
HJILK �NM 3O)P �
K�Q Ö �SRUTVR�W =YX � � TVR�W �
KJZ.O\[^]`_ Ö TLa Qcb <
dMö�� g�à ñ9à ó�éih'à ñ9ó5à óDç\j�ålk�m�å�ßHé?n;Þ�ß#õ�ö7÷�÷�÷qõ#ò�ãfo&p�õ?h!ðqd
¸
π
g#µ!f;h!µ d�o�o�]*^2uXd�h!f$_�i �Mp m�v'_ sDd�i!f?d�m�f$]!h§���2v!fno�v
eDu!s�_�d�i!eÉf;h¬�M]�mDv«i!f;s7_�o�m�f$]!h!eÉf$h«dZk
k�mDv!_�o�v!d�f;hMe��2¨�v*_
¡!_Zk$]�o�f$m9p¢]* �mDv!f;e`µ!f;hMµ¢f;e¥��_�s7]¢iXc!_2m�]rm�v*_�eCp'^�^l_�mDs9f$o�dZk
f;hMfHm�f;dZkÂo�]!h!iMfHm�f$]!h�}*�DÅ���o�]qhXm�s�d�s9p�m9]·m�v*_rf�hMf$mDf�d'k|o�]!h!iMf$g
mDf$]!h�}�Ê������2v!f$o�vbuMs7]!i*cXo�_�e�m�v*_¢µ!f?h!µÉ�2fHmDvbd¢hX]qhX�D_�s�]
¡!_Zk$]�o�f$m9p§���|_� #]!sC_�mDv!_ro�]Mk
k;f$e�fn]qh��y_¢u*c!m�mDv*_¢s�d�iMf$d�mDf°]!h
_�a!cMdZk�m�]��D_�s�]G��ºy_�hXo�_X�G�y_ vXd�¡!_2mDv*_�e7m�dAm�fHo�¸
π
g
µ!f?h!µ¢f;h
mDv!_r 7f;sDe7m�o�v!d�f?hbd�hMiÉm�v'_�^l]q¡!f;hqtĸ
π
g#µ�f$hMµÉf;hÉmDv*_r�D_�s�]
o�v�d�f?h§���{s7]!^ �{fHt��|���&"��y_ye�_�_³mDv�d�mÂm�vX_`¡!_Zk�]Zo�f$m�p�]* |mDv*_
µMf$h�µ!eli*]*_�eyh']qm`o�v!d�hqt'_rd� #m9_�s`o�]!k#knf;e�f$]!h§��¨�v!_�o�]!k#k;f;eDf°]!h
s�_�e7c§k�mDe�]qhªk$p´f?h�m�v*_ÉeD^yd*k#k³eDu!d�o�_Àe�v�f? #m�]' lm�vX_�µ!f?h�µ!e��
�2vMfHo�v�^l_�d�hMelm�vMd�m2mDv!_¢d5t*t�s7_5t�d�mDf°]!h�]' le7cMo�v�e9]Xknfnm9]qhMe
f;hXm9]b^�d�o�s9]*e�o�]*u!f$o�u!vMd�e�_�g#eDk;f;u�o�_�h*m�_�sDe�iX]�_�e�h!]Zm�]*o�o�c�s
f;h½m�vMf�e¥^y]!i*_Zk��
� U*R�Y *$W �A[nU'R �
Ë�h«mDv�f$e�u�d�u*_�sÉ�l_Ãv�d�¡X_Ãe�m9c�i!fn_�i�e�_�¡*_�sDdZk�^l]qiX_�k;e
iX_�eCo�sDf$�Mf;hZt�m�vX_³i*p�hXd�^2f$o�e�]! §o�]*h!¡*_�sDe9f$]*h�]q §o�]qhMi*cMo�mDf°]!h
_Zk�_�o�m�s�]qhMe�f?h!m�]2m�]quX]!k$]�t�f$o�dZk{e7]Mk;f°m�]!h!eÂ]q �mDv*_`o�]!^y^l_�h�eCc�g
sDd�m9_�o�v!d�sCt'_�i*_�h�e�f$m9pr�yd�¡*_X�
Ë�h�d�h�f;h'o�]!^�^`_�hMe7cGs9d�m�_ɤw~`¦��f;h�mDv!_�d��Me9_�h*o�_¢]q
_Zk�_�o�m�sDf$o� 7f$_Zk;i§��m�vX_�f;hXf$m�f;dZk¥o�]!h!iMf$m�fH]!h�mDs9d�hMe9 #]!s9^�e�f$hXm9]
m�vX_�¸
π
g#µ!f;h!µ´k�]*o�dZknf$�5_�i�f;hÉmDv*_ro�_�h!mDs9dZk�o�v�d�f;h�d�h�i�e7cGs9g
s9]Zc�hMi*_�i��!p�o�vMd�s#t�_�i�i!f?u*]Mk�_�e�f?h�m�vX_w]*mDv*_�sÂo�v!d�f;hMe���¨�v*_
o�]!^y^l_�hMe7cMs�d��Mf#knfnm9p¬k$_�d�iXe�m�]�e9cMu!u�sC_�eDe�f$]qh¾]! �e9cXo�v®i!f;g
u*]Mk�_�e��«Ë9hÓmDv*_�uMs7_�e�_�h'o�_�]! ²_�k$_�o�m�s�f$o� 7f$_�k;i �2vX_�h
D × = ��� �wd�h�i�mDv!_` 7fH_�k;i��!_�f;hZt�e�c� 7 7f$o�fH_�hXm�k$p�k;d�sCt!_!�*m�v*_^y_�o�vXd�h!f;e�^ ]! �m9]*u*]Mk�]At�fHo�d'k�o�v!d�sCt'_Ço�s�_�d�m�f$]*hf;e�]*��g
e9_�s7¡X_�i§��Ë7 D × = � ��}��yvMf$o�v¯f$e�^l]!s7_�s7_�dZk;f;e�m�fHoq��m�v*_ 7s�d�o�m�fn]qhMdZk³o�v�d�s�t�_�o�]*h�i*cMo�m�fH¡�f$m�p´d�hMi¾o�sC_�d�mDf$]!h�]! �m�v*_
e9]Xknfnm9]qhMg#d�h!mDf�e�]Xknf$m�]!h�u!d�f;sDe|d�s�_we�c�u!uMs7_�e�eC_�iÚ�q¨�v*_³¸
π
g#µ�f$hMµ
f;e�k�]Zo�d'knfH��_�i�f;h�m�v*_ro�_�hXm�s�d*k�o�v!d�f$h�d�h�i�f$e�e�c�s9s�]Zc�h!iX_�i
�!p¬m�v*_�sDd�i�f$d�mDfH]'h¬f?h¬m�v'_b]*m�v*_�s·o�v!d�f?h�e��j¨�v*_Äe�]Xknf$m�]!h
¡!_�k$]�o�f$m�p½i'_�u*_�hMi!e�]!hrmDv*_ 7fn_�k;i§�
Ë9h�m�vX_� 7s9dZ^`_��y]!s9µ�]! ¥m�v!f;e�^`]!i*_Zk�mDv!_re7]MknfHm�]'hXg
e�]!k;f;g
m9]!hÉf;h*m�_�sDd�o�m�f$]*hÉi!]Z_�e�h*]*m�k�_�d�i�m�]¢m�vX_�d�t*t�s�_�t�d�m�fn]qhÉ]*
m�vX_2e�]!k;f$m9]*h�e¥f;h*m9]r^2d�o�s�]qe�o�]qu!f$o�u!v!dZe7_�g
e5k;f$uro�_�hXm9_�s9eA�
û�ó�Ö
¹XÔ�Ã<ºNƾ¿¾½CÔ"ÏѺ:ÆuÌ�¹»º Ã<½�¹ Á(Æ�Å.À»¿�ƾºV×/Í/¿¾½CÔ���ľÍ�ÁÓ½��ª¿�¹�� � ½IË!¹u¿»ÁÓ½CÆ»¿�Í
��ƾË�Ì�ÆuÄ-¿�Õ-Á ý¥%�ó¥0�ñ�ï¾ôuëXæ�ù
ëu÷Êó1�»ý õ!ç ëX÷/ëuè � ñ�å.ê�æuï�ú&ý � ñ�ìN÷/ä
ìNë�ôXî/ò
ûAþ�ü�+A�»ý�%Êæ�ìNòNí�û®æuï�÷��
� ¹u¿»ÁÓ½:Ã�Ò
gÍ/Ü�¹�Á¥½�¿��ÊÆ
½�Õ-Á�ý�
ªó
!ìNù.. ï¾ëuì
ëX÷ ó¹�»ýÉ&�÷¾÷-ç íNñ¾ï¾äH�̀ ë�íAè�ë�ú ýmõ�ëXæu÷-ç ï� �ý�0�æuíNí:æuôuî�ù/íNëXò:í
ûAþ�þ��A�»ó�-ó��uó��«ó���ìÓç ö¾ë¾ýX&�ó ( ó�õ�ñ��Xî¾æ�ö¾í;��ú�ý�æuï�÷��uó��®ó��!ù/èIç ��ý
½ �»·
½ �»¼¾·
ÉʹuË�Ì�ó�����ý��D.D+
ûAþ�ü����! "��ƾܾ·�#�·�Ç�Æ¾È É�¹uËÑÌη�Ï�лҾÁ»ó��$�-ýG.%��/
ûAþ�ü����$&Aó.-ó ( ó�' ìNæ$�Xñ�ö¾í?�Îç�ç¬æ»ï�÷�,ªó���ç ì�ñ»ö�æ/ý Ö
¹XÔ�Ã<º:ÆÂ¿(��¹
Å)��Ç�ÆuÔXÍ
½ �uÍ-Ã<½£Æ¾¿
Í/¿ÂÕpÏѹuº�½CÆuÕ ½£Ô*��Ä�Ì�¹»ºVÁuÃ<º:ľÔ�Ã�Ä-ºN¹�Á ½C¿+��Ä�Í�ÁÓ½��ª¿�¹ � ½IË!¹u¿»ÁÓ½CÆ»¿�Í
� ½�¹
¹uÔ�Ã<º�½�Ô�ÁAØ��-ƾܾ·��-Ôu½I·-,ª¹uÜ�·�Û/.®ÏÑлÒ/Á óCý0�Xó|0,ó0��î/æ�è�æuò:ïÎç ��ñ�ö
ëX÷ ó¹�»ý21.æ�ì;��ñ�ñ�÷w& ôuæu÷�ëXå«ç ô|%�ù � è�ç íNî�ëXìNíuý3�
û�þ¾üD����ó�-ó ( ó�' ìNæ$�Xñ�ö¾í?�Îç�ç æuï�÷ ( ó!0�æ�òNö¾ëXëXï��/ñ-ý #�·)ÏÑÐÂÒ¾ÁÓ· À54�Ï�Í�ºA½ Á76 �/ý*�%��þ
ûAþ�þÎû��
8�/ý�û�û9)�.
û�þ¾þ-ûD�»ó+-ó � ó�ÿ�ëuç ï � ëXì; bæ�ï¾÷møÎó�ÿ-ìXç ëX÷/ëuè:ý #�·±ÏÑÐ�Ò�ÁÓ·�4�Ï�Í�ºA½ Á76:9<; ý¥��ü�+
ûAþ�ü»üA�»ó
��ó�øÎó � ó�
!ç�è�è:ý #�·&Ï�Ð�Ò¾Á ó3=>� ; ý3�D+�ü¾þ
ûXþ�ü?�5�»ó)�ó ( ó«õ�æuå.æ9��ìAç�í:î¾ï/æ�ý�0,ó|%�ó|0�æ�î/ëXì�ý@�«ó|& å � ë7 ¾æ�ñ��¾æ�ìuý.æuï�÷BA�ó
ã�ô7��ëXìNï�ý�ÏÑÐ�Ò�ÁÓ·C,ª¹uÜ�·ÊÇ�¹�Ã:ÃAó2D�E�ý���/��%�
û�þ¾þD���uó
ü-ó�&ªó ( ó3��ñ¾ö¾æ�è�ëXö�ý8F�ù�ó2�«ó�%)ëXìNíNî-ç ï ý-æ�ï/÷¥&ªó ( ó�õ�ñ���î/æ�ö¾í;��ú ý ÏÑÐÂÒ¾ÁÓ·
,.¹uÜ�ó�G�H�I�ý!û$������)
ûXþ�þ?�5�
½J�»·
½J�»¼¾·!É&¹»Ë�Ì�ó��%�-ý*.��D�
û þ»þK���
Ç�ƾÈ
É�¹uËÑÌ&·&ÏÑÐÂÒ¾Á óC�L�Êý��5+�.
û þ»þK����&Óó
þ-ó��uó��«ó���ìÓç ö¾ë¾ý*&.ó ( ó�õ ñ%�Aî�æuö�í;�¾ú�ý æuï�÷!�®ó*&�ó�õ�ù � æ��/ñ�ö�ý Ïѽ£ÁLM�Ë�Í
N�Ð�·�ÖѼ�ÁNÌ�·«ÉʹXƾºA·
½ � ó 9 D�ý!þ¾þ
ûXþ�ü�)5�� #�ÖÑÉ&Ï Ç�¹�ÃNà ó 9 DÎý®û#��û
ûAþ�ü�)��$&Aó
û9/�ó*&ªó ( ó�õ�ñ���î/æ�ö¾í;��ú ý�F!ù ó��«óM%ÊëXìNíNî-ç ï ý�æ�ï¾÷y&.ó ( ó��!ñ¾ö¾æ�è�ëXö�ý
½ �»·
½J�»¼¾·"É�¹uËÑÌ ó>�LIÊý«û7.D��+
ûXþ�þ�)5�� Ç�ƾÈ]ÉʹuË�Ì�·�ÏÑÐ�Ò�Á ó��<IÎý�þ�þ?�
ûAþ�þ�)��$&Aó
û¾û�ó0F!ù�ó ( ó5��ç ö�íNî/æ�ìwæ�ï/÷·&ªóÂ0,ó5��ñ»í:ëXö/ç�ôXî�ý Ïѽ£ÁLM�Ë�ÍON�о·®Ö�¼�ÁNÌη
ÉʹXƾºA·
½J� óKI?P�ý�+��D�
û�þ¾üD.��@ #�ÖÑÉ&Ï̀ Ç�¹¾Ã:à óKI?P�ý3���¾ü
û�þ¾üD.���&Óó
û7�-óQ�Xó��NíNî�ç�å.ñ�ìAç�æ�ï¾÷2�!óM0�ù�ï�æ9��æuòNæ�ý #�·ÑÏÑÐ�Ò�ÁÓ·��ÊÆuÔu·�#ÎÌο ó�HC�ÂýX.�.%��)
ûAþ�ü��A�
½£×η±Ù· �Iï/ò:ëXìNæuô�òVç£ñ�ï � ëXò;��ëXëXï òIî�ë�í:ñÂèCç�òIñ¾ï¾í`ç ïbò:î/ë
ï¾ë�ç ¾î � ñ»ìXç ï�
ô�î¾æ¾ç ï/íuó
ε =
/�ý Û
=
¶
=
û»ó���î�ëwí:ñÂèIç òNñ�ï�ä�íNñ¾èCç òNñ�ï�ç ï/ò:ëXìNæ�ôXòAç ñ�ï�è�ëXæ�÷¾í
ñ¾ï�è�ú�òNñ«í:åªæ¾èCè�ê¾î�æuíNë.íNî-ç1�Cò�ñ��)òNî/ë�íNñ/èCç òNñ�ï/íuó
% < R�T)(y� %?Q ]
*+* ] K ( T Ø � ] R ],* Q ] X � Ø ] R %&] RVW I�%�Ø � aq� Ø < �SR
T.- % / T K K T <
g�à ñ9à ó�é h!à ñ9ó�à óDç\j�åck�m�å�ßHé?n;Þ�ß#õ�ö7÷�÷�÷*õ#ò�ãfoGpZõ?h!ðqd dMö�p
|