Quantum phases in partially filled Landau levels

http://doc.rero.ch

ikj,lmfn6j,oqp`r,lsOtPskuvmwpxlynOuvlzEz|{w}uvzvzEtP~€lm/~,lj‚t„ƒ…tPzvs

R‡†ˆ†‰,HTB DCcGId Š

‹3Œk

ŽE6J‘“’@Ž(”Ž(•’—–5Žb˜f™6šJ›œŸž( OŽ ¡b¢•œ¤£LŽ(‘“›CœŸ’



Ž%–5Ž¦¥„‘“œ¨§E©5 6‘9ªL¡W˜



Ž(‘v©J«Ÿ«Ž(›E¡¦¬­¯®v°O±J²5²%¥„‘“œ9§C©J O‘9ªL¡…³ ´…œ¤’¤µ(Ž¶‘“«J•–T·

¸J¹

6§E©5‘vJ’@©Jœ¤‘EŽº–5Žb˜W™OšJ›Cœ9ž¶ Ž–5Ž¶›,³©5«œ9–5Ž¶›E¡W»)¼J’|·½T°T²&¾vJ››“©¶¿(œ



Žº5 ‡¬À/Á/³TÂ%ÃT°¶Ä²J½‡ÅƑ“›“Jšx¿Ž–5Ž“Ç3¡¥„‘vJ•¿ŽL·

U†ÈPB SB DCB D

¹

T§C©J‘vJ’@©JœŸ‘vŽº–5Ž¦˜f™6šJ›œŸž( OŽ%–5Ž(›,³©J«œŸ–5Ž(›E¡…»)¼J’|·…½5°T²`¾vJ››©(¿¶œ



ŽJ k¬PÀ,Á—³TÂ(¡fÃ5°(IJJ½‡ÅƑ“›“Jšº¿ŽC–TŽÇL¡¥P‘vJ•¿Ž3·

e,†R&HJDFLGIY/_6gGAEV

‹3Œk

ŽE6J‘“’@Ž(”Ž(•’—–5Žb˜f™6šJ›œŸž( OŽ ¡b¢•œ¤£LŽ(‘“›CœŸ’



Ž%–5Ž¦¥„‘“œ¨§E©5 6‘9ªL¡W˜



Ž(‘v©J«Ÿ«Ž(›E¡¦¬­¯®v°O±J²5²%¥„‘“œ9§C©J O‘9ªL¡…³ ´…œ¤’¤µ(Ž¶‘“«J•–T·

¸3É

•›’9œŸ’¨ 6’@ŽËʓ©J‘ºÌP™OŽ©J‘vŽ(’9œ9¿J«„˜f™6šJ›œŸ¿(›v¡Í¢’¨‘vŽ¿ ™6’¢•œ¤£LŽ¶‘“›œ¤’¨š3¡

¹

Ž¶ O£3Ž(•«5J•!Ä6¡

Î

½T϶ÄЬ„Ñ€¢’¨‘vŽ¿“™O’¤¡b̄™OŽÍÀbŽ¶’Ÿ™OŽ(‘“«J•–J› ·

ÒËB Z¶B GÓ5B S`ÔJÕ%MJN?OBÔJÖJÖL×

ÒËB Ó6GIYCB S

]

BxZ HJghFLDCB%AEVBºB ?B DCdJGIB YHLQ/SGØ B DCB ?TAB KIB Z AEDCHJ?kYEHJKIGISY(لYCNZCVkFLYcNOccKIBºZ DEX6YEACFLKIYÚ—GACVÛACDEGÜ

FL?OdJNKÝFLD,FL?OS)YCÞTNFLDEB¦YEX6ggB AEDEX%FL?S)YvACDEGIhB¯hVFLYEB¶Y¶ÙAEHACVOHJYCB¦HLQZ HJDCDEB¶KÝF3AEB S)ÞTNFL?5ACNgßKIGIÞ6NGISOY

GI?!hFLDEAEGÝFLKIKXaKIKIB S)GI?5AEB¶DEgB SGÝF3ACB,ÈFL?SFLN&KIB“Ó5B KIY(†R&NKAEGIhKIB¯ACDCFL?YCGAEGIHJ?YËcB“A@ÚÆB B¶?&AEVB YCBbhVFLYCB Y

ڗVB ?ÓLFLDEX6GI?d,AEVBÆaKIKIGI?d¯HLQAEVBÆACHJh6Ü@gHJYEAhFLDvACGÝFLKIKX¦aKIKIB SÈFL?SFLNKIB“Ó5B KB“àOhOKÝFLGI?AEVBËHJcYCB DEÓ5B S

DEB B¶?5AEDFL?Z B—HLQAEVBËGI?TAEB dJB DWÞTNFL?TAENgâá/FLKIKB“ØB Z“A¶†6ãËVBÆAEDFL?YEGACGIHJ?OYWcB“A@ÚÆB B¶?B KIB Z“ACDEHJ?OÜ@YEHJKIGISFL?S

ÞTNFL?5ACNOg%Ü@KIGIÞ6NOGIS`hVFLYCB Y¶Ù„FLY/ÚÆB KIKFLY,ACVOHJYCBcB“A@ÚÆB B ?äcONccKIBZ¶DvXOYvAFLKIY/Ú/GAEV`SGØ B DCB ?5A¦?6NOgcB D

HLQ B KIB Z“ACDEHJ?YWhB D…KÝF3AvAEGIZ¶B—YCGAEBJÙ5FLDCBfaDCYEAvÜ@HJDESB D(†LãËVGIYKIB¶FLSYACHbF/ÓLFLDCGIB“A@XHLQgB¶FLYENDFLcKIBÆhOVB ?HJg%Ü

B ?FºYCNOZVFLY/AEVBhOVFLYCBÍZ H6B“à6GIYEAEB¶?OZ¶Bc B“A@ÚÆB B ?ÛF

]

GIdJ?B D¯Z DvXOYvAFLKFL?SF%A@ÚÆHLÜ@B KIB Z“ACDEHJ?cNccKIB

hOVFLYCBxGI?åF)ÈPFL?SFLNOÜ@KIB“Ó5B KÆaKIKIGI?dLܨQ9FLZ“ACHJDÍDFL?OdJBx×æIç¶èé€êåéß×æÔJëOÙPڗVGIZV‡VFLYDEB¶Z B ?5ACKXäcB¶B ?

GI?5Ó5B YEAEGId5F3ACB S`GI?ºACDCFL?YChHJDvA/gB¶FLYENDCB gB ?TAEYËN?SB D—gGIZ DCHLܨÚËF Ó5B,GIDEDFLSGÝF3AEGIHJ?„†

ì

Ž¶šJ´W©J‘v–J›Lí

ÞTNFL?TAENgîá/FLKIKB“Ø B Z“A(ïB KIB Z“ACDEHJ?GIZbZ¶DvXOYvAFLKIY¶ïhVFLYCB¦ACDCFL?YCGAEGIHJ?Y

ð…ñkò

mfn6yóË~/j,ônOuvóWm

"%õ2 ö78Ÿ÷åT…;¶892 ø ù6ùŸO4Jú31(2;,8Ÿåøx0WT130WT78¨45ù9ø 1¦÷åø : Tú(8¨4bû…Tù¨7äü+ýøþøú¶ú(1Lø 45ú(O7÷ۅ4Lý

8Ÿ„ú3T136;¶úÍ7138Ÿ:ú(ýºù¨ø ;¶úbú õ27646ø 7O;b;(8Ÿ4Tú(ýx78¨;(4T2þ T13ÿ2Wú3ýº89„ú(T:T1Íø 7|1Lø 4Jú38Ÿ2øù

ø„ú(÷ =xø ùŸùºWO4JúL;|(<)=!. ø 7ß*,<)=x.x¦1(O;¶0W645ú(89þ 6ùŸÿ ¦“î;(08Ÿú( 2)ú(ý ;(89÷‡89ù¨ø138¤ú ÿ

Tú õ6T ú3ýÛú õ2kf645ú3;6ú3ýT891)2 138Ÿ:8Ÿ 8¨;

8Ÿú(‡78fT13T„úO…2 ú(ýä2 äýø7Ëú(ýÛ(<)=x.

89;xøå÷åø 8|6;¶ú3øú38Ÿ2 2,ú(ý6T13: ÿ

…ø„ú(86øú(892 2¯Tù9645ú(132 ;v÷åø;(; ø…7 4Lý…ø13:

8Ÿ ý89: ýùŸÿ 7T: 6T1Løú3‡-/ø7ø ùŸ6þ Tù¨;v-/-—;JËõ8Ÿú(ý ø ù9Tþ 6ùb;¶60ø1Løú38Ÿ2 2ü Ë"%ý

13øú(892"! #%$'&)(*$,+ 5ú õTT ú(ýå6ùŸO4Jú(132 894‡7T…;¶8Ÿú ÿ$'&-(%ø7 ú(ýk76;(8¤ú ÿ 2;¶ú3øú(6;)0WT1

ùŸ6þ 6ùE.$,+/# ü013245¯75ú(61(÷å896;kú(ý ûù9ùŸ89: 2xú(ý -—-—;6¦ø7€ú3ý (<)=x. 24T4513;‡8

Š65…ܨgºFLGIK

í

dJHTB DCcGId7,KIhOY(†NOÜ@hOYCNS„†QŸD

file:///U|/docs/OA/articles/header_p1.txt22.09.2005 08:32:30

http://doc.rero.ch

Ô

·—Å—·Ë©(Ž¶‘¶§¶œª

! # Íõ8Ÿú(ý8Ÿ„ú(6: 1Løù .bù9645ú(132 ;k01(2÷‡2 ú(O7 ú32 ø ý89: ýT1 -/- õýTîþø 1(ÿP89: ú(ý

÷kø: 5ú(8¨4äûTù¨7Æ 64T2 ÷ååùŸ246øù98667 ÿ 89÷å0138¤ú38ŸO;ø…7 ú3ýT13|21(å72 2úÛ4T2 „ú(138 ú(äú(2

ú(ý6ùŸO4Jú31(2894ú313ø ;(0…21¶ú "%ý89;¯ù96ø7;¯ú32&ø&0ù9øú(6ø ä89‡ú(ý!=xøù9ù136;(89;¶ú3ø 45ø 4T4T2 ÷å0ø 8ŸO7

ÿ ø þø 8¨;¶ý89: ù92 :8¤ú3789øù¦136;(89;¶ú3ø 45 —'! ú3ýk2ú3ýT1`ýø 7Æfú3ý *,<)=!. 8¨;`7‡ú32 ø

; ú31(2: ù9ÿâ4521(13Tù¨øú367

…ø„ú(÷ ùŸ8

8¨7 |2 13÷å67 ÿ ú(ý 6ùŸO4Jú31(2;‡8Ÿîø 0ø1(ú(8¨øù9ù9ÿ ûù9ùŸO7

-—- ø…7 24T4T1L;‡øú ;¶2÷‡ 2xú(ý (÷kø: 8¨4Tø ù ûù9ùŸ89: vø 45ú(213;! #41C^ ø7ßøú

ú(ý68Ÿ1ä0ø1(ú(8¨45ù95öý2ùŸk;(ÿ„÷å÷å5ú31(8¨4‡ûù9ùŸ89:„; ! # 1E —õ8Ÿú(ý 89„ú(6: 1Løù ø 7'

ù¨;¶2 8Ÿ ú3ýû…13;¶úx4T8¤ú367 -/-b |1Lø 45ú(892 ø ù

ø„ú3÷ =xøù9ù/;¶ú3øú(O;ºýøþ 6T 2 ;(T13þ 67 øú

! # L T6ø…7åõýT13 ! # !! 7T2ú(O;¯ú(ýûù9ùŸ89:2…ú3ýú(20÷å2;¶úÍù9Tþ 6ù3

“ ý8Ÿ:ýT1!-—-—;6ú3ý;¶ú(132 :Ё2ùŸ2÷ 13T0ù¨;(8Ÿ2 5ú õT6 Tù964Jú31(2;%89 ú(ý0…ø1(ú(8¨øù9ùŸÿ

ûù9ùŸO7 ù9TþTù¦÷køÿ ù96ø7 ú32 0ýø ;(6;&78fT13T„ú|1(2÷

ø„ú3÷ ù98

8¨7;6—4Tø ù94Tù¨øú(892 …;!89 ú(ý

=xø 1¶ú31(65ö“*24#" ø00132$8Ÿ÷køú(892 âýøþÐ13Tþ6ø ùŸO7 ú(ý %P8¨;¶ú(T…45 2)Tù964Jú31(2ö“;¶2ùŸ8¨7 0ýø;¶O;T

;¶…4Lýßø;‡;¶ú(13890…O;‡ø 1(27 ! # ø 7

ù9 4513ÿ; úLøù¨;Ûõ8Ÿú(ýwþø13ÿP8Ÿ: Tù9645ú(132 P÷‡ö

61&0…61)ù¨øú(ú(8¨45k;(8¤ú3&'(

;¶ú(13890…å0ýø;¶äýø ;)897667 T6 2 ;(T13þ 67 89 ú(1Lø;(0…21¶ú)÷å6øö

;¶1(6÷‡6„ú3;6/õý8¨4Lý€;(ý2õ ø ù9ø 1(: ø89;(2ú31(20„ÿ 89âú(ýÐù92 :8¤ú3789øù%÷kø:5ú32ö1(O;¶8¨;¶ú3ø…45

ø132 …7 !0#*) +6 +66 +-,%,%,.!.Í89;(T;¶ú(68Ÿ0/$1325476 ýøþ |1¶ú3ýT13÷å2 13º÷å6ø;¶1367åøÛ2 ö

÷å2 2 ú(2 894 Tý…øþ„892 12Æú3ý!=!øù9ù…136;(89;¶ú3ø 45x8Ÿkú3ý!û13;¶úÍ%4T8¤ú367 -/-$# 8ºú(ý)*,<)=!.

øú

! # ø 7 89;Ð;¶1(132 …767 ÿ€89;(ù¨øú(89:â6ùŸO4Jú31(2894 0ýø ;(6;6Íõý8¨4Lý‚4Tø ;(

ø 89ú3T:T1

ø„ú38Oøú(892 2ú(ý =!øù9ùb136;(89;¶ú3ø 45Ëø ; |2 1&ú3ý 68Ÿ:ý 21(89: (<)=x.Ë"%ý89;

1(6T„ú(1Lø„úÛ(<)=!. 8¨;Û13T÷å8989;3456„úä2xø âf645ú‡2 ;(T13þ 67 |21(Ð8Ÿ ú3ý ;¶O452 …7 458Ÿú(O7

-—- 9 ýøþ ;¶ý2õâú(ý…øúkú(ý WO4Jú ÷køÿ 7613;¶ú(2P27â89ßú(T13÷k;å2&øwøùŸú(T13øö

ú(892 Tú õ6T

…ø„ú(÷‡öùŸ8

8¨7 ø 7 6ùŸO4Jú(132 ö;(2 ù9897 0ýø ;(6;)õý6 þø13ÿP8Ÿ: ú3ý‡ûùŸù989:Ð2

ú(ý ú(2 0÷‡2„; ú‡-—- : =xT13 —õ0|1(ú(ý61(÷å21(k89Pþ 6;¶ú(89:øú( ù9 4513ÿ; úLøù¨;`õ8¤ú3ýâ78W61(6ú

;¶ÿP÷å÷å5ú31(ÿ ËîýT136ø;&ú(ý

ø„ú(÷äöù98

8¨7 0ýø;¶O;ø13vøþ 2 1367 øú

! # E; 5—øú

!=<# 1C>

ø;¶8ŸöC0…ø1(ú(8¨45ù96;%ø13&458Ÿú(O7 ø 7 13ø 89;()ú(ý`6T13: ÿ 2—ú3ý

ø ú3÷ ù98

ö

8¨7;ºø 2þ )ú3ýøúº2,ú3ý452÷å0…Tú(89:kTù9645ú(132 ;¶2ùŸ8¨7; "%ý`ù¨øú¶ú3T1xø 1(&89;(ù9øú(89: 64Tø ;(

ú(ý6ÿÐø 1(&089O7

ÿ 136;(8¨7øùÆ89÷å0138¤ú38ŸO;%8Ÿ ú3ý`ý2;¶úº÷køú3T1389ø ù3

?ÆñA@ m/t„yCB…{EDälzvôj/zEln6uEó…mGFó…y n6r,tIH uKJÍt„ytPmfnåp`r,lsOtPs

“ 2137T1)ú(2 7O;(4T1(8 ‡ú3ýkùŸ2õ%öTT13: ÿ 7T:1(66;)2 |1(6672÷ Æõý894LýËËøú`2 ö-T61(2 þøù96;

2bú3ýå0ø1(ú(8¨øù/ûù9ùŸ89: vø 45ú(2 1

!fË4T2 ;(89;¶ú!2Í89ú313øö-/-â%4T8¤úLøú38Ÿ2;TWõ‡ø72 0ú&ø ÷å276ù,2

;¶08Ÿö0W2 ù¨ø138667ÐTù964Jú31(2;6

L

M #

ON-PRQ5S UT

V W,

V

UW, õ8Ÿú(ý

Q5S UT #

CX, &

Y T Z S UT

&

õýT13‡2 ù9ÿ ú(ýå4T2 ÷å0W2 6úL;)2Íú3ýk7T…;¶8Ÿú ÿ 2 0WT1Løú32 1)8Ÿ ú(ý$föCú(ý -—-wø 1(Ûú3ø5"T 8Ÿ„ú32

ø 46452 úO

V S UW,#[Z

S

\T

V

UW,]‡"%ýÛ-—- |2 13÷ vø4Jú(21^Z

S

UT#[_

S

UT & P0, T & 89;

: 89þ 6k8Ÿkú3T13÷k;Í2—-—ø:T13130…2ùŸÿP2÷‡8¨øù¨;_

S

K`4"%ý

ø „ú(÷‡ö÷‡O4Lýø8946øù0132 0WT1(ú(896;

2bú3ý‡÷‡276ù¦ø131(6þ Oøù967 ÿ ú(ý‡P;(øù¯452÷å÷ÛúLøú(892 1(6ù9øú(892 ; |2 1!ú(ý‡01325a O4Jú(O7

b ]

B¦NYEBbFYEX6YEAEB gßHLQN?GAEY(ÙGI?xڗVGIZVxACVOBÍgºFLdJ?OB AEGIZ¯KIB ?dLAEVdcfehgji kml#n#oqp ç

http://doc.rero.ch

 J•’¨ 6” ˜f™OJ›“Ž¶›Íœ¤•)˜—J‘“’¨œŸJ«Ÿ«š%¥Wœ¤«Ÿ«Ž–

¹¹

›

7T…;¶8Ÿú ÿÐ20…613øú(213;6

V

\W,

V

' # „;(89UW 'C

V

\Wh'Æ"%ý8¨;º÷å27Tù¯øù9ù92õº;|2 1

øå452 ÷å÷å2 7O;(4T1(890ú(892 2¦øù9ùË-—-/;

"%ý`Tù9645ú(132 ö“;¶2ùŸ8¨7 0ýø ;(6;ø 1(&4Lýø1Lø 45ú(61(8TO7 ÿ ø 2 1L7610…ø1Lø÷å5ú3T1 UW,J…õý8¨4Lý

75ú3T13÷å8ŸO;`ú3ýÐ76;(8¤ú ÿ 0132ûù9 2ú3ý 0ýø ;( ,: 89þ 6 ÿ ú(ý ù92P46øùÍûùŸù989:vø4Jú(21

! y

"%ý ù9øú¶ú3T1k8¨;å1(6ù9øú(67âú(2 ú(ý 2 1L7T1‡0ø1Lø÷åTú(T1 ÿ *2 138Ÿ61‡ú(1Lø; |2 13÷køú(892 — UW,

V

UW,$ + # &

!'y P0 Wy 6 ø7åú3ý!4T2 ýO;¶89þ xT61(:ÿä2Æú(ý!Tù964Jú31(2ö“;¶2ùŸ8¨7

0ýø;¶O;

O452 ÷åO;%8Ÿ ú(ý=xø1(ú(13TTö*24#"åø 00132$8Ÿ÷køú38Ÿ2 &%'(':

!

(

"

!#

$%$ ! # $ +

!jN P'&)(*

S

UT,+ UW,,+& E

õýT13ú3ýå=xø1(ú(13TTö*24#"Ð0W2ú3T„ú(8¨øù

&

(-*

S

\W,ºúLø5"6;!8Ÿ„ú(2 ø 46452 ú

ø„ú(÷äö÷å64Lýø 8¨4Tøù

4Lýø : )f645ú3;

"%ý ù9k4513ÿ; úLøù,õ8¤ú3ý ø ø 1 8Ÿú(1Lø13ÿ ù9øú¶ú(8¨45k;(ÿP÷‡÷åTú(13ÿ 89;&4Lýø 13ø4Jú(61(8TO7 ÿ ú(ý

ùŸ246øùû…ùŸù98Ÿ:vø 45ú(2 1

! y #/.

+"+y 10324+5õýT135.K`4b8¨;¦ú3ý!;¶ú(60|45ú(892 ËPø73032

ø13ú3ýäù¨øú(ú(8¨45‡þ O4Jú(213; …"%ýäþ2 ù9÷åä2¦ú(ýåTù9T÷å6úLø13ÿ ù9øú¶ú(8¨45å456ùŸù 76

"

#^5X98

! 89;

75ú3T13÷å8ŸO7 ÿ&ú3ý0ø1(ú(8¨øùûù9ùŸ89: vø 45ú(21¯ø 7Ûú(ý ùŸ%1Lø 789; + #: ;8 452 „úLø898Ÿ:

8 6ùŸO4Jú(132 …;"%ý&2137610ø1Lø÷åTú(T1%2—ú(ý ù94513ÿ; úLøù

+ <

\W, #

CX : ;8

T =

UT

:

;8 N 2

?>

PA@B%C

ÿP8Ÿ6ù97;ú3ý452ý6;(89þ &T61(:ÿ

+"!D#

$%$D8[ ! #

$,+

!

8 N ( & (*

S

FE ( = &

G: ;8H+E (I+

+E (D+

& v

õýT13bú3ýÍù¨øú(ú(8¨45%;¶ÿP÷å÷å5ú31(ÿ&8¨;/;(0…O458Ÿû672 ù9ÿ

ÿ)ú3ý1364T8Ÿ01(24Tø ù ù¨øú(ú(8¨45Íþ645ú(2 1L;JE ("%ý

ú(61(÷KE ( # Ð8¨;&2 ÷å8¤ú(ú(O7|132 ÷ ú3ýk;¶÷ O4Tø ;¶å8Ÿú`89;`46ø4TTù967 ÿ ú3ýký2 ÷å2: TT2 …;

ø 4#"P:1(27k8¦2 `;(00W2;(6;%2þ 613ø ùŸùf4Lýø 1(:!6ú(1Løù98Ÿú ÿ 2,ú(ý;(ÿ; ú3T÷"

“Ûú3ýº4Tø;¶2f; ú31(890…O;,õ8¤ú3ý‡õ8¨7Pú3ýML&21(89T„ú367ä0ø1Løù9ùŸ6ù ú32)ú(ý7N„ö78Ÿ13645ú(892 ËOú(ýºø;3øú6

! y #/.L O+` =`P24+ù96ø7;ú(2åú3ý`2 1L7610…ø1Lø÷å5ú3T1O

MQ'\W, #

_SRUTWVGX 'Y

;(8Ÿ \T R[Z

Q

!

T\R N 2

W>

V^]

2I_a`

õýT13 Z Q

#OL

!Ð8¨;ú(ý;¶ú(138Ÿ0W`0WT138Ÿ278¨458Ÿú ÿ"%ý8¨;ÿP89Tù¨7;ú(ý4T2 ýO;¶89þ &6T13: ÿ

Q

"

!#

$%$ Z Q

! #

$,+

5X

&

! N

(Fb

c Y & (*

S d

T#

CX

Z

QSef

;¶89

&

UX !

e

e& |

õý8¨4LýÐ8¨;%ú(2 `÷å8Ÿ89÷å8667 õ8Ÿú(ý 136;(0…O4Jú%ú(2åú3ý&þø 1(8¨øú38Ÿ2øùÆ0…ø1Lø÷å5ú3T1 Z Q

"%ý

ø ú3÷‡öCù98

897 0ý…ø ;(6;6 õý8¨4Lý ÷køÿ 2 ú 4Lýø 13ø4Jú(61(8TO7 ÿ ø 21¶ö

7T1 0ø 13ø ÷å5ú(616 ø13 õ6ùŸù 7O;(4T1(8

O7

ÿ -/ø:ýùŸ89Ug;+õøþ%|45ú(892 ; ^"%ýT891 452ö

ý6;(89þ T61(:ÿ 8¨; : 89þ T 89 ú(T13÷k; 2 =xø ù97ø ;g; 0;(T72 0W2ú(6„ú(8¨øù¨;Thji

S

&Dk7l #

E5X am

P Q S

UT _

&Dkl UT

&

P%P0 T

&

5

Von

(

"!D#

$%$ ; ! #

!

XqpN

&Dk7l i S

&Dkl

!,C> î €%s

S

\ E

http://doc.rero.ch

·—Å—·Ë©(Ž¶‘¶§¶œª

õýT13 ú(ý 0ø ;¶892 w452Pk4T8Ÿ6„ú3;

r

&Dk7l

;(0…O458|ÿ ú3ý -—ø : ýùŸ89wõøþ |4Jú38Ÿ2,"%ý

;¶O4527 ú(61(÷ 8Ÿ . CúLø5" O;º89„ú(2 ø4T452„úú(ýäT61(:8ŸO; S

\º2¯ú(ýä458Ÿú(O7

ø ;(8¤ö

0ø1(ú(8¨45ù96;—24Lýø 1(:º E;; øú

!+ E;; Pø7

…ø ;(8¤öý2 ù96;Ë24Lýø 1(:` E> k

øú

! 1C>d 898¤úL;Ð2`ú(ý Tù9645ú(132 8¨4 4Lý…ø13: "%ýTÿw÷køÿ

4Tø ù94Tù¨øú(O7

øø ùŸÿ„ú38946øù9ùŸÿ 8Ÿ ú3ýÐ=!ø÷å89ù¤ú32 8¨ø ú3ýT21(ÿ 2ú(ý *,<)=!.º—O; úLø ù98¨;¶ýO7 ÿ 1¶ú3ý„ÿ ø…7

Pýø "ø1

Ëñ 0 t„sOj,z|n6s

=º61(bõ 4T2 4TT„ú(1Løú3 2 î;¶2÷å ø ;(0…O4Jú3; 2)ú(ý 0ýø ;(6;k89ßú(ý û13;¶ú ø…7ß;(64T2 7ß%„ö

458Ÿú(O7 -/-—;6 $ # åø…7 $ # f136;(0…O4Jú38ŸþTù9ÿ

÷‡21(å7Tú3ø89ù967 789;345…;(;(8Ÿ2Ëf8Ÿ…45ù9789: ø

ø„ú(8Ÿú3øú(89þ `;¶ú(7ÿÐ2/ú(ý`132 ù9&2¯8Ÿ÷å0138Ÿú(896;6÷åøÿ |27 8Ÿ #

*,8Ÿ: ä vø ;¶ý2õº; ú(ýßTT13: 896;"|21 78fT13T„ú 6ùŸO4Jú(132 894 0ýø ;(6; 8Ÿ $ # !"%ý

ø„ú(÷äöù98

8¨7 0ýø ;(6;`ø 1( vøþ 21(O7 ø 1(27

! # ø7ßfõý61(Oø ;&89 ø 8Ÿ„ú(61¶ö

÷å678¨øú313ø : ,I

!î ,øåî89: T1x4T1(ÿ;¶ú3øù vî!)8 # %ýø ;xøäù92õT1TT13: ÿ

“ ú(ý8¨;%13ø : P2 )ú(ýT13|2 13)2 ;(T13þ O;ø Ð89„ú(6: T1

ø ú38Oøú38Ÿ2 2,ú(ý&=!øù9ùÆ1(O;¶8¨;¶ú3ø…45

õýT136ø;b2ºû…7;ú(ý&*,<)=!. ø132 7

! # ø 7 18 2þ

!‚ , ú(ý&*,<)=!.

78¨;(ø 00…Oø1L; O4Tø ;¶ ú3ý

ø„ú3÷ ù98

8¨7ßýø ; ø ý8Ÿ:ýT1 6T13: ÿ ú3ýø‚ø ú õ2öTù9645ú(132

ùŸ‡4513ÿP;¶ú3ø ùEõý894Lý 4T2 ÷å0W5ú(O;ºõ8Ÿú(ý ø ;¶ú(13890…0ýø ;(W"%ýù¨øú¶ú3T1!ýø ;ºø ùŸ2õT16T13: ÿ

ø ;2 &ø001(2„ø 4LýO;býø ù@öCûù9ùŸ89: P. 0…61(89÷åT„ú3ø ùŸù9ÿ „ý2õTþ 616„ø ø 8¨;¶2 ú(132 08¨4ºù92 :8¤ú3789øù

1(O;¶8¨;¶ú3ø…45 ,õý8¨4Lý€8¨;äú(ý ;(8Ÿ:øú313 2); ú31(890… 0ý…ø ;(6;6. ýø ;ä2 ùŸÿ T6€2 ;¶61(þ67 89wø

ú(89ù¤ú367k÷kø : Tú(8¨4%ûTù¨7 Y '!1Í6T13: ÿ‡4Tø ù94Tù9øú(892 ;Í;¶:: O; ú¦ú3ýøú

…ø„ú(÷‡öùŸ8

8¨7å0ýø ;(6;

÷køÿåø ù9;(2 |27 Tù92õ

!# &89kú3ý)ø ;(T4Tx2Ë89÷å0138¤ú38ŸO;P=º2õTþT1Oú3ýx6T13: ÿ

2/ú(ý`‚î8¨;%ù92õ61(O7 ÿ 89÷‡01(8Ÿú(896;67&ú32‡ú(ý7|2 13÷køú(892 Ð2¯8¤úL;%ù9øú¶ú3894T; ú31(45ú(13

"%ý8¨;bf645úÍ8¨;¦÷å2;¶úÍ1(6ùŸ6þø„úb8Ÿåú3ýx789ù9ú(ºù989÷‡8ŸúÍ2Æ;(÷køù9ù !f„ø7‡ú3ýx*,<)=!. 89;¦ú(ý61(|2 13

2úÍ;¶ú3ø ù989‡ú(ý8¨;¦ù98Ÿ÷å8Ÿú6:%õýT132 2 ;(T13þ 6;—ú(ý(<)=x.8"%ý%TT13: 896; |2 1¯ú3ý ùŸ

4513ÿ; úLøù¨;ø13&;(ý2õ 2ú(ý 89 ú(ýä4Tø ;(&2¦ø‡ú(1389ø : ù9ø 1 v452„ú(89„2 ;%ù98Ÿ6;ø7 øk;

ø13

ù9øú¶ú3894Tå;(ÿP÷å÷‡Tú(13ÿ 132>"T ùŸ896;/"%ýä6T13: ÿ 78fT13T4T Tú õ6T ú(ýO;¶‡ú õ2 46ø ;(6;!89;

Pú(13T÷å6ùŸÿ ú38ŸPÿ v2 ú3ýå2 1L7T1)2!Ë*1(2÷ 45ù¨ø ;3;¶8¨4Tø ù,4T2 ;(897T1Løú(892 …;TW2 ‡õ2 ù¨7 %„ö

0…O4Júú(ýøúø)ú(1389ø : ù9ø 1¦ù9øú¶ú(8¨45xýø ;ø&ùŸ2õT1¦6T13: ÿÛú(ýø ø`;

ø 1(ù¨øú(ú(8¨45 º'!1b6T13: ÿ

4Tø ù94Tù9øú(892 ;!8978¨4Tøú3ú3ýøú)ú(ý8¨;)89;)4521(13645úx89 ú(ýäù92õ%ö

! ùŸ89÷å8¤úOWõýT136ø ;!øú&ù9ø 1(:T1x7Tö

;¶8Ÿú(896;ÛøЂ õ8¤ú3ýâ;

ø 1(TöCù¨øú(ú(8¨45å;¶ÿP÷å÷å5ú(13ÿ ýø;`ø ùŸ2õT1&6T13: ÿ ú3ýø ú3ýåú(1389ø : ù9ø 1

2 ;(8Ÿ÷å89ù9ø 1 6ýøþP8Ÿ2189; |2 7 |21ú(ý&ú õ2 öC6ùŸO4Jú(132 ùŸ4T1(ÿ;¶ú3ø ù3=x2õ6þ 616„ú(ý89;

4Lýø: x2—;¶ÿP÷å÷å5ú31(ÿå24T4T13;øúûù9ùŸ89:ö*vø 45ú(21Íþøù96;6PõýT13x2 ú(ý610ýø ;(6;Íýøþ )øù92õ61

T61(:ÿ)$Pú(ý;

ø135öù9øú¶ú3894T);(ÿP÷‡÷åTú(13ÿ 2,ú(ý`î! 8¨; vøþ 2 1367 2 ù9ÿÐø 2þ

! ,

õýT13

ø ú3÷‡öCù98

897Æ ú õ2 öC6ùŸO4Jú31(2

ù9 Pø7k;¶ú(138Ÿ0Wx0ýø ;(6;bø 1(%ú3ýx:1(27å;¶ú3øú3

.bþT 8%2 1&136;(ùŸú3;)ú(ýP;`;(:: 6;¶ú&ú(ýøú;

ø 1(‡Tù9645ú(132 4513ÿP;¶ú3ø ù9;&ø 1(å2 ú`;¶ú3ø ù9 fú(ýTÿ

÷køÿ vøþ 21(O7 8%ú(ý ý2„; úÛ÷køú(T138¨øùbýø;%ø4Jú3ùŸÿ ú(ý8¨;Û;(ÿP÷å÷‡Tú(13ÿ ,;¶4Lýâø;`89 L

ý5ú3T132;¶ú(134Jú3136;

"%ýT61(:ÿ)136;(ùŸú3; |2 1 $#‚!ø13;(ý2õÛ89ä*,89: P “å452„ú(1Lø ;¶úËú(2 $# ø

øö

ú(÷ ù98

897 89;;¶ú3ø

ù9!ø132 7 !# õý61()ø`ú õ2öTù964Jú31(2

ùŸ&4513ÿ; úLøùWýø ;Íú(ý

ùŸ2õ6;¶ú¦T61(:ÿ '!1¦6T13: ÿ46øù¨45ù¨øú38Ÿ2;¦;¶: : O; ú,ú(ý…øúÍø&*,<)=!. ÷å89: ý„ú |27åø132 7

! # ä2 1x2ú3 ý2õ6þ T1O„ú(ýøúºú(ýT61(:8ŸO;%2¯ú(ý

ø„ú(÷äöù98

8¨7 0ýø ;(6;xø13

http://doc.rero.ch

 J•’¨ 6” ˜f™OJ›“Ž¶›Íœ¤•)˜—J‘“’¨œŸJ«Ÿ«š%¥Wœ¤«Ÿ«Ž–

¹¹

› Õ

5 10 15 20 25

-0.2 -0.15 -0.1 -0.05

−0.15

−0.20

−0.10

−0.05 1/9 1/7 1/5 1/3

(a)

0.1 0.2 0.3 0.4 0.5

partial filling factor

cohesive energy

quantum liquid stripes M=1

M=2

5 10 15 20 25

-0.175 -0.15 -0.125 -0.1 -0.075 -0.05 -0.025

0.2

0.1 0.3 0.4 0.5

−0.15

−0.10

−0.05

partial filling factor

cohesive energy

1/9 1/7 1/5 1/3

(b)

quantum liquid M=2

M=1 stripes

mixed phase

GId†WçJ†+efHJVB YCGÓ5BºB ?B DCdJGIB YÍHLQËACVBºSGØ B DCB ?5AhOVFLYCB Y(ÙPGI?‡N?GAEYÍHLQ3n

¸

lce †¨F

í

hVFLYEB YGI?0gîçJ† HJD

AEVB,cONccKIB/hVFLYCB Y¶Ù6cHLAEVACVB—ACDEGÝFL?dJNKÝFLDŸZ HJ?TAEGI?TNHJNYËKIGI?B YFL?SACVB/YCÞTNFLDCB—Z DEX6YEACFLK 9cDEHJB ?!KIGI?B Y…FLDCB

YEVH(ڗ?„†9c

í

hOVFLYCB YËGI?dg ÔO†6ãËVB¯dJDF XºKIGI?B YÆGI?SGIZ¶F3AEB¯ACVB,cNccKIB“Ü@Z DvXOYvAFLKB¶?OB¶DEdJGIB Y—GI?ºAEVB¯hDEB¶YEB ?Z B¦HLQ

FL?!GIghNDCGA@X%h HLAEB ?TAEGÝFLK¨Ù FL?SxACVB¯ACFL?dJB ?5ACY¯DEB hDCB YCB ?5A/FgGàOB SxhVFLYEB5†

þ 61(ÿ 4TùŸ2„;¶‡ú32 ú(ýøú2%ú(ýk‚^ø7Ɨ8Ÿ ú3ý 4Tø;¶å2

! # fú32 ø ÷‡867 0ý…ø ;(‡2%ø

î^ø…7 øÐú õ2öTù9645ú(132

ù9 4513ÿ; úLøùCÆõý8¨4Lý 8¨;`13T0136;(T„ú367

ÿ ú(ýåúLø:T„ú —ú89;

ú(ý61(|2 13å2úä4TùŸOø1`õýTú(ý61ú3ý

ø„ú3÷ ù98

8¨7 13T÷kø89;`;¶ú3ø ùŸ 89 ú(ý 01(O;¶645k2

8Ÿ÷å01(8Ÿú(896;6Ëõý8¨4Lý ù92õT1)ú(ýk6T13: ÿ 2ú3ý 4513ÿ; úLøù¯0ýø;¶O;TËø;`;¶ý2õ ÿ ú3ý 7ø ;(ýO7

4513þ O;,"%ýTÿ ýøþ TT€4Tøù¨45ù9øú(67 |2 1åøâ89÷å0138¤ú ÿ ;¶ú(13T: ú(ýi

Y

# , „ & Y e&+

õýT13 i Y

89;%ú3ýÛ4Lýø 13ø4Jú3T1389;¶ú(8¨4x6T13: ÿ 2¦øk;¶ý21¶ú(öC1Lø: &ø ;3;¶8¨ø 0W2ú(6„ú(8¨øùËõ8Ÿú(ý 4521¶ö

1(6ù9øú(892 ù9T:ú(ý1: . 0…61(89÷åT„ú3ø ùŸù9ÿ Pøä;(÷køù9ùf÷åø58Ÿ÷ä÷ 89 ú(ý)ù92 : 8Ÿú(789ø ùW136;(8¨; úLø4T

ø132 …7

! # 8978¨4Tøú(O; øß8Ÿ…458908Ÿ6„ú ÷‡6ù¤ú38Ÿ: 2)ø 4T1(ÿ;¶ú3øù%0ý…ø ;(9 "%ý89;|Oøú31(

ýø ;&1364TT„ú(ù9ÿ T6â; ú378967 8Ÿ ÷å2 13k75úLø89ù ÿ)61(þø8¨;9 &

õý2 |27 ú(ýøúú(ý89;

÷køC8Ÿ÷ä÷ õý894Lý 7645136ø;¶O;¦õý6 ù92õ61(89:&ú(ýxú3T÷å0…613øú(13P;(0ùŸ8Ÿú3;89ú32ú õ20W6ø5";

;¶60ø1Løú367 ÿßø ;¶÷køù9ùºù924Tøù÷å8989÷Û÷ 01(O458¨;¶6ùŸÿ€øú

! # õ8¤ú3ýß894T1(Oø ;(8Ÿ:

1(6÷å8Ÿ8¨;345T„úºö760…676ú!f64Jú)ýø ; 6T 2 ;(T13þ 67 89 ú(ýۂ 1(6: 89÷‡Û8Ÿ ú3ýÛù92õ6;¶ú

-—- ( .Íþ T 8¦ú(ý89;!f645ú!÷køÿÐ8978¨4Tøú(‡ø

ø„ú(÷äöù98

8¨7 : 132 7 ; úLøú38Ÿ Pú(13T÷åTù9ÿ

013Ð;3ø÷å0ù96;6¯8¤úå÷køÿ ø ù9;(2

7613;¶ú(2P27 89ß78fT13T„úäú3T13÷k;T,õýT136ø;ú3ý 4513ÿP;¶ú3ø ùE

õý8¨4Lý 8Ÿ ú(ý8¨;&;(4TTø 1(892 13T÷kø89;xú(ý # Ð: 132 …7 ; úLøú(f÷‡6ù¤úL;&øú!1Løú3ýT1)ù92õ |2

ú(ý&213761Í2—ú(ý!6T13: ÿ 78fT13T4T 5ú õT6 ú(ý)‚wø 7kú3ý

…ø„ú(÷‡öùŸ8

8¨7 0ýø;¶J

ú(ý

ø„ú3÷ 452ýT13T4Tº2—ú(ý)ùŸ8

8¨7Ð78¨;(0ù9øÿP89:Û*¯<)=x. |Oøú31(O;89;2 ù9ÿ 7O; ú31(2ÿ67køú

ý89: ý61 .

!—ñ

p`r,lsOt#"Íylm,sOu|n6uEó…m,s

'!1`TT13: ÿ 46øù¨45ù¨øú38Ÿ2;`;(: :6;¶ú)ú3ýøúÛú(ýkú313ø ;(8¤ú38Ÿ2; Tú õ6T ú(ý 78W61(6úä0ýø ;(6;

ø13%$'&(*)+&-,&"%ýû13;¶ú¶ö2 1L761—0ýø;¶Íú(1Lø;(8Ÿú(892 ; Tú õ6Tú3ý

…ø„ú(÷‡öùŸ8

8¨7ø7ú(ý

8Ÿ…;¶ù¨øú38Ÿ: ùŸ‡4513ÿP;¶ú3ø ù9;º÷åøÿ 4Tø ;¶äøkýPÿP;¶ú(61(Tú(8¨4Tø ù 6ýøþP8Ÿ21º89 ú(ý‡=xøù9ù—136;(8¨; úLø4T

ø132 …7kú(ý!ú313ø ;(8¤ú38Ÿ2Ð0W2 89„ú3;6õý894Lý—Pú(2äú(ýd"P2õù967:!2—ú3ý`øú3ý2 1L;TPýø;2ú TT

1(60…21¶ú367 ÿ5ú

ù¨;(2 ú(ýä0ý…ø ;(`ú(1Lø;(8Ÿú(892 ;

Tú õ6T

ù9ä4T1(ÿ;¶ú3øù¨;ºõ8Ÿú(ý 78W61(6ú 8

0…61b;¶8Ÿú(ºø 1(û1L;¶úb2 1L7T1O8Ÿkø:1(6T÷åT„ú¯õ8¤ú3ýåú(89÷å5ö“7T0WT7T„úÍ=xø 1¶ú31(65ö“*24#"4Tø ù94Tù9øú(892 ;

ÿ L2ú/. 08 "%ý8¨;`ù96ø7;)ú(2 ø 0ýø;¶k4T2„%89;¶ú(645Ë2 1ø ÷å8fO7 0ýø ;( —ø 1(27 ú(ý

http://doc.rero.ch

è

·—Å—·Ë©(Ž¶‘¶§¶œª

ú(1Lø;(8Ÿú(892 0…28Ÿ„úL;89âø ûù9ùŸ89:ö*vø 45ú(2113ø : Æõý8¨4Lý 89;ä76;345138 67 ÿ ø ú3ø : 6ú2 ú(ý

T61(:ÿ‡4T13þ 6;6 øú ,Ÿ !î ,`89 $ # 4 „*,89: -. 0WT138Ÿ÷åT„úLøù9ùŸÿú(ý61(

89;6þ„8¨7645 |2 1%;¶…4LýÐøä÷‡867 0ýø ;( „õý8¨4Lý 8¨;1(6þ 6ø ùŸO7 ÿ øÛ72 ù95ö0…Oø5"k;¶ú(134Jú31()89

ú(1Lø;(0W2 1(ú¯÷åOø ;(1(6÷åT„ú3;,7T1b÷å8¨45132öõøþb8Ÿ131Lø 78¨øú38Ÿ2Ë1(O45T„ú3ùŸÿ0WT1 |2 13÷å67

ÿä-Ë6õ89;

9

Æñ DäóWm/ôzvj,s6uEó…m,s

“Û45245ù9;(8Ÿ2ËOõýøþ b0WT1 |2 13÷å67&6T13: ÿ&4Tø ù94Tù9øú(892 ;,|2 1¯452÷‡0W5ú38Ÿ:

ø„ú3÷ 0ýø ;(6;

8Ÿ‡89ú3T13÷å678¨øú3%-/-—;

åøùŸú(61(øú(892 Tú õ6T‡8Ÿ;(ù¨øú38Ÿ:)Tù9645ú(132 ö“;(2 ù9897äø7

ø„ú(÷äö

ùŸ8

8¨7 0ýø ;(6;6õý8¨4Lý 78¨;¶0ù¨øÿ ú3ýÛ*¯<)=x.º89;!øúú(ý2 138Ÿ:8Ÿ 2¯ú3ý2 ;¶61(þ67Ð1(6T„ú(1Lø4T

2ú(ýå(<)=x.+89 $ # åø…7 $ # 9 '8å"%ý‡ú(1Lø;(8¤ú38Ÿ2; Tú õ6T ú(ýk78fT13T„ú`0ýø ;(6;

ø13 |2 7€ú32 û1L;¶ú¶ö2 1L7T1åø7ß÷køÿâù96ø7âú32âø þø 1(895ú ÿâ2!2 ;¶61(þø ùŸ 0ýT2÷‡6ø

“ ú(ý 4Tø;¶k2ú313ø ;(8¤ú38Ÿ2; 5ú õTT ù9 4513ÿ; úLøù¨;`õ8Ÿú(ýâ78W61(6„úÛTù9645ú(132 P÷ T1

0…61Ð;(8¤ú3 ø 0ýø;¶ 4T2P89;¶ú(645 8¨; %0…O4Jú(O7 : "%ý8¨; ;3456ø138Ÿ2 8¨; ;(00W2 1(ú(O7 ÿß136456„ú

÷å894T1(2 öCõ%øþ Ð0…61(89÷åT„ú3;6¦89ßõý894Lýwø 72

ùŸTöC0W6ø>" ; ú31(…4Jú(1( ýø ;

T6w2

;(T13þ O7â89

ú(ýÐùŸ2: 8Ÿú(…78Ÿ…øùÍ4T2 7…4Jú(89þP8¤ú ÿ 89 ø ûù9ùŸ89:ö*vø 45ú(2113ø : ,Ÿ ! ,I 9k89 : 2P27

ø:1(6T÷åT„ú%2 1%ú3ýT21(Tú(8¨4TøùÆ89Pþ O; ú38Ÿ:„øú(892 …;:

ô m,óåzEtP~ BWoâtPmfn6s

ø 4#"P2õù967: |1(8¤ú |ù`789;345…;(;(8Ÿ2; õ8Ÿú(ý02 13 a¶; 6ø  %.b8¨;¶6;¶ú(T89Ë%" )8¨øö

÷kø1L4Lý8E ö# ,-—8E¯# 2P6;3;¶T1O/ø…7 4¦4LýT8¨7ù*¦"%ý89;äõ2 1 " õ%ø ;ä;¶00…21¶ú367 ÿ ú(ý

Põ8¨;(;!øú(892 …øù—*2 7øú(892 |2 1x4589T„ú(8Ÿû…4`#O;¶Oø1L4Lý 7T1: 1Lø„úºº2 ö

0 t Ft„ytPm,ô tPs

! #"#$%'&)(+*,.-/1032-45036768-9!:%;=<>@?ABC>D<E3

F+HGGIJLK! MN@KPO'%QRQRS!K #T.U=%$V;WXY!NZ #KPOZ[N"#"7%;&\(Z*],C-^/_032-545036768-5`!a;%;b@>>RAB=>>cE3d

QR'QR'S!K #T.U=%'GGJLK! MN@KPO'%!$VWX'YZ!NZ #K]OZ[NZ"#"7%'&\(Z*],C-e/1032-fg9he%=D@?]<iAB=>>c@E3d'QR

QR!S!K #T.Uj]$VkGI!GIJLK l]N@KPO'%mon.m7p+-fg99;%'><@F]cHAB=>>qE3

<Z!QK+TC[[$!T.Ur$!VHs!tr'u)! #N@T.U=%'&)(+*,.-/1032-!fg9he%?vvciAB=>>c@E3

biQRw5@;"M # yx036{z|M-M%&)(+*,.-/_032-45036768-Z}~;%+<>bABC>>>E3d@ji036^z|M-M%Z€'|mopL€!6‚z]680„ƒ…†g†„‡ˆ'-

‰ :Š;%<D>HABC>>>E3

?+Hs!w5‹^"#[TC$![BŒT."M$Ž036z|M-M%!&\(Z*,.-/1032-45036768-}}%vqcDvA‚Fvv@FE3

cZJ‘'u)K+K’'T.U‘036“z|M-#%&\(Z*],.-e/_032-f‘a!:;%PFD?AB=>>>@E3

q+iQR@”„•rK+T.U–!"#%@w5;T=VT3UT.U=%@]$Vgu+QK]UX"#[YZ—"yŒ%&\(Z*,.-/1032-f‘a};%@F]b=<v@F‘A‚Fvv<@E3d+&)(+*,.-

/_032-!f‘a!Š;%eP?<FqHA‚Fvvb@E3

DZHS)g˜j] lV$T%'&\(Z*],.-e/_032-4e036768-'9

‰

%'cv@?ABC>D<E3

>Zi•„QUŒ+xk$!VkYZ]$!N]U=%/1032-™R=p+-&\(Z*],C-`9;%=vZkA‚F]vv<@E3

Cvš›w{$R036\z|M-M%&\(Z*],.-/1032-'45036768-}œ;%DFvkABC>>>@E3d!QRw5Z"# # yxR036)z|M-M%+‚ž Ÿ¡}!œ;%D@FPbAB=>>>E3

…!)K$[ # 5]$VHG!G'QHPUXVV"#$;%'&\(Z*],C-/_032-!f ‰ 9%e=>?>HABC>@qqE3

=FZH•„'•rT.UO"#[g036“z|M-#%’UTC’U"#$+Œ=¢£CK$!V¤‚—¥]Œ3¦]vbv@FZCc>Z

C<š›w{]$036“z|M-M%!&)(Z*],.-e/_032-;45036768-'}};%PqcDvFA‚FvvFE3

.bHQR'”„•rK+T.U–!"#¥]$VHu'QKUX]"M[rY—"yŒ;%§‡Z¨3©(Z*,.-;45036768-aœ;%q<cHA‚Fvv<@E3

=?ZkIujªKŒZ«T036z|M-M%&)(Z*],.-;/1032-fga};%;P??]<@FqiA‚F]vv<@E3

CckIQR;T.¬_"#[‘036z|M-M%’UT.’U"#$+Œ=¢£.K$VZ¤‚—¥]Œ3¦v]b@vZCb@cFZ