光系統 II 核心複合體能量傳遞動力學的理論研究

全文

(1)੢ΘႨᝯʨዕ୎ዕਖˢዕԦ ၭʦቈ́ 'HSDUWPHQW RI &KHPLVWU\ &ROOHJH RI 6FLHQFH. 1DWLRQDO 7DLZDQ 8QLYHUVLW\ 0DVWHU 7KHVLV. γԦ஀ ,, औ˻ሷϐᝂ঻ඹ෭ჳੂʍዕ‫୎ڄ‬ቈߧԥ $ 7KHRUHWLFDO 6WXG\ RI (QHUJ\ 7UDQVIHU '\QDPLFV LQ WKH 3KRWRV\VWHP ,, &RUH &RPSOH[. ᒧϭࣘ 6KRX7LQJ +VLHK. ‫ݣ‬዗૥૗íቷࢍ‫׫‬૥૗ $GYLVRU <XDQ&KXQJ &KHQJ 3K'. ˀൡͺ੢ ϶ ̇ -XO\ . doi:10.6342/NTU201802891.

(2) LL. doi:10.6342/NTU201802891.

(3) doi:10.6342/NTU201802891.

(4) LY. doi:10.6342/NTU201802891.

(5) ဇ࠱ γϐѕ·‫ݵ‬ϙ୍ʕΆ‫ٵ‬Άϫ༬‫ۍ‬ગࡌ࠱‫ཫڄ‬ദé͟ළֻ‫ؠ‬γϐЂ γሷϐᝂă/+&ĄçЂූ˯෍γՓઅ঻ඹ෭ൂ˫ᏻˀ˻ă5&VĄéѕ޴ यमΆϾ˺ᐂ‫ڄ‬γԦ஀ ,,ă36,,Ąऔ˻ሷϐᝂ‫ݵ‬ᘕᓉ‫ڄ‬γϐѕ·ሷϐ ᝂ˃ɾé36,, औ˻ሷϐᝂ‫ݵ‬ɾࡴ࿬ၳʅ႞ᝂç̸͟҉͗ࡴ˭ለሷϐᝂ ă&3 ֜ &3Ą֜ղࡴ˫ᏻˀ˻ă5&Ąé࠱ʄ༱௠ၲሷᕺ‫ڄ‬γϐѕ· ሷϐᝂˀ‫঻ڄ‬ඹ෭᎔ᄔ࠱Љं‫୎ڄ‬ቈᆦ‫ܓ‬ç௠ᆟ‫ڄ‬ᆦ‫׫̣̈́ܓ‬࿧ϙι ୏Ԧ஀ˀ‫ڄ‬ጒച࿽঻ඹᕢ୰ཫദéϚ௠ෛʳѕˀçӍ࡭੪‫ؠ‬ζ‫˜ڄۮ‬ ʪੂʍዕă0'Ąᆦᐈߧԥ഻‫س‬ಏ̳ʄ 36,, औ˻ሷϐᝂˀጒച࿽঻ඹᕢ ୰‫ڄ‬Љंᆦ‫ܓ‬Փघየ PRGLILHG 5HGILHOG WKHRU\ ࠳ၼጒച࿽˃෇঻ඹᕢ୰ ‫ڄ‬௥୊ગᆚé͟ಇ࠽ʄ . इ &3è&3 ̣˪ 5& ‫ڄ‬ҁЂγᗯ̣˪ 36,, ˀ ࡴചи࿋˃෇‫ڄ‬ηጒച঻ඹᕢ୰ੂʍዕéЏ͙çϚӍ࡭‫ڄ‬ᆦ ‫ܓ‬ˀçʛШᅱʄղၲ̟࠱ྐம˜ᕹ௯ࣜ PD1 ௯ࣜ֜ ChlD1 ௯ࣜéӍ࡭ ച୏Ϛ 36,, औ˻ሷϐ‫ڄٵ‬వᝂˀçન &3ă&3Ąռ &3ă&3Ą ‫ڄ‬ጒച࿽঻෭ჳཫദఛЉ̈́঻௢ཫ 5&éЏ͙çӍ࡭ച୏ &3 Љѕ޴ ঻ඹቆ໢዇‫঻̷ڄ‬ç̣̈́͟෭ჳవᝂ˃෇‫ڄ‬ጒച࿽঻ඹçՓ̝ະղࡴ 5& ˀЉɾࡴϚᘕ௻‫ٶڄ‬࿽इç՟દ 36,, औ˻ሷϐ‫ݠۘٵ‬ਢं୊‫ྐڄ‬ மᕢ୰éఛ݈çӍ࡭ച୏ &/$ ̈́঻‫ݵ‬ղၲ 36,, औ˻ሷϐ‫ٵ‬వᝂ˃ ෇঻ඹ෭ჳ‫ڄ‬ጂᆭéӍ࡭‫ڄ‬഻‫س‬ಏ̳ʄ 36,, औ˻ሷϐ‫ٵ‬ဟܿϾʅ႞ᝂ ഻ဟ‫ࢍ঻̈́ڄ‬ϕéЏ͙çʛ޴୎༱ 36,, औ˻ሷϐᝂˀ‫ڄ‬γࣵᐺಏաʄ ๘‫ڄ‬Գ༱çՓ̝ࣉΕ੪‫˜ؠ‬ʪੂʍዕᆦᐈ֜ඹʪˢዕ࠳ၼ‫୶ڄ‬ɾၲࢍ ୎̣̄ٗ̈́Љंϙ·‫ا ؠ‬ሷᕺγϐሷϐᝂˀγࣵᐺ‫ੂڄ‬ʍዕé. Y. doi:10.6342/NTU201802891.

(6) YL. doi:10.6342/NTU201802891.

(7) $EVWUDFW 7KH 3KRWRV\VWHP ,, 36,,

(8) FRUH FRPSOH[ WKH HQJLQH IRU R[\JHQ JHQHUD WLRQ LV DQ LPSRUWDQW SKRWRV\QWKHWLF FRPSOH[ ,W LV D V\PPHWULF GLPHU WKDW FRQWDLQV IRXU DQWHQQD FRPSOH[HV &3 DQG &3

(9) DQG WZR UHDFWLRQ FHQ WHUV 5&V

(10) 8QGHUVWDQGLQJ HQHUJ\ WUDQVSRUW LQ VXFK FRPSOH[ SKRWRV\QWKHWLF FRPSOH[HV UHTXLUHV WKHRUHWLFDO HIIHFWLYH PRGHOV WKDW FDQ IDLWKIXOO\ UHSURGXFH H[FLWDWLRQ HQHUJ\ WUDQVIHU ((7

(11) G\QDPLFV ,Q WKLV ZRUN ZH SUHVHQW DQ HIIHF WLYH PRGHO IRU ((7 LQ WKH 36,, FRUH FRPSOH[ EDVHG RQ D SUHYLRXV PROHFXODU G\QDPLFV 0'

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doi:10.6342/NTU201802891.

(13) YLLL. doi:10.6342/NTU201802891.

(14) &RQWHQWV LLL. ʤִ༵࢜๡ᅜ‫׆‬ए. Y. ဇ࠱ $EVWUDFW . ,QWURGXFWLRQ . . YLL . /LJKW KDUYHVWLQJ DQG FKDUJH WUDQVIHU RI R[\JHQLF SKRWRV\QWKHVLV . . . 7KH VWUXFWXUH RI SKRWRV\VWHP ,, . . . 3ULPDU\ FKDUJH VHSDUDWLRQ LQ WKH UHDFWLRQ FHQWHU . . . (IILFLHQW ((7 DQG KLJK TXDQWXP \LHOG 4<

(15) RI FKDUJH WUDQVIHU &7

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doi:10.6342/NTU201802891.

(17) . . WLRQ . . 6LPXODWLRQ RI WKH DEVRUSWLRQ VSHFWUXP . . (IIHFWLYH PRGHOV IRU 5& &3 DQG &3. . . 0RGHO +DPLOWRQLDQ . . . 3LJPHQW ODEHOV RI 36,, FRUH FRPSOH[ . . . %ORFN +DPLOWRQLDQV RI 36,, FRUH FRPSOH[ . . $Q HIIHFWLYH PRGHO IRU 5& . . . &DOLEUDWLRQ RI HRC . . . )UHQNHO H[FLWRQ +DPLOWRQLDQ RI 5& . . (IIHFWLYH PRGHOV IRU &3 DQG &3 . . . &DOLEUDWLRQ RI HCP 47 DQG HCP 43 . . . )UHQNHO H[FLWRQ +DPLOWRQLDQ RI &3 . . . )UHQNHO H[FLWRQ +DPLOWRQLDQ RI &3 . . . . . +DUPRQLF TXDQWXP FRUUHFWLRQ RI HQHUJ\ JDS DXWRFRUUHODWLRQ IXQF. (IIHFWLYH PRGHO IRU 36,, FRUH FRPSOH[ PRQRPHU &

(18). . . 0DVWHU HTXDWLRQ DQG UDWH FRQVWDQW PDWUL[ EDVHG RQ 057 . . . ([FLWRQ VWDWHV DQG LQWHUFRPSOH[ H[FLWRQLF FRXSOLQJV IRU 36,, FRUH FRP SOH[ PRQRPHU &

(19) . . ([FLWDWLRQ HQHUJ\ WUDQVIHU G\QDPLFV LQ D PRQRPHU RI 36,, FRUH FRPSOH[ &

(20) . $Q HIIHFWLYH PRGHO IRU 36,, FRUH FRPSOH[ &

(21) . . . ([FLWRQ VWDWHV DQG LQWHUPRQRPHU H[FLWRQLF FRXSOLQJV IRU 36,, FRUH FRP SOH[ &

(22) . . . ([FLWDWLRQ HQHUJ\ WUDQVIHU G\QDPLFV LQ 36,, FRUH FRPSOH[ &

(23) . . . 0XWDWLRQ DQG D FORVHG 5& IRU 36,, FRUH FRPSOH[ . . . ([FLWDWLRQ HQHUJ\ WUDQVIHU IRU 36,, FRUH FRPSOH[ ZLWKRXW &/$V . . ([FLWDWLRQ HQHUJ\ WUDQVIHU IRU 36,, FRUH FRPSOH[ ZLWK D FORVHG 5& . . ([FLWDWLRQ HQHUJ\ WUDQVIHU IRU PXWDQW 36,, FRUH FRPSOH[ ZLWK D FORVHG 5& . . [. doi:10.6342/NTU201802891.

(24) . &RQFOXVLRQ. . %LEOLRJUDSK\. . [L. doi:10.6342/NTU201802891.

(25) [LL. doi:10.6342/NTU201802891.

(26) /LVW RI )LJXUHV . ,OOXVWUDWLRQ RI OLJKW UHDFWLRQ LQ WKH 36,, RI KLJKHU SODQWV . . . $ VWUXFWXUDO PRGHO RI C2 S2 M2 W\SH 36,,ü/+&,, VXSHUFRPSOH[ . . . 7KH FU\VWDO VWUXFWXUH RI 36,, FRUH FRPSOH[ LQ 7 YXOFDQXV DW D UHVROXWLRQ RI c . . . ,OOXVWUDWLRQ RI WKH FKORURSK\OO DUUDQJHPHQW LQ WKH 36,, FRUH FRPSOH[ . . . &KURPRSKRUHV LQ WKH 5& DQG R[\JHQHYROYLQJ FRPSOH[ 2(&

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doi:10.6342/NTU201802891.

(28) . ([FLWRQLF FRXSOLQJV DQG H[FLWRQ VWDWHV LQ WKH 5& . . D

(29) 7KH DEVRUSWLRQ VSHFWUXP RI WKH &3 E

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βFDURWHQHV . . [LY. doi:10.6342/NTU201802891.

(31) /LVW RI 7DEOHV . 7KH GHORFDOL]DWLRQ RI H[FLWRQ VWDWHV LQ WKH 5& . . . 7KH GHORFDOL]DWLRQ RI WKH 5& . . . 7KH GHORFDOL]DWLRQ RI WKH 5& . . [Y. doi:10.6342/NTU201802891.

(32) [YL. doi:10.6342/NTU201802891.

(33) &KDSWHU ,QWURGXFWLRQ . /LJKW KDUYHVWLQJ DQG FKDUJH WUDQVIHU RI R[\JHQLF SKRWRV\QWKHVLV 2[\JHQLF SKRWRV\QWKHVLV LV D W\SH RI SKRWRV\QWKHVLV WKDW FDQ SURGXFH R[\JHQ 7KH. R[LGDWLRQ RI ZDWHU WR PROHFXODU R[\JHQ LV FDUULHG RXW E\ WKH R[\JHQHYROYLQJ FRPSOH[ 2(&

(34) RI SKRWRV\VWHP ,, 36,,

(35) 7KLV SURFHVV UHTXLUHV DEVRUSWLRQ RI PXOWLSOH SKRWRQV 36,, LV D PHPEUDQHERXQG SLJPHQWSURWHLQ FRPSOH[ WKDW FDSWXUHV VXQOLJKW DQG WUDQVIHUV OLJKW HQHUJ\ WR WKH UHDFWLRQ FHQWHU 5&

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doi:10.6342/NTU201802891.

(37) )LJXUH ,OOXVWUDWLRQ RI OLJKW UHDFWLRQ LQ WKH 36,, RI KLJKHU SODQWV 7KH 36,, LV ORFDWHG LQ WKH WK\ODNRLG PHPEUDQH %ODFN OLQHV LQGLFDWH WKH WK\ODNRLG PHPEUDQH <HOORZ DUURZV LQGLFDWH WKH OLJKW KDUYHVWLQJ IURP SHULSKHUDO OLJKW KDUYHVWLQJ FRPSOH[ ,, /+&,,

(38) WR WKH UHDFWLRQ FHQWHU 5&

(39) %OXH DUURZV LQGLFDWH WKH SDWK RI HOHFWURQ WUDQVIHU 3KH LV WKH SKHR SK\WLQ QA DQG QB DUH SODVWRTXLQRQHV 2(& LV WKH R[\JHQHYROYLQJ FRPSOH[. . 7KH VWUXFWXUH RI SKRWRV\VWHP ,,. 36,, LV D FRPSOLFDWHG SLJPHQWSURWHLQ FRPSOH[ HPEHGGHG ZLWKLQ WKH WK\ODNRLG PHP EUDQH RI F\DQREDFWHULD DOJDH DQG KLJKHU SODQWV ,Q JUHHQ SODQWV WKH WK\ODNRLG PHPEUDQH IUHTXHQWO\ IRUP VWDFNV RI GLVNV DQG WKH FRQWLQXRXV DTXHRXV SKDVH HQFORVHG E\ WKH WK\ ODNRLG PHPEUDQH LV WKH WK\ODNRLG OXPHQ 7KH WK\ODNRLG OXPHQ SOD\V DQ LPSRUWDQW UROH IRU SKRWRSKRVSKRU\ODWLRQ GXULQJ SKRWRV\QWKHVLV ,Q )LJ WKH VXUIDFH ZKLFK WKH 2(& DWWDFKHG WR LV WKH OXPHQDO VXUIDFH DQG WKH RWKHU VLGH LV WKH VWRPDO VXUIDFH >@ ,Q SODQWV WKH 36,, VXSHUFRPSOH[ FRQWDLQV D YDULHW\ RI SHULSKHUDO OLJKWKDUYHVWLQJ FRPSOH[HV LQFOXGLQJ WKH PDMRU OLJKWKDUYHVWLQJ FRPSOH[HV ,, /+&,,

(40) PLQRU DQWHQQD FRPSOH[HV &3 &3 DQG &3

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doi:10.6342/NTU201802891.

(42) )LJXUH $ VWUXFWXUDO PRGHO RI C2 S2 M2 W\SH 36,,ü/+&,, VXSHUFRPSOH[ 7KH PRGHO ZDV FRQVWUXFWHG EDVHG RQ WKH HOHFWURQ PLFURVFRS\ PDS DQG WKH FU\VWDO VWUXFWXUHV RI 36,, 3'% $5&

(43) PDM/+&,, 3'% 5:7

(44) DQG &3 3'% 3/

(45) 6XEXQLWV ' ' &3 DQG &3 RI 36,, FRUH DUH FRORUHG LQ SXUSOH VDOPRQ UHG RUDQJH DQG JUHHQ UHVSHFWLYHO\ ĩ6Ī ĩ0Ī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

(46) VLPXODWLRQV DQG TXDQWXP PHFKDQLFV PROHFXODU PHFKDQLFV FDOFXODWLRQV EDVHG RQ WKH ;UD\ VWUXFWXUH RI 7KHUPRV\QHFKRFRFFXV YXOFDQXV > @ 7KURXJK FRO ODERUDWLRQ ZH REWDLQ WKH 0' VLPXODWLRQ GDWH 7KHUHIRUH RXU VWXG\ LV DOVR EDVHG RQ WKH FU\VWDO VWUXFWXUH RI 7 YXOFDQXV 7KH FU\VWDO VWUXFWXUH RI 36,, FRUH FRPSOH[ LQ 7 YXOFDQXV LV VKRZHG LQ )LJ . doi:10.6342/NTU201802891.

(47) )LJXUH VKRZV SURWHLQ VXEXQLWV DQG SRVLWLRQV RI SLJPHQWV $FFRUGLQJ WR SRVLWLRQV RI SLJPHQWV VKRZHG LQ )LJ E ZH FDQ ILQG WKDW 36,, FRUH FRPSOH[ LV D GLPHU ZLWK & V\PPHWU\. E

(48). D

(49). )LJXUH 7KH FU\VWDO VWUXFWXUH RI 36,, FRUH FRPSOH[ LQ 7 YXOFDQXV DW D UHVROXWLRQ RI c D

(50) 7KH VLGH YLHZ RI 36,, FRUH FRPSOH[ E

(51) 7KH WRS YLHZ RI 36,, FRUH FRPSOH[ 7KH KHOLFDO ULEERQV LQ WKH EDFNJURXQG DUH SURWHLQ VXEXQLWV 7KH FKORULQ ULQJ RI FKORURSK\OOV D DQG SKHRSK\WLQV DUH VKRZHG 7KH FRORU FRGH IRU FKURPRSKRUHV DUH &/$ F\DQ

(52) 3+( UHG

(53) DQG %&5 RUDQJH

(54) 36,, FRUH FRPSOH[ IRUPV D & V\PPHWULF GLPHU ,Q HDFK PRQRPHU LW LQFOXGHV WZR DQWHQQD FRPSOH[HV &3 DQG &3

(55) DQG RQH UHDFWLRQ FHQWHU 5&

(56) 7KH ORFDWLRQ RI DQ WHQQD FRPSOH[HV DQG UHDFWLRQ FHQWHUV DUH VKRZQ LQ )LJ 7KH EOXH JUHHQ DQG UHG HOOLSVHV UHSUHVHQW WKH ORFDWLRQ RI &3 &3 DQG 5& 7ZR &3V LQ GLIIHUHQW PRQRPHUV DUH QHDUHVW QHLJKERUV WR HDFK RWKHU ZKLOH WZR &3V LQ GLIIHUHQW PRQRPHU DUH IDU DZD\ IURP HDFK RWKHU 7R XQGHUVWDQG OLJKW KDUYHVWLQJ LQ WKH 36,, FRUH FRPSOH[ RXU VWXG\ IRFXVHG RQ WKH FKURPRSKRUHV LQ WKH 36,, FRUH FRPSOH[ ,W LQFOXGHV FKORURSK\OOV D &/$V

(57) SKHRSK\WLQV 3+(V

(58) ,Q DGGLWLRQ WKHUH DUH &/$V LQ D &3 &/$V LQ D &3 DQG &/$V DQG 3+(V LQ D 5& 7KHUHIRUH WKHUH DUH SLJPHQWV FRQVLGHUHG LQ RXU PRGHO. . doi:10.6342/NTU201802891.

(59) )LJXUH ,OOXVWUDWLRQ RI WKH FKORURSK\OO DUUDQJHPHQW LQ WKH 36,, FRUH FRPSOH[ &KORULQ ULQJV LQ WKH FU\VWDO VWUXFWXUH RI 7 YXOFDQXV 36,, FRUH FRPSOH[ 3'% $5&

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c 7KHUHIRUH D VSHFLDO SDLU LV VWURQJO\ FRXSOHG WR HDFK RWKHU $ LQWHUHVWLQJ SKHQRPHQRQ LV WKDW WKH SULPDU\ FKDUJH VHSDUDWLRQ RQO\ WDNHV SODFH LQ RQH EUDQFK $FFRUGLQJ WR WKH SUHYLRXV VWXGLHV > @ WKHUH ZHUH WZR SDWKZD\V WR FKDUJH WUDQVIHU LQ WKH 5& WKH VRFDOOHG ChlD1 SDWKZD\ DQG PD1 SDWKZD\ >@ 7KH UHDFWLRQV DUH DV IROORZV ChlD1 SDWKZD\ &KO'3KH'

(61) PD1 SDWKZD\ 3'3'&KO'

(62) . ± &KO' 3KH' ± 3' 3'. ± 3' 3KH' ± 3' &KO'. ± 3' 3KH' . ,Q ERWK SDWKZD\V WKH\ ILQDOO\ WUDQVIHU D HOHFWURQ WR SKHRSK\WLQ WR IRUP WKH VDPH UDGLFDO + P he− SDLU PD1 D1 7KHQ WKH HOHFWURQ LV WUDQVIHUUHG WR QA DQG WKHQ WUDQVIHUUHG WR WKH QB LQ. RUGHU WR OHDYH WKH 5& 'XH WR WKLV IXQFWLRQDO DV\PPHWU\ RI WZR EUDQFKHV WKH EUDQFK LQ ZKLFK WKH HOHFWURQ WUDQVIHU WDNHV SODFH LV FDOOHG WKH DFWLYH FKDLQ DQG WKH RWKHU LV FDOOHG WKH LQDFWLYH FKDLQ %HFDXVH RI WKH FKDUJH WUDQVIHU G\QDPLFV LQ WKH 5& DUH RXW RI WKH UDQJH RI RXU ZRUN . doi:10.6342/NTU201802891.

(63) .

(64) .

(65) . . . . . . . .

(66) . )LJXUH &KURPRSKRUHV LQ WKH 5& DQG R[\JHQHYROYLQJ FRPSOH[ 2(&

(67) 7KH FRORU FRGH IRU FKURPRSKRUHV DUH &/$ F\DQ

(68) 3+( UHG

(69) %&5 RUDQJH

(70) SODVWRTXLQRQH JUD\

(71) DQG 2(& SXUSOH

(72) ZH RQO\ FRQVLGHU WZR DSSDUHQW WLPH FRQVWDQWV IRU IRUPDWLRQV RI UDGLFDO SDLU 53

(73) + + − ChlD1 P he− D1 LQ ChlD1 SDWKZD\ DQG UDGLFDO SDLU 53

(74) PD1 ChlD1 LQ PD1 SDWKZD\. ChlD1 SDWKZD\ &KO'3KH'

(75) PD1 SDWKZD\ 3'3'&KO'

(76) . ± &KO' 3KH' τRP 1 ± 3' &KO' τRP 2. IV

(77). SV

(78). LQ WKH PDVWHU HTXDWLRQ WR PLPLF WKH FKDUJH WUDQVIHU LQ WKH 5& >@. . (IILFLHQW ((7 DQG KLJK TXDQWXP \LHOG 4<

(79) RI FKDUJH WUDQVIHU &7

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doi:10.6342/NTU201802891.

(81) E\ ΦCS = 1 −. τavg , τChl.

(82). ZKHUH τavg DQG τChl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doi:10.6342/NTU201802891.

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´H[FLWRQ UDGLFDO SDLU HTXLOLEULXP´ (53(

(84) PRGHO >@ EHFDXVH LW SURSRVHG WKDW WKH H[FLWDWLRQ HQHUJ\ WUDQVIHU WKURXJK WKH DQWHQQD WR WKH 5& LV PXFK IDVWHU WKDQ WKH RYHUDOO FKDUJH VHSDUDWLRQ WLPH $V D UHVXOW WKH HTXLOLEULXP EHWZHHQ H[FLWDWLRQ LQ WKH DQWHQQD DQG WKH FKDUJH VHSDUDWLRQ VWDWH FDQ EH HVWDEOLVKHG +RZHYHU WKH FU\VWDO VWUXFWXUH VKRZHG WKDW WKH GLVWDQFH RI DQWHQQD FKORURSK\OOV DQG 5& FKORURSK\OOV LV ODUJHU WKDQ c >@ DQG WKH GLVWDQFH LV VR IDU WKDW HQHUJ\ WUDQVIHU IURP DQWHQQD FRPSOH[HV WR 5&V VKRXOG EH VORZHU WKDQ WKH RYHUDOO FKDUJH VHSDUDWLRQ LQ WKH 5& 7KHUHIRUH WKH HQHUJ\ WUDQVIHU WR WKH 5& VKRXOG QRW EH UHYHUVLEOH 7KLV OHDGV WR WKH VRFDOOHG ´WUDQVIHUWRWKHWUDS OLPLWHG´ 777/

(85) PRGHO >@ &OHDUO\ WKH UHODWLYH WLPH VFDOHV RI HQHUJ\ WUDQVIHU WR EH YHUVXV WKDW RI FKDUJH WUDQVIHU GLVWLQJXLVKHV WKH (53( PRGHO DQG WKH 777/ PRGHO +RZHYHU WKH UHSRUWHG WLPH VFDOHV RI HQHUJ\ WUDQVIHU DQG FKDUJH WUDQVIHU DUH LQFRQVLVWHQW LQ WKH OLIHWLPH ,W LV GXH WR WKH GLIILFXOW\ WR DVVLJQ D SHDN DV WKH FRQWULEXWLRQ RI D VSHFLILF VLWH EHFDXVH WKH HQHUJ\ GLIIHUHQFH RI WUDQVLWLRQ HQHUJLHV LQ GLIIHUHQW VLWHV DUH WRR FORVH DQG VLWHV VWURQJO\ FRXSOH WR HDFK RWKHU $OVR UDGLFDO SDLU 53

(86) IRUPDWLRQ DQG H[FLWDWLRQ HQHUJ\ WUDQVIHU EHWZHHQ FKORURSK\OOV ERWK VKRZ VSHFWUDO VLJQDWXUHV LQ WKH Qy UHJLRQ LQ 36,, 7KHVH SURFHVVHV JUHDWO\ FRPSOLFDWHV WKH LQWHUSUHWDWLRQ RI WKH WUDQVLHQW DEVRUSWLRQ GDWD 7KHUHIRUH LW OHDGV WR DQ H[WHQVLYH GHEDWH LQ WKH OLWHUDWXUH UHJDUGLQJ WKH PHFKDQLVP DQG WKH WLPHVFDOH RI HQHUJ\ WUDQVIHU DQG FKDUJH WUDQVIHU LQ 36,, >@ 8QWLO QRZ ZKLFK RQH RI WKH WZR NLQHWLF PRGHOV IRU HQHUJ\ DQG HOHFWURQ WUDQVIHU LV FRUUHFW UHPDLQ GHEDWH. . doi:10.6342/NTU201802891.

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¶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c DQG LV VPDOOHU WKDQ WKH GLVWDQFH RI WKH QHDUHVW SLJPHQWV RI WKH &3 DQG WKH 5& LQ GLIIHUHQW PRQRPHUV ZKLFK LV c >@ 7KHUHIRUH WKH HQHUJ\ WUDQVIHU OLQN VKRXOG EH FRQVLGHU EHWZHHQ WZR &3V WRR. . 7KH RXWOLQH RI WKLV ZRUN ,Q WKH SUHYLRXV VWXG\ >@ +XDQJ DQG FRZRUNHUV SHUIRUPHG ILYH LQGHSHQGHQW QV. PROHFXODU G\QDPLFV 0'

(88) VLPXODWLRQV EDVHG RQ WKH FU\VWDO VWUXFWXUH RI 7 YXOFDQXV 7KH\ FDOFXODWHG H[FLWRQLF FRXSOLQJV DQG VLWH HQHUJLHV IRU SLJPHQWV LQ WKH 36,, FRUH FRPSOH[ EDVHG RQ VWUXFWXUH HQVHPEOHV IURP 0' VLPXODWLRQ 7KH HIIHFW RI SURWHLQ HQYLURQPHQW . doi:10.6342/NTU201802891.

(89) ZDV FRQVLGHUHG LQ WKH FDOFXODWLRQ RI WKH DYHUDJH H[FLWRQLF FRXSOLQJ DQG WKH DYHUDJH VLWH HQHUJ\ REWDLQHG IURP 0' VLPXODWLRQ $FFRUGLQJ WR WKHLU VWXG\ WKH VLWH HQHUJ\ RI ChlD1 ZDV ORZHUHG E\ FKDUJHG UHVLGXHV RI WKH SURWHLQ HQYLURQPHQW ,W OHG ChlD1 WR KDYH WKH ORZ HVW VLWH HQHUJ\ DQG H[FLWDWLRQ HQHUJ\ WR IORZ WR ChlD1 HYHQWXDOO\ +RZHYHU WKHLU VWXG\ RQO\ FRQVLGHUHG VWDWLF UHVXOWV DQG GLG QRW DQDO\]H WKH G\QDPLFV RI UHVXOWV IURP 0' VLPXOD WLRQ 7KHUHIRUH WKURXJK FROODERUDWLRQ ZH REWDLQ 0' VLPXODWLRQ GDWD IURP +XDQJ¶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doi:10.6342/NTU201802891.

(90) DQ H[SODQDWLRQ IRU D UHDVRQ ZK\ 36,, FRUH FRPSOH[ IRUP LQWR D GLPHULF VWUXFWXUH LQ QDWXUH DQG SURSRVH D SRVVLEOH LQWHUPRQRPHULF H[FLWDWLRQ HQHUJ\ WUDQVIHU SDWKZD\. . doi:10.6342/NTU201802891.

(91) . doi:10.6342/NTU201802891.

(92) &KDSWHU 7KHRUHWLFDO EDFNJURXQG . 6WUXFWXUHEDVHG PRGHO IRU SKRWRV\QWKHWLF FRPSOH[HV ,Q WKH SDVW GHFDGHV WR XQGHUVWDQG WKH HQHUJ\ WUDQVIHU G\QDPLFV WKH ZHOOHVWDEOLVKHG. PRGHO LV GHYHORSHG ,Q WKH IROORZLQJ VHFWLRQV ZH ZLOO LQWURGXFH WKH V\VWHPEDWK PRGHO WR GHVFULEH WKH SLJPHQWSURWHLQ FRPSOH[HV 33&V

(93) DQG WKH PHWKRG WR REWDLQ WUDQVLWLRQ HQHUJLHV DQG H[FLWRQLF FRXSOLQJV. . 6\VWHPEDWK PRGHO DQG )UHQNHO H[FLWRQ +DPLOWRQLDQ. 7KH GHVFULSWLRQ RI WKH TXDQWXP G\QDPLFV RI H[FLWRQV LQ SLJPHQWSURWHLQ FRPSOH[HV 33&V

(94) LV ZHOO HVWDEOLVKHG > @ 7KH VWDQGDUG +DPLOWRQLDQ RI D 33& XVHG WR VWXG\ HQHUJ\ WUDQVIHU FRQWDLQV WKUHH SDUWV H = Hs + Hb + Hsb.

(95). ZKHUH Hs LV WKH V\VWHP +DPLOWRQLDQ Hb LV WKH EDWK +DPLOWRQLDQ DQG Hsb LV WKH V\VWHP EDWK +DPLOWRQLDQ >@ 7KH V\VWHP +DPLOWRQLDQ LV WKH )UHQNHO H[FLWRQ +DPLOWRQLDQ ,Q WKH SLJPHQWSURWHLQ FRPSOH[ WKH GLVWDQFH EHWZHHQ PRVW RI WKH SLJPHQWV LV WRR ODUJH WR KDYH VSDWLDO RYHUODS EHWZHHQ WKH HOHFWURQLF ZDYH IXQFWLRQV RI WKH GLIIHUHQW SLJPHQWV VR WKH RI )UHQNHO H[FLWRQV. . doi:10.6342/NTU201802891.

(96) FDQ EH DSSOLHG >@ ,W LV JLYHQ E\ Hs =. . En |n n| +. n. . Jnm |n m| ,.

(97). n=m. ZKHUH En LV WKH WUDQVLWLRQ HQHUJ\ RI HDFK VLWHV DQG Jnm LV WKH H[FLWRQLF FRXSOLQJ IRU HDFK SDLUV RI VLWHV ,Q RXU PRGHO WKH ORFDOL]HG H[FLWHG VWDWH |n LV JLYHQ DV WKH SURGXFW RI WKH (e). Qy H[FLWHG VWDWH S1

(98) ZDYHIXQFWLRQ ψn (r) RI SLJPHQW Q DQG JURXQG VWDWH ZDYHIXQFWLRQV (g). ψk (r) RI SLJPHQW N = Q WKDW LV |n = ψn(e) (r). . (g). ψk (r)..

(99). k=n. 7KH H[FLWRQLF FRXSOLQJ FRQWDLQV WZR SDUWV 2QH LV FRXORPE WHUP DQG WKH RWKHU LV H[FKDQJH WHUP ([FKDQJH WHUP LV VKRUWUDQJH FRQWULEXWLRQ GXH WR HOHFWURQ H[FKDQJH &RXORPE WHUP LV WKH FRXORPE LQWHUDFWLRQ EHWZHHQ WKH HOHFWURQV VWD\ DW WKHLU PROHFXOHV 7KH &RXORPE WHUP ZKLFK GRPLQDWHV WKH ODUJH PDMRULW\ RI H[FLWRQLF FRXSOLQJV EHWZHHQ SKRWRV\QWKHWLF SLJPHQWV Jnm LV JLYHQ E\ . Jnm =. (g) d¯ r1 . . . d¯ rN ψn(e) (r1 . . . rN )ψm (¯ r1 . . . r¯N ). dr1 . . . drN ×. i,j. 1 (e) (¯ r1 . . . r¯N ). ψ (g) (r1 . . . rN )ψm |ri − r¯j | n.

(100). %\ XVLQJ 3DXOLĪ V SULQFLSOH IRU WKH H[FKDQJH RI HOHFWURQV DQG FKDQJLQJ QDPHV RI LQWHJUDWLRQ YDULDEOHV WKH DERYH PDWUL[ HOHPHQW FDQ EH ZULWWHQ DV Jnm = Nm Nn. dr1 . . . drN. (g) d¯ r1 . . . d¯ rN ψn(e) (r1 . . . rN )ψm (¯ r1 . . . r¯N ). × =. dr1 dr2 ρn (r1 ) ρn (r1 ) = Nn. 1 (e) ψn(g) (r1 . . . rN )ψm (¯ r1 . . . r¯N ). |r1 − r¯1 |.

(101). 1 ρm (r2 ), r1 − r 2. dr2 . . . drN ψn(e) (r1 . . . rN )ψn(g) (r1 . . . rN ),.

(102). ZKHUH ρn (r1 ) LV WKH WUDQVLWLRQ GHQVLW\ RI WKH SLJPHQW Q >@ . doi:10.6342/NTU201802891.

(103) 7KH EDWK +DPLOWRQLDQ LV JLYHQ DV Hb =. α. 1 ωα (b†α bα + ), 2.

(104). ZKHUH ωα LV WKH HQHUJ\ RI YLEUDWLRQDO TXDQWD LQ WKH PRGH α $FWXDOO\ LW LV KDUG WR GH VFULEH WKH HQYLURQPHQW H[DFWO\ VR ZH DSSO\ D EXQFK RI HIIHFWLYH KDUPRQLF RVFLOODWRUV WR DSSUR[LPDWH WKH PRWLRQV IURP WKH EDWK +HUH ZH RQO\ FRQVLGHU WKH GLDJRQDO WHUP RI V\VWHPEDWK +DPLOWRQLDQ DQG DVVXPH WKH RIIGLDJRQDO WHUP LV ]HUR 7R YHULI\ WKDW WKH DV VXPSWLRQ LV UHDVRQDEOH RU QRW ZH FDOFXODWH WKH UDWLR RI VWDQGDUG GHYLDWLRQV WR DEVROXWH YDOXH RI FRXSOLQJV. σ |J|. 7KLV UDWLR LPSOLHV WKH GHJUHH RI H[FLWRQLF FRXSOLQJ IOXFWXDWLRQ. :H RQO\ FDOFXODWH WKH UDWLR RI H[FLWRQLF FRXSOLQJ ZKLFK LV ODUJHU WKDQ cm−1 EHFDXVH WKH H[FLWRQLF FRXSOLQJ ZKLFK LV VPDOOHU WKDQ cm−1 PD\ UHVXOW LQ D IDNH GHJUHH RI IOXF WXDWLRQ :H ILQG WKDW PRVW RI WKH UDWLR DUH OHVV WKDQ ,W PHDQV WKDW SLJPHQWV ERXQG E\ SURWHLQV FDQ URWDWH DQG YLEUDWH LQ D OLPLWHG VSDFH DQG OHDGV WR VOLJKW IOXFWXDWLRQV RI FRX SOLQJV EHWZHHQ SLJPHQWV 7KHUHIRUH LJQRULQJ WKH RIIGLDJRQDO WHUP RI Hsb LV UHDVRQDEOH DQG ZH MXVW FRQVLGHU H[FLWRQLF FRXSOLQJV DV FRQVWDQW YDOXHV LQ WKH V\VWHP +DPLOWRQLDQ 7KH V\VWHPEDWK +DPLOWRQLDQ LV GHQRWHG E\ Hsb =. α. ωα gα,n (b†α + bα ) |n n|.

(105). n. ZKHUH gα,n LV WKH V\VWHPEDWK FRXSOLQJ FRQVWDQW EHWZHHQ WKH VWDWH Q LQ WKH V\VWHP DQG WKH PRGH α RI WKH EDWK 7KH YLEURQLF FRXSOLQJ RI HDFK HOHPHQW LQ WKH V\VWHPEDWK +DPLOWRQLDQ GHVFULEH WKH PRGXODWLRQ RI VLWH HQHUJLHV DQG H[FLWRQLF FRXSOLQJV E\ QXFOHDU PRWLRQV RI WKH FRPSOH[ ,W LV DVVXPHG WKDW WKH IOXFWXDWLRQV RI VLWH HQHUJLHV DUH OLQHDU FRXSOHG WR WKH GLV SODFHPHQWV RI QXFOHL IURP LWV HTXLOLEULXP SRVLWLRQV DQG HDFK VLWH KDV LWV RZQ LQGHSHQGHQW EDWK ,Q FRQGHQVHG SKDVHG V\VWHP WKH QXPEHU RI YLEUDWLRQDO PRGHV FRXSOHG WR VLWHV LV VR ODUJH 7KHUHIRUH ZH DSSO\ WKH VSHFWUDO GHQVLW\ IXQFWLRQ J(ω) WR GHVFULEH VXFK LQWHUDFWLRQ %DVHG RQ WKH LQGHSHQGHQW EDWK DVVXPSWLRQ WKH VSHFWUDO GHQVLW\ IXQFWLRQ IRU WKH VLWH Q LV. . doi:10.6342/NTU201802891.

(106) GHILQHG DV Jn (ω) =. . 2 gα,n 2 ωα2 δ(ω − ωα )..

(107). α. 7KH VSHFWUDO GHQVLW\ IXQFWLRQ LV WKH GHQVLW\ RI VWDWH RI YLEUDWLRQ PRGHV ZHLJKWHG E\ WKH HIIHFWLYH LQWHUDFWLRQ VWUHQJWK ,Q DGGLWLRQ LQ WKH HQHUJ\ JDS +DPLOWRQLDQ (T

(108) WKH HQHUJ\ JDS IOXFWXDWLRQ JRYHUQV WKH TXDQWXP G\QDPLFV ZKLFK LV GHVFULEHG E\ WKH HQHUJ\ JDS DXWRFRUUHODWLRQ IXQFWLRQ Cn (τ ) ,W LV JLYHQ E\ Cn (τ ) = δEn (τ )δEn (0) βωα 2 ) − isin(ωα τ )] gα,n 2 ωα2 [cos(ωα τ )coth( = 2 α ∞ βωα = ) − isin(ωα τ )], dωJn (ω)[cos(ωα τ )coth( 2 0 ZKHUH β =. 1 kb T.

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

(110) PHWKRG > @ LV RQH RI WKH PHWKRGV EDVHG RQ VWUXFWXUDO . doi:10.6342/NTU201802891.

(111) GDWD DQG LV DSSOLHG WR FDOFXODWH VLWH HQHUJLHV EDVHG RQ 0' WUDMHFWRULHV IURP KXDQJ¶V JURXS ,Q WKLV DSSURDFK WKH UHODWLYH VLWH HQHUJ\ LV FDOFXODWHG UDWKHU WKDQ WKH DEVROXWH VLWH HQHUJ\ )LJXUH VKRZV WKH LGHD RI &'& PHWKRG . . 𝒈. . . )LJXUH 7KH VFKHPDWLF GLDJUDP IRU &'& PHWKRG 7KH JURXQG VWDWH DQG ILUVW H[FLWHG VWDWH RI Qy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n = E0 + ΔEn.

(112). ZKHUH ΔEn LV WKH VLWH HQHUJ\ VKLIW GXH WR WKH GLIIHUHQFH LQ SLJPHQWSURWHLQ &RXORPE LQWHU DFWLRQ EHWZHHQ WKH JURXQG DQG H[FLWHG VWDWHV RI WKH SLJPHQWV 7R VLPSOLI\ WKH FDOFXODWLRQ RI &RXORPE LQWHUDFWLRQ EHWZHHQ SLJPHQWV DQG SURWHLQ UHVLGXHV &KDUJH SURWHLQ UHVLGXHV DUH FRQVLGHUHG DV EDFNJURXQG FKDUJHV qjbg DQG D HOHFWURQLF VWDWH RI D SLJPHQW DUH UHSUH VHQWHG E\ D VHW RI DWRPLF SDUWLDO FKDUJH qi $WRPLF SDUWLDO FKDUJH LV D FKDUJH ORFDOL]HG RQ D DWRP RI D SLJPHQW $ VHW RI DWRPLF SDUWLDO FKDUJHV LV REWDLQ IURP ILWWLQJ RI DE LQLWLR HOHFWURQLF SRWHQWLDO 7KDW LV WKH HOHFWURQLF SRWHQWLDO RI D HOHFWURQLF GHQVLW\ DSSUR[LPDWH. . doi:10.6342/NTU201802891.

(113) WKH HOHFWURQLF SRWHQWLDO RI DWRPLF SDUWLDO FKDUJHV 7KXV ΔEn LV JLYHQ E\ ΔEn = =. 1 ef f. i. j. (. n bg qe,i qj. |rin − rjbg |. bg 1 Δqin qj. ef f. i. j. |rin − rjbg |. −. n bg qg,i qj. |rin − rjbg |. )

(114). ,. n ZKHUH ef f LV DQ HIIHFWLYH GLHOHFWULF FRQVWDQW qe,i LV D DWRPLF SDUWLDO FKDUJH RQ DWRP L IRU n LV D DWRPLF SDUWLDO FKDUJH RQ DWRP L IRU WKH JURXQG VWDWH WKH H[FLWHG VWDWH RI SLJPHQW Q qg,i. RI SLJPHQW Q Δqin LV WKH GLIIHUHQFH RI D DWRPLF SDUWLDO FKDUJH RQ DWRP L IRU SLJPHQW Q DQG rin RU rjbg LV WKH SRVLWLRQ RI DWRPLF SDUWLDO FKDUJHV RU EDFNJURXQG FKDUJHV )LJXUH VKRZV WKH GLIIHUHQFH RI JURXQG DQG H[FLWHG HOHFWURQLF GHQVLW\ RI FKORURSK\OO D DQG WKH GLIIHUHQFH RI JURXQG DQG H[FLWHG HOHFWURQLF SRWHQWLDO RI FKORURSK\OO D. D

(115). E

(116). )LJXUH 6XUIDFH SORW RI WKH GLIIHUHQFH LQ HOHFWURQ GHQVLW\ DQG WKH FRUUHVSRQGLQJ HOHF WURQLF SRWHQWLDO IRU FKORURSK\OO D D

(117) 6XUIDFH SORW RI WKH GLIIHUHQFH LQ HOHFWURQ GHQVLW\ Δρ(r) = ρe (r) − ρg (r) EHWZHHQ WKH H[FLWHG VWDWH S1 DQG WKH JURXQG VWDWH S0 REWDLQHG E\ 7'')7%/<3 E

(118) 7KH FRUUHVSRQGLQJ HOHFWURQLF SRWHQWLDO Δφ(r) = φe (r) − φg (r) 1HJDWLYH YDOXHV DUH UHSUHVHQWHG E\ UHG FRORUV DQG SRVLWLYH YDOXHV E\ EOXH FRORUV >@. . doi:10.6342/NTU201802891.

(119) . 0HWKRGV IRU HVWLPDWLRQ RI WKH H[FLWRQLF FRXSOLQJ. ,Q WKH VXEVHFWLRQ ZH PHQWLRQHG H[FLWRQLF FRXSOLQJ Jnm ,Q WKH IROORZLQJ VXEVHFWLRQ ZH ZLOO SUHVHQW WZR PHWKRGV WR FDOFXODWH H[FLWRQLF FRXSOLQJ $V IDU DV ZH NQRZ H[FLWRQLF FRXSOLQJ LV JLYHQ DV Jnm =. dr1 dr2 ρn (r1 ). 1 ρm (r2 ). r12.

(120). ,Q WKH WUDQVLWLRQ GHQVLW\ FXEH 7'&

(121) PHWKRG >@ WUDQVLWLRQ GHQVLW\ ρ(r) LV UHSUHVHQW DV D VHW RI WKUHH GLPHQVLRQDO JULGV $FFRUGLQJ WR (T H[FLWRQLF FRXSOLQJ LV WKH LQWHJUDO ZLWK UHVSHFW WR r1 DQG r2 RI DFFXUDWH LQWHUDFWLRQ HQHUJLHV EHWZHHQ WUDQVLWLRQ GHQVLW\ FXEHV RI HDFK SLJPHQWV +RZHYHU WKLV PHWKRG LV HYDOXDWHG QXPHULFDOO\ 7KHUHIRUH 7UDQVL WLRQ FKDUJH IURP HOHFWURVWDWLF SRWHQWLDO 7U(VS

(122) PHWKRG ZKLFK LV HTXDO DFFXUDF\ EXW OHVV QXPHULFDO FRVW LV GHYHORSHG )LJXUH VKRZV WKH WUDQVLWLRQ GHQVLW\ RI FKORURSK\OO D DQG WKH FRUUHVSRQGLQJ HOHF WURVWDWLF SRWHQWLDO RI WKH WUDQVLWLRQ GHQVLW\ ,Q WKH 7U(VS PHWKRG >@ WKH HOHFWURVWDWLF. E

(123). D

(124). )LJXUH 6XUIDFH SORW RI WUDQVLWLRQ GHQVLW\ DQG WKH FRUUHVSRQGLQJ HOHFWURVWDWLF SRWHQWLDO IRU FKORURSK\OO D D

(125) 6XUIDFH SORW RI WKH WUDQVLWLRQ GHQVLW\ ρT (r) RI FKORUSK\OO D REWDLQHG E\ 7'')7%/<3 E

(126) 7KH FRUUHVSRQGLQJ HOHFWURQLF SRWHQWLDO φT (r) 1HJDWLYH YDOXHV DUH UHSUHVHQWHG E\ UHG FRORUV DQG SRVLWLYH YDOXHV E\ EOXH FRORUV >@ SRWHQWLDO RI WKH WUDQVLWLRQ GHQVLW\ LV ILWWLQJ E\ WUDQVLWLRQ FKDUJHV ZKLFK ORFDOL]H RQ DWRPV RI D SLJPHQW 7KXV WKH H[FLWRQLF FRXSOLQJ LV JLYHQ DV Jnm = f. qin,T qjm,T , f = 2.68 H[S{−0.27d} + 0.54, n m |R − R | i j i j.

(127). . doi:10.6342/NTU201802891.

(128) ZKHUH I LV D VFDOLQJ IDFWRU WR GHVFULEH VFUHHQLQJ DQG SRODUL]DWLRQ HIIHFW RI WKH SURWHLQ HQYLURQPHQW LQ DQ LPSOLFLW ZD\ > @ qin,T LV WKH WUDQVLWLRQ FKDUJH L RI SLJPHQW Q qjm,T LV WKH WUDQVLWLRQ FKDUJH M RI SLJPHQW P Rin LV WKH SRVLWLRQ RI WUDQVLWLRQ FKDUJH L RI SLJPHQW Q Rjm LV WKH SRVLWLRQ RI WUDQVLWLRQ FKDUJH M RI SLJPHQW P DQG G LV WKH GLVWDQFH EHWZHHQ SLJPHQW Q DQG P 7KH VFKHPDWLF GLDJUDP IRU 7U(VS PHWKRG LV VKRZHG EHOORZ. )LJXUH 7KH VFKHPDWLF GLDJUDP IRU 7U(VS PHWKRG. . 4XDQWXP FRUUHFWLRQ RI FODVVLFDO WLPH FRUUHODWLRQ IXQF WLRQ IURP 0' $V ZH PHQWLRQHG EHIRUH UDZ GDWD RI PROHFXODU G\QDPLFV 0'

(129) VLPXODWLRQ SURSD. JDWHG E\ KXDQJ¶V JURXS DUH VWUXFWXUH HQVHPEOHV RI 36,, FRUH FRPSOH[ :H FDQ FDOFXODWH VLWH HQHUJLHV DQG H[FLWRQLF FRXSOLQJV E\ &'& PHWKRG DQG 7U(VS PHWKRG EDVHG RQ VWUXF WXUH HQVHPEOHV IURP 0' DQG KDYH WUDMHFWRULHV RI VLWH HQHUJLHV DQG WUDMHFWRULHV RI H[FLWRQLF FRXSOLQJV )LJXUH VKRZV WUDMHFWRULHV RI VLWH HQHUJ\ IRU PD1 DQG H[FLWRQLF FRXSOLQJ EH WZHHQ VSHFLDO SDLU PD1 DQG PD2 ,Q WKLV VHFWLRQ ZH GHVFULEH WKH LQWHUDFWLRQ EHWZHHQ RXU V\VWHP DQG EDWK E\ WKH HQHUJ\ JDS DXWRFRUUHODWLRQ IXQFWLRQ (T

(130) IURP 0' WUDMHFWRULHV DQG REWDLQ TXDQWXP WLPH FRUUHODWLRQ IXQFWLRQ T7&)

(131) E\ TXDQWXP FRUUHFWLRQ. . doi:10.6342/NTU201802891.

(132) D

(133). E

(134). )LJXUH 7KH WUDMHFWRULHV RI VLWH HQHUJ\ DQG H[FLWRQLF FRXSOLQJ IURP 0' D

(135) 7KH WUD MHFWRU\ RI VLWH HQHUJ\ REWDLQ E\ &'& PHWKRG IRU PD1 ; D[LV LV WKH VLPXODWLRQ WLPH RI 0'< D[LV LV WKH HQHUJ\ JDS RI VLWH HQHUJ\ DQG XQLW LV cm−1 E

(136) 7KH WUDMHFWRU\ RI H[FL WRQLF FRXSOLQJ - REWDLQ E\ 7U(VS PHWKRG EHWZHHQ VSHFLDO SDLU ; D[LV LV WKH VLPXODWLRQ WLPH RI 0' 7KH XQLW RI < D[LV LV cm−1 . . &ODVVLFDO WLPH FRUUHODWLRQ IXQFWLRQ IURP 0'. $V ZH PHQWLRQHG EHIRUH ZH DSSO\ HQHUJ\ JDS DXWRFRUUHODWLRQ IXQFWLRQ WR GHVFULEH WKH LQWHUDFWLRQ RI WKH V\VWHP DQG WKH EDWK 7R REWDLQ HQHUJ\ JDS DXWRFRUUHODWLRQ IXQFWLRQ ZH QHHG WR KDYH WKH WUDMHFWRU\ RI HQHUJ\JDS IOXFWXDWLRQ )RU HDFK SLJPHQWV ZH KDYH VL[ WUDMHFWRULHV RI VLWH HQHUJ\ ΔEn (t) 7KHQ WKH DYHUDJH YDOXH ΔEn RI VLWH HQHUJ\ IRU DOO WUDMHFWRULHV LV DSSOLHG LQ WKH GLDJRQDO WHUP RI V\VWHP +DPLOWRQLDQ ,Q DGGLWLRQ ZH FDQ REWDLQ HQHUJ\ JDS IOXFWXDWLRQ δEn (t) IRU HDFK SLJPHQWV 7KH HQHUJ\ JDS IOXFWXDWLRQ LV JLYHQ E\ δEn (t) = ΔEn (t) − ΔEn ..

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doi:10.6342/NTU201802891.

(138) )LJXUH 2QH RI WKH WUDMHFWRULHV IRU HQHUJ\JDS IOXFWXDWLRQ RI PD1 ; D[LV LV WKH VLPX ODWLRQ WLPH RI 0'< D[LV LV WKH HQHUJ\JDS IOXFWXDWLRQ RI VLWH HQHUJ\ DQG XQLW LV cm−1 GHU RI HQHUJ\ JDS IOXFWXDWLRQ DUH PL[LQJ LQ WKH WUDMHFWRU\ 7KHUHIRUH ZH WU\ WR ´ILOWHU´ WKH VWDWLF GLVRUGHU E\ GLYLGLQJ WKH SV WUDMHFWRU\ WR ILYH LQWHUYDOV (DFK LQWHUYDO LV SV DQG GRPLQDWHV E\ WKH G\QDPLF GLVRUGHU 7KHQ ZH FDQ FDOFXODWH HQHUJ\ JDS DXWRFRUUHODWLRQ IXQFWLRQ EDVHG RQ SV WUDMHFWR ULHV RI HQHUJ\ JDS IOXFWXDWLRQ IRU HDFK SLJPHQW 7KH HQHUJ\ JDS WLPH FRUUHODWLRQ IXQFWLRQ LV JLYHQ DV Cn (τ ) = δEn (τ )δEn (0) ..

(139). $FFRUGLQJ WR HUJRGLF WKHRU\ DV ORQJ DV PHDVXUHPHQWV DUH SHUIRUPHG RYHU D ORQJ WLPH DQG WKDW GXH WR WKH IORZ RI WKH V\VWHP WKURXJK VWDWH VSDFH WKH WLPH DYHUDJH LV WKH WKH VDPH DV WKH HQVHPEOH DYHUDJH >@ 7KHUHIRUH ZH FDQ UHZULWH WKH WLPH FRUUHODWLRQ IXQFWLRQ 7&)

(140) DV WLPH DYHUDJH DQG LW LV JLYHQ DV 1 Cn (τ ) = T. 0. T. δEn (τ + t)δEn (t)dt..

(141). (DFK SLJPHQW KDV WUDMHFWRULHV IRU SV DQG KDV FRUUHVSRQGLQJ HQHUJ\ JDS DXWR FRUUHODWLRQ IXQFWLRQV :H DYHUDJH HQHUJ\ JDS DXWR FRUUHODWLRQ IXQFWLRQV DQG HDFK SLJPHQW KDV RQH DYHUDJH HQHUJ\ JDS DXWRFRUUHODWLRQ IXQFWLRQV 0RUHRYHU ZH DVVXPH SLJPHQWV DUH FRXSOHG WR LQGHSHQGHQW EDWKV RI WKH VDPH IRUP 7KHUHIRUH ZH DYHUDJH HQ HUJ\ JDS DXWRFRUUHODWLRQ IXQFWLRQV RI HDFK SLJPHQW LQ WKH 5& DQG WKLV 7&) LV GHQRWHG DV. . doi:10.6342/NTU201802891.

(142) avg CM D ,W LV JLYHQ DV. avg CM D (τ ). 1 = Cn,i,j (τ ), 30 × 8 × 2 n=1 i=1 j=1 8. 30. 2.

(143). ZKHUH i LV WKH LQGH[ RI WUDMHFWRULHV RI HQHUJ\ JDS IOXFWXDWLRQ IRU HDFK SLJPHQW DQG j LV WKH LQGH[ IRU PRQRPHU 0

(144) RU PRQRPHU 0

(145) )LJXUH VKRZV WKH DYHUDJH HQHUJ\ JDS DXWRFRUUHODWLRQ IXQFWLRQ IURP SLJPHQWV. )LJXUH 7KH DYHUDJH HQHUJ\ JDS DXWRWLPH FRUUHODWLRQ IXQFWLRQ EDVHG RQ 0' VLPXOD WLRQ 7KH XQLW RI [ D[LV LV SV 7KH XQLW RI \ D[LV LV cm−2 . . +DUPRQLF TXDQWXP FRUUHFWLRQ RI HQHUJ\ JDS DXWRFRUUHODWLRQ IXQFWLRQ. 7R FRUUHFWO\ VLPXODWH H[FLWDWLRQ HQHUJ\ WUDQVIHU G\QDPLFV WKH EHKDYLRU RI RXU PRGHO V\VWHP KDV WR REH\ GHWDLOHG EDODQFH $V IDU DV ZH NQRZ TXDQWXP WLPH FRUUHODWLRQ IXQF WLRQ T7&)

(146) GHVFULEH WKH TXDQWXP G\QDPLFV RI D V\VWHP DQG DOVR REH\ GHWDLOHG EDODQFH 4XDQWXP WLPH FRUUHODWLRQ IXQFWLRQ LV FRPSOH[ ,W FDQ¶W EH GLUHFWO\ PHDVXUHG EXW REVHUY DEOHV DUH RIWHQ UHODWHG WR WKH UHDO RU LPDJLQDU\ SDUW RI FRUUHODWLRQ IXQFWLRQ ,Q RXU ZRUN HQHUJ\ JDS DXWRFRUUHODWLRQ IXQFWLRQ DOVR NQRZQ DV FODVVLFDO WLPH FRUUHODWLRQ IXQFWLRQ F7&)

(147) REWDLQHG E\ VLWH HQHUJ\ IOXFWXDWLRQ IURP 0' VLPXODWLRQ UHODWHV WR WKH UHDO SDUW . doi:10.6342/NTU201802891.

(148) RI TXDQWXP WLPH FRUUHODWLRQ IXQFWLRQ 7KHUHIRUH ZH QHHG WR DSSO\ TXDQWXP FRUUHFWLRQ WR F7&) WR REWDLQ T7&) :H DSSO\ KDUPRQLF TXDQWXP FRUUHFWLRQ WR F7&) REWDLQHG E\ 0' +DUPRQLF TXDQWXP FRUUHFWLRQ FRUUHFWV WKH F7&) LQ WKH IUHTXHQF\ GRPDLQ VR ZH DSSO\ WKH )RXULHU WUDQVIRUP WR F7&) WR REWDLQ FODVVLFDO WLPH FRUUHODWLRQ IXQFWLRQ LQ IUHTXHQF\ GRPDLQ >@ 7KH FODVVLFDO WLPH FRUUHODWLRQ IXQFWLRQ LQ IUHTXHQF\ GRPDLQ LV JLYHQ DV avg CM D (ω). =. ∞. −∞. avg eiωτ CM D (τ )dτ,.

(149). avg ZKHUH ω LV WKH DQJXODU IUHTXHQF\ :H DSSO\ WKH +DQQ ZLQGRZ WR CM D (ω) WR ILOWHU RXW avg WKH KLJKHU IUHTXHQF\ PRGHV 7KHQ CM D (ω) LV PXOWLSOLHG E\ D KDUPRQLF TXDQWXP FRU. UHFWLRQ IDFWRU Qhar (ω) WR REWDLQ TXDQWXP WLPH FRUUHODWLRQ IXQFWLRQ LQ IUHTXHQF\ GRPDLQ +DUPRQLF TXDQWXP FRUUHFWLRQ LV JLYHQ DV avg Cqc (ω) = Qhar (ω)CM D (ω) =. ZKHUH β =. 1 kb T. βω C avg (ω), 1 − eβω M D.

(150). DQG 7 LV WKH WHPSHUDWXUH 7KHQ Cqc (ω) LV DSSOLHG E\ LQYHUVH )RXULHU. WUDQVIRUP WR REWDLQ TXDQWXP WLPH FRUUHODWLRQ IXQFWLRQ LQ WLPH GRPDLQ Cqc (τ ) 7KH TXDQ WXP WLPH FRUUHODWLRQ IXQFWLRQ T7&)

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doi:10.6342/NTU201802891.

(152) D

(153). E

(154). )LJXUH 7KH TXDQWXP WLPH FRUUHODWLRQ IXQFWLRQ EDVHG RQ 0' VLPXODWLRQ D

(155) 7KH 5HDO SDUW RI TXDQWXP WLPH FRUUHODWLRQ IXQFWLRQ E

(156) 7KH LPDJLQDU\ SDUW RI TXDQWXP WLPH FRUUHODWLRQ IXQFWLRQ 7KH XQLW RI [ D[LV LV SV 7KH XQLW RI \ D[LV LV cm−2 36,, FRUH FRPSOH[ 7KH H[FLWRQ VWDWH |α GHQRWH DV Hs |α = Eα |α , |α =. . Cnα |n ..

(157). n. ZKHUH Eα LV WKH H[FLWRQ HQHUJ\ IRU WKH H[FLWRQ VWDWH α Cnα LV WKH FRHIILFLHQW IRU WKH VLWH Q LQ WKH H[FLWRQ VWDWH α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

(158) WR VLPXODWH. . doi:10.6342/NTU201802891.

(159) WKH DEVRUSWLRQ VSHFWUXP > @ 7KH RSWLFDO GHQVLW\ LV JLYHQ DV OD(ω) = ω. . μ2α Re. 0. α. μα =. n. Rαααα = −. ∞. dtei(ω−ωα )t−gαααα (t)−Rαααα t ;. Cnα μn ;. .

(160)

(161)

(162). Rββαα ,. β=α. ZKHUH μα DQG ωα GHQRWH WKH WUDQVLWLRQ GLSROH PRPHQW DQG IUHTXHQF\ RI WKH αWK H[FLWRQ VWDWH gαααα (t) LV WKH OLQHEURDGHQLQJ IXQFWLRQ Rαααα LV WKH LQYHUVH OLIHWLPH RI WKH αWK H[FLWRQ VWDWH 7KH FRHIILFLHQW Cnα IRU WKH VLWH Q LQ WKH H[FLWRQ VWDWH α DVVRFLDWHV WKH WUDQ VLWLRQ GLSROH RI WKH H[FLWRQ VWDWH ZLWK WKH PROHFXODU WUDQVLWLRQ GLSROH μn ,W LV LPSRUWDQW WR QRWH WKDW WKH RSWLFDO GHQVLW\ WDNHV LQWR DFFRXQW D UHOD[DWLRQLQGXFHG EURDGHQLQJ RI WKH H[FLWRQ VWDWHV JLYHQ E\ WKHLU LQYHUVH OLIHWLPHV LH Rαααα Rαααα LV JLYHQ E\ D VXP RI WKH UHOD[DWLRQ UDWHV IURP WKH αWK H[FLWRQ VWDWH WR WKH RWKHUV H[FLWRQ VWDWHV Rββαα LV WKH WUDQVLWLRQ UDWH EDVHG RQ PRGLILHG 5HGILHOG WKHRU\ IURP αWK H[FLWRQ VWDWH WR βWK H[FLWRQ VWDWH DQG LV JLYHQ E\ >@ Rββαα = −2Re. ∞ 0. ˆ (ωβα , t){¨ dtW gβααβ (t)−{g˙ αβαα (t) − g˙ αβββ (t) + 2iλαβαα } ×{g˙ ααβα (t) − g˙ βββα (t) + 2iλααβα }};

(163). ˆ (ωβα , t) = H[S{−iωβ−α t−gαααα (t)−gββββ (t)+2gααββ +2i(λααββ −λαααα )t}

(164) W ZKHUH ωβα = ωβ − ωα λαααα LV WKH UHRUJDQL]DWLRQ HQHUJ\ IRU αWK H[FLWRQ VWDWH 7KH OLQHVKDSH IXQFWLRQ g(t) DQG λYDOXH LQ (T DQG GHILQHG DV gαβγδ (t) =. t 0. dτ Cαβγδ (τ )(t − τ ).

(165). . doi:10.6342/NTU201802891.

(166) λαβγδ = − Cαβγδ (τ ) =. ∞ 0. ∞ 0. Im(Cαβγδ (τ ))dτ. dωJαβγδ (ω)[cos(ωα τ )coth(.

(167). βωα ) − isin(ωα τ )], 2.

(168). ZKHUH Jαβγδ (ω) LV WKH PDWUL[ RI WKH VSHFWUDO GHQVLWLHV LQ WKH HLJHQVWDWH H[FLWRQ

(169) UHS UHVHQWDWLRQ DQG FDQ EH REWDLQHG IURP WKH PDWUL[ RI WKH VSHFWUDO GHQVLWLHV LQ WKH VLWH UHSUH VHQWDWLRQJnmn m (ω) :H IXUWKHU DVVXPH WKDW WKH VSHFWUDO GHQVLW\ RI HDFK VXFK EDWK LV VLWH LQGHSHQGHQW 7KDW LV Jnmn m (ω) = δnm δnn δmm J(ω) 7KHUHIRUH WUDQVIRUPDWLRQ WR WKH HLJHQVWDWH UHSUHVHQWDWLRQ \LHOGV Jαβγδ (ω) =. . Cnα Cnβ Cnγ Cnδ J(ω).

(170). n. 7KHUHIRUH HQHUJ\ JDS DXWRFRUUHODWLRQ IXQFWLRQ LQ H[FLWRQ UHSUHVHQWDWLRQ Cαβγδ (τ ) FDQ DOVR EH REWDLQ IURP WKH VLWH UHSUHVHQWDWLRQ ,W LV JLYHQ E\ Cαβγδ (τ ) =. n. =. . Cnα Cnβ Cnγ Cnδ. . ∞ 0. dωJ(ω)[cos(ωα τ )coth(. βωα ) − isin(ωα τ )] 2.

(171). Cnα Cnβ Cnγ Cnδ C(τ ),. n. ZKHUH C(τ ) LV HQHUJ\ JDS DXWRFRUUHODWLRQ IXQFWLRQ LQ VLWH UHSUHVHQWDWLRQ DQG ZH DVVXPH avg C(τ ) LV HTXDO WR Cqc (τ ) REWDLQHG E\ CM D (τ ) 7KDW LV WR VD\ ZH FDQ FDOFXODWH WKH (T . EDVHG RQ WKH Cqc (τ ) DQG H[FLWRQ HQHUJLHV DQG FRHIILFLHQWV RI H[FLWRQ VWDWHV +RZHYHU ZH KDYH WR FRQVLGHU WKH KRPRJHQHRXV EURDGHQLQJ DQG LQKRPRJHQHRXV EURDGHQLQJ ZKLFK DUH GXH WR WKH G\QDPLF GLVRUGHU DQG WKH VWDWLF GLVRUGHU RI HQHUJ\ JDS IOXFWXDWLRQ ZKHQ ZH VLPXODWH WKH DEVRUSWLRQ VSHFWUXP 6LQFH WKH VLPXODWLRQ WLPH RI HDFK 0' WUDMHFWRULHV LV RQO\ SV WKH LQKRPRJHQHRXV EURDGHQLQJ REWDLQHG E\ 0' LV ELDVHG ZH VHW WKH LQKRPRJHQHRXV EURDGHQLQJ DV cm−1 IRU DOO H[FLWRQ VWDWHV 7KH KRPRJH QHRXV EURDGHQLQJ IRU WKH SHDN RI WKH αth H[FLWRQ VWDWH LV UHSUHVHQWHG E\ WKH DEVRUSWLRQ OLQH VKDSH IXQFWLRQ RI WKH αth H[FLWRQ VWDWH gαααα (t) )XUWKHUPRUH $IWHU YHULI\LQJ RXU PRGHO E\ ILWWLQJ DEVRUSWLRQ VSHFWUXP ZH FDQ SURSD . doi:10.6342/NTU201802891.

(172) JDWH H[FLWDWLRQ HQHUJ\ WUDQVIHU G\QDPLFV E\ FRQVWUXFW WKH UDWH FRQVWDQW PDWUL[ 7KH PDWUL[ HOHPHQW RI UDWH FRQVWDQW PDWUL[ FDQ EH REWDLQHG E\ (T 7KH GHWDLOV ZLOO EH PHQWLRQHG LQ VHFWLRQ . . doi:10.6342/NTU201802891.

(173) &KDSWHU (IIHFWLYH PRGHOV IRU 5& &3 DQG &3 . 0RGHO +DPLOWRQLDQ ,Q WKLV FKDSWHU ZH SUHVHQW WKH HIIHFWLYH PRGHO LQ RXU ZRUN EDVHG RQ VLWH HQHUJLHV FDO. FXODWHG E\ KXDQJ¶V JURXS DQG H[FLWRQLF FRXSOLQJV FDOFXODWHG E\ RXUVHOI EDVHG RQ FU\VWDO VWUXFWXUH 3'% ,'$5&

(174) ,Q IROORZLQJ VXEVHFWLRQV ZH SUHVHQW SLJPHQWV ODEHOV IRU FKURPRSKRUHV LQ WKH 36,, FRUH FRPSOH[ WR LQWURGXFH PDWUL[ HOHPHQWV RI V\VWHP +DPLOWR QLDQ 7KH V\VWHP +DPLOWRQLDQ LV E\ PDWUL[ VR WKH V\VWHP +DPLOWRQLDQ LV GLYLGHG LQWR EORFN +DPLOWRQLDQV WR GLVFXVV LQGLYLGXDOO\. . 3LJPHQW ODEHOV RI 36,, FRUH FRPSOH[. ,Q WKH LQWURGXFWLRQ ZH VKRZ WKH FU\VWDO VWUXFWXUH RI 36,, FRUH FRPSOH[ EXW ZH GRQ¶W DVVLJQ DOO WKH SLJPHQW ODEHOV WR HDFK SLJPHQWV +RZHYHU WKH GLDJRQDO WHUP RI V\VWHP +DPLOWRQLDQ LV VLWH HQHUJ\ RI HDFK SLJPHQW 7KHUHIRUH ZH SUHVHQW SLJPHQWV FRQVLGHUHG LQ RXU PRGHO LQ )LJ 7KH ODEHO RI SLJPHQWV DUH VKRZQ EHORZ ,Q )LJ ZH RQO\ VKRZ WKH PRQRPHU RI 36,, FRUH FRPSOH[ EHFDXVH WKH ODEHO DUH WKH VDPH LQ WZR PRQRPHUV 7KHUH DUH FKORURSK\OOV D LQ WKH &3 DQG WKHVH SLJPHQWV DUH ODEHOHG IURP &/$ WR &/$ 7KHUH DUH FKORURSK\OOV D LQ WKH &3 DQG WKHVH. . doi:10.6342/NTU201802891.

(175) .

(176). . . . .

(177).

(178) .

(179).

(180) . .

(181). . . .

(182) .

(183)

(184).

(185). .

(186).

(187). . .

(188) .

(189) . . .

(190) .

(191) .

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hlD1 DQG ChlD2 DUH DOVR NQRZQ DV DFFHVVRU\ FKORURSK\OOV ChlzD1 DQG ChlzD2 DUH DOVR NQRZQ DV SHULSKHUDO FKORURSK\OOV. . %ORFN +DPLOWRQLDQV RI 36,, FRUH FRPSOH[. 7R FOHDUO\ XQGHUVWDQG DQG DQDO\]H PDWUL[ HOHPHQWV RI RXU V\VWHP +DPLOWRQLDQ ZH GLYLGH WKH V\VWHP +DPLOWRQLDQ LQWR EORFN +DPLOWRQLDQV 7KHUH DUH SLJPHQWV LQ WKH 36,, FRUH FRPSOH[ SLJPHQWV DUH LQ HDFK PRQRPHUV Q UHSUHVHQW SLJPHQWV LQ 0 DQG Q UHSUHVHQW SLJPHQWV LQ 0 6LWH HQHUJLV En DUH FDOFXODWH EDVHG RQ 0' VLPXODWLRQ E\ KXDQJ¶V JURXS DQG H[FLWRQLF FRXSOLQJV Jnm DUH FDOFXODWH EDVHG RQ FU\VWDO VWUXFWXUH E\ RXUVHOI )LJXUH VKRZV EORFN +DPLOWRQLDQV LQ WKH V\VWHP +DPLOWRQLDQ. . doi:10.6342/NTU201802891.

(193) )LJXUH %ORFN +DPLOWRQLDQV LQ WKH V\VWHP +DPLOWRQLDQ 7KH ZKROH PDWUL[ LV D E\ V\VWHP +DPLOWRQLDQ 7KH QDPH RI HDFK EORFN +DPLOWRQLDQ LV VKRZQ LQ WKH FHQWHU RI WKH EORFN HRC DQG HRC DUH E\ PDWUL[HV HCP 47 DQG HCP 47 DUH E\ PDWUL[HV HCP 43 DQG HCP 43 DUH E\ PDWUL[HV HCP 47−RC DQG HCP 47−RC DUH E\ PDWUL[HV HCP 43−RC DQG HCP 43−RC DUH E\ PDWUL[HV HCP 43−CP 47 DQG HCP 43−CP 47 DUH E\ PDWUL[HV HRC−CP 47 LV WKH WUDQVSRVH RI HCP 47−RC HRC−CP 43 LV WKH WUDQVSRVH RI HCP 43−RC HCP 47−CP 43 LV WKH WUDQVSRVH RI HCP 43−CP 47 HRC−CP 47 LV WKH WUDQVSRVH RI HCP 47−RC HRC−CP 43 LV WKH WUDQVSRVH RI HCP 43−RC HCP 47−CP 43 LV WKH WUDQVSRVH RI HCP 43−CP 47 HM 1−M 2 DQG HM 2−M 1 DUH E\ PDWUL[H[ HRC HCP 47 DQG HCP 43 DUH )UHQNHO H[FLWRQ +DPLOWRQLDQ IRU 5& &3 DQG &3 7KHVH DUH JLYHQ DV HRC =. 8 . En |n n| +. n=1. HCP 47 =. HCP 43 =. 8 . 24 . Jnm (|n m| + |m n|),. n=1,n<m. En |n n| +. 24 . n=9. n=9,n<m. 37 . 37 . n=25.

(194). En |n n| +. Jnm (|n m| + |m n|),.

(195). Jnm (|n m| + |m n|),.

(196). n=25,n<m. . doi:10.6342/NTU201802891.

(197) ZKHUH En LV WKH DYHUDJH VLWH HQHUJLHV RI SLJPHQW Q REWDLQHG IURP 0' WUDMHFWRU\ HCP 47−RC HCP 43−RC HCP 43−CP 47 HRC−CP 47 HRC−CP 43 DQG HCP 47−CP 43 DUH RIIGLDJRQDO WHUP RI WKH V\VWHP +DPLOWRQLDQ DQG DOO RI WKH PDWUL[ HOHPHQWV DUH H[FLWRQLF FRXSOLQJV EHWZHHQ SLJPHQWV RI GLIIHUHQW FRPSOH[HV ZLWKLQ D PRQRPHU )RU H[DPSOH PDWUL[ HOHPHQWV RI HCP 47−RC DUH H[FLWRQLF FRXSOLQJV EHWZHHQ SLJPHQWV LQ &3 DQG SLJPHQWV LQ 5&7KHVH DUH JLYHQ DV HCP 47−RC =. 24 8 . Jnm |n m| = (HRC−CP 47 )T ,.

(198). Jnm |n m| = (HRC−CP 43 )T ,.

(199). Jnm |n m| = (HCP 47−CP 43 )T ..

(200). n=9 m=1. HCP 43−RC =. 37 8 n=25 m=1. HCP 43−CP 47 =. 37 24 n=25 m=9. $ERYH EORFN +DPLOWRQLDQV GHVFULEH RQH RI PRQRPHUV LQ 36,, FRUH FRPSOH[ %ORFN +DPLOWRQLDQV ZLWK DSRVWURSKH GHVFULEH WKH RWKHU PRQRPHU LQ 36,, FRUH FRPSOH[ 7R GLV WLQJXLVK WZR PRQRPHUV WZR PRQRPHUV GHQRWH DV PRQRPHU 0

(201) DQG PRQRPHU 0

(202) . )RU H[DPSOH HRC LV )UHQNHO +DPLOWRQLDQ IRU 5& LQ WKH 0 ZKLOH HRC LV )UHQNHO +DPLO . WRQLDQ IRU 5& LQ WKH 0 7KH IRUP RI HRC DQG HRC DUH WKH VDPH EXW YDOXHV RI PDWUL[ HOHPHQWV DUH VOLJKWO\ GLIIHUHQW 7KHVH DUH JLYHQ DV 45 . . HRC =. n=38. . HCP 47 =. . HCP 43 =. 45 . En |n n| +. 61 .

(203). n=38,n<m. En |n n| +. 61 . n=46. n=46,n<m. 74 . 74 . En |n n| +. n=62. . Jnm (|n m| + |m n|),. HCP 47−RC =. Jnm (|n m| + |m n|),.

(204). Jnm (|n m| + |m n|)..

(205). n=62,n<m. 61 45 . . Jnm |n m| = (HRC−CP 47 )T ,.

(206). n=46 m=38. . doi:10.6342/NTU201802891.

(207) . HCP 43−RC =. 45 74 . .

(208). .

(209). Jnm |n m| = (HRC−CP 43 )T ,. n=62 m=38. . HCP 43−CP 47 =. 74 61 . Jnm |n m| = (HCP 47−CP 43 )T .. n=62 m=46. HM 1−M 2 DUH RIIGLDJRQDO WHUP RI WKH V\VWHP +DPLOWRQLDQ WRR ,W LV D E\ PDWUL[ +RZHYHU PDWUL[ HOHPHQWV LQ HM 1−M 2 DUH H[FLWRQLF FRXSOLQJV EHWZHHQ SLJPHQWV LQ WZR PRQRPHUV HM 1−M 2 LV JLYHQ DV HM 1−M 2 =. 37 74 . Jnm |n m| = (HM 2−M 1 )T ..

(210). n=1 m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

(211) PHWKRG WR FDOFXODWH H[FLWRQLF FRXSOLQJ 6LQFH PRVW RI H[FLWRQ VWDWHV GHORFDOL]H DW SLJPHQWV ZLWKLQ c ZH FRQVLGHU WKH H[FLWRQLF FRX SOLQJ RQO\ LI WKH GLVWDQFH EHWZHHQ SLJPHQWV LV OHVV WKDQ c ,Q WKLV ZRUN ZH HPSOR\ WKH 36,, FRUH FRPSOH[ FU\VWDO VWUXFWXUH DV VWUXFWXUH UHIHUHQFH >@ ([FLWRQLF FRXSOLQJV VKRZHG LQ VXEVHFWLRQ DUH DYHUDJH UHVXOWV. . doi:10.6342/NTU201802891.

(212) . $Q HIIHFWLYH PRGHO IRU 5&. . &DOLEUDWLRQ RI HRC. ,Q WKH HRC EHFDXVH ZH GLGQ¶W KDYH WKH VLWH HQHUJLHV RI SKHRSK\WLQV IURP 0' ZH . WDNH 5HQJHU¶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nth VLWH LV JLYHQ E\ Ens = E0 + ΔEns ,.

(213). . doi:10.6342/NTU201802891.

(214) ΔEns (τ ). = f ΔEn (τ ) =. f ef f. i. j. Δqin qjbg |rin (τ ) − rjbg (τ )|. ,.

(215). ZKHUH I LV WKH VFDOLQJ IDFWRU ef f LV WKH HIIHFWLYH GLHOHFWULF FRQVWDQW Δqin LV WKH GLIIHU HQFH RI JURXQG VWDWH DQG H[FLWHG VWDWH DWRPLF SDUWLDO FKDUJH L LQ WKH VLWH Q DQG qjbg LV WKH EDFNJURXQG SDUWLDO FKDUJH RI FKDUJHG UHVLGXH M rin DQG rjbg DUH WKH SRVLWLRQ YHFWRUV RI HDFK DWRPV 7KHQ WKH PRGLILHG FODVVLFDO WLPH FRUUHODWLRQ IXQFWLRQ CM D (τ ) LV (T PXOWLSOLHG E\ f 2 avg CM D (τ ) = f 2 CM D =. f2 δEn (τ )δEn (0) N n.