UNIVERSIDADE FEDERAL DE SÃO CARLOS CENTRO DE CIÊNCIAS EXATAS E DE TECNOLOGIA PROGRAMA DE PÓS-GRADUAÇÃO EM FÍSICA

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❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❙➹❖ ❈❆❘▲❖❙

❈❊◆❚❘❖ ❉❊ ❈■✃◆❈■❆❙ ❊❳❆❚❆❙ ❊ ❉❊ ❚❊❈◆❖▲❖●■❆

P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❋❮❙■❈❆

❘❛♣❤❛❡❧ ❋♦rt❡s ■♥❢❛♥t❡ ●♦♠❡s

❚❡❧❡tr❛♥s♣♦rt❡ ◗✉â♥t✐❝♦ ♥❛ Pr❡s❡♥ç❛ ❞❡ ❘✉í❞♦

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❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❙➹❖ ❈❆❘▲❖❙

❈❊◆❚❘❖ ❉❊ ❈■✃◆❈■❆❙ ❊❳❆❚❆❙ ❊ ❉❊ ❚❊❈◆❖▲❖●■❆

P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❋❮❙■❈❆

❘❛♣❤❛❡❧ ❋♦rt❡s ■♥❢❛♥t❡ ●♦♠❡s

❚❡❧❡tr❛♥s♣♦rt❡ ◗✉â♥t✐❝♦ ♥❛ Pr❡s❡♥ç❛ ❞❡ ❘✉í❞♦

❊st❛ t❡s❡ ❝♦♥té♠ ❛s ❝♦rr❡çõ❡s ❡ ❛❧t❡r❛çõ❡s s✉❣❡r✐❞❛s ♣❡❧❛ ❈♦♠✐ssã♦ ❏✉❧❣❛❞♦r❛ ❞✉r❛♥t❡ ❛ ❞❡❢❡s❛ r❡❛❧✐③❛❞❛ ♣♦r ❘❛♣❤❛❡❧ ❋♦rt❡s ■♥❢❛♥t❡ ●♦♠❡s ❡♠ 01✴04✴2016✳ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❙ã♦ ❈❛r❧♦s✳ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛✳ ➪r❡❛ ❞❡ ❈♦♥❝❡♥tr❛çã♦✿ ❋ís✐❝❛ ❊st❛tíst✐❝❛✳ ❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ●✉st❛✈♦ ●❛r❝✐❛ ❘✐❣♦❧✐♥✳

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Ficha catalográfica elaborada pelo DePT da Biblioteca Comunitária UFSCar Processamento Técnico

com os dados fornecidos pelo(a) autor(a)

G633t

Gomes, Raphael Fortes Infante

Teletransporte quântico na presença de ruído / Raphael Fortes Infante Gomes. -- São Carlos : UFSCar, 2016.

155 p.

Tese (Doutorado) -- Universidade Federal de São Carlos, 2016.

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✐✈

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UNI VERSI DADE FEDERAL DE sÃo CARLOS

Cent ro de Ciênci as Exat as e de Tecno 】agi a

Programa de Pl i s-Gradua ç ão em Físi ca

Fol ha de _Aprovag ão

Ass , na \uras dos membros da cam íqsi \n examinadora que aval,OU e _aprovou a Def esa de Tese de Dout orado do candi dat o

Raphael Fort es I nf ant eGomes , real i zada em 01/04/2016 :

Pro_四_回西_西・stâvo Garci a Ri g口【i”

Prof. Dr. Al ex Eduardo de Bemardi ni UFSCar

Prof. Dr. MUed Hi t qqan You , sef M" " sa

USP

Prof. Dr. Marcos Ces âr de Ol . Ei ra

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❆❣r❛❞❡❝✐♠❡♥t♦s

❆❣r❛❞❡ç♦ ❞❡ ❝♦r❛çã♦ ❛♦s ♠❡✉s ♣❛✐s✱ ❘❡❣✐♥❛ ❡ ❘✐❝❛r❞♦✱ ❡ ❛♦ ♠❡✉ ✐r♠ã♦✱ ❇❡r♥❛r❞♦✱ ♣❡❧♦ ❝❛r✐♥❤♦✱ s♦❧✐❞❛r✐❡❞❛❞❡✱ ❝♦♠♣r❡❡♥sã♦✱ ♣❡❧♦ ❛♣♦✐♦ ✐♥❝♦♥❞✐❝✐♦♥❛❧ ❡♠ t♦❞♦s ♦s ♠♦♠❡♥t♦s✱ ❡✱ ♥♦✈❛♠❡♥t❡✱ ♣♦r ♠❡ ❢❛③❡r❡♠ ❛❝r❡❞✐t❛r q✉❡ s♦♥❤♦s sã♦ ♣♦ssí✈❡✐s✳ ❙❡♠ ❡❧❡s✱ ❡st❡ tr❛❜❛❧❤♦ t❛♠❜é♠ ♥ã♦ ❡①✐st✐r✐❛✳

❆♦ ♣r♦❢❡ss♦r ●✉st❛✈♦ ●❛r❝✐❛ ❘✐❣♦❧✐♥✱ ♣❡❧❛ ♦♣♦rt✉♥✐❞❛❞❡ ❞❡ ❞❡s❡♥✈♦❧✈❡r ❡st❡ tr❛❜❛❧❤♦✱ ♣❡❧♦ ❝♦♥❤❡❝✐♠❡♥t♦ tr❛♥s♠✐t✐❞♦ ❡ ♣❡❧♦ ✐♥✈❡st✐♠❡♥t♦ ♥❛ ♠✐♥❤❛ ❢♦r♠❛çã♦ ✐♥t❡❧❡❝✲ t✉❛❧ ❡ ♣r♦✜ss✐♦♥❛❧ ❞✉r❛♥t❡ ♦s ú❧t✐♠♦s ❛♥♦s✳

❆♦ ❛♠✐❣♦ ❆❧❡①❛♥❞r❡ ❈✉r②✱ ♥ã♦ só ♣❡❧♦ ❛✉①í❧✐♦ ✐♠❡❞✐❛t♦ ❝♦♠ t♦❞❛s ❛s q✉❡s✲ tõ❡s té❝♥✐❝❛s ♠❛s ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣❡❧❛ ❛♠✐③❛❞❡✱ ♠♦t✐✈❛çã♦ ❡ ♣❡❧♦s ❝♦♥s❡❧❤♦s ✈❛❧✐♦s♦s✳

❆♦s ❛♠✐❣♦s ▲❡♦♥❛r❞♦ ●✉✐♠❛rã❡s✱ ❚❤✐❛❣♦ ❋r❡✐r❡✱ ▲❡♦♥❛r❞♦ ❘♦s❛✱ ▼❛r❝❡❧♦ ❙✐r✐♠❛r❝♦✱ ▼❛t❤❡✉s P✐✈❛✱ ❋❧á✈✐♦ ▲❛③③❛r♦tt♦✱ ❉✐❡❣♦ ▼❛rt✐♥s✱ ▲✉ís ❋❡r♥❛♥❞♦ ▼❛❣♥❛♥✐♥✐✱ ❘❛❢❛❡❧ ❙❛❧❧❛✱ ❘✐❝❤❛r❞ ◆❡✐❧✱ ▼❛r❝❡❧♦ ▲❡✐t❡✱ ❇r✉♥♦ ●rü♥✐♥❣❡r✱ ❱✐✈❛❧❞♦ ▲♦♣❡s✱ ❏❛❧❞❛✐r ◆ó✲ ❜r❡❣❛✱ ❋❡r♥❛♥❞♦ ❞❡ ❙♦✉③❛ ❡ ❊♠❛♥✉❡❧ ❉✐♥✐③✱ ♣❡❧❛ ❛♠✐③❛❞❡ ✈❡r❞❛❞❡✐r❛✱ ♣❡❧❛ ❛❥✉❞❛ ❝♦♠ q✉❡stõ❡s r❡❧❡✈❛♥t❡s ❡ ♣❡❧♦ s✉♣♦rt❡ ❡♠ ♠♦♠❡♥t♦s ❞✐❢í❝❡✐s✳

❆♦s ❢❛♠✐❧✐❛r❡s✱ ♣❡❧♦ ✐♥❝❡♥t✐✈♦✱ ♣❡❧❛ ✉♥✐ã♦ ❡ ♣❡❧❛ s❡♥s❛çã♦ ❞❡ ♣r♦①✐♠✐❞❛❞❡ ♠❡s♠♦ ❡♠ ❣r❛♥❞❡s ❞✐stâ♥❝✐❛s✳

❆♦s ❛♠✐❣♦s ❉❛✈✐❞ ❚❛♥❣❛♥❡❧❧✐✱ ❋❛❜✐❛♥♦ ◆✉♥❡s✱ ❆♥❞ré ❞❡ ❙♦✉③❛ ❡ P❛✉❧♦ ❈❛r✲ ✈❛❧❤♦✱ ♣❡❧❛ ❛♠✐③❛❞❡✱ ♣❡❧♦s ❡♥s✐♥❛♠❡♥t♦s✱ ♣❡❧♦ ❡♥t✉s✐❛s♠♦ ❡ ♣♦r ♠♦♠❡♥t♦s ❞❡ ❛❧❡❣r✐❛ ✐♥❡sq✉❡❝í✈❡✐s✳

➚ ❇✐❛♥❝❛ ❘❛♥t✐♥✱ ♣❡❧♦ ❝❛r✐♥❤♦✱ ✐♥❝❡♥t✐✈♦✱ ♣❡❧❛ ❝♦♠♣r❡❡♥sã♦ ❡♠ ♠♦♠❡♥t♦s ❝r✉❝✐❛✐s ❡ ♣❡❧♦ s✉♣♦rt❡ ❝♦♥st❛♥t❡ ❛♦ ❧♦♥❣♦ ❞♦s ú❧t✐♠♦s ♠❡s❡s✳

❆♦s ♣r♦❢❡ss♦r❡s ●✐❧♠❛r ❊✉❣ê♥✐♦ ▼❛rq✉❡s✱ ❈❡❧s♦ ❱✐❧❧❛s✲❇ô❛s ❡ ❋❡r♥❛♥❞♦ ▼✳ ❆r❛✉❥♦✲▼♦r❡✐r❛✱ ♣❡❧❛ ✐♥s♣✐r❛çã♦ ❝♦♠♦ ❡①❝❡❧❡♥t❡s ♣r♦❢❡ss♦r❡s✱ ♣❡❧❛ ❛♠✐③❛❞❡ ❡ ♣❡❧♦ ❛♣♦✐♦ ❝♦rr❡s♣♦♥❞✐❞♦ ❡♠ t♦❞♦s ♦s ♠♦♠❡♥t♦s r❡q✉✐s✐t❛❞♦s✳

❆♦s ♣r♦❢❡ss♦r❡s ❏♦ã♦ ❈❤❛✜✱ ❏♦ã♦ ❇❛t✐st❛ ❞❡ ❖❧✐✈❡✐r❛✱ ▲✉✐③ ❍❡♥r✐q✉❡ ❇❛r✲ ❜♦s❛✱ ❏♦sé ❈❛r❧♦s ●r✐③❡♥❞✐✱ ◆❡❧s♦♥ ❘❛❣❛③③✐✱ ◆✐❧❝✐❧é❛ P❡✐①♦t♦✱ ❈❛r❧♦s ❊❞✉❛r❞♦ ◆♦❣✉ér❡s ❡ ❋❛❜rí❝✐♦✱ ♣❡❧❛ ♠♦t✐✈❛çã♦ ❡ ✐♥s♣✐r❛çã♦ ❛tr✐❜✉í❞❛s ♥♦ ✐♥í❝✐♦ ❞❡st❛ ❥♦r♥❛❞❛✳

❆♦s ❡♥t❡s q✉❡r✐❞♦s q✉❡ ♥ã♦ ❡stã♦ ♠❛✐s ❝♦♥♦s❝♦ ❡ q✉❡ ♣❛rt✐❝✐♣❛r❛♠ ❞❡st❛ ❤✐stór✐❛✳

❆♦s ❛♠✐❣♦s✱ ♣r♦❢❡ss♦r❡s ❡ ❝♦❧❡❣❛s ♥❛ ❯♥✐✈❡rs✐❞❛❞❡ q✉❡ ♥ã♦ t✐✈❡r❛♠ s❡✉s ♥♦♠❡s ❝✐t❛❞♦s✳

❊ à ❈❛♣❡s✱ ♣❡❧♦ ❛✉①í❧✐♦ ✜♥❛♥❝❡✐r♦ ❞✉r❛♥t❡ ♦s q✉❛tr♦ ❛♥♦s ❞❡ ❞♦✉t♦r❛❞♦✳

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✈✐

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✈✐✐

❘❡s✉♠♦

❖ ❢♦❝♦ ❞♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ ❝♦♥s✐st❡ ❡♠ ❡①♣❧♦r❛r ❛ ✈✐❛❜✐❧✐❞❛❞❡ ❞❡ s❡ r❡❛❧✐③❛r ♦ t❡❧❡tr❛♥s♣♦rt❡ ❞❡ ❡st❛❞♦s q✉â♥t✐❝♦s ❛r❜✐trár✐♦s ❡♠ ❝❡♥ár✐♦s ♦♥❞❡ ❛ ♣r❡s❡♥ç❛ ❞❡ ✉♠ ❛♠❜✐❡♥t❡ ❡①t❡r♥♦ r❡❞✉③ ❛ ♣✉r❡③❛ ❞♦ ❡st❛❞♦ ❞❡ ❡♥tr❛❞❛ ❡ ❞♦ ❝❛♥❛❧ ❞❡ tr❛♥s♠✐ssã♦ ❞❡ ✐♥❢♦r♠❛çã♦✳ P❛r❛ ✐♥✈❡st✐❣❛r ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡st❡s ♣r♦t♦❝♦✲ ❧♦s ❡♠ ❝♦♥❞✐çõ❡s r❡❛❧✐st❛s✱ s❡❧❡❝✐♦♥❛♠♦s ♦s ♣r✐♥❝✐♣❛✐s ♠❛♣❛s ❞❡ ❞❡❝♦❡rê♥❝✐❛ r❡❣✐str❛❞♦s ♥❛ ❧✐t❡r❛t✉r❛ r❡❧❛t✐✈♦s à ❞❡s❝r✐çã♦ ❞❡st❡ ❢❡♥ô♠❡♥♦✱ ✐♥❝❧✉✐♥❞♦ ❛ r❡✲ ♣r❡s❡♥t❛çã♦ ❞❡ ❡st❛❞♦s ♠✐st♦s ❛tr❛✈és ❞♦s ♦♣❡r❛❞♦r❡s ❞❡ ❑r❛✉s ❡ ❞❡ s✐st❡♠❛s ❡♠ ❡q✉✐❧í❜r✐♦ tér♠✐❝♦ ❝✉❥♦ ❍❛♠✐❧t♦♥✐❛♥♦ é ❞❡s❝r✐t♦ ♣❡❧♦ ♠♦❞❡❧♦ ❞❡ ❍❡✐s❡♥✲ ❜❡r❣✳ ◆❡st❡ ❝♦♥t❡①t♦✱ ♣r♦✈❛♠♦s q✉❡ ❡①✐st❡♠ ❝❛s♦s ♥♦s q✉❛✐s ❛ ✐♥✢✉ê♥❝✐❛ ❞❡ ❢❛t♦r❡s ❡①t❡r♥♦s ✭❝♦♠♦ ♦ ❛✉♠❡♥t♦ ❞❛ t❡♠♣❡r❛t✉r❛ ❡ ❞❛s t❛①❛s ❞❡ ❞❡❝♦❡rê♥✲ ❝✐❛✮ ❡ ❛ ✐♠❡rsã♦ ❞❡ q✉❜✐ts ❡♠ ❛♠❜✐❡♥t❡s ❞✐st✐♥t♦s ❝♦♥tr✐❜✉✐ ♣❛r❛ ❛✉♠❡♥t❛r ❛ s❡♠❡❧❤❛♥ç❛ ❡♥tr❡ ❛s ♣r♦♣r✐❡❞❛❞❡s ❞❛ ✐♥❢♦r♠❛çã♦ ♦r✐❣✐♥❛❧ ❡ ❛s ❞♦ ❡st❛❞♦ t❡❧❡tr❛♥s♣♦rt❛❞♦✳ ❆❧é♠ ❞✐ss♦✱ ❡st✉❞❛♠♦s ♦ ♠ét♦❞♦ ❞❡ t❡❧❡tr❛♥s♣♦rt❡ ♣r♦❜❛❜✐✲ ❧íst✐❝♦ s♦❜ ❛ ✐♥✢✉ê♥❝✐❛ ❞♦s ♠❡s♠♦s t✐♣♦s ❞❡ r✉í❞♦s ❛♥❛❧✐s❛❞♦s ♣❛r❛ ♦ ♣r♦t♦❝♦❧♦ ❞❡t❡r♠✐♥íst✐❝♦✱ ❡ ♦s r❡s✉❧t❛❞♦s ❛q✉✐ ❛♣r❡s❡♥t❛❞♦s ❞❡♠♦♥str❛♠ q✉❡ ♦ ♣r✐♠❡✐r♦ ♣r♦❝❡ss♦ é ❝❛♣❛③ ❞❡ ❛✉♠❡♥t❛r ❛✐♥❞❛ ♠❛✐s ♦ ✈❛❧♦r ❡s♣❡r❛❞♦ ❞❛ ✜❞❡❧✐❞❛❞❡ ♠é❞✐❛ ❞♦ ❡st❛❞♦ t❡❧❡tr❛♥s♣♦rt❛❞♦✳

(8)

✈✐✐✐

❆❜str❛❝t

❚❤❡ ♠❛✐♥ ❢♦❝✉s ♦❢ t❤✐s ✇♦r❦ ✐s t♦ ❡①♣❧♦r❡ t❤❡ ❢❡❛s✐❜✐❧✐t② ♦❢ ❝♦♥❞✉❝t✐♥❣ t❤❡ t❡❧❡♣♦rt❛t✐♦♥ ♣r♦t♦❝♦❧ ✐♥ s❝❡♥❛r✐♦s ✇❤❡r❡ t❤❡ ♣r❡s❡♥❝❡ ♦❢ ❛♥ ❡①t❡r♥❛❧ ❡♥✈✐r♦♥✲ ♠❡♥t r❡❞✉❝❡s t❤❡ ♣✉r✐t② ♦❢ t❤❡ ✐♥♣✉t st❛t❡ ❛♥❞ t❤❡ tr❛♥s♠✐ss✐♦♥ ❝❤❛♥♥❡❧✳ ❚♦ ✐♥✈❡st✐❣❛t❡ t❤❡ ❜❡❤❛✈✐♦r ♦❢ t❤❡s❡ ♣r♦t♦❝♦❧s ✉♥❞❡r r❡❛❧✐st✐❝ ❝♦♥❞✐t✐♦♥s✱ ✇❡ s❡✲ ❧❡❝t❡❞ t❤❡ ♠❛✐♥ ❞❡❝♦❤❡r❡♥❝❡ ♠❛♣s r❡♣♦rt❡❞ ✐♥ t❤❡ ❧✐t❡r❛t✉r❡ ❝♦♥❝❡r♥✐♥❣ t❤❡ ❞❡s❝r✐♣t✐♦♥ ♦❢ t❤✐s ♣❤❡♥♦♠❡♥♦♥✱ ✐♥❝❧✉❞✐♥❣ t❤❡ r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ ♠✐①❡❞ st❛t❡s t❤r♦✉❣❤ t❤❡ ❑r❛✉s ♦♣❡r❛t♦rs ❛♥❞ s②st❡♠s ✐♥ t❤❡r♠❛❧ ❡q✉✐❧✐❜r✐✉♠ ✇❤♦s❡ ❍❛✲ ♠✐❧t♦♥✐❛♥ ✐s ❞❡s❝r✐❜❡❞ ❜② t❤❡ ❍❡✐s❡♥❜❡r❣ ♠♦❞❡❧✳ ■♥ t❤✐s ❝♦♥t❡①t✱ ✇❡ ♣r♦✈❡❞ t❤❛t t❤❡r❡ ❛r❡ ❝❛s❡s ✐♥ ✇❤✐❝❤ t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ ❡①t❡r♥❛❧ ❢❛❝t♦rs ✭s✉❝❤ ❛s ✐♥❝r❡❛✲ s✐♥❣ t❡♠♣❡r❛t✉r❡ ❛♥❞ ❞❡❝♦❤❡r❡♥❝❡ r❛t❡s✮ ❛♥❞ t❤❡ ✐♠♠❡rs✐♦♥ ♦❢ t❤♦s❡ q✉❜✐ts ✐♥ ❞✐st✐♥❝t ❡♥✈✐r♦♥♠❡♥ts ❤❡❧♣ ✐♥❝r❡❛s✐♥❣ t❤❡ s✐♠✐❧❛r✐t② ❜❡t✇❡❡♥ t❤❡ ♣r♦♣❡rt✐❡s ♦❢ t❤❡ ♦r✐❣✐♥❛❧ ✐♥❢♦r♠❛t✐♦♥ ❛♥❞ t❤❡ t❡❧❡♣♦rt❡❞ st❛t❡✳ ■♥ ❛❞❞✐t✐♦♥✱ ✇❡ st✉❞✐❡❞ t❤❡ ♣r♦❜❛❜✐❧✐st✐❝ t❡❧❡♣♦rt❛t✐♦♥ ♣r♦t♦❝♦❧ ✉♥❞❡r t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ t❤❡ s❛♠❡ ♥♦✐s❡ ❝♦♥✲ ❞✐t✐♦♥s ❛♥❛❧②s❡❞ ❢♦r t❤❡ ❞❡t❡r♠✐♥✐st✐❝ ♣r♦t♦❝♦❧✱ ❛♥❞ t❤❡ r❡s✉❧ts ❤❡r❡ ♦❜t❛✐♥❡❞ s❤♦✇ t❤❛t t❤❡ ✜rst ♣r♦❝❡ss ❝❛♥ ♦✉t♣❡r❢♦r♠ t❤❡ ❡①♣❡❝t❡❞ ✈❛❧✉❡ ♦❢ t❤❡ ❛✈❡r❛❣❡ ✜❞❡❧✐t② ♦❢ t❤❡ t❡❧❡♣♦rt❡❞ st❛t❡✳

(9)

❙✉♠ár✐♦

▲✐st❛ ❞❡ ❋✐❣✉r❛s ①✐✐✐

▲✐st❛ ❞❡ ❚❛❜❡❧❛s ①①✐✐✐

✶ ■♥tr♦❞✉çã♦ ✶

✶✳✶ ❈♦♥s✐❞❡r❛çõ❡s Pr❡❧✐♠✐♥❛r❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷

✶✳✷ ❖❜❥❡t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷

✶✳✸ ❈♦♥tr✐❜✉✐çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸

✶✳✹ ❖r❣❛♥✐③❛çã♦ ❞♦ ❚r❛❜❛❧❤♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸

✷ ❋✉♥❞❛♠❡♥t♦s ❞❡ ■♥❢♦r♠❛çã♦ ◗✉â♥t✐❝❛ ✺

✷✳✶ ◗✉❜✐ts ❡ ❙✐st❡♠❛s ❞❡ ❉♦✐s ◆í✈❡✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺

✷✳✷ ❖ ❖♣❡r❛❞♦r ❉❡♥s✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽

✷✳✷✳✶ ❖ ❖♣❡r❛❞♦r ❉❡♥s✐❞❛❞❡ ♣❛r❛ ✉♠ ◗✉❜✐t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷

✷✳✷✳✷ ❖ ❖♣❡r❛❞♦r ❉❡♥s✐❞❛❞❡ ♣❛r❛ ❙✐st❡♠❛s ❈♦♠♣♦st♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹

✷✳✸ ❆ ❉❡❝♦♠♣♦s✐çã♦ ❞❡ ❙❝❤♠✐❞t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻

✷✳✹ P✉r✐✜❝❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶

✷✳✺ ❖s ❖♣❡r❛❞♦r❡s ❞❡ ❑r❛✉s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸

✷✳✻ ❊♥tr♦♣✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽

✷✳✻✳✶ ❆ ❊♥tr♦♣✐❛ ❞❡ ❙❤❛♥♥♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾

✷✳✻✳✷ ❆ ❊♥tr♦♣✐❛ ❞❡ ❱♦♥ ◆❡✉♠❛♥♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷

✷✳✼ ❈♦♥❝❡♥tr❛çã♦ ❞❡ ❊♠❛r❛♥❤❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺

✷✳✽ ❙❡♣❛r❛❜✐❧✐❞❛❞❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽

✷✳✾ ❉❡❝♦❡rê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵

✷✳✾✳✶ ■♥✈❡rsã♦ ❞❡ ❇✐t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼

✷✳✾✳✷ ■♥✈❡rsã♦ ❞❡ ❋❛s❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾

✷✳✾✳✸ ■♥✈❡rsã♦ ❞❡ ❇✐t ❡ ❋❛s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵

✷✳✾✳✹ ❉❡s♣♦❧❛r✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶

✷✳✾✳✺ ❆t❡♥✉❛çã♦ ❞❡ ❋❛s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷

✷✳✾✳✻ ❆t❡♥✉❛çã♦ ❞❡ ❆♠♣❧✐t✉❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺

✷✳✶✵ ❘❡❞✉çã♦ ❞❡ ❊♠❛r❛♥❤❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼

✷✳✶✶ ▼❡❝â♥✐❝❛ ❊st❛tíst✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽

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① ❙❯▼➪❘■❖

✷✳✶✷ ❖ ●❛t♦ ❞❡ ❙❝❤rö❞✐♥❣❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶

✸ ❚❡❧❡tr❛♥s♣♦rt❡ ◗✉â♥t✐❝♦ ❉✐r❡t♦ ✻✸

✸✳✶ ❚❡❧❡tr❛♥s♣♦rt❡ ❞❡ ❊st❛❞♦s ❆r❜✐trár✐♦s ❛tr❛✈és ❞❡ ❈❛♥❛✐s P✉r♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸

✸✳✶✳✶ ❖ Pr♦t♦❝♦❧♦ ❖r✐❣✐♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸

✸✳✷ ❚❡❧❡tr❛♥s♣♦rt❡ ❞❡ ❊st❛❞♦s ❆r❜✐trár✐♦s ❛tr❛✈és ❞❡ ❈❛♥❛✐s ▼✐st♦s ✳ ✳ ✳ ✳ ✳ ✳ ✻✼

✸✳✷✳✶ ❖ ▼♦❞❡❧♦ ●❡r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼

✸✳✷✳✷ ❈❛♥❛✐s ▼✐st♦s ❝♦♠ ❉❡❝♦❡rê♥❝✐❛ ❍♦♠♦❣ê♥❡❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷

✸✳✷✳✸ ❈❛♥❛✐s ▼✐st♦s ❝♦♠ ❉❡❝♦❡rê♥❝✐❛ ❍❡t❡r♦❣ê♥❡❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵

✸✳✸ ❆♥á❧✐s❡ ❞♦ ❱❛❧♦r ❊s♣❡r❛❞♦ ❞❛ ❋✐❞❡❧✐❞❛❞❡ ▼é❞✐❛ ❚♦t❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵

✸✳✸✳✶ ❊♥tr❛❞❛ P✉r❛ ❡♠ ❈❛♥❛✐s ❝♦♠ ❉❡❝♦❡rê♥❝✐❛ ❍♦♠♦❣ê♥❡❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵

✸✳✸✳✷ ❊♥tr❛❞❛ ▼✐st❛ ❡♠ ❈❛♥❛✐s ❝♦♠ ❉❡❝♦❡rê♥❝✐❛ ❍♦♠♦❣ê♥❡❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽

✸✳✸✳✸ ❊♥tr❛❞❛ P✉r❛ ❡♠ ❈❛♥❛✐s ❝♦♠ ❉❡❝♦❡rê♥❝✐❛ ❍❡t❡r♦❣ê♥❡❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷

✸✳✸✳✹ ❊♥tr❛❞❛ ▼✐st❛ ❡♠ ❈❛♥❛✐s ❝♦♠ ❉❡❝♦❡rê♥❝✐❛ ❍❡t❡r♦❣ê♥❡❛ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹

✹ ❚❡❧❡tr❛♥s♣♦rt❡ ◗✉â♥t✐❝♦ ❈♦♥❞✐❝✐♦♥❛❧ ✾✼

✹✳✶ ❊♥tr❛❞❛ P✉r❛ ❡♠ ❈❛♥❛✐s ❝♦♠ ❉❡❝♦❡rê♥❝✐❛ ❍♦♠♦❣ê♥❡❛ ❡ ❍❡t❡r♦❣ê♥❡❛ ✳ ✳ ✳ ✾✾

✹✳✷ ❊♥tr❛❞❛ ▼✐st❛ ❡♠ ❈❛♥❛✐s ❝♦♠ ❉❡❝♦❡rê♥❝✐❛ ❍♦♠♦❣ê♥❡❛ ❡ ❍❡t❡r♦❣ê♥❡❛ ✳ ✳ ✳ ✶✵✺

✺ ❚❡❧❡tr❛♥s♣♦rt❡ ◗✉â♥t✐❝♦ ❡♠ ❈❛❞❡✐❛s ❞❡ ❙♣✐♥ ✶✶✶

✺✳✶ ❚❡❧❡tr❛♥s♣♦rt❡ ❉✐r❡t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✸

✺✳✶✳✶ ❖ ▼♦❞❡❧♦ ❳❨ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✸

✺✳✶✳✷ ❖ ▼♦❞❡❧♦ ❳❳❩ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✵

✺✳✷ ❚❡❧❡tr❛♥s♣♦rt❡ ❈♦♥❞✐❝✐♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✺

✺✳✷✳✶ ❖ ▼♦❞❡❧♦ ❳❨❩ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✺

✻ ❈♦♥❝❧✉sõ❡s ✶✷✼

❆ ❱❡t♦r❡s✱ ❖♣❡r❛❞♦r❡s ❡ ▼❛tr✐③❡s ✶✸✶

❆✳✶ ❱❡t♦r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✶

❆✳✶✳✶ ■♥tr♦❞✉çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✶

❆✳✶✳✷ ■♥❞❡♣❡♥❞ê♥❝✐❛ ▲✐♥❡❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✶

❆✳✶✳✸ ❖ Pr♦❞✉t♦ ❊s❝❛❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✷

❆✳✶✳✹ ◆♦r♠❛❧✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✷

❆✳✶✳✺ ❖rt♦♥♦r♠❛❧✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✷

❆✳✶✳✻ ❖ Pr♦❞✉t♦ ❚❡♥s♦r✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✸

❆✳✷ ❖♣❡r❛❞♦r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✹

❆✳✷✳✶ ■♥tr♦❞✉çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✹

❆✳✷✳✷ ❆ ❘❡❧❛çã♦ ❞❡ ❈♦♠♣❧❡t❡③❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✹

❆✳✷✳✸ ❈♦♠✉t❛❞♦r❡s ❡ ❆♥t✐❝♦♠✉t❛❞♦r❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✺

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❙❯▼➪❘■❖ ①✐

❆✳✷✳✺ ❖♣❡r❛❞♦r❡s ❍❡r♠✐t✐❛♥♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✺

❆✳✷✳✻ ❖ Pr♦❞✉t♦ ❚❡♥s♦r✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✻

❆✳✸ ❘❡♣r❡s❡♥t❛çã♦ ▼❛tr✐❝✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✼

❆✳✸✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✼

❆✳✸✳✷ ❖ ❖♣❡r❛❞♦r ■♥✈❡rs♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✾

❆✳✸✳✸ ❖ Pr♦❞✉t♦ ❚❡♥s♦r✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✾

❆✳✸✳✹ ❖♣❡r❛❞♦r❡s ❍❡r♠✐t✐❛♥♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✵

❆✳✸✳✺ ❆s ▼❛tr✐③❡s ❞❡ P❛✉❧✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✶

❆✳✸✳✻ ❈♦♠✉t❛❞♦r❡s ❡ ❆♥t✐✲❈♦♠✉t❛❞♦r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✷

❇ ❖s P♦st✉❧❛❞♦s ❞❛ ▼❡❝â♥✐❝❛ ◗✉â♥t✐❝❛ ✶✹✸

❇✳✶ P♦st✉❧❛❞♦ ■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✸

❇✳✷ P♦st✉❧❛❞♦ ■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✹

❇✳✸ P♦st✉❧❛❞♦ ■■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✻

❈ P♦rt❛s ▲ó❣✐❝❛s ◗✉â♥t✐❝❛s ✶✹✾

❈✳✵✳✶ P♦rt❛s ❞❡ ✉♠ ◗✉❜✐t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✾

❈✳✵✳✷ P♦rt❛s ❞❡ ❞♦✐s ◗✉❜✐ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✵

(12)

(13)

▲✐st❛ ❞❡ ❋✐❣✉r❛s

✷✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ |Ψ_i ♥❛ ❊s❢❡r❛ ❞❡ ❇❧♦❝❤✳

❋♦♥t❡✿ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❡ ◆✐❡❧s❡♥ ❛♥❞ ❈❤✉❛♥❣✱ ✷✵✶✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻

✷✳✷ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❡ ✉♠ ❝✐r❝✉✐t♦ q✉❡ s✐♠✉❧❛ ♦ ♣r♦❝❡ss♦ ❞❡ ❞❡❝♦✲

❡rê♥❝✐❛ s♦❜r❡ ✉♠ ❡st❛❞♦ ❞❡ ❡♥tr❛❞❛ ❛r❜✐trár✐♦ ρ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸

✷✳✸ ❊♥tr♦♣✐❛ ❞❡ ❙❤❛♥♥♦♥ ♣❛r❛ ✉♠ s✐st❡♠❛ ❜✐♥ár✐♦✳

❋♦♥t❡✿ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❡ ❇❡♥❡♥t✐ ❡t ❛❧✳✱ ✷✵✵✼✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵

✷✳✹ ❊①❡♠♣❧♦ ❞❡ ✉♠ ♣❛r ❡st❛❞♦s ♥ã♦✲♦rt♦❣♦♥❛✐s✳

❋♦♥t❡✿ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❡ ❇❡♥❡♥t✐ ❡t ❛❧✳✱ ✷✵✵✼✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹

✷✳✺ ❊♥tr♦♣✐❛ ❞❡ ❱♦♥ ◆❡✉♠❛♥♥ ❞♦ ♦♣❡r❛❞♦r ❞❡♥s✐❞❛❞❡ r❡❧❛t✐✈♦ ❛♦ ♣❛r ❞❡ ❡st❛❞♦s

♥ã♦✲♦rt♦❣♦♥❛✐s|˜0i❡|˜1i❡♠ ❢✉♥çã♦ ❞❡θ✳ ❖s r❡s♣❡❝t✐✈♦s í♥❞✐❝❡s ❞❡1❛5❡stã♦

❛ss♦❝✐❛❞♦s ❛♦s ✈❛❧♦r❡s ❞❡ θ=_{0; 0.2π

4; 0.4 π 4; 0.6

π 4 ❡0.8

π 4}✳

❋♦♥t❡✿ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❡ ❇❡♥❡♥t✐ ❡t ❛❧✳✱ ✷✵✵✼✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺

✷✳✻ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❡ ✉♠ ❝✐r❝✉✐t♦ q✉❡ s✐♠✉❧❛ ♦ ♣r♦❝❡ss♦ ❞❡ ❞❡❝♦✲ ❡rê♥❝✐❛ ♠❛✐s s✐♠♣❧❡s ♣♦ssí✈❡❧ q✉❡ ♣♦❞❡ ❛t✉❛r s♦❜r❡ ✉♠ ❡st❛❞♦ ❞❡ ❡♥tr❛❞❛

❛r❜✐trár✐♦ ρ✿ ❛ ♣♦rt❛ CN OTa,b✳ ❖ ❝ír❝✉❧♦ ♣r❡❡♥❝❤✐❞♦ ♥♦ q✉❜✐t ❞❡ ❝♦♥tr♦❧❡

❞❡♥♦t❛ q✉❡ ❛ ❛t✐✈❛çã♦ ❞❛ ♣♦rt❛ ♦❝♦rr❡ q✉❛♥❞♦ ♦ ❡st❛❞♦ ❞❡ ❡♥tr❛❞❛ é ✐❣✉❛❧ ❛ |1_i✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶

✷✳✼ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❡ ✉♠ ❝✐r❝✉✐t♦ q✉❡ s✐♠✉❧❛ ♦ ♣r♦❝❡ss♦ ❝♦♠♣❧❡t♦

❞❡ ❞❡❝♦❡rê♥❝✐❛ s♦❜r❡ ✉♠ q✉❜✐t ❛r❜✐trár✐♦ρ✳ ❖s ❝ír❝✉❧♦s ✈❛③✐♦s ❡ ♣r❡❡♥❝❤✐❞♦s

❞❡♥♦t❛♠ q✉❡ ❛ ❛t✐✈❛çã♦ ❞❛s ♣♦rt❛s σx✱ σy ❡ σz ♦❝♦rr❡ q✉❛♥❞♦ ♦s ❡st❛❞♦s

❞♦s q✉❜✐ts ❞❡ ❝♦♥tr♦❧❡ sã♦ r❡s♣❡❝t✐✈❛♠❡♥t❡ ✐❣✉❛✐s ❛ |00_i✱_|01_i ❡_|10_i✳ ✳ ✳ ✳ ✳ ✹✺

✷✳✽ ❊❢❡✐t♦ ❞♦ ♠❛♣❛ ❞❡ ■♥✈❡rsã♦ ❞❡ ❇✐t ♥❛ ❡s❢❡r❛ ❞❡ ❇❧♦❝❤ ♣❛r❛ ♣❂✵✳✸✳

❆♣❡♥❛s ♦ ❡✐①♦ x ♥ã♦ s♦❢r❡ ❝♦♥tr❛çã♦✳

❋♦♥t❡✿ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❡ ◆✐❡❧s❡♥ ❛♥❞ ❈❤✉❛♥❣✱ ✷✵✶✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽

✷✳✾ ❊❢❡✐t♦ ❞♦ ♠❛♣❛ ❞❡ ■♥✈❡rsã♦ ❞❡ ❋❛s❡ ♥❛ ❡s❢❡r❛ ❞❡ ❇❧♦❝❤ ♣❛r❛ ♣❂✵✳✸✳

❆♣❡♥❛s ♦ ❡✐①♦ z ♥ã♦ s♦❢r❡ ❝♦♥tr❛çã♦✳

❋♦♥t❡✿ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❡ ◆✐❡❧s❡♥ ❛♥❞ ❈❤✉❛♥❣✱ ✷✵✶✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵

✷✳✶✵ ❊❢❡✐t♦ ❞♦ ♠❛♣❛ ❞❡ ■♥✈❡rsã♦ ❞❡ ❇✐t ❡ ❋❛s❡ ♥❛ ❡s❢❡r❛ ❞❡ ❇❧♦❝❤ ♣❛r❛ ♣❂✵✳✸✳

❆♣❡♥❛s ♦ ❡✐①♦ y ♥ã♦ s♦❢r❡ ❝♦♥tr❛çã♦✳

❋♦♥t❡✿ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❡ ◆✐❡❧s❡♥ ❛♥❞ ❈❤✉❛♥❣✱ ✷✵✶✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶

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①✐✈ ▲■❙❚❆ ❉❊ ❋■●❯❘❆❙

✷✳✶✶ ❊❢❡✐t♦ ❞♦ ♠❛♣❛ ❞❡ ❉❡s♣♦❧❛r✐③❛çã♦ ♥❛ ❡s❢❡r❛ ❞❡ ❇❧♦❝❤ ♣❛r❛ ♣❂✵✳✸✳

❖s ❡✐①♦s x✱y ❡ z sã♦ ❝♦♥tr❛í❞♦s ❞❡ ❢♦r♠❛ s✐♠étr✐❝❛✳

❋♦♥t❡✿ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❡ ◆✐❡❧s❡♥ ❛♥❞ ❈❤✉❛♥❣✱ ✷✵✶✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸

✷✳✶✷ ❊❢❡✐t♦ ❞♦ ♠❛♣❛ ❞❡ ❆t❡♥✉❛çã♦ ❞❡ ❆♠♣❧✐t✉❞❡ ♥❛ ❡s❢❡r❛ ❞❡ ❇❧♦❝❤ ♣❛r❛ ♣❂✵✳✸✳

❖s ❡✐①♦sx✱ y ❡z ❝♦♥tr❛❡♠✲s❡ ♥❛ ❞✐r❡çã♦ ❞♦ ♣♦♥t♦ ✭✵✱✵✱✶✮ q✉❡ r❡♣r❡s❡♥t❛ ♦

❡st❛❞♦|0_i✳

❋♦♥t❡✿ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❡ ◆✐❡❧s❡♥ ❛♥❞ ❈❤✉❛♥❣✱ ✷✵✶✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻

✷✳✶✸ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❡ ✉♠ ❝✐r❝✉✐t♦ q✉❡ s✐♠✉❧❛ ♦ ♣r♦❝❡ss♦ ❞❡ ❞❡❝♦✲

❡rê♥❝✐❛ s♦❜r❡ ❛♣❡♥❛s ✉♠ ❞♦s q✉❜✐ts ❞♦ ❡st❛❞♦ρ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼

✸✳✶ ❚❡❧❡tr❛♥s♣♦rt❡ ❞❡ ✐♥❢♦r♠❛çã♦ q✉â♥t✐❝❛ ❡♥tr❡ ❞♦✐s ♣♦♥t♦s ❞✐st✐♥t♦s ❛tr❛✈és ❞❡ ✉♠ ❡st❛❞♦ ❡♠❛r❛♥❤❛❞♦ ❞❡ ❞♦✐s q✉❜✐ts✳ ❆s ❝♦r❡s ✈❡r♠❡❧❤❛ ❡ ❛③✉❧ r❡❢❡r❡♠✲ s❡ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛ ❆❧✐❝❡ ❡ ❇♦❜✱ ❡ ❛ ❜❛rr❛ ✐♥t❡r♠❡❞✐ár✐❛ r❡♣r❡s❡♥t❛ ♦ ❝❛♥❛❧

❣❡r❛❞♦ ♣❡❧♦ ❡♠❛r❛♥❤❛♠❡♥t♦ ❡♥tr❡ ❡st❡s q✉❜✐ts✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹

✸✳✷ ❈❛♥❛❧ ❣❡r❛❞♦ ♣❡❧♦ ❡♠❛r❛♥❤❛♠❡♥t♦ ✭r❡♣r❡s❡♥t❛❞♦ ♣❡❧♦ s✐♥❛❧ ♦♥❞✉❧❛tór✐♦ ❡♠ ✈❡r❞❡✮ ❡♥tr❡ ♦s q✉❜✐ts ❞❡ ❆❧✐❝❡ ✭✈❡r♠❡❧❤♦✮ ❡ ❇♦❜ ✭❛③✉❧✮✳ ➚ ❡sq✉❡r❞❛✱ ❛

✐♥❢♦r♠❛çã♦ ♦r✐❣✐♥❛❧ ❞❡ ❆❧✐❝❡ ✭r❡♣r❡s❡♥t❛❞❛ ♣❡❧❛ ❝♦r ❛♠❛r❡❧❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹

✸✳✸ ❊❧❡♠❡♥t♦s ♥❡❝❡ssár✐♦s ♣❛r❛ ❛ r❡❛❧✐③❛çã♦ ❞❡ ✉♠ t❡❧❡tr❛♥s♣♦rt❡ q✉â♥t✐❝♦✿ ♦s ❝❛❜♦s ❞❡ ❝♦♥❡①ã♦ ❡ ♦s ♠♦♥✐t♦r❡s r❡♣r❡s❡♥t❛♠ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛ ❜❛s❡ ❞❡ ♠❡❞✐❞❛s ✉t✐❧✐③❛❞❛ ♣♦r ❆❧✐❝❡ ❡ ♦ r❡s✉❧t❛❞♦ ♦❜t✐❞♦ ❛♣ós ❛ r❡❛❧✐③❛çã♦ ❞❛s

♠❡s♠❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺

✸✳✹ ❈♦♥✜r♠❛çã♦ ❞♦ r❡s✉❧t❛❞♦ ❞❛ ♠❡❞✐❞❛ ❞❡ ❆❧✐❝❡ ❛tr❛✈és ❞❡ ✉♠ ❝❛♥❛❧ ❝❧ás✲ s✐❝♦✿ ❇♦❜ ♠❛♥✐♣✉❧❛ s❡✉ ❡st❛❞♦ ❞❡ ❢♦r♠❛ q✉❡ ♦ ♠❡s♠♦ t♦r♥❛✲s❡ ✐❞ê♥t✐❝♦ à

✐♥❢♦r♠❛çã♦ ♦r✐❣✐♥❛❧ ❡♥✈✐❛❞❛ ♣♦r ❆❧✐❝❡✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻

✸✳✺ ●rá✜❝♦ ❞❡ hF_i ❡♠ ❢✉♥çã♦ ❞❡ φ ♣❛r❛ θ = π/4 ❡ pa = pb = 1✳ ❆s ❝♦r❡s

❛③✉❧ ❡ ✈❡r♠❡❧❤❛ r❡❢❡r❡♠✲s❡ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛hF_i_0|0|IF ❡hFi0|IF|IF✱ ❡ ❛ ❧✐♥❤❛

❤♦r✐③♦♥t❛❧ tr❛❝❡❥❛❞❛ r❡♣r❡s❡♥t❛ ♦ ❧✐♠✐t❡ ❝❧áss✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛ hF_i =

2/3✳ ❖s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ❡stã♦ ❛ss♦❝✐❛❞♦s ❛♦ ♠♦❞❡❧♦ 0_|IF_|IF✳ ✳ ✳ ✳ ✳ ✳ ✽✶

✸✳✻ ●rá✜❝♦ ❞❡ hF_i ❡♠ ❢✉♥çã♦ ❞❡ φ ♣❛r❛ θ =π/4 ❡ pa =pb = 1✳ ❆s ❝♦r❡s ❛③✉❧

❡ ✈❡r♠❡❧❤❛ r❡❢❡r❡♠✲s❡ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛ hF_i_0|0|_IB ❡ _hF_i_0|_IB_|_IB✱ ❡ ❛ ❧✐♥❤❛

❤♦r✐③♦♥t❛❧ tr❛❝❡❥❛❞❛ r❡♣r❡s❡♥t❛ ♦ ❧✐♠✐t❡ ❝❧áss✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛ hF_i =

2/3✳ ❖s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ❡stã♦ ❛ss♦❝✐❛❞♦s ❛♦ ♠♦❞❡❧♦ 0_|IB_|IB✳ ✳ ✳ ✳ ✳ ✳ ✽✷

✸✳✼ ●rá✜❝♦ ❞❡hF_i❡♠ ❢✉♥çã♦ ❞❡φ♣❛r❛θ =π/4❡pa =pb = 0.95✳ ❆s ❝♦r❡s ❛③✉❧

❡ ✈❡r♠❡❧❤❛ r❡❢❡r❡♠✲s❡ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛hF_i_0|0|D ❡ hFi0|D|D✳ ◆❡♥❤✉♠❛ ❞❛s

❝✉r✈❛s ❛t✐♥❣❡ ♦ ❧✐♠✐t❡ ❝❧áss✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛ hF_i = 2/3✳ ❖s r❡s✉❧t❛❞♦s

(15)

▲■❙❚❆ ❉❊ ❋■●❯❘❆❙ ①✈

✸✳✽ ●rá✜❝♦ ❞❡ hF_i ❡♠ ❢✉♥çã♦ ❞❡ φ ♣❛r❛ pa = 0.5 ❡ pb = 0.82✳ ❆s ❝♦r❡s ❛③✉❧ ❡

✈❡r♠❡❧❤❛ r❡❢❡r❡♠✲s❡ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛ hF_i_0|0|_AA ❡ _hF_i_0|_AA_|_AA✱ ❡ ❛ ❧✐♥❤❛ ❤♦✲

r✐③♦♥t❛❧ tr❛❝❡❥❛❞❛ r❡♣r❡s❡♥t❛ ♦ ❧✐♠✐t❡ ❝❧áss✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛ hF_i= 2/3✳

❖ ✈❛❧♦r ♠á①✐♠♦ ❞❡ ❛♠❜❛s ❛s ❢✉♥çõ❡s ♣❛r❛ ✭❛✮θ = 0.7s✉♣❡r❛ ♦s r❡s✉❧t❛❞♦s

❡①✐❜✐❞♦s ♣❛r❛ ✭❜✮ θ = π/4✱ ❡ ♦s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ❡stã♦ ❛ss♦❝✐❛❞♦s ❛♦

♠♦❞❡❧♦ 0_|AA_|AA✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹

✸✳✾ ●rá✜❝♦ ❞❡hF_i❡♠ ❢✉♥çã♦ ❞❡φ ♣❛r❛pa= 0.1❡pb = 0.3✳ ❆s ❝♦r❡s ❛③✉❧✱ ✈❡r✲

♠❡❧❤❛✱ ♠❛rr♦♠ ❡ ✈❡r❞❡ r❡❢❡r❡♠✲s❡ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛ hF_i_0|IF|IF✱ hFi0|IB|IB✱

hF_i_0|D|D ❡hFi0|AA|AA✱ ❡ ❛ ❧✐♥❤❛ ❤♦r✐③♦♥t❛❧ tr❛❝❡❥❛❞❛ r❡♣r❡s❡♥t❛ ♦ ❧✐♠✐t❡ ❝❧ás✲

s✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛ hF_i = 2/3✳ ❖s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ❡stã♦ ❛ss♦❝✐❛❞♦s

r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛♦s ♠♦❞❡❧♦s ✭❛✮ 0_|AA_|AA❀ ✭❜✮0_|IB_|IB ❡ ✭❝✮ 0_|IF_|IF✳ ✳ ✳ ✽✺

✸✳✶✵ ●rá✜❝♦ ❞❡hF_i❡♠ ❢✉♥çã♦ ❞❡pb ♣❛r❛pa = 0.1❡φ =π/4✳ ❆s ❝♦r❡s ❛③✉❧✱ ✈❡r✲

♠❡❧❤❛✱ ♠❛rr♦♠ ❡ ✈❡r❞❡ r❡❢❡r❡♠✲s❡ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛ hF_i_0|_IF_|_IF✱ _hF_i_0|_IB_|_IB✱

r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛♦s ♠♦❞❡❧♦s ✭❛✮ 0_|AA_|AA❀ ✭❜✮0_|IB_|IB ❡ ✭❝✮ 0_|IF_|IF✳ ✳ ✳ ✽✻

✸✳✶✶ ●rá✜❝♦ ❞❡hF_i ❡♠ ❢✉♥çã♦ ❞❡pa =pb =p♣❛r❛ φ=π/4✳ ❆s ❝♦r❡s ❛③✉❧✱ ✈❡r✲

♠❡❧❤❛✱ ♠❛rr♦♠ ❡ ✈❡r❞❡ r❡❢❡r❡♠✲s❡ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛ hF_i_0|IF|IF✱ hFi0|IB|IB✱

r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛♦s ♠♦❞❡❧♦s ✭❛✮ 0_|AA_|AA❀ ✭❜✮0_|IB_|IB ❡ ✭❝✮ 0_|IF_|IF✳ ✳ ✳ ✽✼

✸✳✶✷ ●rá✜❝♦ ❞❡hF_i ❡♠ ❢✉♥çã♦ ❞❡ φ ♣❛r❛ θ =π/4✱ p0 =pa = 0.8❡ pb = 0.2✳ ❆s

❝♦r❡s ❛③✉❧ ❡ ✈❡r♠❡❧❤❛ r❡❢❡r❡♠✲s❡ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛ hF_i_0|IB|IB ❡hFiIB|IB|IB✱

❡ ❛ ❧✐♥❤❛ ❤♦r✐③♦♥t❛❧ tr❛❝❡❥❛❞❛ r❡♣r❡s❡♥t❛ ♦ ❧✐♠✐t❡ ❝❧áss✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛

hF_i= 2/3✳ ❖s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ❡stã♦ ❛ss♦❝✐❛❞♦s ❛♦ ♠♦❞❡❧♦IB_|IB_|IB✳ ✽✽

✸✳✶✸ ●rá✜❝♦ ❞❡ hF_i ❡♠ ❢✉♥çã♦ ❞❡ φ ♣❛r❛ θ = π/4✱ p0 = 0.2 ❡ pa = pb = 1✳

❆s ❝♦r❡s ❛③✉❧✱ ✈❡r♠❡❧❤❛ ❡ ♠❛rr♦♠ r❡❢❡r❡♠✲s❡ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛ hF_i_0|0|IF✱

hF_i_0|IF|IF ❡ hFiIF|IF|IF✱ ❡ ❛ ❧✐♥❤❛ ❤♦r✐③♦♥t❛❧ tr❛❝❡❥❛❞❛ r❡♣r❡s❡♥t❛ ♦ ❧✐♠✐t❡

❝❧áss✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛ hF_i = 2/3✳ ❖s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ❡stã♦ ❛ss♦❝✐✲

❛❞♦s ❛♦s ♠♦❞❡❧♦s 0_|IF_|IF ❡ IF_|IF_|IF✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽

✸✳✶✹ ●rá✜❝♦ ❞❡ hF_i ❡♠ ❢✉♥çã♦ ❞❡ φ ♣❛r❛ θ = π/4✱ p0 = 0.4 ❡ pa = pb = 1✳

❆s ❝♦r❡s ❛③✉❧✱ ✈❡r♠❡❧❤❛ ❡ ♠❛rr♦♠ r❡❢❡r❡♠✲s❡ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛ hF_i_0|0|IB✱

hF_i_0|IB|IB ❡ hFiIB|IB|IB✱ ❡ ❛ ❧✐♥❤❛ ❤♦r✐③♦♥t❛❧ tr❛❝❡❥❛❞❛ r❡♣r❡s❡♥t❛ ♦ ❧✐♠✐t❡

❝❧áss✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛ hF_i = 2/3✳ ❖s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ❡stã♦ ❛ss♦❝✐✲

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①✈✐ ▲■❙❚❆ ❉❊ ❋■●❯❘❆❙

✸✳✶✺ ●rá✜❝♦ ❞❡ hF_i ❡♠ ❢✉♥çã♦ ❞❡ φ ♣❛r❛ θ = π/4✱ p0 = 0.5 ❡ pa = pb = 0.95✳

❆s ❝♦r❡s ❛③✉❧✱ ✈❡r♠❡❧❤❛ ❡ ♠❛rr♦♠ r❡❢❡r❡♠✲s❡ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛ hF_i_0|0|_D✱

hF_i_0|_D_|_D ❡_hF_i_D_|_D_|_D✳ ◆❡♥❤✉♠❛ ❞❛s ❝✉r✈❛s ❛t✐♥❣❡ ♦ ❧✐♠✐t❡ ❝❧áss✐❝♦ ❝♦rr❡s♣♦♥✲

❞❡♥t❡ ❛ hF_i= 2/3✳ ❖s r❡s✉❧t❛❞♦s ❛ss♦❝✐❛❞♦s ❛♦s ♠♦❞❡❧♦s 0_|D_|D ❡D_|D_|D

sã♦ ✐♥❢❡r✐♦r❡s ❛♦s ❞♦ ♠♦❞❡❧♦0_|0_|D✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾

✸✳✶✻ ●rá✜❝♦ ❞❡hF_i❡♠ ❢✉♥çã♦ ❞❡φ♣❛r❛θ =π/4✱p0 = 0.3✱pa = 0.5❡pb = 0.82✳

❆s ❝♦r❡s ❛③✉❧✱ ✈❡r♠❡❧❤❛ ❡ ♠❛rr♦♠ r❡❢❡r❡♠✲s❡ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛ hF_i_0|0|AA✱

hF_i_0|AA|AA ❡ hFiAA|AA|AA✱ ❡ ❛ ❧✐♥❤❛ ❤♦r✐③♦♥t❛❧ tr❛❝❡❥❛❞❛ r❡♣r❡s❡♥t❛ ♦ ❧✐♠✐t❡

❝❧áss✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛ hF_i= 2/3✳ ❖s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ❡stã♦ ❛ss♦❝✐✲

❛❞♦s ❛♦s ♠♦❞❡❧♦s0_|AA_|AA ❡ 0_|0_|AA✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵

✸✳✶✼ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♠♦❞❡❧♦s q✉❡ ♣♦ss✉❡♠ ❡♥tr❛❞❛s ♠✐st❛s ❡ ❝❛♥❛✐s ❤♦♠♦❣ê✲ ♥❡♦s ♦♥❞❡ ♦ ❡st❛❞♦ ❞❡ ❡♥tr❛❞❛ é ♠❛♥t✐❞♦ ✐♥❛❧t❡r❛❞♦✳ ❆s ✜❣✉r❛s ❡①✐❜❡♠ ♦s

❣rá✜❝♦s ❞❡ hF_i ❡♠ ❢✉♥çã♦ ❞❡ φ ❡ ❛ ❧✐♥❤❛ ❤♦r✐③♦♥t❛❧ tr❛❝❡❥❛❞❛ r❡♣r❡s❡♥t❛ ♦

❧✐♠✐t❡ ❝❧áss✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛ hF_i = 2/3✳ ❖s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ❡stã♦

❛ss♦❝✐❛❞♦s r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛♦s ♠♦❞❡❧♦s ✭❛✮ IF_|AA_|AA❀ ✭❜✮ IB_|AA_|AA❀

✭❝✮ D_|AA_|AA ❡ ✭❞✮ AA_|IF_|IF✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵

✸✳✶✽ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♠♦❞❡❧♦s q✉❡ ♣♦ss✉❡♠ ❡♥tr❛❞❛s ♠✐st❛s ❡ ❝❛♥❛✐s ❤♦♠♦❣ê✲ ♥❡♦s ♦♥❞❡ ♦ ❝❛♥❛❧ é ♠❛♥t✐❞♦ ✐♥❛❧t❡r❛❞♦✳ ❆s ✜❣✉r❛s ❡①✐❜❡♠ ♦s ❣rá✜❝♦s ❞❡

hF_i❡♠ ❢✉♥çã♦ ❞❡ φ ❡ ❛ ❧✐♥❤❛ ❤♦r✐③♦♥t❛❧ tr❛❝❡❥❛❞❛ r❡♣r❡s❡♥t❛ ♦ ❧✐♠✐t❡ ❝❧ás✲

r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛♦s ♠♦❞❡❧♦s ✭❛✮ AA_|IF_|IF❀ ✭❜✮ AA_|IB_|IB❀ ✭❝✮ AA_|D_|D

❡ ✭❞✮ IF_|AA_|AA✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶

✸✳✶✾ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♠♦❞❡❧♦s q✉❡ ♣♦ss✉❡♠ ❡♥tr❛❞❛s ♣✉r❛s ❡ ❝❛♥❛✐s ❤❡t❡r♦❣ê✲ ♥❡♦s ♦♥❞❡ ♦ q✉❜✐t ❞❡ ❆❧✐❝❡ ♥♦ ❝❛♥❛❧ é ♠❛♥t✐❞♦ ✐♥❛❧t❡r❛❞♦✳ ❆s ✜❣✉r❛s ❡①✐❜❡♠

♦s ❣rá✜❝♦s ❞❡hF_i ❡♠ ❢✉♥çã♦ ❞❡φ ❡ ❛ ❧✐♥❤❛ ❤♦r✐③♦♥t❛❧ tr❛❝❡❥❛❞❛ r❡♣r❡s❡♥t❛

♦ ❧✐♠✐t❡ ❝❧áss✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛ hF_i = 2/3✳ ❖s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ❡s✲

tã♦ ❛ss♦❝✐❛❞♦s r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛♦s ♠♦❞❡❧♦s ✭❛✮0_|IF_|AA❀ ✭❜✮0_|IB_|AA❀ ✭❝✮

0_|D_|AA ❡ ✭❞✮ 0_|AA_|IB✱ 0_|AA_|D ❡0_|AA_|IF✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷

✸✳✷✵ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♠♦❞❡❧♦s q✉❡ ♣♦ss✉❡♠ ❡♥tr❛❞❛s ♠✐st❛s ❡ ❝❛♥❛✐s ❤❡t❡r♦✲ ❣ê♥❡♦s ♦♥❞❡ ♦ q✉❜✐t ❞❡ ❆❧✐❝❡ ♥♦ ❝❛♥❛❧ ❡ ♦ ❡st❛❞♦ ❞❡ ❡♥tr❛❞❛ sã♦ ♠❛♥t✐✲

❞♦s ✐♥❛❧t❡r❛❞♦s✳ ❆s ✜❣✉r❛s ❡①✐❜❡♠ ♦s ❣rá✜❝♦s ❞❡ hF_i ❡♠ ❢✉♥çã♦ ❞❡ φ ❡

❛ ❧✐♥❤❛ ❤♦r✐③♦♥t❛❧ tr❛❝❡❥❛❞❛ r❡♣r❡s❡♥t❛ ♦ ❧✐♠✐t❡ ❝❧áss✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛

hF_i = 2/3✳ ❖s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ❡stã♦ ❛ss♦❝✐❛❞♦s r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛♦s

(17)

▲■❙❚❆ ❉❊ ❋■●❯❘❆❙ ①✈✐✐

✸✳✷✶ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♠♦❞❡❧♦s q✉❡ ♣♦ss✉❡♠ ❡♥tr❛❞❛s ♠✐st❛s ❡ ❝❛♥❛✐s ❤❡t❡r♦❣ê✲ ♥❡♦s ♦♥❞❡ ♦ q✉❜✐t ❞❡ ❇♦❜ ♥♦ ❝❛♥❛❧ é ♠❛♥t✐❞♦ ✐♥❛❧t❡r❛❞♦✳ ❆s ✜❣✉r❛s ❡①✐❜❡♠

♦s ❣rá✜❝♦s ❞❡hF_i❡♠ ❢✉♥çã♦ ❞❡φ ❡ ❛ ❧✐♥❤❛ ❤♦r✐③♦♥t❛❧ tr❛❝❡❥❛❞❛ r❡♣r❡s❡♥t❛

♦ ❧✐♠✐t❡ ❝❧áss✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛ hF_i= 2/3✳ ❖s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ❡stã♦

❛ss♦❝✐❛❞♦s r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛♦s ♠♦❞❡❧♦s ✭❛✮ AA_|AA_|IF❀ ✭❜✮ AA_|AA_|IB❀

✭❝✮ AA_|AA_|D ❡ ✭❞✮ IF_|IF_|AA✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺

✹✳✶ ●rá✜❝♦s ❞❡pi ✭♥❛ ❝♦❧✉♥❛ à ❡sq✉❡r❞❛✮ ❡hFi✭♥❛ ❝♦❧✉♥❛ à ❞✐r❡✐t❛✮ ❡♠ ❢✉♥çã♦

❞❡ φ ♣❛r❛ pa = pb = 0.2✳ ❆s ❧✐♥❤❛s ❤♦r✐③♦♥t❛✐s tr❛❝❡❥❛❞❛s r❡♣r❡s❡♥t❛♠

r❡s♣❡❝t✐✈❛♠❡♥t❡ pi = 1/4 ❡ ♦ ❧✐♠✐t❡ ❝❧áss✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡ à hFi = 2/3✳

P❛r❛ θ = π/4✱ t♦❞❛s ❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s sã♦ ✐❣✉❛✐s ❡ ❛ ❢✉♥çã♦ _hF_i_0|_IF_|_IF

é ✐❞ê♥t✐❝❛ ❛♦s ♣❛r❡s hF_iI/hFiIV ❡ hFiII/hFiIII r❡❧❛t✐✈♦s ❛♦ t❡❧❡tr❛♥s♣♦rt❡

❝♦♥❞✐❝✐♦♥❛❧ ❞♦ ♠♦❞❡❧♦0_|IF_|IF✳ P❛r❛θ ₆=π/4✱ ♦s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ❡stã♦

❛ss♦❝✐❛❞♦s às ✜❞❡❧✐❞❛❞❡s ❝♦♥❞✐❝✐♦♥❛✐s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶

✹✳✷ ●rá✜❝♦s ❞❡pi ✭♥❛ ❝♦❧✉♥❛ à ❡sq✉❡r❞❛✮ ❡hFi✭♥❛ ❝♦❧✉♥❛ à ❞✐r❡✐t❛✮ ❡♠ ❢✉♥çã♦

❞❡ ✭❛✲❜✮ φ ❡ ✭❝✲❢✮ θ ♣❛r❛ pa = pb = 0.2✳ ❆s ❧✐♥❤❛s ❤♦r✐③♦♥t❛✐s tr❛❝❡❥❛❞❛s

r❡♣r❡s❡♥t❛♠ r❡s♣❡❝t✐✈❛♠❡♥t❡ pi = 1/4 ✭à ❡sq✉❡r❞❛✮ ❡ ♦ ❧✐♠✐t❡ ❝❧áss✐❝♦ ❝♦r✲

r❡s♣♦♥❞❡♥t❡ à hF_i= 2/3✭à ❞✐r❡✐t❛✮✳ P❛r❛θ=π/4✱ t♦❞❛s ❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s

sã♦ ✐❣✉❛✐s✱ ❡♠❜♦r❛ ❛ ❢✉♥çã♦ hF_i_0|0|AA ❡ ♦s ♣❛r❡shFiI/hFiIV ❡ hFiII/hFiIII

r❡❧❛t✐✈♦s ❛♦ t❡❧❡tr❛♥s♣♦rt❡ ❝♦♥❞✐❝✐♦♥❛❧ ❞♦ ♠♦❞❡❧♦ 0_|0_|AA ❡①✐❜❛♠ ❝♦♠♣♦r✲

t❛♠❡♥t♦s ❞✐st✐♥t♦s✳ ❖s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ❡stã♦ ❛ss♦❝✐❛❞♦s às ✜❞❡❧✐❞❛❞❡s

❝♦♥❞✐❝✐♦♥❛✐s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸

✹✳✸ ●rá✜❝♦ ❞❡ hF_i ❡♠ ❢✉♥çã♦ ❞❡ φ ♣❛r❛ pa = 0.1 ❡ pb = 0.3✳ ❆s ❝♦r❡s

❛③✉❧✱ ✈❡r♠❡❧❤❛✱ ♠❛rr♦♠ ❡ ✈❡r❞❡ r❡❢❡r❡♠✲s❡ r❡s♣❡❝t✐✈❛♠❡♥t❡ às ♠❡❞✐❞❛s ❞❡

|Φ+_φ_i❡ _|Ψ−_φ_i r❡❧❛t✐✈❛s ❛♦ t❡❧❡tr❛♥s♣♦rt❡ ❝♦♥❞✐❝✐♦♥❛❧ ❞♦s ♠♦❞❡❧♦s _hF_i_0|IF|IF✱

hF_i_0|IB|IB✱ hFi0|D|D ❡ hFi0|AA|AA✱ ❡ ❛ ❧✐♥❤❛ ❤♦r✐③♦♥t❛❧ tr❛❝❡❥❛❞❛ r❡♣r❡s❡♥t❛

♦ ❧✐♠✐t❡ ❝❧áss✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛ hF_i = 2/3✳ ❖s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ❡s✲

tã♦ ❛ss♦❝✐❛❞♦s às ✜❞❡❧✐❞❛❞❡s ❝♦♥❞✐❝✐♦♥❛✐s ❞♦s ♠♦❞❡❧♦s ✭❛✮ 0_|AA_|AA✱ ✭❜✮

0_|IB_|IB❀ 0_|IF_|IF ❡ ✭❝✮ 0_|IF_|IF✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹

✹✳✹ ●rá✜❝♦s ❞❡pi ✭♥❛ ❝♦❧✉♥❛ à ❡sq✉❡r❞❛✮ ❡hFi✭♥❛ ❝♦❧✉♥❛ à ❞✐r❡✐t❛✮ ❡♠ ❢✉♥çã♦

❞❡φ♣❛r❛p0 =pa =pb = 0.25✳ ❆s ❧✐♥❤❛s ❤♦r✐③♦♥t❛✐s tr❛❝❡❥❛❞❛s r❡♣r❡s❡♥t❛♠

r❡s♣❡❝t✐✈❛♠❡♥t❡ pi = 1/4 ✭à ❡sq✉❡r❞❛✮ ❡ ♦ ❧✐♠✐t❡ ❝❧áss✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡

à hF_i = 2/3 ✭à ❞✐r❡✐t❛✮✳ P❛r❛ φ =₆ π/4 ❡ θ ₆= π/4✱ ❛s q✉❛tr♦ ✜❞❡❧✐❞❛❞❡s

❝♦♥❞✐❝✐♦♥❛✐s sã♦ ❞✐st✐♥t❛s✳ P❛r❛ θ = π/4✱ ❛ ❢✉♥çã♦ _hF_iAA|IF|IF ❡ ♦s ♣❛r❡s

hF_iI/hFiIV ❡ hFiII/hFiIII r❡❧❛t✐✈♦s ❛♦ t❡❧❡tr❛♥s♣♦rt❡ ❝♦♥❞✐❝✐♦♥❛❧ ❞♦ ♠♦✲

❞❡❧♦ AA_|IF_|IF ❡①✐❜❡♠ ❝♦♠♣♦rt❛♠❡♥t♦s ❞✐st✐♥t♦s✳ ❖s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s

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①✈✐✐✐ ▲■❙❚❆ ❉❊ ❋■●❯❘❆❙

✹✳✺ ●rá✜❝♦s ❞❡ pi ✭♥❛ ❝♦❧✉♥❛ à ❡sq✉❡r❞❛✮ ❡hFi✭♥❛ ❝♦❧✉♥❛ à ❞✐r❡✐t❛✮ ❡♠ ❢✉♥çã♦

❞❡θ♣❛r❛p0 =pa=pb = 0.25✳ ❆s ❧✐♥❤❛s ❤♦r✐③♦♥t❛✐s tr❛❝❡❥❛❞❛s r❡♣r❡s❡♥t❛♠

à hF_i = 2/3 ✭à ❞✐r❡✐t❛✮✳ P❛r❛ φ =₆ π/4 ❡ θ ₆= π/4✱ ❛s q✉❛tr♦ ✜❞❡❧✐❞❛❞❡s

❝♦♥❞✐❝✐♦♥❛✐s sã♦ ❞✐st✐♥t❛s✳ P❛r❛ φ = π/4✱ ❛ ❢✉♥çã♦ _hF_iAA|IF|IF ❡ ♦s ♣❛r❡s

hF_iI/hFiII ❡ hFiIII/hFiIV r❡❧❛t✐✈♦s ❛♦ t❡❧❡tr❛♥s♣♦rt❡ ❝♦♥❞✐❝✐♦♥❛❧ ❞♦ ♠♦✲

❞❡❧♦AA_|IF_|IF ❡①✐❜❡♠ ❝♦♠♣♦rt❛♠❡♥t♦s ❞✐st✐♥t♦s✳ ❖s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s

❡stã♦ ❛ss♦❝✐❛❞♦s às ✜❞❡❧✐❞❛❞❡s ❝♦♥❞✐❝✐♦♥❛✐s✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✼

✹✳✻ ●rá✜❝♦s ❞❡ pi ✭♥❛ ❝♦❧✉♥❛ à ❡sq✉❡r❞❛✮ ❡hFi✭♥❛ ❝♦❧✉♥❛ à ❞✐r❡✐t❛✮ ❡♠ ❢✉♥çã♦

❞❡φ♣❛r❛p0 =pa=pb = 0.25✳ ❆s ❧✐♥❤❛s ❤♦r✐③♦♥t❛✐s tr❛❝❡❥❛❞❛s r❡♣r❡s❡♥t❛♠

à hF_i = 2/3 ✭à ❞✐r❡✐t❛✮✳ P❛r❛ φ =₆ π/4 ❡ θ ₆= 0.96✱ ❛s q✉❛tr♦ ✜❞❡❧✐❞❛❞❡s

❝♦♥❞✐❝✐♦♥❛✐s sã♦ ❞✐st✐♥t❛s✳ P❛r❛ θ _≈ 0.96✱ ❛ ❢✉♥çã♦ _hF_i_AA_|_AA_|_AA ❡ ♦s ♣❛r❡s

hF_iI/hFiIV ❡ hFiII/hFiIII r❡❧❛t✐✈♦s ❛♦ t❡❧❡tr❛♥s♣♦rt❡ ❝♦♥❞✐❝✐♦♥❛❧ ❞♦ ♠♦✲

❞❡❧♦AA_|AA_|AA❡①✐❜❡♠ ❝♦♠♣♦rt❛♠❡♥t♦s ❞✐st✐♥t♦s✳ ❖s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s

❡stã♦ ❛ss♦❝✐❛❞♦s às ✜❞❡❧✐❞❛❞❡s ❝♦♥❞✐❝✐♦♥❛✐s✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽

✹✳✼ ●rá✜❝♦ ❞❡ hF_i ❡♠ ❢✉♥çã♦ ❞❡ φ ♣❛r❛ θ = 0.5✱ p0 = pa = 0.8 ❡ pb =

0.2✳ ❆s ❝♦r❡s ❛③✉❧ ❡ ✈❡r♠❡❧❤❛ r❡❢❡r❡♠✲s❡ r❡s♣❡❝t✐✈❛♠❡♥t❡ às ♠❡❞✐❞❛s ❞❡

|Φ+_φ_i ❡ _|Ψ_φ−_i r❡❧❛t✐✈❛s ❛♦ t❡❧❡tr❛♥s♣♦rt❡ ❝♦♥❞✐❝✐♦♥❛❧ ❞♦s ♠♦❞❡❧♦s _hF_i_0|IB|IB

❡ hF_i_IB_|_IB_|_IB✱ ❡ ❛ ❧✐♥❤❛ ❤♦r✐③♦♥t❛❧ tr❛❝❡❥❛❞❛ r❡♣r❡s❡♥t❛ ♦ ❧✐♠✐t❡ ❝❧áss✐❝♦

❝♦rr❡s♣♦♥❞❡♥t❡ ❛ hF_i = 2/3✳ ❖s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ❡stã♦ ❛ss♦❝✐❛❞♦s às

✜❞❡❧✐❞❛❞❡s ❝♦♥❞✐❝✐♦♥❛✐s ❞♦ ♠♦❞❡❧♦ IB_|IB_|IB✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾

✹✳✽ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♠♦❞❡❧♦s ❝♦♠ ❡♥tr❛❞❛s ♠✐st❛s ❡♠ ❞✐✈❡rs♦s ❝❡♥ár✐♦s✿ ✭❛✮ ❝❛♥❛✐s ❤♦♠♦❣ê♥❡♦s ♦♥❞❡ ♦ ❡st❛❞♦ ❞❡ ❡♥tr❛❞❛ é ♠❛♥t✐❞♦ ✐♥❛❧t❡r❛❞♦❀ ✭❜✮ ❝❛♥❛✐s ❤♦♠♦❣ê♥❡♦s ♦♥❞❡ ♦ ❝❛♥❛❧ é ♠❛♥t✐❞♦ ✐♥❛❧t❡r❛❞♦❀ ✭❝✮ ❝❛♥❛✐s ❤❡t❡r♦✲ ❣ê♥❡♦s ♦♥❞❡ ♦ q✉❜✐t ❞❡ ❆❧✐❝❡ ♥♦ ❝❛♥❛❧ ❡ ♦ ❡st❛❞♦ ❞❡ ❡♥tr❛❞❛ sã♦ ♠❛♥t✐❞♦s ✐♥❛❧t❡r❛❞♦s ❡ ✭❞✮ ❝❛♥❛✐s ❤❡t❡r♦❣ê♥❡♦s ♦♥❞❡ ♦ q✉❜✐t ❞❡ ❇♦❜ ♥♦ ❝❛♥❛❧ é ♠❛♥✲

t✐❞♦ ✐♥❛❧t❡r❛❞♦✳ ❆s ✜❣✉r❛s ❡①✐❜❡♠ ♦s ❣rá✜❝♦s ❞❡ hF_i ❡♠ ❢✉♥çã♦ ❞❡ φ ❡

❛ ❧✐♥❤❛ ❤♦r✐③♦♥t❛❧ tr❛❝❡❥❛❞❛ r❡♣r❡s❡♥t❛ ♦ ❧✐♠✐t❡ ❝❧áss✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛

hF_i = 2/3✳ ❖s ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ❡stã♦ ❛ss♦❝✐❛❞♦s r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛♦s

♠♦❞❡❧♦s ✭❛✮ IF_|AA_|AA❀ ✭❜✮ AA_|IF_|IF❀ IB_|IF_|IF❀ ✭❝✮ IF_|IF_|AA ❡ ✭❞✮

AA_|AA_|IF❀ IB_|IB_|IF✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾

✺✳✶ ●rá✜❝♦ ❞❡ hF_iX,Y ❡♠ ❢✉♥çã♦ ❞❡ kT ♣❛r❛φ =π/4❡ jy = 10✳ ❆s ❝♦r❡s ❛③✉❧✱

✈❡r♠❡❧❤❛ ❡ ♠❛rr♦♠ r❡❢❡r❡♠✲s❡ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛♦s ✈❛❧♦r❡s ❞❡ jx = −1✱

jx =−2❡jx =−3✱ ❡ ❛ ❧✐♥❤❛ ❤♦r✐③♦♥t❛❧ tr❛❝❡❥❛❞❛ r❡♣r❡s❡♥t❛ ♦ ❧✐♠✐t❡ ❝❧áss✐❝♦

❝♦rr❡s♣♦♥❞❡♥t❡ ❛ hF_i = 2/3✳ ❆ ✜❞❡❧✐❞❛❞❡ é ✐♥✈❡rs❛♠❡♥t❡ ♣r♦♣♦r❝✐♦♥❛❧ à

(19)

▲■❙❚❆ ❉❊ ❋■●❯❘❆❙ ①✐①

✺✳✷ ●rá✜❝♦ ❞❡ hF_iX,Y ❡♠ ❢✉♥çã♦ ❞❡ jx ♣❛r❛ φ = 3π/4 ❡ jy = −40✳ ❆s ❝♦r❡s

❛③✉❧✱ ✈❡r♠❡❧❤❛ ❡ ♠❛rr♦♠ r❡❢❡r❡♠✲s❡ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛♦s ✈❛❧♦r❡s ❞❡kT = 4✱

kT = 8❡kT = 16✱ ❡ ❛ ❧✐♥❤❛ ❤♦r✐③♦♥t❛❧ tr❛❝❡❥❛❞❛ r❡♣r❡s❡♥t❛ ♦ ❧✐♠✐t❡ ❝❧áss✐❝♦

❝♦rr❡s♣♦♥❞❡♥t❡ ❛ hF_i = 2/3✳ ❆ ✜❞❡❧✐❞❛❞❡ é ♣r♦♣♦r❝✐♦♥❛❧ à ❝♦♥st❛♥t❡ ❞❡

❛❝♦♣❧❛♠❡♥t♦ jx✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✻

✺✳✸ ●rá✜❝♦ ❞❡ hF_iX,Y ❡♠ ❢✉♥çã♦ ❞❡ kT ♣❛r❛ φ = π/4 ❡ jy = −0.05✳ ❆s ❝♦r❡s

❛③✉❧✱ ✈❡r♠❡❧❤❛ ❡ ♠❛rr♦♠ r❡❢❡r❡♠✲s❡ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛♦s ✈❛❧♦r❡s ❞❡ jx =

−1✱ jx = −5 ❡ jx = −10✱ ❡ ❛ ❧✐♥❤❛ ❤♦r✐③♦♥t❛❧ tr❛❝❡❥❛❞❛ r❡♣r❡s❡♥t❛ ♦

❧✐♠✐t❡ ❝❧áss✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛ hF_i = 2/3✳ ❆ ✜❞❡❧✐❞❛❞❡ é ♣r♦♣♦r❝✐♦♥❛❧ à

t❡♠♣❡r❛t✉r❛ ♥❛ r❡❣✐ã♦ 0< kT < kTc ♣❛r❛ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ✈❛❧♦r ❝rít✐❝♦ Tc✳ ✶✶✼

✺✳✹ ●rá✜❝♦ ❞❡ hF_i_X,Y,hz ❡♠ ❢✉♥çã♦ ❞❡ hz ♣❛r❛ φ = π/4✱ jx = −10 ❡ jy = 10✳

❆s ❝♦r❡s ❛③✉❧✱ ✈❡r♠❡❧❤❛ ❡ ♠❛rr♦♠ r❡❢❡r❡♠✲s❡ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛♦s ✈❛❧♦r❡s

❞❡ kT = 1✱ kT = 2.5 ❡ kT = 5✳ ❚♦❞❛s ❛s ❝✉r✈❛s s✉♣❡r❛♠ ♦ ❧✐♠✐t❡ ❝❧ás✲

s✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛ hF_i = 2/3✳ ❆ r❡❧❛çã♦ ❞❡ ♣r♦♣♦r❝✐♦♥❛❧✐❞❛❞❡ ❡♥tr❡ ❛

✜❞❡❧✐❞❛❞❡ ❡ ♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❞❡♣❡♥❞❡ ❞❛ t❡♠♣❡r❛t✉r❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✽

✺✳✺ ●rá✜❝♦ ❞❡ hF_i_X,Y,hz ❡♠ ❢✉♥çã♦ ❞❡ φ ♣❛r❛ kT = 5✱ jx =−10 ❡ jy =−0.01✳

❆s ❝♦r❡s ❛③✉❧✱ ✈❡r♠❡❧❤❛✱ ♠❛rr♦♠ ❡ ✈❡r❞❡ r❡❢❡r❡♠✲s❡ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛♦s

✈❛❧♦r❡s ❞❡hz = 0✱hz = 5✱hz = 7.5❡hz = 10✱ ❡ ❛ ❧✐♥❤❛ ❤♦r✐③♦♥t❛❧ tr❛❝❡❥❛❞❛

r❡♣r❡s❡♥t❛ ♦ ❧✐♠✐t❡ ❝❧áss✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛ hF_i = 2/3✳ ❆ ✜❞❡❧✐❞❛❞❡ é

♠á①✐♠❛ ♣❛r❛ φ=π/4✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✾

✺✳✻ ●rá✜❝♦ ❞❡ hF_i_X,Y,hz ❡♠ ❢✉♥çã♦ ❞❡ jx ♣❛r❛ φ = 3π/4✱ kT = 5 ❡ jy = −10✳

✈❛❧♦r❡s ❞❡hz = 0✱hz = 5✱hz = 7.5❡hz = 10✱ ❡ ❛ ❧✐♥❤❛ ❤♦r✐③♦♥t❛❧ tr❛❝❡❥❛❞❛

r❡♣r❡s❡♥t❛ ♦ ❧✐♠✐t❡ ❝❧áss✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛ hF_i = 2/3✳ ❆ ✜❞❡❧✐❞❛❞❡ é

♣r♦♣♦r❝✐♦♥❛❧ à ❝♦♥st❛♥t❡ ❞❡ ❛❝♦♣❧❛♠❡♥t♦ jx✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✾

✺✳✼ ●rá✜❝♦ ❞❡ hF_i_X,Y,hz ❡♠ ❢✉♥çã♦ ❞❡ kT ♣❛r❛ φ=π/4✱ jx =−20✱ jy =−0.1✳

✈❛❧♦r❡s ❞❡ hz = 0✱ hz = 0.6✱hz = 0.7❡hz = 0.71✳ ❚♦❞❛s ❛s ❝✉r✈❛s s✉♣❡r❛♠

♦ ❧✐♠✐t❡ ❝❧áss✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛ hF_i = 2/3✳ ❆ ✜❞❡❧✐❞❛❞❡ é ♣r♦♣♦r❝✐♦♥❛❧

à t❡♠♣❡r❛t✉r❛ ♥❛ r❡❣✐ã♦ 0 < kT < kTc ❡ ♥♦ ✐♥t❡r✈❛❧♦ 0 < hz < hz c ♣❛r❛

❞❡t❡r♠✐♥❛❞♦s ✈❛❧♦r❡s ❝rít✐❝♦s Tc ❡hz c✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✵

✺✳✽ ●rá✜❝♦ ❞❡ hF_iX,X+∆,Z ❡♠ ❢✉♥çã♦ ❞❡ kT ♣❛r❛ φ = π/4✱ j = 2 ❡ jz = −10✳

✈❛❧♦r❡s ❞❡ ∆ = 0✱ ∆ = ₋0.5✱ ∆ = ₋1 ❡ ∆ = ₋1.5✱ ❡ ❛ ❧✐♥❤❛ ❤♦r✐③♦♥✲

t❛❧ tr❛❝❡❥❛❞❛ r❡♣r❡s❡♥t❛ ♦ ❧✐♠✐t❡ ❝❧áss✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛ hF_i = 2/3✳ ❆

(20)

①① ▲■❙❚❆ ❉❊ ❋■●❯❘❆❙

✺✳✾ ●rá✜❝♦ ❞❡ hF_iX,X+∆,Z ❡♠ ❢✉♥çã♦ ❞❡ jz ♣❛r❛ φ =π/4✱ kT = 1 ❡ ∆ =−0.5✳

❆s ❝♦r❡s ❛③✉❧✱ ✈❡r♠❡❧❤❛ ❡ ♠❛rr♦♠ r❡❢❡r❡♠✲s❡ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛♦s ✈❛❧♦r❡s

❞❡ j = 1✱ j = 1.5 ❡ j = 2✱ ❡ ❛ ❧✐♥❤❛ ❤♦r✐③♦♥t❛❧ tr❛❝❡❥❛❞❛ r❡♣r❡s❡♥t❛ ♦

❧✐♠✐t❡ ❝❧áss✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛ hF_i = 2/3✳ ❆ ✜❞❡❧✐❞❛❞❡ é ✐♥✈❡rs❛♠❡♥t❡

♣r♦♣♦r❝✐♦♥❛❧ à ❝♦♥st❛♥t❡ ❞❡ ❛❝♦♣❧❛♠❡♥t♦jz✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✸

✺✳✶✵ ●rá✜❝♦ ❞❡hF_iX,X+∆,Z ❡♠ ❢✉♥çã♦ ❞❡kT ♣❛r❛φ=π/4✱j =−10❡∆ =−0.1✳

❆s ❝♦r❡s ❛③✉❧✱ ✈❡r♠❡❧❤❛ ❡ ♠❛rr♦♠ r❡❢❡r❡♠✲s❡ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛♦s ✈❛❧♦r❡s ❞❡

jz =−9.6✱jz =−9.7❡jz =−9.8✳ ❚♦❞❛s ❛s ❝✉r✈❛s s✉♣❡r❛♠ ♦ ❧✐♠✐t❡ ❝❧áss✐❝♦

❝♦rr❡s♣♦♥❞❡♥t❡ ❛ hF_i = 2/3✳ ❆ ✜❞❡❧✐❞❛❞❡ é ❞✐r❡t❛♠❡♥t❡ ♣r♦♣♦r❝✐♦♥❛❧ à

t❡♠♣❡r❛t✉r❛ ♥❛ r❡❣✐ã♦ 0< kT < kTc ♣❛r❛ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ✈❛❧♦r ❝rít✐❝♦ Tc✳ ✶✷✹

✺✳✶✶ ●rá✜❝♦ ❞❡hF_iX,X+∆,Z,hz ❡♠ ❢✉♥çã♦ ❞❡hz ♣❛r❛φ =π/4✱j =−9.5✱jz =−10

❡∆ =₋0.2✳ ❆s ❝♦r❡s ❛③✉❧✱ ✈❡r♠❡❧❤❛ ❡ ♠❛rr♦♠ r❡❢❡r❡♠✲s❡ r❡s♣❡❝t✐✈❛♠❡♥t❡

❛♦s ✈❛❧♦r❡s ❞❡ kT = 1.5✱ kT = 2 ❡ kT = 2.5✳ ❚♦❞❛s ❛s ❝✉r✈❛s s✉♣❡r❛♠ ♦

❧✐♠✐t❡ ❝❧áss✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛hF_i= 2/3✳ ❆ r❡❧❛çã♦ ❞❡ ♣r♦♣♦r❝✐♦♥❛❧✐❞❛❞❡

❡♥tr❡ ❛ ✜❞❡❧✐❞❛❞❡ ❡ ♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❞❡♣❡♥❞❡ ❞❛ t❡♠♣❡r❛t✉r❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✹

✺✳✶✷ ●rá✜❝♦ ❞❡ hF_iX,X+∆,Z,hz ❡♠ ❢✉♥çã♦ ❞❡kT ♣❛r❛ φ =π/4✱ j =−10✱ jz =−9

❡ ∆ =₋0.2✳ ❆s ❝♦r❡s ❛③✉❧✱ ✈❡r♠❡❧❤❛✱ ♠❛rr♦♠ ❡ ✈❡r❞❡ r❡❢❡r❡♠✲s❡ r❡s♣❡❝t✐✲

✈❛♠❡♥t❡ ❛♦s ✈❛❧♦r❡s ❞❡ hz = 0✱ hz = 0.4✱ hz = 0.5 ❡ hz = 0.55✳ ❚♦❞❛s ❛s

❝✉r✈❛s s✉♣❡r❛♠ ♦ ❧✐♠✐t❡ ❝❧áss✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡ à hF_i= 2/3✳ ❆ ✜❞❡❧✐❞❛❞❡

é ❞✐r❡t❛♠❡♥t❡ ♣r♦♣♦r❝✐♦♥❛❧ à t❡♠♣❡r❛t✉r❛ ♥❛ r❡❣✐ã♦ 0 < kT < kTc ❡ ♥♦

✐♥t❡r✈❛❧♦ 0< hz < hz c ♣❛r❛ ❞❡t❡r♠✐♥❛❞♦s ✈❛❧♦r❡s ❝rít✐❝♦s Tc ❡ hz c✳ ✳ ✳ ✳ ✳ ✳ ✶✷✺

✺✳✶✸ ●rá✜❝♦ ❞❡hF_i❡♠ ❢✉♥çã♦ ❞❡kT ♣❛r❛φ= 0.9✱jx=−10✱jy = 10✱jz =−10

❡ hz = 1✳ ❆s ❝♦r❡s ♠❛rr♦♠✱ ❛③✉❧ ❡ ✈❡r♠❡❧❤❛ r❡❢❡r❡♠✲s❡ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛

hF_i_0|IF|IF ❡ ❛♦s ♣❛r❡shFiI/hFiIV ❡ hFiII/hFiIII r❡❧❛t✐✈♦s ❛♦ t❡❧❡tr❛♥s♣♦rt❡

❝♦♥❞✐❝✐♦♥❛❧ ❞♦ ♠♦❞❡❧♦ ❣❡r❛❧XY Z✳ ❚♦❞❛s ❛s ❝✉r✈❛s s✉♣❡r❛♠ ♦ ❧✐♠✐t❡ ❝❧ás✲

s✐❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛ hF_i= 2/3✳ ❆ ✜❞❡❧✐❞❛❞❡ s❡ ♠❛♥té♠ ❡stá✈❡❧ ♥❛ r❡❣✐ã♦

0< kT < kTc ♣❛r❛ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ✈❛❧♦r ❝rít✐❝♦Tc ❡ t♦r♥❛✲s❡ ✐♥✈❡rs❛♠❡♥t❡

♣r♦♣♦r❝✐♦♥❛❧ à t❡♠♣❡r❛t✉r❛ ♣❛r❛T > Tc✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✻

❈✳✶ P♦rt❛s s✐♠♣❧❡s q✉❡ ❛t✉❛♠ s♦❜r❡ ✉♠ q✉❜✐t✱ s✉❛s r❡s♣❡❝t✐✈❛s ♥♦♠❡♥❝❧❛t✉r❛s ❡

r❡♣r❡s❡♥t❛çõ❡s ♠❛tr✐❝✐❛✐s✳ ❋♦♥t❡✿ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❡◆✐❡❧s❡♥ ❛♥❞ ❈❤✉❛♥❣✱

✷✵✶✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✵

❈✳✷ ❋✐❣✉r❛ ❡sq✉❡♠át✐❝❛ ♣❛r❛ ♣♦rt❛s ❞❡ ❞♦✐s q✉❜✐ts✳ ❊♠(a₎✿ ❝♦♥tr♦❧❡ ♥♦ ♣r✐♠❡✐r♦

q✉❜✐t✳ ❊♠ (b₎✿ ❝♦♥tr♦❧❡ ♥♦ s❡❣✉♥❞♦ q✉❜✐t✳ ❖ ❝ír❝✉❧♦ ♠❡♥♦r ♣r❡❡♥❝❤✐❞♦ ♥♦

q✉❜✐t ❞❡ ❝♦♥tr♦❧❡ ❞❡♥♦t❛ q✉❡ ❛ ❛t✐✈❛çã♦ ❞❛ ♣♦rt❛ ♦❝♦rr❡ q✉❛♥❞♦ ♦ ❡st❛❞♦ ❞❡

❡♥tr❛❞❛ é ✐❣✉❛❧ ❛|1_i✱ ❡ ♦ ❝ír❝✉❧♦ ♠❡♥♦r ✈❛③✐♦ ♥♦ q✉❜✐t ❞❡ ❝♦♥tr♦❧❡ r❡♣r❡s❡♥t❛

❛ ❛t✐✈❛çã♦ ❞❛ ♣♦rt❛ q✉❛♥❞♦ ♦ ❡st❛❞♦ ❞❡ ❡♥tr❛❞❛ é ✐❣✉❛❧ ❛|0_i✳ ❋♦♥t❡✿ ❋✐❣✉r❛

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▲■❙❚❆ ❉❊ ❋■●❯❘❆❙ ①①✐

❈✳✸ P♦rt❛s q✉❡ ❛t✉❛♠ s♦❜r❡ ❞♦✐s q✉❜✐ts✱ s✉❛s r❡s♣❡❝t✐✈❛s ♥♦♠❡♥❝❧❛t✉r❛s ❡ r❡✲

♣r❡s❡♥t❛çõ❡s ♠❛tr✐❝✐❛✐s✳ ❋♦♥t❡✿ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❡ ◆✐❡❧s❡♥ ❛♥❞ ❈❤✉❛♥❣✱

✷✵✶✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✶

❈✳✹ ❈♦♥str✉✐♥❞♦ ♣♦rt❛s ❞❡ ❞♦✐s q✉❜✐ts ❛ ♣❛rt✐r ❞❡ ♣♦rt❛s ❞❡ ✉♠ q✉❜✐t✳ ❊♠(a₎✿

❛ ♣♦rt❛ CN OT ❝♦♠ ❝♦♥tr♦❧❡ ♥♦ s❡❣✉♥❞♦ q✉❜✐t✳ ❊♠ (b)✿ ❛ ♣♦rt❛ Sw✳ ❊♠

(c₎✿ ❛ ♣♦rt❛_Z₋_Controlada❝♦♠ ❝♦♥tr♦❧❡ ♥♦ ♣r✐♠❡✐r♦ q✉❜✐t✳ ❋♦♥t❡✿ ❋✐❣✉r❛

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▲✐st❛ ❞❡ ❚❛❜❡❧❛s

✸✳✶ ❘❡s✉❧t❛❞♦s ❛ss♦❝✐❛❞♦s às ♠❡❞✐❞❛s ❞❡ ❆❧✐❝❡ ❡ ❛s r❡s♣❡❝t✐✈❛s ❝♦rr❡çõ❡s q✉❡

❞❡✈❡♠ s❡r ❛♣❧✐❝❛❞❛s ♣♦r ❇♦❜✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻

✸✳✷ ❮♥❞✐❝❡s ❛ss♦❝✐❛❞♦s ❛♦s ❡st❛❞♦s ❞❛ ❇❛s❡ ❞❡ ❇❡❧❧ ●❡♥❡r❛❧✐③❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷

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