❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❖ ❈❊❆❘➪ ❈❊◆❚❘❖ ❉❊ ❈■✃◆❈■❆❙
❉❊P❆❘❚❆▼❊◆❚❖ ❉❊ ❋❮❙■❈❆
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❋❮❙■❈❆
❉✐❡❣♦ ❆r❛✉❥♦ ❋r♦t❛
❊st✉❞♦ ❞❡ ✉♠ s✐st❡♠❛ s✉♣❡r❝♦♥❞✉t♦r✲❢❡rr♦♠❛❣♥❡t♦✿
❡❢❡✐t♦s ❞❛ ❛♣❧✐❝❛çã♦ ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❡ ❝♦rr❡♥t❡
❡❧étr✐❝❛
❉✐❡❣♦ ❆r❛✉❥♦ ❋r♦t❛
❊st✉❞♦ ❞❡ ✉♠ s✐st❡♠❛ s✉♣❡r❝♦♥❞✉t♦r✲❢❡rr♦♠❛❣♥❡t♦✿
❡❢❡✐t♦s ❞❛ ❛♣❧✐❝❛çã♦ ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❡ ❝♦rr❡♥t❡
❡❧étr✐❝❛
❚❡s❡ ❞❡ ❞♦✉t♦r❛❞♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦✲ ❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❋ís✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá✱ ❝♦♠♦ r❡✲ q✉✐s✐t♦ ♣❛r❝✐❛❧ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ ❚ít✉❧♦ ❞❡ ❉♦✉t♦r ❡♠ ❋ís✐❝❛✳ ➪r❡❛ ❞❡ ❝♦♥❝❡♥✲ tr❛çã♦✿ ❋ís✐❝❛ ❞❛ ▼❛tér✐❛ ❈♦♥❞❡♥s❛❞❛✳
❖r✐❡♥t❛❞♦r✿
❲❛♥❞❡♠❜❡r❣ P❛✐✈❛ ❋❡rr❡✐r❛
❈♦✲♦r✐❡♥t❛❞♦r✿▼✐❧♦r❛❞ ❱❧❛❞♦ ▼✐❧♦➨❡✈✐➣
❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❖ ❈❊❆❘➪ ✲ ❉❊P❆❘❚❆▼❊◆❚❖ ❉❊ ❋❮❙■❈❆
❉❛❞♦s ■♥t❡r♥❛❝✐♦♥❛✐s ❞❡ ❈❛t❛❧♦❣❛çã♦ ♥❛ P✉❜❧✐❝❛çã♦ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá
❇✐❜❧✐♦t❡❝❛ ❞♦ ❈✉rs♦ ❞❡ ❋ís✐❝❛ ❋✾✻✶❡ ❋r♦t❛✱ ❉✐❡❣♦ ❆r❛✉❥♦
❊st✉❞♦ ❞❡ ✉♠ s✉♣❡r❝♦♥❞✉t♦r✲❢❡rr♦♠❛❣♥❡t♦✿ ❡❢❡✐t♦s ❞❛ ❛♣❧✐❝❛çã♦ ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❡ ❝♦rr❡♥t❡ ❡❧étr✐❝❛✳ ✴ ❉✐❡❣♦ ❆r❛✉❥♦ ❋r♦t❛✳ ✲ ❋♦rt❛❧❡③❛✱
2016✳
✽✽ ❢✳✿✐❧✳ ❝♦❧♦r✳ ❡♥❝✳❀ ✸✵ ❝♠✳
❖r✐❡♥t❛çã♦✿ Pr♦❢✳ ❉r✳ ❲❛♥❞❡♠❜❡r❣ P❛✐✈❛ ❋❡rr❡✐r❛✳ ❈♦♦r✐❡♥t❛çã♦✿ Pr♦❢✳ ❉r✳ ▼✐❧♦r❛❞ ▼✐❧♦➨❡✈✐➣✳
➪r❡❛ ❞❡ ❝♦♥❝❡♥tr❛çã♦✿ ❋ís✐❝❛ ❞❛ ▼❛tér✐❛ ❈♦♥❞❡♥s❛❞❛✳
❚❡s❡ ✭❉♦✉t♦r❛❞♦✮ ✲ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá✱❋♦rt❛❧❡③❛✱2016✳
✶✳ ❋ís✐❝❛ ❞❛ ▼❛tér✐❛ ❈♦♥❞❡♥s❛❞❛✳ ✷✳ ❱órt✐❝❡s✳ ✸✳ ❙✉♣❡r❝♦♥❞✉t✐✈✐✲ ❞❛❞❡✳ ✹✳ ❍í❜r✐❞♦s ❙❋✳
■✳ ❚ít✉❧♦✳
❉✐❡❣♦ ❆r❛✉❥♦ ❋r♦t❛
❊st✉❞♦ ❞❡ ✉♠ s✐st❡♠❛ s✉♣❡r❝♦♥❞✉t♦r✲❢❡rr♦♠❛❣♥❡t♦✿
❡❢❡✐t♦s ❞❛ ❛♣❧✐❝❛çã♦ ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❡ ❝♦rr❡♥t❡
❡❧étr✐❝❛
❚❡s❡ ❞❡ ❞♦✉t♦r❛❞♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❋ís✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá✱ ❝♦♠♦ r❡q✉✐s✐t♦ ♣❛r❝✐❛❧ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ ❚ít✉❧♦ ❞❡ ❉♦✉t♦r ❡♠ ❋ís✐❝❛✳ ➪r❡❛ ❞❡ ❝♦♥❝❡♥tr❛çã♦✿ ❋ís✐❝❛ ❞❛ ▼❛tér✐❛ ❈♦♥❞❡♥s❛❞❛✳
❆♣r♦✈❛❞❛ ❡♠ ✷✼✴✵✶✴✷✵✶✻✳
❇❆◆❈❆ ❊❳❆▼■◆❆❉❖❘❆
Pr♦❢✳ ❉r✳ ❲❛♥❞❡♠❜❡r❣ P❛✐✈❛ ❋❡rr❡✐r❛ ✭❖r✐❡♥t❛❞♦r✮ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá ✭❯❋❈✮
Pr♦❢✳ ❉r✳ ❆♥❞ré ❆✉t♦ ▼♦r❡✐r❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá ✭❯❋❈✮
Pr♦❢✳ ❉r✳ ❆s❝â♥✐♦ ❉✐❛s ❆r❛✉❥♦ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá ✭❯❋❈✮
Pr♦❢✳ ❉r✳ ❆r✐st❡✉ ❘♦s❡♥❞♦ P♦♥t❡s ▲✐♠❛
❆❣r❛❞❡❝✐♠❡♥t♦s
■♥✐❝✐❛❧♠❡♥t❡✱ ❣♦st❛r✐❛ ❞❡ ❞❡✐①❛r r❡❣✐str❛❞♦ ❛q✉✐✱ ♦ ♠❡✉ ✐♠❡♥s♦ ❛❣r❛❞❡❝✐♠❡♥t♦ ❛♦s ♣r♦❢❡ss♦r❡s ❲❛♥❞❡♠❜❡r❣ P❛✐✈❛ ❡ ▼✐❧♦r❛❞ ▼✐❧♦➨❡✈✐➣✳ ❆♠❜♦s ♠❡ r❡❝❡❜❡r❛♠ ❡♠ s❡✉s r❡s♣❡❝t✐✈♦s ❣r✉♣♦s ❞❡ ♣❡sq✉✐s❛✱ ❛q✉✐ ♥❛ ❯❋❈✱ ❡♠ ❋♦rt❛❧❡③❛✱ ❡ ♥❛ ❯❆✱ ♥❛ ❆♥t✉ér♣✐❛ ♠❡ ❞❛♥❞♦ t♦❞♦ ♦ s✉♣♦rt❡✱ ❛t❡♥çã♦ ❡ ♣❛❝✐ê♥❝✐❛ ♣❛r❛ ❛ r❡❛❧✐③❛çã♦ ❞♦ ♠❡✉ tr❛❜❛❧❤♦ ❞❡ ❞♦✉t♦r❛❞♦✳ ❙♦✉✱ r❡❛❧♠❡♥t❡✱ ♠✉✐t♦ ❣r❛t♦ à ❛♠❜♦s✱ ♣♦✐s ❛❝❡✐t❛r❛♠ ♠❡ ♦r✐❡♥t❛r ♠❡s♠♦ ❝♦♠ t♦❞❛s ❛s ❞✐✜❝✉❧❞❛❞❡s q✉❡ t✐♥❤❛ à é♣♦❝❛✱ q✉❛♥❞♦ ❞❡♠❛♥❞❛r✐❛ ❞❡❧❡s ♠✉✐t♦ tr❛❜❛❧❤♦ ✭❛❧é♠ ❞♦ ❥á ár❞✉♦ tr❛❜❛❧❤♦ ❞❡ ♦r✐❡♥t❛çã♦✮ ♣❛r❛ q✉❡ ❡✉ ♣✉❞❡ss❡ r❡❛❧✐③❛r ❡ ❝♦♥❝❧✉✐r ♠✐♥❤❛ ♣❡sq✉✐s❛✳
❆♦ ♣r♦❢❡ss♦r ❆♥❞r❡② ❈❤❛✈❡s ♣❡❧❛s ❢r✉tí❢❡r❛s ❞✐s❝✉ssõ❡s✱ ♣❛❝✐ê♥❝✐❛ ❡ ♦r✐❡♥t❛çã♦ ♥♦ ❞❡❝♦rr❡r ❞♦ ♠❡✉ tr❛❜❛❧❤♦ ❞❡ t❡s❡✳ ❆♦s ♣r♦❢❡ss♦r❡s ●✐❧ ❞❡ ❆q✉✐♥♦ ❡ ❋r❛♥ç♦✐s P❡❡t❡rs q✉❡✱ ❝♦♠♦ ❧í❞❡r❡s ❞♦s ❣r✉♣♦s ❞❡ ♣❡sq✉✐s❛ ❡♠ q✉❡ ❡st✐✈❡✱ ♠❡ r❡❝❡❜❡r❛♠ ♠✉✐t♦ ❝♦r❞✐❛❧♠❡♥t❡ ❡ ❞❡r❛♠ t♦❞♦ ♦ ❛♣♦✐♦ ♣❛r❛ ❛ r❡❛❧✐③❛çã♦ ❞❡st❛ t❡s❡✳
❆♦ ♣r♦❢❡ss♦r ❆♥tô♥✐♦ ●♦♠❡s ❞❡ ❙♦✉s❛ ❋✐❧❤♦✱ à é♣♦❝❛ ❝♦♦r❞❡♥❛❞♦r ❞♦ ♣r♦❣r❛♠❛ ❞❡ ♣ós✲❣r❛❞✉❛çã♦ ❡♠ ❢ís✐❝❛✱ ♣❡❧♦ ✐♥❝❡♥t✐✈♦ ❡ ❡♠♣❡♥❤♦ ❡♠ ♣r♦❧ ❞❛ ♣ós✲❣r❛❞✉❛çã♦ ❡ ❞♦s ❡st✉❞❛♥t❡s ❞♦ ❝✉rs♦ ❞❡ ❋ís✐❝❛ ♥♦ ❞❡❝♦rr❡r ❞❡ s❡✉ ♠❛♥❞❛t♦❀ ❆♦ ❛t✉❛❧ ❝♦♦r❞❡♥❛❞♦r ❞♦ ♣r♦❣r❛♠❛ ❞❡ ♣ós✲❣r❛❞✉❛çã♦ ❡♠ ❢ís✐❝❛ ♦ ♣r♦❢❡ss♦r ❆❧❡❥❛♥❞r♦ P❡❞r♦ ❆②❛❧❛✱ q✉❡ t❡♥❤❛ ✉♠ ❡①❝❡❧❡♥t❡ ♣❡rí♦❞♦ ❛ ❢r❡♥t❡ ❞❛ ❝♦♦r❞❡♥❛çã♦ ❞♦ ♣r♦❣r❛♠❛ ❞❡ ♣ós✲❣r❛❞✉❛çã♦❀ ❆♦s ♣r♦❢❡ss♦r❡s P❛✉❧♦ ❞❡ ❚❛rs♦✱ ❊✉❝❧✐♠❛r✱ ❏❡❛♥❧❡① ❡ ▼✉r✐❧♦ ♣❡❧❛s ❝♦♥tr✐❜✉✐çõ❡s à ♠✐♥❤❛ ❢♦r♠❛çã♦ ♥♦ ♠❡str❛❞♦ ❡ ❞♦✉t♦r❛❞♦ ❡ às ❢✉♥❝✐♦♥ár✐❛s ❞❛ ♣ós✲❣r❛❞✉❛çã♦ ❘❡❥❛♥❡ ❡ ❆♥❛ ❈❧❡✐❞❡ ♣❡❧♦ s✉♣♦rt❡ ❜✉r♦❝rát✐❝♦ q✉❛♥❞♦ ♥❡❝❡ssár✐♦✳
❆♦s ❛♠✐❣♦s ❞♦ ❞❡♣❛rt❛♠❡♥t♦ ❞❡ ❢ís✐❝❛ ❞❛ ❯❋❈✱ ❈❡s❛r ❙❛♠♣❛✐♦✱ ❈és❛r ▼❡♥❡③❡s✱ ❉❛✈✐ ❉❛♥t❛s✱ ❉❛✈✐ ❋✐❣✉❡✐r❡❞♦✱ ❉❛♥✐❧♦✱ ❉✐❡❣♦ ❈❛♠❛rã♦✱ ❉✐❡❣♦ ❘❛❜❡❧♦✱ ❊❞✉❛r❞♦✱ ❋r❛♥✲ ❝✐s❝♦ ▲❡❛♥❞r♦✱ ❍❡✐t♦r✱ ❍②❣♦r P✐❛❣❡t✱ ■❣♦r ❘♦❝❤❛✐❞✱ ❏♦ã♦ P❤✐❧✐♣❡✱ ❏♦r❣❡ ❆♥❞ré✱ ❏♦r❣❡ ❈♦❡❧❤♦ ✭❈❛♣✉❛♥✮✱ ❏♦r❣❡ ▲✉✐③✱ ❏♦sé ❊✉❝❧✐❞❡s✱ ❏♦sé ❘♦❜s♦♥✱ ▲❡❛♥❞r♦ P✐t♦♠❜❡✐r❛✱ ▲❡✈✐ ▲❡✐t❡✱ ▼❛r❝❡❧✐❛♥♦ ❖❧✐✈❡✐r❛✱ ◆á❞✐❛ ❋❡rr❡✐r❛✱ ❘♦❝✐❝❧❡r ❍♦❧❛♥❞❛ ❡ ❱❛❣♥❡r ❇❡ss❛✳ ❆♦s ♠❡✉s ❛♠✐❣♦s ❧á ❞❛ ❯❆✱ ❉♦♥❥❛♥✱ ▲✉❝❛s✱ ❱✐❝t♦r ❡ ❘❡❜❡❝❛✳
➚ ♠✐♥❤❛ ❢❛♠í❧✐❛✱ ❆♥❛ P❛✉❧❛✱ P❡❞r✐♥❤♦✱ ▼❛r✐❛ ▲❡tí❝✐❛ ❡ ▼❛r✐❛♥✐♥❤❛✱ ♠✉✐t♦ ♦❜r✐❣❛❞♦ ♣♦r t♦❞❛ ❛ ❝♦♠♣r❡❡♥sã♦ ❞❡ ✈♦❝ês✳ ❱♦❝ês sã♦ ❛ ♠✐♥❤❛ ♠❛✐♦r ♠♦t✐✈❛çã♦✳ ➚ ♠✐♥❤❛ ♠ã❡ ▼❛r❣❛r✐❞❛✱ ♠✐♥❤❛ ♠❛❞r✐♥❤❛ ❋✁át✐♠❛✱ ♠✐♥❤❛ s♦❣r❛ ❋r❛♥sq✉✐♥❤❛✱ à ♠✐♥❤❛ ♣r✐♠❛ ❱❛❧ér✐❛ ❡ s❡✉ ♣❛✐✱ sr✳ ❖③❛♥✐ ❡ ❛♦ ♠❡✉ ♣r✐♠♦ ❘♦❜❡rt♦ ♣❡❧♦ ❛♠♦r ❡ ✐♥❝❡♥t✐✈♦❀ ❆♦s ♣r♦❢❡ss♦r❡s ❡ ❣r❛♥❞❡s ♠❡str❡s ❆♥tô♥✐♦ ❏♦sé ❡ ❆♥tô♥✐♦ ❙✐q✉❡✐r❛✱ ♣❡❧❛ ♠✐♥❤❛ ❢♦r♠❛çã♦ ❡ ❛♣♦✐♦ ❞✉r❛♥t❡ t♦❞❛ ❛ ❣r❛❞✉❛çã♦✳
✏▲❡t ♠❡ t❡❧❧ ②♦✉ s♦♠❡t❤✐♥❣ ②♦✉ ❛❧r❡❛❞② ❦♥♦✇✳ ❚❤❡ ✇♦r❧❞ ❛✐♥✬t ❛❧❧ s✉♥s❤✐♥❡ ❛♥❞ r❛✐♥❜♦✇s✳ ■t✬s ❛ ✈❡r② ♠❡❛♥ ❛♥❞ ♥❛st② ♣❧❛❝❡✱ ❛♥❞ ■ ❞♦♥✬t ❝❛r❡ ❤♦✇ t♦✉❣❤ ②♦✉ ❛r❡✱ ✐t ✇✐❧❧ ❜❡❛t ②♦✉ t♦ ②♦✉r ❦♥❡❡s ❛♥❞ ❦❡❡♣ ②♦✉ t❤❡r❡ ♣❡r♠❛♥❡♥t❧② ✐❢ ②♦✉ ❧❡t ✐t✳ ❨♦✉✱ ♠❡✱ ♦r ♥♦❜♦❞② ✐s ❣♦♥♥❛ ❤✐t ❛s ❤❛r❞ ❛s ❧✐❢❡✳ ❇✉t ✐t ❛✐♥✬t ❛❜♦✉t ❤♦✇ ❤❛r❞ ②♦✉ ❤✐t✳ ■t✬s ❛❜♦✉t ❤♦✇ ❤❛r❞ ②♦✉ ❝❛♥ ❣❡t ❤✐t ❛♥❞ ❦❡❡♣ ♠♦✈✐♥❣ ❢♦r✇❛r❞❀ ❤♦✇ ♠✉❝❤ ②♦✉ ❝❛♥ t❛❦❡ ❛♥❞ ❦❡❡♣ ♠♦✈✐♥❣ ❢♦r✇❛r❞✳ ❚❤❛t✬s ❤♦✇ ✇✐♥♥✐♥❣ ✐s ❞♦♥❡✦✑
❘❡s✉♠♦
❆❜str❛❝t
❙✉♠ár✐♦
✶ ■♥tr♦❞✉çã♦ ✶
✶✳✶ ■♥tr♦❞✉çã♦ ❛ s✉♣❡r❝♦♥❞✉t✐✈✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷ ✶✳✷ ❆ t❡♦r✐❛ ❞❡ ▲♦♥❞♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✶✳✸ ❆ t❡♦r✐❛ ❞❡ ●✐♥③❜✉r❣✲▲❛♥❞❛✉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✶✳✸✳✶ ❉❡r✐✈❛çã♦ ❞❛ ♣r✐♠❡✐r❛ ❡q✉❛çã♦ ❞❡ ●✐♥③❜✉r❣✲▲❛♥❞❛✉ ❡ ❞❛ ❝♦♥❞✐çã♦ ❞❡ ❝♦♥t♦r♥♦
❣❡r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✶✳✸✳✷ ❉❡r✐✈❛çã♦ ❞❛ s❡❣✉♥❞❛ ❡q✉❛çã♦ ❞❡ ●✐♥③❜✉r❣✲▲❛♥❞❛✉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✶✳✹ ❈♦♠♣r✐♠❡♥t♦s ❝❛r❛❝t❡ríst✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✶✳✺ ❚✐♣♦s ❞❡ s✉♣❡r❝♦♥❞✉t♦r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✶✳✻ ❚❡♦r✐❛ ❇❈❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✶✳✼ ▼❛tér✐❛ ❞❡ ✈órt✐❝❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✶✳✼✳✶ ◗✉❛♥t✐③❛çã♦ ❞♦ ✢✉①♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✶✳✼✳✷ ❆ ❡str✉t✉r❛ ❞❡ ✉♠ ✈órt✐❝❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✶✳✼✳✸ ❘❡❞❡ ❞❡ ✈órt✐❝❡s ✲ ❝♦♥s✐❞❡r❛çõ❡s ❣❡r❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✶✳✼✳✹ ❋✐①❛çã♦ ✭❵♣✐♥♥✐♥❣✬✮ ❞♦ ✢✉①♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾
✷ ▼ét♦❞♦ ◆✉♠ér✐❝♦ ✸✶
✷✳✶ ❆s ❡q✉❛çõ❡s ❞❡ ●▲ ❛❞✐♠❡♥s✐♦♥❛✐s ❡ ❛ ❢♦r♠❛ ❞❡♣❡♥❞❡♥t❡ ❞♦ t❡♠♣♦ ❞❛ ♣r✐♠❡✐r❛ ❡q✉❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✷✳✷ ▼ét♦❞♦ ❞❛s ✈❛r✐á✈❡✐s ❞❡ ❧✐❣❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✷✳✸ ❉✐s❝r❡t✐③❛çã♦ ❞❛ ❡q✉❛çã♦ ❞❡ ❚❉●▲ ❡ ❞❛ s✉♣❡r❝♦rr❡♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✷✳✸✳✶ ❊①♣r❡ssã♦ ♣❛r❛ ❛ ❡♥❡r❣✐❛ ❧✐✈r❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✷✳✹ ❈♦♥❞✐çõ❡s ❞❡ ❝♦♥t♦r♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✷✳✹✳✶ ❋✐❧♠❡ ❢❡rr♦♠❛❣♥ét✐❝♦✿ ♠♦❞❡❧♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾
✸ ❘❡s✉❧t❛❞♦s ✹✶
✸✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✸✳✷ ▼♦❞❡❧♦ t❡ór✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✸✳✸ ▼❛tér✐❛ ❞❡ ✈órt✐❝❡✲❛♥t✐✈órt✐❝❡ ♥❛ ❛✉sê♥❝✐❛ ❞❡ ❝❛♠♣♦ ❛♣❧✐❝❛❞♦ ❡ ❝♦rr❡♥t❡ ✳ ✳ ✳ ✹✺ ✸✳✹ ❈♦♠♣♦rt❛♠❡♥t♦ ❞♦s ♣❛r❡s ✈órt✐❝❡✲❛♥t✐✈órt✐❝❡ ♥❛ ♣r❡s❡♥ç❛ ❞❡ ✉♠ ❝❛♠♣♦ ♠❛❣✲
♥ét✐❝♦ ❡①t❡r♥♦ ❤♦♠♦❣ê♥✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✸✳✺ ❉✐♥â♠✐❝❛ ❞❡ ✈órt✐❝❡✲❛♥t✐✈órt✐❝❡ ❡ ❛ ❝♦rr❡♥t❡ ❝rít✐❝❛ ❛♥✐s♦tró♣✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸
❆ ❖ P♦t❡♥❝✐❛❧ ❱❡t♦r ✻✶ ❇ ❆ tr❛♥s❢♦r♠❛❞❛ ❞❡ ❋♦✉r✐❡r ❞❛ s❡❣✉♥❞❛ ❡q✉❛çã♦ ❞❡ ●▲ ✻✹
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✶ ❉✐❛❣r❛♠❛ r❡♣r❡s❡♥t❛♥❞♦ ♦s ♣❛râ♠❡tr♦s ❝rít✐❝♦s ❞♦ ❡st❛❞♦ s✉♣❡r❝♦♥❞✉t♦r ❡ ❛ s✉❛ ♣♦ssí✈❡❧ ❡①♣❛♥sã♦✳ ❋✐❣✉r❛ r❡t✐r❛❞❛ ❞❡ ❬✶❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶ ✷ ❘❡s✐stê♥❝✐❛ ❡♠ ♦❤♠s ❞❡ ✉♠❛ ❛♠♦str❛ ❞❡ ♠❡r❝úr✐♦ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛
❡♠ ❦❡❧✈✐♥s✱ ♦❜t✐❞❛ ♣♦r ❖♥♥❡s ❬✷❪✳ ❋✐❣✉r❛ r❡t✐r❛❞❛ ❞❡ ❬✸❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸ ✸ ❊❢❡✐t♦ ▼❡✐ss♥❡r✿ ✉♠ ♠❛t❡r✐❛❧ ❛♣r❡s❡♥t❛ ❝♦♠♣♦rt❛♠❡♥t♦ ♥♦r♠❛❧ à t❡♠♣❡r❛t✉r❛
T > Tc✱ ♥♦ q✉❛❧ ♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❛tr❛✈❡ss❛ ❛ ❛♠♦str❛✱ ❡ ♣❛ss❛ ❛ r❡♣❡❧✐r ♦
❝❛♠♣♦ ♠❛❣♥ét✐❝♦✱ ♥♦ ❡st❛❞♦ s✉♣❡r❝♦♥❞✉t♦r✱ q✉❛♥❞♦T < Tc✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹
✹ ■❧✉str❛çã♦ ❞❛ tr♦❝❛ ❞❡ ✉♠ ❢ô♥♦♥ ❡♥tr❡ ❞♦✐s ❡❧étr♦♥s q✉❡ ❞á ♦r✐❣❡♠ à s✉❛ ✐♥t❡r❛çã♦ ❛tr❛t✐✈❛ ♥❛ t❡♦r✐❛ ❇❈❙✳ ❖ ❡❧étr♦♥ k1 ❡♠✐t❡ ✉♠ ❢ô♥♦♥ q✉❡ é ❛❜s♦r✈✐❞♦ ♣♦r ✉♠
s❡❣✉♥❞♦ ❡❧étr♦♥ k2✳ ❋✐❣✉r❛ r❡t✐r❛❞❛ ❞❡ ❬✹❪✱ ❝♦♠ ♦ ❛✉tó❣r❛❢♦ ❞❡ ▲❡♦♦♥ ❈♦♦♣❡r✱
✉♠ ❞♦s ❛✉t♦r❡s ❞❛ t❡♦r✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✺ ❋✐❣✉r❛ ✐❧✉str❛♥❞♦ ♦ ❡❢❡✐t♦ ❞♦ r❡s❢r✐❛♠❡♥t♦ ❞❡ ✉♠❛ ❛♠♦str❛ s✉♣❡r❝♦♥❞✉t♦r❛ ✭à
❡sq✉❡r❞❛✮ ❡ ❞❡ ✉♠ ❝♦♥❞✉t♦r ♣❡r❢❡✐t♦ ✭à ❞✐r❡✐t❛✮ ✐♥❝✐❛❧♠❡♥t❡ ❛ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❛♣❧✐❝❛❞♦ ③❡r♦ ❬❡✛❡❝t ♦❢ ③❡r♦ ✜❡❧❞ ❝♦♦❧✐♥❣ ✭❩❋❈✮❪ ✭❛✮ ❡ ✭❝✮✱ r❡s♣❡❝t✐✈❛♠❡♥t❡❀ ❡ ❞♦ r❡s❢r✐❛♠❡♥t♦ q✉❛♥❞♦ ❛s ❛♠♦str❛s✱ ✐♥✐❝✐❛❧♠❡♥t❡✱ ❡stã♦ ✐♥✐❝✐❛❧♠❡♥t❡ s✉❜♠❡t✐❞❛s ❛ ✉♠ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❛♣❧✐❝❛❞♦ ❬✜❡❧❞ ❝♦♦❧✐♥❣ ✭❋❈✮❪ ♣❛r❛ ✭❜✮ ♦ s✉♣❡r❝♦♥❞✉t♦r ❡ ✭❞✮ ♦ ❝♦♥❞✉t♦r ♣❡r❢❡✐t♦✳ ❋✐❣✉r❛ r❡t✐r❛❞❛ ❞❡ ❬✺❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✻ ❈♦♠♣♦rt❛♠❡♥t♦ ❞❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❡♥❡r❣✐❛ ♣❛r❛ ♦ ❝❛s♦ s❡♠ ❝❛♠♣♦s ❡ ❣r❛❞✐❡♥t❡s✳
◆❛ ✜❣✉r❛ ✭❛✮α >0✱ t❡♠♦s ♦ ❡st❛❞♦ ♥♦r♠❛❧ ❡ ♥❛ ✜❣✉r❛ ✭❜✮α <0✱ t❡♠♦s ♦ ❡st❛❞♦
s✉♣❡r❝♦♥❞✉t♦r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✼ ■❧✉str❛çã♦ ❞❛ ✐♥t❡r❢❛❝❡ s✉♣❡r❝♦♥❞✉t♦r✴ ♠❡t❛❧✱ ♠♦str❛♥❞♦ ❛ ❞❡♣❡♥❞ê♥❝✐❛ ❡s♣❛❝✐❛❧
❞♦ ♣❛râ♠❡tr♦ ❞❡ ♦r❞❡♠ |Ψ|✱ ♦♥❞❡b é ♦ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ❡①tr❛♣♦❧❛çã♦ ❬✶❪✳ ✳ ✳ ✳ ✳ ✶✸ ✽ ❉✐str✐❜✉✐çã♦ ❡s♣❛❝✐❛❧ ❞♦ ♣❛râ♠❡tr♦ ❞❡ ♦r❞❡♠ ψ ❡ ❞♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ H~ ♥❛
✐♥t❡r❢❛❝❡ s✉♣❡r❝♦♥❞✉t♦r✴ ♠❡t❛❧ ♥♦r♠❛❧ ❬✶❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✾ P❡♥❡tr❛çã♦ ❞❡ ✉♠ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❛♣❧✐❝❛❞♦ H~a ❡♠ ✉♠ s✉♣❡r❝♦♥❞✉t♦r s❡♠✐✲
✐♥✜♥✐t♦✳ ❖ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♣❡♥❡tr❛çã♦ λ é ❞❡✜♥✐❞♦ ❝♦♠♦ ❛ ❞✐stâ♥❝✐❛ ❛♦ ❧♦♥❣♦ ❞❛ q✉❛❧ ♦ ❝❛♠♣♦ ❞✐♠✐♥✉✐ ♣❛r❛ ✉♠ ✈❛❧♦r ✐❣✉❛❧ ❛♦ ✈❛❧♦r ♦r✐❣✐♥❛❧ ❞✐✈✐❞✐❞♦ ♣♦r e✳ ❊♠ s✉♣❡r❝♦♥❞✉t♦r❡s ♣✉r♦s✱λ é ❞❛ ♦r❞❡♠ ❞❡ ✺✵✵ ❆ ❬✸❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼o ✶✵ ❊str✉t✉r❛ s✐♠♣❧✐✜❝❛❞❛ ❞❡ ✉♠ ✈órt✐❝❡✱ ❡♠ q✉❡ é ♠♦str❛❞♦ ♦ ❝r❡s❝✐♠❡♥t♦ ❞❛ ❞❡♥✲
s✐❞❛❞❡ ❞❡ ❡❧étr♦♥s s✉♣❡r❝♦♥❞✉t♦r❡s ns ❡ ♦ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ❝♦❡rê♥❝✐❛ ξ ❬✻❪✳ ✳ ✳ ✳ ✳ ✶✽
✶✶ ❉✐❛❣r❛♠❛ ❞❡ ❢❛s❡H−T✱ ♣❛r❛ ✭❛✮ s✉♣❡r❝♦♥❞✉t♦r❡s ❞♦ t✐♣♦✲■✱ ✭❜✮ ♣❛r❛ s✉♣❡r❝♦♥✲ ❞✉t♦r❡s ❞♦ t✐♣♦✲■■ ❡ ✭❝✮ s✉♣❡r❝♦♥❞✉t♦r❡s ❞♦ t✐♣♦✲✶✳✺✳ ❋✐❣✉r❛ ❛❞❛♣❛t❛❞❛ ❞❡ ❬✼❪✳
✶✷ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ s✉♣❡r❝♦♥❞✉t♦r❡s ❞♦ t✐♣♦✲■ ❡ ❞♦ t✐♣♦✲■■✱ ❝♦♠ ♦ ♠❡s♠♦ ❝❛♠♣♦ ❝rít✐❝♦ t❡r♠♦❞✐♥â♠✐❝♦ Hc✳ ◆♦ s✉♣❡r❝♦♥❞✉t♦r ❞♦ t✐♣♦ ■■✱ ♦ ❝✉st♦ ❞❡ ❡♥❡r❣✐❛
❞✐❛♠❛❣♥ét✐❝♦ ♣❛r❛ ♠❛♥t❡r ❛ s✉♣❡r❝♦♥❞✉t✐✈✐❞❛❞❡ é ♠❡♥♦r q✉❡ ♥♦ s✉♣❡r❝♦♥❞✉t♦r ❞♦ t✐♣♦ ■✱ ♦ q✉❡ ♣❡r♠✐t❡ ♦ ❝❛♠♣♦ Hc2 s❡r ♠✉✐t♦ ♠❛✐♦r q✉❡ ♦ ❝❛♠♣♦ Hc✳ ✳ ✳ ✳ ✳ ✷✵
✶✸ ❉✐str✐❜✉✐çã♦ ❞❡ ✈órt✐❝❡s ♦❜s❡r✈❛❞♦ ♣♦r ❍❡ss ❡t ❛❧✳ ❝♦♠♣r♦✈❛♥❞♦ ❛ ♣r❡❞✐çã♦ ❞❡ ❆❜r✐❦♦s♦✈✳ ❋✐❣✉r❛ r❡t✐r❛❞❛ ❞❡ ❬✽❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✶✹ ▼❛❣♥❡t✐③❛çã♦ ❝♦♠♦ ✉♠❛ ❢✉♥çã♦ ❞♦ ❝❛♠♣♦ ❛♣❧✐❝❛❞♦ ♣❛r❛ ✭❛✮ s✉♣❡r❝♦♥❞✉t♦r❡s ❞♦
t✐♣♦ ■ ❡ ✭❜✮ s✉♣❡r❝♦♥❞✉t♦r❡s ❞♦ t✐♣♦ ■■✳ ❋✐❣✉r❛ r❡t✐r❛❞❛ ❞❡ ❬✾❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✶✺ ❋✐❣✉r❛ ✐❧✉str❛♥❞♦ ❛ ❡str✉t✉r❛ ❡s♣❛❝✐❛❧ ❞❡ ✉♠ ú♥✐❝♦ ✈órt✐❝❡✳ ❆ ❡sq✉❡r❞❛ é ♠♦str❛❞♦
❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝♦rr❡♥t❡j(r)q✉❡ é ③❡r♦ ♥♦ ❝❡♥tr♦ ❞♦ ✈órt✐❝❡ ❡✱ ❞❡ ✉♠❛ ❞✐stâ♥❝✐❛ ≈ ξ✱ t❡♠ ✈❛❧♦r ❞✐❢❡r❡♥t❡ ❞❡ ③❡r♦ ❡ ❞❡❝❛✐ ♥♦✈❛♠❡♥t❡ ❛ ③❡r♦ ❛tr❛✈és ❞❡ ✉♠ ❝♦♠✲
♣r✐♠❡♥t♦ ❞♦ ♦r❞❡♠ ❞❡ λ✱ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♣❡♥❡tr❛çã♦✳ ❆ ❞✐r❡✐t❛ é ♠♦str❛❞♦ ❛ ❞✐str✐❜✉✐çã♦ r❛❞✐❛❧ ❞♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❧♦❝❛❧ h(r) ❡ ❞❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❡❧étr♦♥s
s✉♣❡r❝♦♥❞✉t♦r❡snsc(r)✳ ❋✐❣✉r❛ r❡t✐r❛❞❛ ❞❡ ❬✼❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻
✶✻ ❉✐❛❣r❛♠❛ ❡sq✉❡♠át✐❝♦ ❞❡ ✉♠❛ r❡❞❡ tr✐❛♥❣✉❧❛r ❞❡ ✈órt✐❝❡s ❝♦♠ ✉♠ ♣❡rí♦❞♦ av✳
❋✐❣✉r❛ r❡t✐r❛❞❛ ❞❡ ❬✼❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✶✼ ❊str✉t✉r❛ ❞❡ ✉♠ ❡st❛❞♦ ✐♥t❡r♠❡❞✐ár✐♦✱ ❞✐✈✐❞✐❞♦ ❡♠ ❢❛✐①❛s ♥♦r♠❛✐s ❡ s✉♣❡r❝♦♥✲
❞✉t♦r❛s ✭❧✐♥❤❛s ❡s❝✉r❛s✮✱ ❡♠ ✉♠ ❞✐s❝♦ ❞❡ ❝r✐st❛❧ ❞❡ P❜ ❛ ✺❑ ♦❜t✐❞♦ ♣♦r té❝♥✐❝❛ ó♣t✐❝♦✲♠❛❣♥ét✐❝❛✳ ❆ ❛♠♦str❛ ❞❛ ❡sq✉❡r❞❛ ❢♦✐ ♦❜t✐❞❛ ❛♣ós ♦ ❛✉♠❡♥t♦ ❞♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❛♣❧✐❝❛❞♦ ❝♦♠ ❛ ❛♠♦str❛ ✐♥✐❝✐❛❧♠❡♥t❡ r❡s❢r✐❛❞❛ ❛ ❝❛♠♣♦ ③❡r♦ ✭❩❋❈✮✱ ❡♥q✉❛♥t♦ q✉❡ ❛ ❛♠♦str❛ ❞❛ ❞✐r❡✐t❛ ❢♦✐ ♦❜t✐❞❛ ❝♦♠ ♦ ❞❡❝rés❝✐♠♦ ❞♦ ❝❛♠♣♦ ♠❛❣✲ ♥ét✐❝♦✳ ❋✐❣✉r❛ r❡t✐r❛❞❛ ❞❡ ❬✶✵❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✶✽ ❊sq✉❡♠❛ ❞♦ ♠ét♦❞♦ ❞❛s ✈❛r✐á✈❡✐s ❞❡ ❧✐❣❛çã♦ ♣❛r❛ ✉♠❛ r❡❞❡ q✉❛❞r❛❞❛✱ ❝♦♠
❡s♣❛ç❛♠❡♥t♦ ❞❛ ❣r❛❞❡ ax✱ ♥❛ ❞✐r❡çã♦ ❞❡ x ❡ ay✱ ♥❛ ❞✐r❡çã♦ ❞❡ y✱ ❝♦♠♦ ♦ ✉s❛❞♦
♥❛s s✐♠✉❧❛çõ❡s✳ ❋✐❣✉r❛ r❡t✐r❛❞❛ ❞❡ ❬✾❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✶✾ ●r✐❞ ❞❡ ❞✐♣♦❧♦s ♠❛❣♥ét✐❝♦s✱ ❝♦♠ ❞♦♠í♥✐♦s ❛❞❥❛❝❡♥t❡s ❞❡ ♣♦❧❛r✐❞❛❞❡ ♠❛❣♥ét✐❝❛
❛❧t❡r♥❛❞❛ r❡♣r❡s❡♥t❛♥❞♦ ♦ ✜❧♠❡ ❢❡rr♦♠❛❣♥ét✐❝♦ ❝♦♥s✐❞❡r❛❞♦ ♥❛s s✐♠✉❧❛çõ❡s✳ ✳ ✳ ✹✵ ✷✵ ❱✐sã♦ ❡sq✉❡♠át✐❝❛ ❞❡ ✉♠ ✜❧♠❡ s✉♣❡r❝♦♥❞✉t♦r ✭❝♦♠ ❡s♣❡ss✉r❛d✮ ❝♦♠ ✉♠❛ ✉♠❛
❝❛♠❛❞❛ ❞❡ ó①✐❞♦ ❡♠ ❝✐♠❛ ✭❡s♣❡ss✉r❛l✮✱ s♦❜ ✉♠ ✜❧♠❡ ❢❡rr♦♠❛❣♥ét✐❝♦ ✭❡s♣❡ss✉r❛ D✮ ❝♦♠ ✉♠❛ ♠❛❣♥❡t✐③❛çã♦ M~ ❞❡ ♦r✐❡♥t❛çã♦ ♣❡r♣❡♥❞✐❝✉❧❛r ❛♦ ✜❧♠❡ ❡ s❡♥t✐❞♦ ❛❧t❡r♥❛❞♦ ❡♠ ❞♦♠í♥✐♦s ♣❛r❛❧❡❧♦s ❝✉❥♦ ♦ ❝♦♠♣r✐♠❡♥t♦ éw✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✷✶ P❡r✜❧ ❡s♣❛❝✐❛❧ ❞❛ ❝♦♠♣♦♥❡♥t❡ z ❞♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ♥ã♦✲❤♦♠♦❣ê♥✐♦ ❞♦ ✜❧♠❡
✷✷ ❊♥❡r❣✐❛ ❧✐✈r❡ ❞❡ ●✐❜❜s ❞♦ ✜❧♠❡ s✉♣❡r❝♦♥❞✉t♦r ✭d = 200 ♥♠✱ ξ(0) = 12 ♥♠✱
T /Tc = 0.674✱ κ = 5.1✮ ❝♦♠ ✉♠ ó①✐❞♦ ✭l = 10 ♥♠✮ ❡ ✉♠ ✜❧♠❡ ❢❡rr♦♠❛❣♥ét✐❝♦
❝♦♠ ❞♦♠í♥✐♦s ❛❧t❡r♥❛❞♦s ❡♠ s❡✉ t♦♣♦ ✭D = 1 µ♠✮✱ ❝♦♠♦ ✉♠❛ ❢✉♥çã♦ ❞❛ ♠❛❣✲
♥❡t✐③❛çã♦ ❞♦ ❢❡rr♦♠❛❣♥❡t♦✳ ✭❛✮✲✭❢✮ ♠♦str❛ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ♣❛r❡s ❞❡ ❈♦♦♣❡r ❞❡ ❡st❛❞♦s ❢✉♥❞❛♠❡♥t❛✐s ❞❡ ❛❧❣✉♠❛s ❝♦♥✜❣✉r❛çõ❡s ❞❡ ✈órt✐❝❡✲❛♥t✐✈órt✐❝❡ ✭❱✲❆❱✮✳ ✭❣✮✲✭❥✮ ♠♦str❛ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ♣❛r❡s ❞❡ ❈♦♦♣❡r ❞❡ ❞✐✈❡rs♦s ❡st❛❞♦s ❡stá✈❡✐s✱ ♠❛s ❞❡ ❡♥❡r❣✐❛ ♠❛✐♦r❡s✱ ❝♦♠ ✉♠ ♥ú♠❡r♦ ❞✐❢❡r❡♥t❡ ❞❡ ♣❛r❡s ❞❡ ❱✲❆❱ ❡♠ ❞✐❢❡r❡♥t❡s ♣❛r❡❞❡s ❞❡ ❞♦♠í♥✐♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✷✸ ❊♥❡r❣✐❛ ❧✐✈r❡ ❞❡ ●✐❜❜s ❞❡ ✉♠ ✜❧♠❡ s✉♣❡r❝♦♥❞✉t♦r ❝♦♠♦ ✉♠❛ ❢✉♥çã♦ ❞♦ ❝❛♠♣♦
♠❛❣♥ét✐❝♦ ❡①t❡r♥♦ ♣❛r❛ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡ ♠❛❣♥❡t✐③❛çã♦ ❞❛ ❝❛♠❛❞❛ ❢❡rr♦♠❛❣✲ ♥ét✐❝❛✳ ❖ ♥ú♠❡r♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❞❡ ✢✉①♦ q✉â♥t✐❝♦ ♥❛ r❡❣✐ã♦ ❞❡ s✐♠✉❧❛çã♦ ♣❛r❛ ❝❛❞❛ ✈❛❧♦r ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ é ✐♥❞✐❝❛❞♦ ♥♦ ❡✐①♦ s✉♣❡r✐♦r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✷✹ ❉❡♥s✐❞❛❞❡ ❞❛s ❝♦rr❡♥t❡s ❞❡ ▼❡✐ss♥❡r ♥♦ ✜❧♠❡ s✉♣❡r❝♦♥❞✉t♦r s♦❜ ✉♠❛ ❝❛♠❛❞❛
❢❡rr♦♠❛❣♥ét✐❝❛ ❞❡ ♠❛❣♥❡t✐③❛çã♦ M = 20 ●✱ ♥❛ ❛✉sê♥❝✐❛ ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦
❡①t❡r♥♦ ❬❝♦♠ ❛ ✐♥❞✐❝❛çã♦ ✈❡t♦r✐❛❧ ❞❛s ❝♦rr❡♥t❡s ❞❡ ▼❡✐ss♥❡r ✐♥❞✉③✐❞❛s ✐♥❝❧✉s❛✱ ♣❛✐♥❡❧ ✭❛✮❪✱ ❡ ♣❛r❛ ❝❛♠♣♦s ❛♣❧✐❝❛❞♦s ❤♦♠♦❣ê♥✐♦s ❝♦rr❡s♣♦♥❞❡♥❞♦ ❛♦s ✢✉①♦s ♠❛❣✲ ♥ét✐❝♦s ❞❡ Φ/Φ0 = 2 ✭❜✮✱ ✺ ✭❝✮ ❡ ✶✶ ✭❞✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶
✷✺ ❘❡s♣♦st❛ ♠❛❣♥ét✐❝❛ ❞❡ ✉♠ ✜❧♠❡ s✉♣❡r❝♦♥❞✉t♦r s♦❜ ✉♠ ✜❧♠❡ ❢❡rr♦♠❛❣♥ét✐❝♦ M = 50 ●✱ ♥❛ ♣r❡s❡♥ç❛ ❞❡ ✉♠ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❡①t❡r♥♦ ❝♦rr❡s♣♦♥❞❡♥❞♦ ❛
❛❞✐çã♦ ❞❡ ✢✉①♦ ✭❛✮ Φ/Φ0 = 5✱ ✭❜✮ Φ/Φ0 = 8✱ ✭❝✮ Φ/Φ0 = 17 ❡ ✭❞✮ Φ/Φ0 = 43
✭❝♦♥❢♦r♠❡ ♦ ❞✐❛❣r❛♠❛ ❞❡ ❡♥❡r❣✐❛ ♥❛ ❋✐❣✳ ❬✷✸❪✮✳ ❆s ❧✐♥❤❛s ❜r❛♥❝❛s ✐♥❞✐❝❛♠ ❛s ♣❛r❡❞❡s ❞♦s ❞♦♠í♥✐♦ ❢❡rr♦♠❛❣♥ét✐❝♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✷✻ ❈♦rr❡♥t❡ ❝rít✐❝❛ ❞♦ ✜❧♠❡ s✉♣❡r❝♦♥❞✉t♦r ✈❡rs✉s ♦ â♥❣✉❧♦ ✭❞✐r❡çã♦✮ ❞❛ ❝♦rr❡♥t❡
❛♣❧✐❝❛❞❛θ✱ ♣❛r❛ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡ ♠❛❣♥❡t✐③❛çã♦M ❞♦ ✜❧♠❡ ❢❡rr♦♠❛❣♥ét✐❝♦ ♥❛ ❜✐❝❛♠❛❞❛✳ θ = 0 ❞❡♥♦t❛ ❛ ♦r✐❡♥t❛çã♦ ❞❛ ❝♦rr❡♥t❡ ❛♣❧✐❝❛❞❛ ♣❡r♣❡♥❞✐❝✉❧❛r♠❡♥t❡
❛s ♣❛r❡❞❡s ❞❡ ❞♦♠í♥✐♦ ❡θ =π/2❛ ♦r✐❡♥t❛çã♦ ❞❛ ❝♦rr❡♥t❡ ❛♣❧✐❝❛❞❛ ♣❛r❛❧❡❧❛♠❡♥t❡
❛s ♣❛r❡❞❡s ❞❡ ❞♦♠í♥✐♦s✳ ❖s sí♠❜♦❧♦s ❛❜❡rt♦s ♠♦str❛♠ ❛ ❝♦rr❡♥t❡ ❝rít✐❝❛ ♦❜t✐❞❛ ❛♣ós s✉❛ ❛♣❧✐❝❛çã♦ ❛ ✉♠❛ ❛♠♦str❛ ✐♥✐❝✐❛❧♠❡♥t❡ ♥♦ ❡st❛❞♦ ▼❡✐ss♥❡r✱ ❡ ♦s sí♠❜♦❧♦s ♣r❡❡♥❝❤✐❞♦s ❛ ❝♦rr❡♥t❡ ❝rít✐❝❛ ♦❜t✐❞❛ q✉❛♥❞♦ ❛♣❧✐❝❛❞❛ à ❛♠♦str❛ ✐♥✐❝✐❛❧♠❡♥t❡ ♥❛ ❝♦♥✜❣✉r❛çã♦✱ ❝♦♠ ✈órt✐❝❡s ❡ ❛♥t✐✈órt✐❝❡s✱ ❞❡ ❡st❛❞♦ ❢✉♥❞❛♠❡♥t❛❧ ♣❛r❛ ✉♠ ❞❛❞♦ M✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✷✼ ❖ ♣❡r✜❧ ❞❛ ♠❛❣♥✐t✉❞❡ ❞❛ ❝♦rr❡♥t❡ t♦t❛❧ ❛♦ ❧♦♥❣♦ ❞❛ ❧✐♥❤❛ ❞❡y= 0 ❞♦ s✉♣❡r❝♦♥✲
❞✉t♦r s♦❜ ♦ ✜❧♠❡ ❢❡rr♦♠❛❣♥ét✐❝♦ ❝♦♠ ♠❛❣♥❡t✐③❛çã♦ M = 15 ● ✭s❡♠ q✉❛❧q✉❡r
✷✽ ❉✐❛❣r❛♠❛ ❞❡ ❡♥❡r❣✐❛ ❧✐✈r❡ ❡ ❛s ❝♦rr❡s♣♦♥❞❡♥t❡s ❞❡♥s✐❞❛❞❡s ❞❡ ♣❛r❡s ❞❡ ❈♦♦♣❡r ❞♦ ❡st❛❞♦ s✉♣❡r❝♦♥❞✉t♦r s♦❜ ✉♠ ✜❧♠❡ ❢❡rr♦♠❛❣♥ét✐❝♦ ❝♦♠ M = 50 ●✱ ❝♦♠♦
✉♠❛ ❢✉♥çã♦ ❞❛ ❝♦rr❡♥t❡ ❡①t❡r♥❛ ❛♣❧✐❝❛❞❛ ♥❛ ❞✐r❡çã♦ θ = 0.58 r❛❞✱ ♠♦str❛♥❞♦
♠✉❞❛♥ç❛s s✉❜t❛s ♥❛s ❝♦♥✜❣✉r❛çõ❡s ❞❡ ✈órt✐❝❡✲❛♥t✐✈órt✐❝❡ ❝❛✉s❛❞❛s ♣❡❧❛ ❝♦rr❡♥t❡ ❛♣❧✐❝❛❞❛ ❡ s✉❛ ✐♥t❡r❛çã♦ ❝♦♠ ❛s ❝♦rr❡♥t❡s ▼❡✐ss♥❡r✳ ❆ ❧✐♥❤❛ só❧✐❞❛ ♠♦str❛ ❛ s❡q✉ê♥❝✐❛ ❞❡ ❡st❛❞♦s ♣❛r❛ ❛ ✉♠ ❛✉♠❡♥t♦ ❣r❛❞✉❛❧✱ ❛ ♣❛rt✐r ❞❡ ③❡r♦✱ ❞❛ ❝♦rr❡♥t❡ ❛♣❧✐❝❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✷✾ ❯♠ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ✉♥✐❢♦r♠❡B~ ♥❛ ❞✐r❡çã♦z❝♦rr❡s♣♦♥❞❡ ❛ ✉♠ ♣♦t❡♥❝✐❛❧ ✈❡t♦r
q✉❡ ❣✐r❛ ❡♠ t♦r♥♦ ❞♦ ❡✐①♦ z✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✸✵ ❋✉♥çã♦ ❞❡❣r❛✉ Π(z,−d/2, d/2) ✉t✐❧✐③❛❞❛ ♥❛ ❞❡✜♥✐çã♦ ❞❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝♦rr❡♥t❡
✶
✶ ■♥tr♦❞✉çã♦
❆♣ós ♦ ❡①♣❡r✐♠❡♥t♦ r❡✈♦❧✉❝✐♦♥ár✐♦ ❞❡ ❖♥♥❡s ❡♠ ✶✾✶✶ ❬✷❪✱ ✈ár✐❛s ❛♣❧✐❝❛çõ❡s ♣rát✐❝❛s ♣❛r❛ ❛ s✉♣❡r❝♦♥❞✉t✐✈✐❞❛❞❡ ❢♦r❛♠ ♣r♦♣♦st❛s ❬✶✶❪✳ ❊♥tr❡t❛♥t♦✱ ❞❡✈✐❞♦ ❛ ❢r❛❣✐❧✐❞❛❞❡ ❞♦ ❡st❛❞♦ s✉♣❡r❝♦♥❞✉t♦r ✲ ❡❧❡ é ❞❡str✉í❞♦ q✉❛♥❞♦ ♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ H✱ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝♦rr❡♥t❡ j ♦✉ ❛ t❡♠♣❡r❛t✉r❛ T ❡①❝❡❞❡♠ s❡✉s ❝♦rr❡s♣♦♥❞❡♥t❡s ✈❛❧♦r❡s ❝rít✐❝♦s ✲ ❛s ♣♦ss✐❜✐❧✐❞❛❞❡s ❞❡ ❛♣❧✐❝❛çõ❡s ♣rát✐❝❛s ❞♦s ♠❛t❡r✐❛✐s s✉♣❡r❝♦♥❞✉t♦r❡s ❡stã♦ ❧✐♠✐t❛❞❛s ♣♦r s❡✉s ♣❛râ♠❡tr♦s ❝rít✐❝♦s✳ ❊ss❡ ❝♦♥❥✉♥t♦ ❞❡ ♣❛râ♠❡tr♦s ❞❡✜♥❡ ✉♠❛ s✉♣❡r❢í❝✐❡ ❝rít✐❝❛ q✉❡ s❡♣❛r❛ ♦ ❡st❛❞♦ s✉♣❡r❝♦♥❞✉t♦r ❞♦ ❡st❛❞♦ ♥♦r♠❛❧ ♥♦ ❡s♣❛ç♦ ❞❡✜♥✐❞♦ ♣♦r ❡❧❡ ❬✼❪✱ ❝♦♥❢♦r♠❡ ♣♦❞❡ s❡r ✈✐st♦ ♥♦ ❞✐❛❣r❛♠❛ ❞❛ ❋✐❣✳ ✶✳ ❖ ❡st❛❞♦ ❞❡ r❡s✐stê♥❝✐❛ ③❡r♦ ❡♥❝♦♥tr❛✲s❡ ❛❜❛✐①♦ ❞❛ s✉♣❡r❢í❝✐❡ ❝➥✐t✐❝❛✱ ♣♦rt❛♥t♦✱ ✉♠ ❞♦s ♣r✐♥❝✐♣❛✐s ♦❜❥❡t✐✈♦s ❞❛ ❢ís✐❝❛ ❡ ❞❛ ❝✐ê♥❝✐❛ ❞♦s ♠❛t❡r✐❛✐s s✉♣❡r❝♦♥❞✉t♦r❡s✱ é ❛♠♣❧✐❛r ♦ ♠á①✐♠♦ ♣♦ssí✈❡❧ ♦s ❧✐♠✐t❡s ❞❡✜♥✐❞♦s ♣❡❧❛ s✉♣❡r❢í❝✐❡ ❝rít✐❝❛ ✭❋✐❣✳ ✶✮✳ ❆s ❛♣❧✐❝❛çõ❡s ❝♦♠❡r❝✐❛✐s ❞♦s s✉♣❡r❝♦♥❞✉t♦r❡s t♦r♥❛r❛♠✲s❡ ♣♦ssí✈❡✐s ♥❛ ❞é❝❛❞❛ ❞❡ ✻✵✱ ❝♦♠ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ s✉♣❡r❝♦♥❞✉t♦r❡s ❜❛s❡❛❞♦s ❡♠ ♥✐ó❜✐♦ ✭◆❜✮ ❬✶✷❪✱ ♠❛s ♠❡s♠♦ ❝♦♠ t♦❞♦ ♦ ♣r♦❣r❡ss♦ ❛❧❝❛♥ç❛❞♦✱ ❞❡s❛✜♦s ❝♦♠♦ ❝✉st♦ ❡ r❡❢r✐❣❡r❛çã♦✱ ♣♦r ❡①❡♠♣❧♦✱ tê♠ ❡st✐♠✉❧❛❞♦ ❛ ♣❡sq✉✐s❛ ❡♠ s✉♣❡r❝♦♥❞✉t✐✈✐❞❛❞❡✳ ▼✉✐t♦ ❡s❢♦rç♦ t❡♠ s✐❞♦ ❞❡❞✐❝❛❞♦ ❛ ❜✉s❝❛ ♣♦r ♥♦✈♦s ♠❛t❡r✐❛✐s s✉♣❡r❝♦♥❞✉t♦r❡s ❡ ❛♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ s✐st❡♠❛s ❤í❜r✐❞♦s ❝♦♠ ❛❧t♦s ♣❛râ♠❡tr♦s ❝rít✐❝♦s❬✶✸✱ ✶✹✱ ✶✺❪✳
❋✐❣✉r❛ ✶✿ ❉✐❛❣r❛♠❛ r❡♣r❡s❡♥t❛♥❞♦ ♦s ♣❛râ♠❡tr♦s ❝rít✐❝♦s ❞♦ ❡st❛❞♦ s✉♣❡r❝♦♥❞✉t♦r ❡ ❛ s✉❛ ♣♦s✲ sí✈❡❧ ❡①♣❛♥sã♦✳ ❋✐❣✉r❛ r❡t✐r❛❞❛ ❞❡ ❬✶❪✳
❉❛r❡♠♦s ❡♥❢♦q✉❡ ❛♦ ❡st✉❞♦ ❞♦ ❡st❛❞♦ s✉♣❡r❝♦♥❞✉t♦r ❡♠ s✉♣❡r❝♦♥❞✉t♦r❡s ❞♦ t✐♣♦✲■■ ✲ ♦s q✉❛✐s ♣♦ss✉❡♠ κ > 1/√2 ❡ ♣❡r♠✐t❡♠ ❛ ♣❛ss❛❣❡♠ ❞❡ ✢✉①♦ ♠❛❣♥ét✐❝♦✱ ❝♦♠
✶ ■♥tr♦❞✉çã♦ ✷
s✐❞♦ ❛♠♣❧❛♠❡♥t❡ ❡st✉❞❛❞❛ ♣♦r s❡✉ ❣r❛♥❞❡ ♣♦t❡♥❝✐❛❧ ❡♠ ❛♣❧✐❝❛çõ❡s ♣❛r❛ ❛ ❛♠♣❧✐❛çã♦ ❞❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝♦rr❡♥t❡ ❡❧étr✐❝❛ ❝rít✐❝❛ q✉❡ ❡st❡s ♠❛t❡r✐❛✐s ♣♦❞❡♠ s✉♣♦rt❛r ❬✶✸❪✳ ❊♠ ❣❡r❛❧✱ ❛s ❡str✉t✉r❛s ❞❡ ✜①❛çã♦ ❜❛s❡❛❞❛s ❡♠ ❞❡❢❡✐t♦s✱ q✉❡ sã♦ ✐♥tr♦❞✉③✐❞♦s ♥♦s s✉♣❡r❝♦♥❞✉t♦r❡s ♦✉ sã♦ ♣❛rt❡ ❞❡❧❡s ♣♦r ❝♦♥t❛ ❞❡ ✐♠♣✉r❡③❛s✱ ♥ã♦ tê♠ ✉♠ ♣♦t❡♥❝✐❛❧ ❞❡ ❛♣r✐s✐♦♥❛♠❡♥t♦ ❢♦rt❡ ♦ s✉✜❝✐❡♥t❡ ♣❛r❛ ✐♠♣❡❞✐r ♦ ♠♦✈✐♠❡♥t♦ ❞♦s ✈órt✐❝❡s ❝❛✉s❛❞♦ ♣❡❧❛ ❢♦rç❛ ❞❡ ▲♦r❡♥t③ ❡ ♣♦r ✢✉t✉❛çõ❡s tér♠✐❝❛s ❬✶✻❪✳ ❊♥tr❡t❛♥t♦✱ ❛ ✜①❛çã♦ ♣♦r ♠❡✐♦s ♠❛❣♥ét✐❝♦s✱ ❝♦♠♦ ♣♦♥t♦s ♦✉ ✜❧♠❡s ❢❡rr♦♠❛❣♥ét✐❝♦s✱ sã♦ ♠❛✐s ✐♥t❡♥s❛s q✉❡ ❛s ♥ã♦ ♠❛❣♥ét✐❝❛s✳ ❆❧é♠ ❞♦ ♠❛✐s✱ ♣♦♥t♦s ❢❡rr♦♠❛❣♥ét✐❝♦s ❝♦♠ ❛❧t❛ ♠❛❣♥❡t✐③❛çã♦ ❡ ♦ ❝❛♠♣♦ ♥ã♦ ❤♦♠♦❣ê♥❡♦ ❞♦s ✜❧♠❡s ❢❡rr♦♠❛❣✲ ♥ét✐❝♦s ♣♦❞❡♠ ✐♥❞✉③✐r ❛ ❝r✐❛çã♦ ❞❡ ✈órt✐❝❡s ❬✶✼✱ ✶✽❪ ❡ ❛ ❢♦r♠❛çã♦ ❡s♣♦♥tâ♥❡❛ ❞❡ ♣❛r❡s ❞❡ ✈órt✐❝❡ ❡ ❛♥t✐ ✈órt✐❝❡ ✭❱✲❆❱✮ ❬✶✾✱ ✷✵✱ ✷✶✱ ✷✷✱ ✶✻❪✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ P♦rt❛♥t♦✱ ❛❧é♠ ❞♦ ❡❢❡✐t♦ ❞❡ ✜①❛çã♦✱ ✉♠ r✐❝♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞✐♥â♠✐❝♦ ❞♦s ✈órt✐❝❡s s✉r❣❡ ♥♦s ❡❧❡♠❡♥t♦s ❤í❜r✐❞♦s✱ ♦ q✉❡ ❧❡✈❛ ❛ ❞✐✈❡rs❛s ♣♦ss✐❜✐❧✐❞❛❞❡s ❞❡ ❛♠♣❧✐❛çã♦ ❞❛ ❝♦rr❡♥t❡ ❝rít✐❝❛ ♥♦s s✉♣❡r❝♦♥❞✉t♦r❡s✳
❍í❜r✐❞♦s s✉♣❡r❝♦♥❞✉t♦r✲❢❡rr♦♠❛❣♥❡t♦ tê♠ s✐❞♦ ✐♥t❡♥s❛♠❡♥t❡ ✐♥✈❡st✐❣❛❞♦s ♣♦r ♦❢❡r❡❝❡r❡♠ ❞✐✈❡rs❛s ♣♦ss✐❜✐❧✐❞❛❞❡s ♣❛r❛ ♦ ❝♦♥tr♦❧❡ ❞❛ s✉♣❡r❝♦♥❞✉t✐✈✐❞❛❞❡ ❡♠ ♥❛♥♦ ❡s❝❛❧❛ ❬✷✸✱ ✷✹✱ ✷✷✱ ✶✻✱ ✷✺✱ ✷✶❪✳ ◆❡st❛ t❡s❡✱ ❞❡s❡♥✈♦❧✈❡♠♦s ❛ t❡♦r✐❛ ❡ ♦s ♠ét♦❞♦s ♥❡❝❡ssár✐♦s ♣❛r❛ ❛ ❞❡s❝r✐çã♦ ❞❛ s✉♣❡r❝♦♥❞✉t✐✈✐❞❛❞❡ ♥❡st❡s s✐st❡♠❛s ❤í❜r✐❞♦s✱ ❛❝♦♣❧❛❞♦s ♠❛❣♥❡t✐❝❛♠❡♥t❡✱ ♥❛ q✉❛❧✱ t❡♠♦s ❝♦♠♦ ♦❜❥❡t✐✈♦ ♣r✐♥❝✐♣❛❧ ✐♥✈❡st✐❣❛r ❝♦♠♦ ❡ss❛ ❜✐❝❛♠❛❞❛ ❞❡ s✉♣❡r❝♦♥❞✉t♦r ❡ ❢❡rr♦♠❛❣♥❡t♦ s❡ ❝♦♠♣♦rt❛ s♦❜ ❛ ✐♥✢✉ê♥❝✐❛ ❞❡ ♠❡❝❛♥✐s♠♦s ❡①t❡r♥♦s✱ ❝♦♠♦ ✉♠ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❡ ❝♦rr❡♥t❡ ❡❧étr✐❝❛ ❛♣❧✐❝❛❞♦s✱ ❡ ♦ ♣❛♣❡❧ ❞❡s❡♠♣❡♥❤❛❞♦ ♣❡❧❛ ♠❛tér✐❛ ❞❡ ✈órt✐❝❡s ❢♦r♠❛❞❛ ♥♦ s✉♣❡r❝♦♥❞✉t♦r✳ ❆ss✐♠✱ t❡♠♦s ❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ t❡r ✉♠ ♠❡❧❤♦r ❡♥t❡♥❞✐♠❡♥t♦ ❞❛ ✐♥✢✉ê♥❝✐❛ ❞♦s ♣❛râ♠❡tr♦s ❝rít✐❝♦s ♥♦ ❡st❛❞♦ s✉♣❡r❝♦♥❞✉t♦r ❡ ❝♦♠♦ ❡❧❡s ♣♦❞❡♠ s❡r ♠❡❧❤♦r❛❞♦s✳
✶✳✶ ■♥tr♦❞✉çã♦ ❛ s✉♣❡r❝♦♥❞✉t✐✈✐❞❛❞❡
❆ ❞❡s❝♦❜❡rt❛ ❞♦ ❢❡♥ô♠❡♥♦ ❞❛ s✉♣❡r❝♦♥❞✉❝t✐✈✐❞❛❞❡ é ❝r❡❞✐t❛❞❛ ❛ ✉♠ ❞♦s ♣✐♦✲ ♥❡✐r♦s ❞❛ ❝r✐♦❣❡♥✐❛✱ q✉❡♠ ♣❡❧❛ ♣r✐♠❡✐r❛ ✈❡③ ❝♦♥s❡❣✉✐✉ ❧✐q✉❡❢❛③❡r ♦ ❤é❧✐♦✱ ❍❡✐❦❡ ❑❛♠❡r❧✐♥❣❤ ❖♥♥❡s ❡♠ ✶✾✾✶✱ ❡♠ ▲❡✐❞❡♥ ♥❛ ❍♦❧❛♥❞❛ ❬✶✶❪✳ ❈♦♠ ❛ s✉❛ ❞❡s❝♦❜❡rt❛✱ ❞✐✈❡rs❛s ♣♦ss✐❜✐❧✐✲ ❞❛❞❡s ❞❡ ❛♣❧✐❝❛çõ❡s ♣rát✐❝❛s ❢♦r❛♠ ♣r♦♣♦st❛s ❬✶✶✱ ✷✻✱ ✷✼❪✳ P❛r❛ ❝✐t❛r ❛❧❣✉♠❛s✱ tê♠✲s❡ ♦s ✜♦s s✉♣❡r❝♦♥❞✉t♦r❡s✱ ♣❛r❛ ♦ tr❛♥s♣♦rt❡ ❞❡ ❡♥❡r❣✐❛ ❡❧étr✐❝❛❀ ♠❛❣♥❡t♦s s✉♣❡r❝♦♥❞✉t♦r❡s ✭s♦❧❡♥ó✐❞❡s ♣❛r❛ ❣❡r❛çã♦ ❞❡ ❝❛♠♣♦s ♠❛❣♥ét✐❝♦s ❡❧❡✈❛❞♦s✮✱ ✉t✐❧✐③❛❞♦s ❡♠ ❡q✉✐♣❛♠❡♥t♦s ❞❡ r❡ss♦♥â♥❝✐❛ ♥✉❝❧❡❛r ♠❛❣♥ét✐❝❛❀ ❛r♠❛③❡♥❛♠❡♥t♦ ❞❡ ❡♥❡r❣✐❛ ♠❛❣♥ét✐❝❛ ♣♦r s✉♣❡r❝♦♥❞✉t✐✈✐✲ ❞❛❞❡❀ ❧❡✈✐t❛çã♦ ♠❛❣♥ét✐❝❛✱ q✉❡ ♣♦❞❡ s❡r ✉t✐❧✐③❛❞❛ ❡♠ ✈❡í❝✉❧♦s ❞❡ ❧❡✈✐t❛çã♦ ♠❛❣♥ét✐❝❛❀ ❡ ❡♠ ❞✐s♣♦s✐t✐✈♦s ❡❧❡trô♥✐❝♦s ♣❛r❛ s❡r❡♠ ❡♠♣r❡❣❛❞♦s ❡♠ ❝✐r❝✉✐t♦s ❡❧❡trô♥✐❝♦s ❬✷✻✱ ✷✽❪✳
❖♥♥❡s ❡ s❡✉ ❣r✉♣♦✱ ✐♥✈❡st✐❣❛r❛♠ ❛s ♣r♦♣r✐❡❞❛❞❡s ❡❧étr✐❝❛s ❞❡ ✈ár✐❛s s✉❜stâ♥❝✐❛s r❡s❢r✐❛❞❛s ♣❡❧♦ ❤é❧✐♦ ❧íq✉✐❞♦✱ ❛ ✉♠❛ t❡♠♣❡r❛t✉r❛ ❡①tr❡♠❛♠❡♥t❡ ❜❛✐①❛ ❞❡ ✹✱✷ ❑ ✭✲✷✻✽✱✾✺◦❈✮✳
✶ ■♥tr♦❞✉çã♦ ✸
❋✐❣✉r❛ ✷✿ ❘❡s✐stê♥❝✐❛ ❡♠ ♦❤♠s ❞❡ ✉♠❛ ❛♠♦str❛ ❞❡ ♠❡r❝úr✐♦ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ❡♠ ❦❡❧✈✐♥s✱ ♦❜t✐❞❛ ♣♦r ❖♥♥❡s ❬✷❪✳ ❋✐❣✉r❛ r❡t✐r❛❞❛ ❞❡ ❬✸❪✳
❝♦♠♦ ♦ ❝❤✉♠❜♦ ❡ ♦ ❡st❛♥❤♦✱ ❝❛í❛♠ ❛❜r✉♣t❛♠❡♥t❡ ❛ ✈❛❧♦r❡s tã♦ ♣❡q✉❡♥♦s q✉❡ s✉♣❡r❛✈❛♠ ❛ r❡s♦❧✉çã♦ ❞❡ s❡✉s ✐♥str✉♠❡♥t♦s ❬✶✱ ✸✱ ✾❪✳ ❚❛❧ ❢❡♥ô♠❡♥♦ ❢♦✐ ❝❤❛♠❛❞♦ ♣❡❧❛ ♣r✐♠❡✐r❛ ✈❡③ ♣♦r ❖♥♥❡s ❞❡ s✉♣r❛✲❝♦♥❞✉t✐✈✐❞❛❞❡ ❡♠ s✉❛ ♣✉❜❧✐❝❛çã♦ q✉❡ r❡♣♦rt❛✈❛ ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣♦r s❡✉ ❣r✉♣♦✱ ❝♦♥❢♦r♠❡ ❘❡❢✳ ❬✷❪✳ ❋♦✐ ❞❡s❝♦❜❡rt♦✱ ♣♦rt❛♥t♦✱ ❞✉❛s ❢❛s❡s ❞✐st✐♥t❛s ❞❡st❡s ♠❛t❡r✐❛✐s✿ ♦ ❡st❛❞♦ ♥♦r♠❛❧ ❡ ♦ ❡st❛❞♦ s✉♣❡r❝♦♥❞✉t♦r✳
◆♦ ❡st❛❞♦ s✉♣❡r❝♦♥❞✉t♦r✱ ❛ r❡s✐st✐✈✐❞❛❞❡ ❡❧étr✐❝❛ ♣❛r❛ ❝♦rr❡♥t❡ ❝♦♥tí♥✉❛ é ③❡r♦ ♦✉✱ ❡♠ ♦✉tr❛s ♣❛❧❛✈r❛s✱ ❛ ❝♦♥❞✉t✐✈✐❞❛❞❡ é ✐♥✜♥✐t❛✳ ❯♠❛ ❞❛s ❡✈✐❞ê♥❝✐❛s ♠❛✐s ❝♦♥✈✐♥❝❡♥t❡s ❞❡ q✉❡ ❛ r❡s✐st✐✈✐❞❛❞❡ ρ = 0✱ é ❛ ♦❜s❡r✈❛çã♦ ❞❡ ❝♦rr❡♥t❡s ♣❡rs✐st❡♥t❡s✳ ❖s ❝✐❡♥t✐st❛s ❥á
♦❜s❡r✈❛r❛♠ ❝♦rr❡♥t❡s ❝✐r❝✉❧❛r❡♠ s❡♠ ❛t❡♥✉❛çã♦ ❡♠ ❛♥é✐s s✉♣❡r❝♦♥❞✉t♦r❡s ❞✉r❛♥t❡ ♠❛✐s ❞❡ ✉♠ ❛♥♦ ❬✸✱ ✷✾❪✳ ❏✳ ❋✐❧❡ ❡ ❘✳ ●✳ ▼✐❧❧s ❬✸✵❪✱ ❡st✉❞❛r❛♠ ♦ ❞❡❝❛✐♠❡♥t♦ ❞❡ s✉♣❡r❝♦rr❡♥t❡s ❡♠ ✉♠ s♦❧❡♥ó✐❞❡ ✉s❛♥❞♦ ♠ét♦❞♦s ❞❡ r❡ss♦♥â♥❝✐❛ ♠❛❣♥ét✐❝❛ ♥✉❝❧❡❛r ♣❛r❛ ♠❡❞✐r ♦ ❝❛♠♣♦ ❛ss♦❝✐❛❞♦ ❛ s✉♣❡r❝♦rr❡♥t❡ ❡ ❝♦♥❝❧✉ír❛♠ q✉❡ ♦ t❡♠♣♦ ❞❡ ❞❡❝❛✐♠❡♥t♦ ❞❛ s✉♣❡r❝♦rr❡♥t❡ ♥ã♦ ❡r❛ ♠❡♥♦r ❞♦ q✉❡ ✶✵✵✵✵✵ ❛♥♦s ❬✸❪✳
✶ ■♥tr♦❞✉çã♦ ✹
❋✐❣✉r❛ ✸✿ ❊❢❡✐t♦ ▼❡✐ss♥❡r✿ ✉♠ ♠❛t❡r✐❛❧ ❛♣r❡s❡♥t❛ ❝♦♠♣♦rt❛♠❡♥t♦ ♥♦r♠❛❧ à t❡♠♣❡r❛t✉r❛T > Tc✱
♥♦ q✉❛❧ ♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❛tr❛✈❡ss❛ ❛ ❛♠♦str❛✱ ❡ ♣❛ss❛ ❛ r❡♣❡❧✐r ♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦✱ ♥♦ ❡st❛❞♦ s✉♣❡r❝♦♥❞✉t♦r✱ q✉❛♥❞♦T < Tc✳
❊st❡ ❡❢❡✐t♦ ❢❛③ ❝♦♠ q✉❡ ❝♦rr❡♥t❡s ❞❡ ❜❧✐♥❞❛❣❡♠ ✢✉❛♠ ❡ ♣r♦❞✉③❛♠ ✉♠ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ♥♦ ✐♥t❡r✐♦r ❞♦ s✉♣❡r❝♦♥❞✉t♦r q✉❡ ✐rã♦ ❜❛❧❛♥❝❡❛r ♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❛♣❧✐❝❛❞♦ q✉❡✱ ❡♠ ♦✉tr♦ ❝❛s♦✱ ✐r✐❛ ♣❡♥❡tr❛r ♦ ♠❛t❡r✐❛❧✳
■♠♣♦rt❛♥t❡ ♠❡♥❝✐♦♥❛r q✉❡✱ s♦♠❡♥t❡ ❞❡♣♦✐s ❞❡ ✈✐♥t❡ ❛♥♦s ❞❛ ❞❡s❝♦❜❡rt❛ ❞❛ s✉♣❡r❝♦♥❞✉t✐✈✐❞❛❞❡✱ ❡♠ ✶✾✸✺✱ s✉r❣✐✉ ❛ ♣r✐♠❡✐r❛ t❡♦r✐❛ ❢❡♥♦♠❡♥♦❧ó❣✐❝❛ q✉❡ ❞❡s❝r❡✈✐❛ ❛s ❞✉❛s ♣r✐♥❝✐♣❛✐s ♣r♦♣r✐❡❞❛❞❡s ❞♦s s✉♣❡r❝♦♥❞✉t♦r❡s✿ ❛ ❝♦♥❞✉t✐✈✐❞❛❞❡ ♣❡r❢❡✐t❛ ❡ ♦ ❡❢❡✐t♦ ▼❡✐ss♥❡r✱ ❞❡s❡♥✈♦❧✈✐❞❛ ♣❡❧♦s ✐r♠ã♦s ▲♦♥❞♦♥ ❬✸✸❪✳ ❊st❛ t❡♦r✐❛ t❛♠❜é♠ ❞❡♠♦♥str❛ q✉❡ ♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❞❡❝❛✐ ♥♦ ✐♥t❡r✐♦r ❞♦ s✉♣❡r❝♦♥❞✉t♦r ❛té ✉♠❛ ❞✐stâ♥❝✐❛ ❝❛r❛❝t❡ríst✐❝❛ ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♣❡♥❡tr❛çã♦ λ✳ ❆♣❡s❛r ❞❡ ♠❛❝r♦s❝ó♣✐❝❛✱ ❛ t❡♦r✐❛ ❞♦s ✐r♠ã♦s ▲♦♥❞♦♥ s❡ ♠♦str♦✉ út✐❧ ❡♠ ❞❡s❝r❡✈❡r ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦ ❡st❛❞♦ s✉♣❡r❝♦♥❞✉t♦r ❡ ❞♦ ❡st❛❞♦ ❞❡ ✈órt✐❝❡s ❡♠ s✉♣❡r❝♦♥❞✉t♦r❡s ❞♦ t✐♣♦✲■■ ❡①tr❡♠♦s ✭κ ≫ 1✮ ❬✷✾✱ ✼✱ ✸✹✱ ✸✺❪✱
❛♣❡s❛r ❞❡ tr❛tá✲❧♦s ❝♦♠♦ ♣♦♥t♦s ❡ ♥ã♦ ❧❡✈❛r❡♠ ❡♠ ❝♦♥t❛ ♦ s❡✉ t❛♠❛♥❤♦ ❡ ❡str✉t✉r❛ ✐♥t❡r♥❛✳ ❊♠ ✶✾✺✵✱ ❱✐t❛❧② ●✐♥③❜✉r❣ ❡ ▲❡✈ ▲❛♥❞❛✉✱ ♣r♦♣✉s❡r❛♠ ✉♠❛ t❡♦r✐❛ ❢❡♥♦♠❡♥♦❧ó❣✲ ✐❝❛ ♣❛r❛ ❛ s✉♣❡r❝♦♥❞✉t✐✈✐❞❛❞❡ ❬✸✻❪✱ ♦♥❞❡ ✐♥tr♦❞✉③✐r❛♠ t❛♠❜é♠ ♦ ❝♦♥❝❡✐t♦ ❞❡ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ❝♦❡rê♥❝✐❛ ξ✱ r❡❧❛❝✐♦♥❛❞♦ ❝♦♠ ❛ ✈❛r✐❛çã♦ ❡s♣❛❝✐❛❧ ❞♦ ♣❛râ♠❡tr♦ ❞❡ ♦r❞❡♠✳ ❊st❛ t❡♦✲ r✐❛ t❡✈❡ ❣r❛♥❞❡ s✉❝❡ss♦ ❡♠ ❡①♣❧✐❝❛r ❛s ♣r♦♣r✐❡❞❛❞❡s ♠❛❝r♦s❝ó♣✐❝❛s ❞♦s s✉♣❡r❝♦♥❞✉t♦r❡s✳ P♦❞❡✲s❡ ❞❡st❛❝❛r✱ ❡♠ ♣❛rt✐❝✉❧❛r✱ ❛ ♣r❡❞✐çã♦ ❢❡✐t❛ ♣♦r ❆❜r✐❦♦s♦✈✱ ✉t✐❧✐③❛♥❞♦ ❛ t❡♦r✐❛ ❞❡ ●▲✱ ❞❛ ❡①✐stê♥❝✐❛ ❞❡ ❞✉❛s ❝❛t❡❣♦r✐❛s ❞❡ s✉♣❡r❝♦♥❞✉t♦r❡s✿ ♦s ❞❡ t✐♣♦✲■ ❡ ❞❡ t✐♣♦✲■■✱ ❡ ❞❡s❝r✐t♦✱ ❛✐♥❞❛✱ ❛ ❡①✐stê♥❝✐❛ ❞❡ ✉♠ ❡st❛❞♦ ♠✐st♦ ♥♦s s✉♣❡r❝♦♥❞✉t♦r❡s ❞♦ t✐♣♦✲■■ ❬✸✼❪✳
✶ ■♥tr♦❞✉çã♦ ✺
❋✐❣✉r❛ ✹✿ ■❧✉str❛çã♦ ❞❛ tr♦❝❛ ❞❡ ✉♠ ❢ô♥♦♥ ❡♥tr❡ ❞♦✐s ❡❧étr♦♥s q✉❡ ❞á ♦r✐❣❡♠ à s✉❛ ✐♥t❡r❛çã♦ ❛tr❛t✐✈❛ ♥❛ t❡♦r✐❛ ❇❈❙✳ ❖ ❡❧étr♦♥k1 ❡♠✐t❡ ✉♠ ❢ô♥♦♥ q✉❡ é ❛❜s♦r✈✐❞♦ ♣♦r ✉♠ s❡❣✉♥❞♦
❡❧étr♦♥k2✳ ❋✐❣✉r❛ r❡t✐r❛❞❛ ❞❡ ❬✹❪✱ ❝♦♠ ♦ ❛✉tó❣r❛❢♦ ❞❡ ▲❡♦♦♥ ❈♦♦♣❡r✱ ✉♠ ❞♦s ❛✉t♦r❡s
❞❛ t❡♦r✐❛✳
❞❡ ❢ô♥♦♥s✱ ♦♥❞❡✱ ♣❛r❛ ✉♠ ♣❛r✱ ✉♠ ❡❧étr♦♥ ❛♦ ♠✉❞❛r s✉❛ tr❛❥❡tór✐❛✱ ❞❡✈✐❞♦ ❛ ✐♥t❡r❛çã♦ ❝♦♠ ❛ r❡❞❡ ❝r✐st❛❧✐♥❛✱ ❡♠✐t❡ ✉♠ ❢ô♥♦♥ ❡ ✉♠ ♦✉tr♦ ❡❧étr♦♥ ❛❜s♦r✈❡ ❡ss❡ ❢ô♥♦♥ ♠✉❞❛♥❞♦ t❛♠❜é♠ s✉❛ tr❛❥❡tór✐❛✳ P♦rt❛♥t♦✱ ❡ss❡ ♣r♦❝❡ss♦ ❞❡ tr♦❝❛ ❞❡ ❢ô♥♦♥✱ ❝r✐❛ ✉♠ ❡st❛❞♦ ❝♦rr❡❧❛✲ ❝✐♦♥❛❞♦ ❡♥tr❡ ❡ss❡ ❞♦✐s ❡❧étr♦♥s q✉❡✱ ❞❡ ♦✉tr❛ ❢♦r♠❛✱ ❡st❛r✐❛♠ ♠♦✈✐♠❡♥t❛♥❞♦✲s❡ ❞❡ ❢♦r♠❛ ✐♥❞❡♣❡♥❞❡♥t❡ ✉♠ ❞♦ ♦✉tr♦ ❬✹❪✱ t❛❧ ♣❛r ❞❡ ❡❧étr♦♥s é ❝❤❛♠❛❞❛♦ ❞❡ ♣❛r ❞❡ ❈♦♦♣❡r ✭❋✐❣✳ ✹✮✳ ❊ss❛ t❡♦r✐❛ ❛ss✉♠❡ q✉❡ ♦s ❡❧étr♦♥s ❛ss✐♠ ❧✐❣❛❞♦s ❝❛rr❡❣❛♠ ❛ s✉♣❡r❝♦rr❡♥t❡ ❡ ✉♠ ❵❣❛♣✬ ❞❡ ❡♥❡r❣✐❛ é ❝r✐❛❞♦ ❡♥tr❡ ♦s ❡st❛❞♦s ♥♦r♠❛❧ ❡ s✉♣❡r❝♦♥❞✉t♦r ❬✺❪✳ P♦r ❡st❡ tr❛❜❛❧❤♦✱ ❇❛r❞❡❡♥✱ ❈♦♦♣❡r ❡ ❙❝❤r✐❡✛❡r r❡❝❡❜❡r❛♠ ♦ ♣rê♠✐♦ ♥♦❜❡❧ ❞❡ ❢ís✐❝❛ ❞❡ ✶✾✼✷✳
▼❛✐♦r❡s ❞❡t❛❧❤❡s s♦❜r❡ ❛s t❡♦r✐❛s ❛❝✐♠❛ ♠❡♥❝✐♦♥❛❞❛s s❡rã♦ ❞❛❞♦s ♥❛s s❡çõ❡s q✉❡ s❡❣✉✐♥t❡s✳
✶✳✷ ❆ t❡♦r✐❛ ❞❡ ▲♦♥❞♦♥
❆s ❞✉❛s ❝❛r❛❝t❡ríst✐❝❛s q✉❡ ❞❡✜♥❡♠ ❛ s✉♣❡r❝♦♥❞✉t✐✈✐❞❛❞❡✱ ❝♦♥❞✉t✐✈✐❞❛❞❡ ❡ ♦ ❞✐❛♠❛❣♥❡t✐s♠♦ ♣❡r❢❡✐t♦s✱ ♥ã♦ ♣♦❞❡♠ s❡r ❡①♣❧✐❝❛❞❛s ♣♦r ✉♠❛ t❡♦r✐❛ ♥ã♦ q✉â♥t✐❝❛✳ P❛r❛ ✉♠ ❝♦♥❞✉t♦r ♣❡r❢❡✐t♦✱ t❡♠✲s❡ q✉❡ ❛ r❡s✐st✐✈✐❞❛❞❡ ❞♦ ♠❛t❡r✐❛❧ ρ → 0✳ ▲❡✈❛♥❞♦ ❡♠ ❝♦♥t❛
q✉❡E~ =ρ~j✱ ♣❡❧❛ ❝♦♥❞✐çã♦ ❞❡ ❝♦♥❞✉t✐✈✐❞❛❞❡ ♣❡r❢❡✐t❛✱ t❡♠♦s q✉❡ ♦ ❝❛♠♣♦ ❡❧étr✐❝♦E~ ❞❡✈❡ s❡r ③❡r♦✳ ■ss♦ ✐♠♣❧✐❝❛✱ ♣❡❧❛ ❧❡✐ ❞❡ ❋❛r❛❞❛②
∇ ×E~ =−∂ ~B/∂t, ✭✶✳✶✮ q✉❡ ∂ ~B/∂t = 0✱ ♦✉ s❡❥❛✱ q✉❡ ✉♠❛ ❛♠♦str❛ s✉❜♠❡t✐❞❛ ❛ ✉♠ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❞❡✈❡
❛♣r✐s✐♦♥á✲❧♦✳ ❯♠ ❡①❡♠♣❧♦ ❞✐ss♦ é ♦ ♣❧❛s♠❛✱ q✉❡ é ✉♠ ót✐♠♦ ❝♦♥❞✉t♦r ❡ ❛♣r✐s✐♦♥❛ ♦ ✢✉①♦ ♠❛❣♥ét✐❝♦ ❬✸✾❪✳
✶ ■♥tr♦❞✉çã♦ ✻
♠❛❣♥ét✐❝♦✱ ♦❜s❡r✈❛✲s❡ q✉❡ ✢✉①♦ ❞❡ ❝❛♠♣♦ s❡rá ♠❛♥t✐♥❞♦ ❢♦r❛ ❞❛ ❛♠♦str❛✱ ♦✉ s❡❥❛✱ t❡♠♦s ❛ ❡①❝❧✉sã♦ ❞♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❬❋✐❣✳ ✺ ✭❛✮❪✳ ❈❧❛ss✐❝❛♠❡♥t❡✱ t❛❧ ❢❡♥ô♠❡♥♦ ♥ã♦ r❡♣r❡s❡♥t❛ ♣r♦❜❧❡♠❛ ❛❧❣✉♠✱ ✉♠ ❝♦♥❞✉t♦r ♣❡r❢❡✐t♦ ❛♣r❡s❡♥t❛ ♦ ♠❡s♠♦ ❡❢❡✐t♦✳ ◗✉❛♥❞♦ ✉♠ ❝♦♥❞✉t♦r é ❝♦❧♦❝❛❞♦ ♥❛ ♣r❡s❡♥ç❛ ❞❡ ✉♠ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ H~0✱ ❛♣❛r❡❝❡♠ ❝♦rr❡♥t❡s tr❛♥s✐❡♥t❡s q✉❡ r❛♣✐❞❛♠❡♥t❡ ❞❡s❛♣❛r❡❝❡♠ ✭❡♠ ✉♠ ✜♦ ❞❡ ❝♦❜r❡ ❞❡ ✶✺ ❝♠ ❞❡ ❞✐â♠❡tr♦✱ ♣♦r ❡①❡♠♣❧♦✱ ❛ ❝♦♥✲ st❛♥t❡ ❞❡ t❡♠♣♦ ❞❡ ❞❡❝❛✐♠❡♥t♦ ❞❛ ❝♦rr❡♥t❡ é ❞❡ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ✵✱✹✷ ♠s ❬✺❪✮✱ r❡❣✐❞❛s ♣❡❧❛ ❡q✉❛çã♦
−A~· d ~H0
dt =Ri+L di
dt, ✭✶✳✷✮
♦♥❞❡ A~ r❡♣r❡s❡♥t❛ ❛ ár❡❛ ♣❡r♣❡♥❞✐❝✉❧❛r à ❞✐r❡çã♦ ❞♦ ❝❛♠♣♦ ❛♣❧✐❝❛❞♦✱ R ❛ r❡s✐stê♥❝✐❛ ❞♦ ❝♦♥❞✉t♦r✱L❛ s✉❛ ✐♥❞✉tâ♥❝✐❛ ❡i❛ ❝♦rr❡♥t❡ tr❛♥s✐❡♥t❡ ✐♥❞✉③✐❞❛ ❞❡✈✐❞♦ ❛ ✈❛r✐❛çã♦ ❞♦ ✢✉①♦ q✉❛♥❞♦ ♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ é ❛♣❧✐❝❛❞♦✳ ❈♦♥s✐❞❡r❛♥❞♦ q✉❡✱ ♣❛r❛ ✉♠ ❝♦♥❞✉t♦r ♣❡r❢❡✐t♦✱ R≈0✱ ♦❜t❡♠♦s ❞❛ ❊q✳ ✭✶✳✷✮✱ ❞❛❞♦
ΦT otal =Li+A~·H~0, ✭✶✳✸✮
q✉❡ ♦ ✢✉①♦ t♦t❛❧ ♣❡r♠❛♥❡❝❡ ❝♦♥st❛♥t❡ q✉❛♥❞♦ ♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ é ❛♣❧✐❝❛❞♦ ❡ é ③❡r♦ s❡ ♥❡♥❤✉♠ ❝❛♠♣♦ ♦✉ ❝♦rr❡♥t❡ ❥á ❡①✐st✐❛ ♥❛ ❛♠♦str❛✳ ❖ ✢✉①♦ ❞♦ ❝❛♠♣♦H~0 é ❝❛♥❝❡❧❛❞♦ ♣❡❧♦ ✢✉①♦ ✐♥❞✉③✐❞♦Li✱ ♠❛♥t❡♥❞♦ ♦ ❝❛♠♣♦ ♥♦ ✐♥t❡r✐♦r ❞♦ ❝♦♥❞✉t♦r ♣❡r❢❡✐t♦ B~ = 0 ❬❋✐❣✳ ✺ ✭❝✮❪✳ ❊♥tr❡t❛♥t♦✱ ❛❞♦t❛♥❞♦ ♦ ♣r♦❝❡❞✐♠❡♥t♦ ✐♥✈❡rs♦✱ ♦✉ s❡❥❛✱ ✐♥✐❝✐❛❧♠❡♥t❡ s✉❜♠❡✲ t❡♥❞♦ ❛ ❛♠♦str❛ ❛ ✉♠ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❡ ❡♠ s❡❣✉✐❞❛ r❡s❢r✐❛♥❞♦✲❛ ❛té t♦r♥❛r✲s❡ s✉♣❡r✲ ❝♦♥❞✉t♦r❛✱ ♦ ❝❛♠♣♦ ❡♠ s❡✉ ✐♥t❡r✐♦r s❡rá ❡①♣✉❧s♦ ❬❋✐❣✳ ✺ ✭❜✮❪✱ ♦ q✉❡ ♥ã♦ ♣♦❞❡ s❡r ❡①♣❧✐❝❛❞♦ ❝❧❛ss✐❝❛♠❡♥t❡✱ ✉♠❛ ✈❡③ q✉❡ ♦ ✢✉①♦ ❞❡✈❡r✐❛ s❡r ❛♣r✐s✐♦♥❛❞♦ ♣❛r❛ ✉♠ ❝♦♥❞✉t♦r ♣❡r❢❡✐t♦ ❬❋✐❣✳ ✺ ✭❞✮❪✱ ♠❛s ♦ q✉❡ ♦❜s❡r✈❛✲s❡ é q✉❡ ∂ ~B/∂t6= 0✳
❖s ✐r♠ã♦s ▲♦♥❞♦♥ ❛❞❛♣t❛r❛♠ ❛s ❧❡✐s ❞❛ ❡❧❡tr♦❞✐♥â♠✐❝❛ ❞❡ ❢♦r♠❛ q✉❡ ♦ ❡❢❡✐t♦ ▼❡✐ss♥❡r ♣✉❞❡ss❡ s❡r ❡①♣❧✐❝❛❞♦ t❛♠❜é♠ ♣❛r❛ ❡st❡ s❡❣✉♥❞♦ ❝❛s♦✱ ♦ ✜❡❧❞ ❝♦♦❧✐♥❣ ❬✸✸❪✳ ❆ t❡♦r✐❛ ❞♦s ✐r♠ã♦s ▲♦♥❞♦♥ ❛ss✉♠❡ q✉❡ ❛ s❡❣✉♥❞❛ ❧❡✐ ❞❡ ◆❡✇t♦♥ ♣♦ss❛ s❡r ❡s❝r✐t❛ ♥❛ ❢♦r♠❛
m∗d ~vs
dt =−e
∗E,~ ✭✶✳✹✮
♦♥❞❡m∗ é ❛ ♠❛ss❛ ❞♦s ♣♦rt❛❞♦r❡s ❞❡ ❝❛r❣❛ ❞❛ s✉♣❡r❝♦rr❡♥t❡✱e∗ é ❛ ❝❛r❣❛ ❞♦s ♣♦rt❛❞♦r❡s
❞❡ ❝❛r❣❛✱~vsé ❛ ✈❡❧♦❝✐❞❛❞❡ ❞❛ s✉♣❡r❝♦rr❡♥t❡ ❡E~ é ♦ ❝❛♠♣♦ ❡❧étr✐❝♦ ❛♣❧✐❝❛❞♦✳ ❘❡❡s❝r❡✈❡♥❞♦
~vs❡♠ t❡r♠♦s ❞❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝♦rr❡♥t❡✱j~s =−e∗ns~vs✱ ♦♥❞❡nsé ❛ ❞❡♥s✐❞❛❞❡ ❞♦s ♣♦rt❛❞♦r❡s
❞❡ ❝❛r❣❛ s✉♣❡r❝♦♥❞✉t♦r❡s✱ ❛ ❊q✳ ✭✶✳✹✮ ♣♦❞❡ s❡r ❡s❝r✐t❛ ❝♦♠♦ d~js
dt = nse∗2
✶ ■♥tr♦❞✉çã♦ ✼
(a) (b) (c) (d)
✶ ■♥tr♦❞✉çã♦ ✽
❈♦♥s✐❞❡r❛♥❞♦ ❛ ❧❡✐ ❞❡ ❋❛r❛❞❛②✱ ❊q✳ ✭✶✳✶✮✱ ♦❜t❡♠♦s ❛ r❡❧❛çã♦ ❛ s❡❣✉✐r ∂
∂t
∇ ×j~s+
nse∗2
m∗ B~
= 0. ✭✶✳✻✮
❊st❛ ❡q✉❛çã♦ é ✈❛❧✐❞❛ ♣❛r❛ q✉❛❧q✉❡r ❝♦♥❞✉t♦r ♣❡r❢❡✐t♦✳ ❊♥tr❡t❛♥t♦✱ à ✜♠ ❞❡ ❝♦♥t♦r♥❛r ♦ ♣r♦❜❧❡♠❛ ❝♦♠ ♦ ❛♣r✐s✐♦♥❛♠❡♥t♦ ❞♦ ❝❛♠♣♦ ♥♦ ✐♥t❡r✐♦r ❞❛ ❛♠♦str❛✱ ✉♠❛ ✈❡③ q✉❡ q✉❛❧q✉❡r ❝♦rr❡♥t❡ ❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❝♦♥st❛♥t❡s s❛t✐s❢❛③❡♠ ❡ss❛ r❡❧❛çã♦✱ ❡ ❛ ❡q✉❛çã♦ ❞❡s❝r❡✈❡r ❝♦rr❡t❛♠❡♥t❡ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦ s✉♣❡r❝♦♥❞✉t♦r ♣❛r❛ ♦ ✜❡❧❞ ❝♦♦❧✐♥❣✱ ♦s ✐r♠ã♦s ▲♦♥❞♦♥ ♣r♦♣✉s❡r❛♠ ❛ r❡str✐çã♦ ❞❛ ❢❛♠í❧✐❛ ❞❡ s♦❧✉çõ❡s ❞❛ ❊q✳ ✭✶✳✻✮ ♣❛r❛ àq✉❡❧❛s q✉❡ s❛t✐s❢❛③❡♠
∇ ×j~s =−
nse∗2
m∗ B.~ ✭✶✳✼✮
❊st❛ ❡q✉❛çã♦ ❞✐③ q✉❡ ❛ s✉♣❡r❝♦rr❡♥t❡ ❜❧✐♥❞❛ ♦ ✐♥t❡r✐♦r ❞❛ ❛♠♦str❛ ❞❡ ✉♠ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❡①t❡r♥♦ ❡ t❛♠❜é♠ q✉❡ q✉❛❧q✉❡r ✢✉①♦ ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ q✉❡✱ ✐♥✐❝✐❛❧♠❡♥t❡✱ ♣♦ss❛ ❡st❛r ❛tr❛✈❡ss❛♥❞♦ ♦ ♠❛t❡r✐❛❧ s❡rá ❡①♣✉❧s♦ q✉❛♥❞♦ ❡❧❡ s❡ t♦r♥❛r s✉♣❡r❝♦♥❞✉t♦r✳ ❙✉❛ ❝♦♠❜✐♥❛çã♦ ❝♦♠ ❛ ❧❡✐ ❞❡ ❆♠♣èr❡
∇ ×B~ =µ0j~s, ✭✶✳✽✮
❝♦♥s✐❞❡r❛♥❞♦ ❛ ✐❞❡♥t✐❞❛❞❡ ✈❡t♦r✐❛❧ ∇ × ∇ ×F~ = ∇(∇ ·F~)− ∇2F~ ❡ q✉❡ ∇ ·B~ = 0✱ ♥♦s
❧❡✈❛ ❛
∇2B~ = 1
λ2
L
~
B, ✭✶✳✾✮
❝♦♠
λL=
r m∗
nse∗2µ0
. ✭✶✳✶✵✮
❆ s♦❧✉çã♦ ❞❡ss❛ ❡q✉❛çã♦ é ✉♠ ❞❡❝❛✐♠❡♥t♦ ❡①♣♦♥❡♥❝✐❛❧ ❝♦♠ ❛ ❢♦r♠❛ ❞❡B =B0exp(−x/λL)✱
♦✉ s❡❥❛✱ ♥♦ ❡st❛❞♦ s✉♣❡r❝♦♥❞✉t♦r ♦ ú♥✐❝♦ ❝❛♠♣♦ ♣❡r♠✐t✐❞♦ ♥❛ ❛♠♦str❛ é ❛t❡♥✉❛❞♦ ❡①♣♦✲ ♥❡♥❝✐❛❧♠❡♥t❡ ❛ ♣❛rt✐r ❞❡ s✉❛ s✉♣❡r❢í❝✐❡✳ P♦rt❛♥t♦✱ λL é ✉♠❛ ♠❡❞✐❞❛ ❞❛ ♣r♦❢✉♥❞✐❞❛❞❡ ❞❡
♣❡♥❡tr❛çã♦ ❞♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦✱ q✉❡ é ✉♠ ❝♦♠♣r✐♠❡♥t♦ ❝❛r❛❝t❡ríst✐❝♦ ❞♦ s✉♣❡r❝♦♥❞✉t♦r ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♣❡♥❡tr❛çã♦ ❞❡ ▲♦♥❞♦♥✳
✶ ■♥tr♦❞✉çã♦ ✾
✶✳✸ ❆ t❡♦r✐❛ ❞❡ ●✐♥③❜✉r❣✲▲❛♥❞❛✉
❖ ❡st❛❞♦ s✉♣❡r❝♦♥❞✉t♦r ❡ ♦ ❡st❛❞♦ ♠❡tá❧✐❝♦ ♥♦r♠❛❧ sã♦ ❢❛s❡s t❡r♠♦❞✐♥â♠✐❝❛s s❡♣❛r❛❞❛s ❞❛ ♠❛tér✐❛✱ ❞❛ ♠❡s♠❛ ♠❛♥❡✐r❛ q✉❡ ❣❛s❡s✱ ❧íq✉✐❞♦s ❡ só❧✐❞♦s sã♦ ❢❛s❡s ❞✐❢❡r❡♥t❡s✳ ❊ss❡s ❡st❛❞♦s✱ ❡stã♦ s❡♣❛r❛❞♦s ♣♦r ✉♠❛ tr❛♥s✐çã♦ ❞❡ ❢❛s❡ q✉❡ ♣♦❞❡ s❡r ❝❛r❛❝t❡r✐③❛❞❛ ♣♦r s✐♥❣✉❧❛r✐❞❛❞❡s ❡♠ ❝❡rt❛s ✈❛r✐á✈❡✐s t❡r♠♦❞✐♥â♠✐❝❛s ♥❛ tr❛♥s✐çã♦✱ ❡♠ Tc✳ P♦❞❡♠♦s ❛ss✐♠✱
tr❛t❛r ❛ s✉♣❡r❝♦♥❞✉t✐✈✐❞❛❞❡ ❞♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❞❛s tr❛♥s✐çõ❡s ❞❡ ❢❛s❡ t❡r♠♦❞✐♥â♠✐❝❛s✳ ❆ t❡♦r✐❛ ❞❡ ●✐♥③❜✉r❣✲▲❛♥❞❛✉ ✭●▲✮ ❞❛ s✉♣❡r❝♦♥❞✉t✐✈✐❞❛❞❡ é ✉♠❛ t❡♦r✐❛ ❢❡♥♦♠❡✲ ♥♦❧ó❣✐❝❛ ❝♦♥str✉í❞❛ s♦❜r❡ ❛ t❡♦r✐❛ ❞❛s tr❛♥s✐çõ❡s ❞❡ ❢❛s❡ ❞❡ s❡❣✉♥❞❛ ♦r❞❡♠ ❞❡s❡♥✈♦❧✈✐❞❛ ♣♦r ▲❛♥❞❛✉ ❡♠ ♠❡❛❞♦s ❞❡ ✶✾✸✵✳ ▲❛♥❞❛✉ ♥♦t♦✉ q✉❡ ✉♠❛ tr❛♥s✐çã♦ ❞❡ ❢❛s❡ ❞❡ s❡❣✉♥❞❛ ♦r❞❡♠ tí♣✐❝❛ ❡♥✈♦❧✈❡ ❛❧❣✉♠❛ ♠✉❞❛♥ç❛ ♥❛ s✐♠❡tr✐❛ ❞♦ s✐st❡♠❛✳ ❯♠ ❡①❡♠♣❧♦ é ✉♠ ❢❡r✲ r♦♠❛❣♥❡t♦ à t❡♠♣❡r❛t✉r❛ ❞❡ ❈✉r✐❡✱ ♣❛r❛ ♦ q✉❛❧✱ ❛❝✐♠❛ ❞❛ t❡♠♣❡r❛t✉r❛ ❞❡ ❈✉r✐❡✱ Tc✱ ♦
s✐st❡♠❛ ❛♣r❡s❡♥t❛ ✉♠ ♠♦♠❡♥t♦ ♠❛❣♥ét✐❝♦ t♦t❛❧ ♥✉❧♦✱ ♠❛s ❛❜❛✐①♦ ❞❡ Tc✱ ✉♠ ♠♦♠❡♥t♦
♠❛❣♥ét✐❝♦ ❛♣❛r❡❝❡ ❡s♣♦♥t❛♥❡❛♠❡♥t❡ ❡ ❝♦♠ ✉♠❛ ❞✐r❡çã♦ ♣❛rt✐❝✉❧❛r ♣r❡❢❡r❡♥❝✐❛❧✳ ◆❛ t❡♦r✐❛ ❞❡ ▲❛♥❞❛✉✱ t❛✐s tr❛♥s✐çõ❡s sã♦ ❝❛r❛❝t❡r✐③❛❞❛s ♣♦r ✉♠ ♣❛râ♠❡tr♦ ❞❡ ♦r❞❡♠ q✉❡ é ③❡r♦ ♥♦ ❡st❛❞♦ ❞❡s♦r❞❡♥❛❞♦✱ ❛❝✐♠❛ ❞❡ Tc✱ ♠❛s t♦r♥❛✲s❡ ❞✐❢❡r❡♥t❡ ❞❡ ③❡r♦ ❛❜❛✐①♦ ❞❡ Tc✳ ◆♦
❝❛s♦ ❞♦ ❢❡rr♦♠❛❣♥❡t♦✱ ❛ ♠❛❣♥❡t✐③❛çã♦ s❡r✐❛ ❛ ❡s❝♦❧❤❛ ❛❞❡q✉❛❞❛ ♣❛r❛ ♣❛râ♠❡tr♦ ❞❡ ♦r❞❡♠ ❬✸✷✱ ✹✵✱ ✹✶❪✳
P❛r❛ ❛ s✉♣❡r❝♦♥❞✉t✐✈✐❞❛❞❡✱ ●✐♥③❜✉r❣ ❡ ▲❛♥❞❛✉ ♣♦st✉❧❛r❛♠ ❛ ❡①✐stê♥❝✐❛ ❞❡ ✉♠ ♣❛râ♠❡tr♦ ❞❡ ♦r❞❡♠ ❝♦♠♣❧❡①♦ ❞❡♥♦t❛❞♦ ♣♦r ψ✱ q✉❡ ❝❛r❛❝t❡r✐③❛ ♦ ❡st❛❞♦ ❞♦ s✐st❡♠❛✳ ◗✉❛♥❞♦ ♦ s✐st❡♠❛ ❡stá ♥♦ ❡st❛❞♦ ♥♦r♠❛❧✱ ❛❝✐♠❛ ❞❛ t❡♠♣❡r❛t✉r❛ ❝rít✐❝❛ Tc✱ ❡❧❡ é ③❡r♦✱
❡♥q✉❛♥t♦ q✉❡ ♣❛r❛ ♦ ❡st❛❞♦ s✉♣❡r❝♦♥❞✉t♦r✱ ❛❜❛✐①♦ ❞❡Tc✱ ❡❧❡ é ❞✐❢❡r❡♥t❡ ❞❡ ③❡r♦✱ ♦✉ s❡❥❛✱
ψ =
0 T > Tc,
ψ(T)6= 0 T < Tc.
✭✶✳✶✶✮
◆❛ é♣♦❝❛ ❞❡ s❡✉ tr❛❜❛❧❤♦ ♦r✐❣✐♥❛❧✱ ♦ s✐❣♥✐✜❝❛❞♦ ❢ís✐❝♦ ❞♦ ♣❛râ♠❡tr♦ ❞❡ ♦r❞❡♠ ❝♦♠♣❧❡①♦✱ψ✱ ♥ã♦ ❡r❛ ❝❧❛r♦✱ ♠❛s ❝♦♠ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ t❡♦r✐❛ ♠✐❝r♦s❝ó♣✐❝❛ ❞❡ ❇❈❙ ❞❛ s✉♣❡r❝♦♥❞✉t✐✈✐❞❛❞❡✱ ●♦r✬❦♦✈ ❢♦✐ ❝❛♣❛③ ❞❡ ❞❡r✐✈❛r ❞❛ t❡♦r✐❛ ❇❈❙ ❛ t❡♦r✐❛ ❞❡ ●▲ ❡ ♠♦str❛r q✉❡|ψ|2✱ ❛ ♠❡♥♦s ❞❡ ❛❧❣✉♠❛s ❝♦♥st❛♥t❡s ♥✉♠ér✐❝❛s✱ ❡r❛ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ✏♣❛r❡s ❞❡ ❈♦♦♣❡r✑✱ ❞❛ t❡♦r✐❛ ❇❈❙✱ ♣r❡s❡♥t❡s ♥❛ ❛♠♦str❛✳
❖ ♣♦st✉❧❛❞♦ ❜ás✐❝♦ ❞❡ ●▲✱ é q✉❡ s❡ψ ❢♦r ♣❡q✉❡♥♦ ❡ ✈❛r✐❛r ♣♦✉❝♦ ♥♦ ❡s♣❛ç♦✱ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❡♥❡r❣✐❛ ❧✐✈r❡f ♣♦❞❡ s❡r ❡①♣❛♥❞✐❞❛ ❡♠ ✉♠❛ sér✐❡ ❞❛ ❢♦r♠❛ ❬✹✵❪
f =fn0+α|Ψ|2 +
β
2 |Ψ|
4
+ 1
2m∗
−i~∇ −e
∗
cA~ Ψ 2 + ~ H−H~o
8π
2
✶ ■♥tr♦❞✉çã♦ ✶✵
✭❛✮ ✭❜✮
❋✐❣✉r❛ ✻✿ ❈♦♠♣♦rt❛♠❡♥t♦ ❞❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❡♥❡r❣✐❛ ♣❛r❛ ♦ ❝❛s♦ s❡♠ ❝❛♠♣♦s ❡ ❣r❛❞✐❡♥t❡s✳ ◆❛ ✜❣✉r❛ ✭❛✮ α > 0✱ t❡♠♦s ♦ ❡st❛❞♦ ♥♦r♠❛❧ ❡ ♥❛ ✜❣✉r❛ ✭❜✮ α < 0✱ t❡♠♦s ♦ ❡st❛❞♦ s✉♣❡r❝♦♥❞✉t♦r✳
❞♦ ♠❛t❡r✐❛❧✱ m∗ é ❛ ♠❛ss❛ ❡ e∗ é ❛ ❝❛r❣❛ ❞♦s ♣❛r❡s ❞❡ ❈♦♦♣❡r✱ A~ é ♦ ♣♦t❡♥❝✐❛❧ ✈❡t♦r
r❡❧❛❝✐♦♥❛❞♦ ❝♦♠ ♦ ❝❛♠♣♦ ❧♦❝❛❧H~ =∇ ×A~ ❡ H~0 é ♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❛♣❧✐❝❛❞♦✳
➱ ó❜✈✐♦ q✉❡✱ s❡ψ = 0✱ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❡♥❡r❣✐❛ s❡ r❡❞✉③ à ❞❡♥s✐❞❛❞❡ ❞❡ ❡♥❡r❣✐❛
❞♦ ❡st❛❞♦ ♥♦r♠❛❧ fn0 +h2/8π✱ ♦♥❞❡ h é ❛ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❧♦❝❛❧ ❡
♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❛♣❧✐❝❛❞♦✳ ❖s ♦✉tr♦s três t❡r♠♦s r❡st❛♥t❡s ❞❡s❝r❡✈❡♠ ♦s ❡❢❡✐t♦s ❞❛ s✉♣❡r❝♦♥❞✉t✐✈✐❞❛❞❡ q✉❡ ♣❛ss❛r❡♠♦s ❛ ❡①❛♠✐♥❛r ❛ s❡❣✉✐r✳
◆❛ ❛✉sê♥❝✐❛ ❞❡ ❝❛♠♣♦s ❡ ❣r❛❞✐❡♥t❡s✱ ✜❝❛♠♦s ❝♦♠
f−fn0 =α|Ψ|2+
β
2|Ψ|
4
, ✭✶✳✶✸✮
♦ q✉❛❧ ♣♦❞❡ s❡r ✈✐st♦ ❝♦♠♦ ✉♠❛ ❡①♣❛♥sã♦ ❡♠ sér✐❡ ❞❡ ♣♦tê♥❝✐❛s ❞❡ |Ψ|2 ❞❛ ❞✐❢❡r❡♥ç❛
❡♥tr❡ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❡♥❡r❣✐❛ ❞♦s ❡st❛❞♦s s✉♣❡r❝♦♥❞✉t♦r ❡ ♥♦r♠❛❧ ♣❛r❛ ✉♠ s✉♣❡r❝♦♥❞✉t♦r ❤♦♠♦❣ê♥❡♦ ❡ ♥❛ ❛✉sê♥❝✐❛ ❞❡ ❝❛♠♣♦s ♠❛❣♥ét✐❝♦s✱ ♥❛ q✉❛❧ s♦♠❡♥t❡ ♦s ❞♦✐s ♣r✐♠❡✐r♦s t❡r♠♦s sã♦ ❝♦♥s✐❞❡r❛❞♦s ❬✶❪✳ ❆ ❛✉sê♥❝✐❛ ❞❡ ❣r❛❞✐❡♥t❡s ❝♦rr❡s♣♦♥❞❡ ❛ ✉♠❛ r❡❣✐ã♦ ❜❡♠ ✐♥t❡r♥❛ ❞♦ s✉♣❡r❝♦♥❞✉t♦r ♦♥❞❡ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ♣❛r❡s ❞❡ ❈♦♦♣❡r ♥ã♦ ✈❛r✐❛ ❝♦♠ ❛ ♣♦s✐çã♦✳ ❆ss✉♠❡✲ s❡ q✉❡✱ ♥✉♠ ♣❡q✉❡♥♦ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣❡r❛t✉r❛s ♣ró①✐♠♦s ❞❡ Tc✱ ♦ ♣❛râ♠❡tr♦ β é ✉♠❛
❝♦♥st❛♥t❡ ♣♦s✐t✐✈❛ ❡ ✐♥❞❡♣❡♥❞❡♥t❡ ❞❛ t❡♠♣❡r❛t✉r❛ ❡α ❞❡♣❡♥❞❡ ❞❛ t❡♠♣❡r❛t✉r❛ ❞❛❞♦ ♣♦r α≈ −αo(1−T /Tc)✱ ♦♥❞❡αo é ✉♠❛ ❝♦♥st❛♥t❡ ♣♦s✐t✐✈❛✳
◗✉❛♥❞♦ α > 0 ❬❋✐❣✳ ✻ ✭❛✮❪✱ T > Tc✱ ♦ s✐st❡♠❛ ❡♥❝♦♥tr❛✲s❡ ♥♦ ❡st❛❞♦ ♥♦r♠❛❧ ❡
♦ ♠í♥✐♠♦ ❞❡ ❡♥❡r❣✐❛ ❧♦❝❛❧✐③❛✲s❡ ❡♠ Ψ = 0✳ P❛r❛ α < 0 ❬❋✐❣✳ ✻ ✭❜✮❪✱ T < Tc✱ ♦ s✐st❡♠❛
❡♥❝♦♥tr❛✲s❡ ♥♦ ❡st❛❞♦ s✉♣❡r❝♦♥❞✉t♦r ❡ ❛ ❡♥❡r❣✐❛ ♣♦ss✉✐ ❞♦✐s ♠í♥✐♠♦s✱ ❧♦❝❛❧✐③❛❞♦s ❡♠
Ψ =±p−α/β ✱ ❝♦♠ ✉♠ ✈❛❧♦r ❞❡ ❡♥❡r❣✐❛
f−fn0 =−
α2
