❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❖ ❈❊❆❘➪ ❈❊◆❚❘❖ ❉❊ ❈■✃◆❈■❆❙
❉❊P❆❘❚❆▼❊◆❚❖ ❉❊ ❋❮❙■❈❆
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❋❮❙■❈❆
❉❯❆❘❚❊ ❏❖❙➱ P❊❘❊■❘❆ ❉❊ ❙❖❯❙❆
P❘❖P❘■❊❉❆❉❊❙ ❊▲❊❚❘Ô◆■❈❆❙ ❉❖ ❋❖❙❋❖❘❊◆❖
❉❯❆❘❚❊ ❏❖❙➱ P❊❘❊■❘❆ ❉❊ ❙❖❯❙❆
P❘❖P❘■❊❉❆❉❊❙ ❊▲❊❚❘Ô◆■❈❆❙ ❉❖ ❋❖❙❋❖❘❊◆❖
❚❡s❡ ❞❡ ❉♦✉t♦r❛❞♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ ❈✉rs♦ ❞❡ Pós✲ ❣r❛❞✉❛çã♦ ❡♠ ❋ís✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ♥❡❝❡ssár✐♦s ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ❉♦✉t♦r ❡♠ ❋ís✐❝❛✳
❖r✐❡♥t❛❞♦r✿
Pr♦❢✳ ❉r✳ ❏♦ã♦ ▼✐❧t♦♥ P❡r❡✐r❛ ❏✉♥✐♦r ❈♦✲♦r✐❡♥t❛❞♦r✿
❉r✳ ❉✐❡❣♦ ❘❛❜❡❧♦ ❞❛ ❈♦st❛
❉❖❯❚❖❘❆❉❖ ❊▼ ❋❮❙■❈❆ ❉❊P❆❘❚❆▼❊◆❚❖ ❉❊ ❋❮❙■❈❆
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❋❮❙■❈❆ ❈❊◆❚❘❖ ❉❊ ❈■✃◆❈■❆❙
❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❖ ❈❊❆❘➪
❋♦rt❛❧❡③❛ ✲ ❈❊
❉❛❞♦s ■♥t❡r♥❛❝✐♦♥❛✐s ❞❡ ❈❛t❛❧♦❣❛çã♦ ♥❛ P✉❜❧✐❝❛çã♦ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá
❇✐❜❧✐♦t❡❝❛ ❞♦ ❈✉rs♦ ❞❡ ❋ís✐❝❛
❈✽✼✶t ❙♦✉s❛✱ ❉✉❛rt❡ ❏♦sé P❡r❡✐r❛ ❞❡
Pr♦♣r✐❡❞❛❞❡s ❊❧❡trô♥✐❝❛s ❞♦ ❋♦s❢♦r❡♥♦ ✴ ❉✉❛rt❡ ❏♦sé P❡r❡✐r❛ ❞❡ ❙♦✉s❛✳ ✲ ❋♦rt❛❧❡③❛✱2018✳
✷✵✶ ❢✳✿✐❧✳ ❛❧❣✉♠❛s ❝♦❧♦r✳ ❡♥❝✳❀ ✸✵ ❝♠✳
❚❡s❡ ✭❉♦✉t♦r❛❞♦ ❡♠ ❋ís✐❝❛✮ ✲ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá✱ ❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s✱ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛✱ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❋ís✐❝❛✱ ❋♦rt❛❧❡③❛✱2018✳
❖r✐❡♥t❛çã♦✿ Pr♦❢✳ ❉r✳ ❏♦ã♦ ▼✐❧t♦♥ P❡r❡✐r❛ ❏✉♥✐♦r✳ ❈♦♦r✐❡♥t❛çã♦✿ ❉r✳ ❉✐❡❣♦ ❘❛❜❡❧♦ ❞❛ ❈♦st❛✳
➪r❡❛ ❞❡ ❝♦♥❝❡♥tr❛çã♦✿ ❋ís✐❝❛ ❞❛ ▼❛tér✐❛ ❈♦♥❞❡♥s❛❞❛✳ ■♥❝❧✉✐ í♥❞✐❝❡✳
✶✳ ◆❛♥♦t❡❝♥♦❧♦❣✐❛✳ ✷✳ ▼✉❧t✐❝❛♠❛❞❛s ❞❡ ❢♦s❢♦r❡♥♦✳ ✸✳ ❙✐st❡♠❛s ❞❡ ❜❛✐①❛ ❞✐♠❡♥s✐♦♥❛❧✐❞❛❞❡✳ ✹✳ ◆❛♥♦✜t❛s ❞❡ ❢♦s❢♦r❡♥♦✳ ✺✳ Pr♦♣r✐❡❞❛❞❡s ❡❧❡trô♥✐❝❛s✳ ■✳ ❏✉♥✐♦r✱ ❏♦ã♦ ▼✐❧t♦♥ P❡r❡✐r❛✳ ■■✳ ❘❛❜❡❧♦ ❞❛ ❈♦st❛✱ ❉✐❡❣♦✳ ■❱✳ ❚ít✉❧♦✳
❉❯❆❘❚❊ ❏❖❙➱ P❊❘❊■❘❆ ❉❊ ❙❖❯❙❆
P❘❖P❘■❊❉❆❉❊❙ ❊▲❊❚❘Ô◆■❈❆❙ ❉❖ ❋❖❙❋❖❘❊◆❖
❚❡s❡ ❞❡ ❞♦✉t♦r❛❞♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ ❈✉rs♦ ❞❡ Pós✲❣r❛❞✉❛çã♦ ❡♠ ❋ís✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ♥❡❝❡ssár✐♦s ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ❉♦✉t♦r ❡♠ ❋ís✐❝❛✳
❆♣r♦✈❛❞❛ ❡♠✿ ✷✹✴✵✼✴✷✵✶✽✳
❇❆◆❈❆ ❊❳❆▼■◆❆❉❖❘❆
Pr♦❢✳ ❉r✳ ❏♦ã♦ ▼✐❧t♦♥ P❡r❡✐r❛ ❏✉♥✐♦r ✭❖r✐❡♥t❛❞♦r✮ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛ ✕ ❯❋❈
❉r✳ ❉✐❡❣♦ ❘❛❜❡❧♦ ❞❛ ❈♦st❛ ✭❈♦♦r✐❡♥t❛❞♦r✮
❉❡♣❛rt♠❡♥t ♦❢ ❊❧❡❝tr✐❝❛❧ ❛♥❞ ❈♦♠♣✉t❡r ❊♥❣✐♥❡❡r✐♥❣ ✕ ❯♥✐✈❡rs✐t② ♦❢ ▼✐♥♥❡s♦t❛
Pr♦❢✳ ●✐❧ ❞❡ ❆q✉✐♥♦ ❋❛r✐❛s ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛ ✕ ❯❋❈
Pr♦❢✳ ❊❞✉❛r❞♦ ❈♦st❛ ●✐rã♦ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ P✐❛✉í ✕ ❯❋P■
Pr♦❢✳ ❙✐❧✈✐❛ ❍❡❧❡♥❛ ❘♦❜❡rt♦ ❞❡ ❙❡♥❛
❆❣r❛❞❡❝✐♠❡♥t♦s
Pr✐♠❡✐r❛♠❡♥t❡✱ ❣♦st❛r✐❛ ❞❡ ❡①♣r❡ss❛r ♦s ♠❡✉s ♠❛✐s ♣r♦❢✉♥❞♦s ❛❣r❛❞❡❝✐♠❡♥t♦s à ♠✐♥❤❛ ❢❛♠í❧✐❛✱ ❡s♣❡❝✐❛❧♠❡♥t❡ ❛♦s ♠❡✉s ♣❛✐s ❘❛✐♠✉♥❞♦ ◆♦♥❛t♦ ❡ ▼❛r✐❛ ❞❛s ●r❛ç❛s ♣❡❧❛ ❡❞✉❝❛çã♦ q✉❡ à ♠✐♠ ❢♦✐ ❞❛❞❛ ❡ ♣❡❧♦s ✐♥❝❡♥t✐✈♦s ❛ss♦❝✐❛❞♦s às ♦♣♦rt✉♥✐❞❛❞❡s ❞❡ ❡st✉❞♦✳ ❚❛♠❜é♠ ❣♦st❛r✐❛ ❞❡ ❛❣r❛❞❡❝❡r à ♠✐♥❤❛ ❡s♣♦s❛ ❆♥❣❡❧✐❝❛ ❙❛♠❛r❛ ♣❡❧♦ ❛♠♦r✱ ❝♦♠♣❛♥❤❡✐r✐s♠♦ ❡ s✉♣♦rt❡✳
❆❣r❛❞❡ç♦ ❛♦ ♣r♦❢❡ss♦r ❆♥❞r❡② ❈❤❛✈❡s ♣♦r s✉❛s ❝♦♦r✐❡♥t❛çõ❡s✱ ❡♥s✐♥❛♠❡♥t♦s ❡ ❛♠✐③❛❞❡ ❞✉r❛♥t❡ ❣r❛♥❞❡ ♣❛rt❡ ❞❡ ♠✐♥❤❛ ❥♦r♥❛❞❛ ❛❝❛❞ê♠✐❝❛✱ ❛♦ Pr♦❢❡ss♦r ●✐❧ ❞❡ ❆q✉✐♥♦ ❋❛r✐❛s ♣❡❧♦ s✉♣♦rt❡ ❡ ❡♥❝♦r❛❥❛♠❡♥t♦ ❡ ❛♦ ♣r♦❢❡ss♦r ❏♦ã♦ ▼✐❧t♦♥ P❡r❡✐r❛ ❏r✳ ♣❡❧❛ ♦r✐❡♥t❛çã♦✱ ❛♠✐③❛❞❡✱ ❝♦♥✜❛♥ç❛ ❡ ♣❛❝✐ê♥❝✐❛ ❞✉r❛♥t❡ ♦s s❡✐s ❛♥♦s ❡♠ q✉❡ ♣❡r♠❛♥❡❝✐ ❝♦♠♦ s❡✉ ♦r✐❡♥t❛♥❞♦✳ ❆❣r❛✲ ❞❡ç♦ t❛♠❜é♠ ❛♦ ❉r✳ ❉✐❡❣♦ ❘❛❜❡❧♦ ❞❛ ❈♦st❛ ♣♦r s✉❛ ❝♦♦r✐❡♥t❛çã♦ ❡ ❛♠✐③❛❞❡ ❞✉r❛♥t❡ t♦❞♦ ♦ ♠❡✉ ♣❡rí♦❞♦ ❞❡ ❞♦✉t♦r❛♠❡♥t♦✳ ❆❣r❡❞❡ç♦ à t♦❞♦s ♦s ♣r♦❢❡ss♦r❡s ❞♦ ❞❡♣❛rt❛♠❡♥t♦ ❞❡ ❢ís✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá ✭❯❋❈✮✱ ❡ ❡♠ ❡s♣❡❝✐❛❧ àq✉❡❧❡s q✉❡ t✐✈❡r❛♠ ♣❛♣❡❧ ❢✉♥❞❛♠❡♥t❛❧ ♥❛ ♠✐♥❤❛ ❢♦r♠❛çã♦ ❛❝❛❞ê♠✐❝❛ ❛tr❛✈és ❞❡ s❡✉s ❝✉rs♦s ❡ ❞✐s❝✉ssõ❡s✳
❆♦s ♠❡✉s ❣r❛♥❞❡s ❛♠✐❣♦s ❞♦ ❞❡♣❛rt❛♠❡♥t♦ ❞❡ ❢ís✐❝❛✱ ❡♠ ❡s♣❡❝✐❛❧ ❛ ▲✉❛♥ ❱✐❡✐r❛✱ ♣❡❧❛ ✈❛❧✐♦s❛ ❛♠✐③❛❞❡✱ ♣❛r❝❡r✐❛ ❡ ❞✐s❝✉ssõ❡s q✉❡ ❛❥✉❞❛r❛♠ ❛ ❡♥r✐q✉❡❝❡r ♦s tr❛❜❛❧❤♦s ❞❡s❡♥✲ ✈♦❧✈✐❞♦s ❞✉r❛♥t❡ t♦❞❛ ♠✐♥❤❛ ❝❛rr❡✐r❛ ❛❝❛❞ê♠✐❝❛ ❡ ♠✐♥❤❛ ❢♦r♠❛çã♦✳ ❚❛♠❜é♠ ❡①♣r❡ss♦ ♠❡✉s ❛❣r❛❞❡❝✐♠❡♥t♦s ❛♦ ♠❡✉s ❡st✐♠❛❞♦s ❛♠✐❣♦s ●❛❜r✐❡❧ ❖❧✐✈❡✐r❛✱ ▲✉❝❛s ❙❛♠✐r✱ ❏♦❤♥❛t❤❛s ❉✬❛r❢✱ ❮❝❛r♦ ❘♦❞r✐❣✉❡s✱ ❱✐❝t♦r ◆♦❝r❛t♦ ❡ ▲❡✈✐ ❋❡❧✐① ♣❡❧♦ ✐♠❡♥s♦ ❝❛r✐♥❤♦ ❡ ❛♠✐③❛❞❡✳
✏❚❤❡r❡ ✐s ♥♦ ❣r❡❛t❡r ❡❝st❛s② t❤❛♥ t♦ ❦♥♦✇ ✇❤♦ ②♦✉ ❛r❡✳✑
✈✐✐✐
❘❡s✉♠♦
❆ ♣r♦❝✉r❛ ♣♦r ♥♦✈♦s ♠❛t❡r✐❛✐s ❝♦♠ ♣r♦♣r✐❡❞❛❞❡s ❡❧❡trô♥✐❝❛s út❡✐s t❡♠ ❧❡✈❛❞♦ ❛ ✉♠ ❝r❡s❝❡♥t❡ ✐♥t❡r❡ss❡ ♥❛ ✐♥✈❡st✐❣❛çã♦ ❞❡ ✉♠❛ ❝❧❛ss❡ ❞❡ só❧✐❞♦s ❧❛♠❡❧❛r❡s q✉❡ ♣♦❞❡♠ s❡r ❡s❢♦✲ ❧✐❛❞♦s ❛té ♦❜t❡r✲s❡ ♣♦✉❝❛s ❝❛♠❛❞❛s✳ ❊ss❡s ♥♦✈♦s ♠❛t❡r✐❛✐s ❜✐❞✐♠❡♥s✐♦♥❛✐s ✭✷❉✮✱ q✉❡ ❢♦r❛♠ tr❛③✐❞♦s à ❛t❡♥çã♦ ♣❡❧❛ ♣r♦❞✉çã♦ ❞♦ ❣r❛❢❡♥♦ ❡♠ ✷✵✵✹✱ t❡♠ ♠♦str❛❞♦ ♣♦ss✉✐r ♣r♦♣r✐❡❞❛❞❡s q✉❡ ♥ã♦ sã♦ ❡♥❝♦♥tr❛❞❛s ❡♠ s✉❛ ❢♦r♠❛ ❜✉❧❦✳ ❉❡♥tr❡ ❡ss❡s ♠❛t❡r✐❛✐s✱ ✉♠❛ ❛t❡♥çã♦ ❝♦♥s✐✲ ❞❡rá✈❡❧ t❡♠ s✐❞♦ ❞✐r❡❝✐♦♥❛❞❛ ❛♦ ❢ós❢♦r♦ ♥❡❣r♦✱ ✉♠ ❛❧ótr♦♣♦ ❞♦ ❢ós❢♦r♦✳ ❉✐❢❡r❡♥t❡♠❡♥t❡ ❞♦ ❣r❛❢❡♥♦✱ ♦ ❢ós❢♦r♦ ♥❡❣r♦ é ✉♠ s❡♠✐❝♦♥❞✉t♦r✱ ❡ s✉❛ ❛❧t❛ ♠♦❜✐❧✐❞❛❞❡ ❡❧❡trô♥✐❝❛ t♦r♥❛✲♦ ✉♠ ♣♦ssí✈❡❧ ❝❛♥❞✐❞❛t♦ ♣❛r❛ ❛♣❧✐❝❛çõ❡s ❡♠ ❞✐s♣♦s✐t✐✈♦s ❡❧❡trô♥✐❝♦s✳ ❯♠ ❛s♣❡❝t♦ ✐♠♣♦rt❛♥t❡ ❞❛ ❡str✉t✉r❛ ❡❧❡trô♥✐❝❛ ❞♦ ❢ós❢♦r♦ ♥❡❣r♦✱ ♣♦r ❡①❡♠♣❧♦✱ é ❛ ❞❡♣❡♥❞ê♥❝✐❛ ❞♦ ❣❛♣ ❞❡ ❡♥❡r❣✐❛s ❝♦♠ ♦ ♥ú♠❡r♦ ❞❡ ❝❛♠❛❞❛s✳ ❊①♣❡r✐♠❡♥t♦s ♠♦str❛r❛♠ q✉❡ ❡ss❛ ♣r♦♣r✐❡❞❛❞❡ ✈❛r✐❛ ❞❡≈2.0
❡❱ ✭♣❛r❛ ❛ ♠♦♥♦❝❛♠❛❞❛✮ à≈0.3❡❱ ✭♣❛r❛ ♦ ❜✉❧❦✮✱ ❝♦❜r✐♥❞♦ ✉♠❛ ❢❛✐①❛ ❞❡ ❢r❡q✉ê♥❝✐❛ ♥ã♦
♦❜s❡r✈❛❞❛ ❛♥t❡r✐♦r♠❡♥t❡ ♣❛r❛ ♦✉tr♦s ♠❛t❡r✐❛✐s ✷❉✳
❘❡❝❡♥t❡♠❡♥t❡✱ ✉♠❛ sér✐❡ ❞❡ ❡st✉❞♦s ♦❜t✐✈❡r❛♠ ❛ ❡str✉t✉r❛ ❞❡ ❜❛♥❞❛s ❞♦ ❢ós❢♦r♦ ♥❡❣r♦ ❛tr❛✈és ❞❡ ❝á❧❝✉❧♦s ❞❡ ♣r✐♠❡✐r♦s ♣r✐♥❝í♣✐♦s✱ ♠ét♦❞♦sk·p✱ ❛ss✐♠ ❝♦♠♦ ❛tr❛✈és ❞♦s ♠♦❞❡❧♦s
t✐❣❤t✲❜✐♥❞✐♥❣ ❡ ❞♦ ❝♦♥tí♥✉♦✳ ❖s r❡s✉❧t❛❞♦s ♠♦str❛r❛♠ q✉❡ ♦ ❢ós❢♦r♦ ♥❡❣r♦ ❛♣r❡s❡♥t❛ ✉♠❛ ❣r❛♥❞❡ ❛♥✐s♦tr♦♣✐❛ ♥❛s ♠❛ss❛ ❡❢❡t✐✈❛s ❡✱ ❛❞✐❝✐♦♥❛❧♠❡♥t❡✱ q✉❡ ♦ ❣❛♣ ♣♦❞❡ s❡r ♠♦❞✐✜❝❛❞♦ ❛tr❛✈és ❞❛ ❛♣❧✐❝❛çã♦ ❞❡ ♣♦t❡♥❝✐❛✐s ❡①t❡r♥♦s✳ ❆ ♠❛✐♦r✐❛ ❞❡ss❡s tr❛❜❛❧❤♦s ♥ã♦ ❝♦♥s✐❞❡r❛r❛♠ ♦s ❡❢❡✐t♦s ❞❛s t❡r♠✐♥❛çõ❡s ❞❛s ❜♦r❞❛s ❡ s♦♠❡♥t❡ ❝♦♥s✐❞❡r❛r❛♠ ♠♦♥♦❝❛♠❛❞❛s ❡ ❜✐❝❛♠❛❞❛s ❞❡ ❢ós❢♦r♦ ♥❡❣r♦✱ ❞❡✈✐❞♦ às ❝r❡s❝❡♥t❡s ❞❡♠❛♥❞❛s ❝♦♠♣✉t❛❝✐♦♥❛✐s ❝♦♠ ♦ ❛✉♠❡♥t♦ ❞♦ ♥ú♠❡r♦ ❞❡ ❝❛♠❛❞❛s✳
◆❡st❡ tr❛❜❛❧❤♦✱ ♣r♦♣♦♠♦s ❝♦♥❞✐çõ❡s ❞❡ ❝♦♥t♦r♥♦ ❜❛s❡❛❞❛s ♥❛s s✐♠❡tr✐❛s ❞❛s s✉❜r❡❞❡s ♣❛r❛ ♥❛♥♦✜t❛s ❞❡ ❢♦s❢♦r❡♥♦ ❝♦♠ ❜♦r❞❛s ③✐❣③❛❣ ❡ ❛r♠❝❤❛✐r ✉t✐❧✐③❛♥❞♦ ♦ ♠♦❞❡❧♦ ❞♦ ❝♦♥✲ tí♥✉♦ ❡ ♠♦str❛♠♦s q✉❡ ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♣❛r❛ ♦s ❡s♣❡❝tr♦s ❞❡ ❡♥❡r❣✐❛s ❡①✐❜❡♠ ❜♦❛ ❝♦♥❝♦r❞â♥❝✐❛ ❝♦♠ ♦ ♠♦❞❡❧♦ t✐❣❤t✲❜✐♥❞✐♥❣ ❞❡ ❝✐♥❝♦ ❤♦♣♣✐♥❣s✳ ❈♦♠♦ ✉♠❛ ❝♦♥s❡q✉ê♥❝✐❛✱ ❞❡♠♦♥str❛♠♦s q✉❡ ♦s ❣❛♣s ❞❡ ❡♥❡r❣✐❛s ♣❛r❛ ♥❛♥♦✜t❛s ❝♦♠ ❞✐❢❡r❡♥t❡s t❡r♠✐♥❛çõ❡s ♣♦s✲ s✉❡♠ ❞✐❢❡r❡♥t❡s ❧❡✐s ❞❡ ❡s❝❛❧❛✳ ❚❛♠❜é♠ ❡st❡♥❞❡♠♦s ♦ ♠♦❞❡❧♦ t✐❣❤t✲❜✐♥❞✐♥❣ ❡ ❞♦ ❝♦♥tí♥✉♦ ♣❛r❛ ❝♦♥s✐❞❡r❛r ❛♠♦str❛s ❞❡ ❢ós❢♦r♦ ♥❡❣r♦ ❝♦♠ ✉♠ ♥ú♠❡r♦ ❛r❜✐trár✐♦ ❞❡ ❝❛♠❛❞❛s✳ ▼♦s✲ tr❛♠♦s q✉❡ ♦ s✐st❡♠❛ ❞❡ ◆ ❝❛♠❛❞❛s ❛❝♦♣❧❛❞❛s ♣♦❞❡ s❡r ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ♠❛♣❡❛❞♦ ❡♠ ✉♠ s✐st❡♠❛ ❞❡ ◆ ❝❛♠❛❞❛s ❞❡s❛❝♦♣❧❛❞❛s✳ ❊①♣r❡ssõ❡s ♣❛r❛ ❛s ❜❛♥❞❛s ❞❡ ♠❡♥♦r❡s ❡♥❡r❣✐❛s ❞❡ ❡❧étr♦♥s ❡ ❜✉r❛❝♦s✱ ❛ss✐♠ ❝♦♠♦ s✉❛s ♠❛ss❛ ❡❢❡t✐✈❛s✱ sã♦ ❞❡r✐✈❛❞❛s✳ ❚❛❧ ❛♥á❧✐s❡ ♣❡r♠✐t❡ ♦ ❝á❧❝✉❧♦ ❞✐r❡t♦ ❞♦s ♥í✈❡✐s ❞❡ ▲❛♥❞❛✉ ❞♦ s✐st❡♠❛✱ ❝♦♠♦ s❡rá ❞✐s❝✉t✐❞♦✳
❆❜str❛❝t
❚❤❡ s❡❛r❝❤ ❢♦r ♥❡✇ ♠❛t❡r✐❛❧s ✇✐t❤ ✉s❡❢✉❧ ❡❧❡❝tr♦♥✐❝ ♣r♦♣❡rt✐❡s ❤❛s ❧❡❞ t♦ ❛♥ ✐♥❝r❡❛s✐♥❣ ✐♥t❡r❡st ♦♥ t❤❡ ✐♥✈❡st✐❣❛t✐♦♥ ♦❢ ❛ ❝❧❛ss ♦❢ ❧❛②❡r❡❞ s♦❧✐❞s t❤❛t ❝❛♥ ❜❡ ♣r♦❞✉❝❡❞ ❛s s✐♥❣❧❡ ♦r ❢❡✇ ❧❛②❡rs✳ ❚❤❡s❡ ♥❡✇ t✇♦✲❞✐♠❡♥s✐♦♥❛❧ ✭✷❉✮ ♠❛t❡r✐❛❧s✱ ✇❤✐❝❤ ✇❡r❡ ✜rst ❜r♦✉❣❤t t♦ ❛tt❡♥t✐♦♥ ❜② t❤❡ ♣r♦❞✉❝t✐♦♥ ♦❢ ❣r❛♣❤❡♥❡ ✐♥2004✱ ❤❛✈❡ ❜❡❡♥ s❤♦✇♥ t♦ ❞✐s♣❧❛② ♣r♦♣❡rt✐❡s t❤❛t ❛r❡ ♥♦t
❢♦✉♥❞ ✐♥ t❤❡✐r ❜✉❧❦ ❢♦r♠✳ ❆♠♦♥❣ t❤❡s❡ s✉❜st❛♥❝❡s✱ t❤❡r❡ ❤❛s ❜❡❡♥ ❝♦♥s✐❞❡r❛❜❧❡ ✐♥t❡r❡st ♦♥ t❤❡ st✉❞② ♦❢ ❜❧❛❝❦ ♣❤♦s♣❤♦r✉s✱ ❛♥ ❛❧❧♦tr♦♣❡ ♦❢ ♣❤♦s♣❤♦r✉s✳ ■♥ ❝♦♥tr❛st ✇✐t❤ ❣r❛♣❤❡♥❡✱ ❜❧❛❝❦ ♣❤♦s♣❤♦r✉s ✐s ❛ s❡♠✐❝♦♥❞✉❝t♦r✱ ❛♥❞ ✐ts ❤✐❣❤ ❡❧❡❝tr♦♥✐❝ ♠♦❜✐❧✐t② ♠❛❦❡s ✐t ❛ ♣♦ss✐❜❧❡ ❝❛♥❞✐❞❛t❡ ❢♦r ❞❡✈✐❝❡ ❛♣♣❧✐❝❛t✐♦♥s✳ ❖♥❡ ✐♠♣♦rt❛♥t ❛s♣❡❝t ♦❢ t❤❡ ❡❧❡❝tr♦♥✐❝ str✉❝t✉r❡ ♦❢ ❜❧❛❝❦ ♣❤♦s♣❤♦r✉s✱ ❢♦r ✐♥st❛♥❝❡✱ ✐s t❤❡ ❞❡♣❡♥❞❡♥❝❡ ♦❢ t❤❡ ❣❛♣ ♦♥ t❤❡ ♥✉♠❜❡r ♦❢ ❧❛②❡rs✳ ❊①♣❡r✐♠❡♥ts ❤❛✈❡ s❤♦✇♥ t❤❛t t❤✐s ♣r♦♣❡rt② ✈❛r✐❡s ❢r♦♠ ≈2.0 ❡❱ ✭❢♦r t❤❡ ♠♦♥♦❧❛②❡r✮ t♦ ≈0.3 ❡❱ ✭❢♦r t❤❡ ❜✉❧❦✮✱ ❝♦✈❡r✐♥❣ ❛ ❢r❡q✉❡♥❝② r❛♥❣❡ ♥♦t ♣r❡✈✐♦✉s❧② ♦❜s❡r✈❡❞ ✐♥ ♦t❤❡r ✷❉
♠❛t❡r✐❛❧s
❘❡❝❡♥t❧②✱ ❛ s❡r✐❡s ♦❢ ❝❛❧❝✉❧❛t✐♦♥s ❤❛✈❡ ♦❜t❛✐♥❡❞ t❤❡ ❜❛♥❞ str✉❝t✉r❡ ♦❢ ❜❧❛❝❦ ♣❤♦s♣❤♦r✉s✱ ❜♦t❤ ❢r♦♠ ❛ ✜rst ♣r✐♥❝✐♣❧❡s ❛♣♣r♦❛❝❤❡s✱k·p♠❡t❤♦❞s✱ ❛s ✇❡❧❧ ❛s t✐❣❤t✲❜✐♥❞✐♥❣ ❛♥❞ ❝♦♥t✐✲
♥✉✉♠ ♠♦❞❡❧s✳ ❚❤❡ r❡s✉❧ts ❤❛✈❡ s❤♦✇♥ t❤❛t ❜❧❛❝❦ ♣❤♦s♣❤♦r✉s ♣r❡s❡♥ts ❛ ❧❛r❣❡ ❛♥✐s♦tr♦♣✐❝ ❡✛❡❝t✐✈❡ ♠❛ss❡s ❛♥❞✱ ✐♥ ❛❞❞✐t✐♦♥✱ t❤❛t t❤❡ ❣❛♣ ✐ts❡❧❢ ❝❛♥ ❜❡ ♠♦❞✐✜❡❞ ❜② t❤❡ ❛♣♣❧✐❝❛t✐♦♥ ♦❢ ❛♥ ❡①t❡r♥❛❧ ❜✐❛s✳ ▼♦st ♦❢ t❤❡s❡ ✇♦r❦s ❤❛✈❡ ♥♦t ❝♦♥s✐❞❡r❡❞ t❤❡ ❡✛❡❝ts ♦❢ ❡❞❣❡ t❡r✲ ♠✐♥❛t✐♦♥ ❛♥❞ ♦♥❧② ❝♦♥s✐❞❡r❡❞ s✐♥❣❧❡ ♦r ❜✐❧❛②❡r ❜❧❛❝❦ ♣❤♦s♣❤♦r✉s✱ ❞✉❡ t♦ t❤❡ ✐♥❝r❡❛s✐♥❣ ❝♦♠♣✉t❛t✐♦♥❛❧ ❞❡♠❛♥❞s ❛s t❤❡ ♥✉♠❜❡r ♦❢ ❧❛②❡rs ✐s ✐♥❝r❡❛s❡❞✳
■♥ t❤✐s ✇♦r❦✱ ✇❡ ♣r♦♣♦s❡ ❜♦✉♥❞❛r② ❝♦♥❞✐t✐♦♥s ❜❛s❡❞ ♦♥ s✉❜❧❛tt✐❝❡ s②♠♠❡tr✐❡s ❢♦r ❜❧❛❝❦ ♣❤♦s♣❤♦r✉s ♥❛♥♦r✐❜❜♦♥s ✇✐t❤ ③✐❣③❛❣ ❛♥❞ ❛r♠❝❤❛✐r ❡❞❣❡s ✉s✐♥❣ t❤❡ ❝♦♥t✐♥✉✉♠ ❛♣♣r♦❛❝❤ ❛♥❞ s❤♦✇ t❤❛t ♦✉r r❡s✉❧ts ❢♦r t❤❡ ❡♥❡r❣② s♣❡❝tr❛ ❡①❤✐❜✐t ❣♦♦❞ ❛❣r❡❡♠❡♥t ✇✐t❤ t❤♦s❡ ♦❜t❛✐✲ ♥❡❞ ❜② ✉s✐♥❣ t❤❡ ✜✈❡✲♣❛r❛♠❡t❡r t✐❣❤t✲❜✐♥❞✐♥❣ ♠♦❞❡❧✳ ❆s ❛ ❝♦♥s❡q✉❡♥❝❡✱ ✇❡ ❞❡♠♦♥str❛t❡ t❤❛t t❤❡ ❜❛♥❞s ❣❛♣s ❢♦r ♥❛♥♦r✐❜❜♦♥s ✇✐t❤ ❞✐✛❡r❡♥t t❡r♠✐♥❛t✐♦♥s ❤❛✈❡ ❞✐✛❡r❡♥t s❝❛❧✐♥❣ ❧❛✇s✳ ❲❡ ❛❧s♦ ❡①t❡♥❞ t❤❡ ♣r❡✈✐♦✉s ♣r♦♣♦s❡❞ t✐❣❤t✲❜✐♥❞✐♥❣ ❛♥❞ ❝♦♥t✐♥✉✉♠ ❛♣♣r♦❛❝❤❡s t♦ ❝♦♥s✐❞❡r ❜❧❛❝❦ ♣❤♦s♣❤♦r✉s ✜❧♠s ✇✐t❤ ❛r❜✐tr❛r② ♥✉♠❜❡rs ♦❢ ❧❛②❡rs✳ ❲❡ s❤♦✇ t❤❛t ❛ s②st❡♠ ♦❢ ◆ ❝♦✉♣❧❡❞ ❜❧❛❝❦ ♣❤♦s♣❤♦r✉s ❧❛②❡rs ❝❛♥ ❜❡ ❛♣♣r♦①✐♠❛t❡❧② ♠❛♣♣❡❞ ✐♥t♦ ❛ s②st❡♠ ♦❢ ◆ ✉♥❝♦✉♣❧❡❞ s✐♥❣❧❡ ❧❛②❡rs✳ ❊①♣r❡ss✐♦♥s ❢♦r t❤❡ ❧♦✇✲❡♥❡r❣② ❡❧❡❝tr♦♥ ❛♥❞ ❤♦❧❡ ❜❛♥❞s✱ ❛s ✇❡❧❧ ❛s t❤❡✐r ❡✛❡❝t✐✈❡ ♠❛ss❡s ❛r❡ ❞❡r✐✈❡❞✳ ❚❤✐s ✐♥ t✉r♥ ♣❡r♠✐ts ❛ str❛✐❣❤t❢♦r✇❛r❞ ❝❛❧❝✉❧❛t✐♦♥ ♦❢ t❤❡ ▲❛♥❞❛✉ ❧❡✈❡❧ s♣❡❝tr✉♠ ♦❢ t❤❡ s②st❡♠✱ ❛s ✇✐❧❧ ❜❡ ❛❧s♦ ❞✐s❝✉ss❡❞ ❤❡r❡✳
❙✉♠ár✐♦
▲✐st❛ ❞❡ ❋✐❣✉r❛s ①✐✐
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ①✈✐✐✐
✶ ■♥tr♦❞✉çã♦ ✷✷
✷ ❋♦s❢♦r❡♥♦ ✷✺
✷✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✷ ❊str✉t✉r❛ ❡ ♣r♦♣r✐❡❞❛❞❡s ❞♦ ♠❛t❡r✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✷✳✶ ❊str✉t✉r❛ ❝r✐st❛❧✐♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✷✳✷✳✷ ❊str✉t✉r❛ ❞❡ ❜❛♥❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✷✳✷✳✸ Pr♦♣r✐❡❞❛❞❡s ót✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✷✳✸ ❆♣❧✐❝❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✷✳✸✳✶ ❉✐s♣♦s✐t✐✈♦s ❡❧❡trô♥✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✷✳✸✳✷ ❉✐s♣♦s✐t✐✈♦s ♦♣t♦❡❧❡trô♥✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✷✳✹ ❙í♥t❡s❡ ❡ ❞❡s❛✜♦s r❡♠❛♥❡s❝❡♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✷✳✹✳✶ ❙í♥t❡s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✷✳✹✳✷ ❉❡s❛✜♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼
✸ ▼♦❞❡❧♦ t❡ór✐❝♦ ✹✵
✸✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✸✳✷ ❖ ♠♦❞❡❧♦ t✐❣❤t✲❜✐♥❞✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✸✳✸ ❆♣r♦①✐♠❛çã♦ ❞♦ ❝♦♥tí♥✉♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✸✳✹ ❆♣r♦①✐♠❛çã♦ ❞❛ ♠❛ss❛ ❡❢❡t✐✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷
✹ ◆❛♥♦✜t❛s ❞❡ ❢♦s❢♦r❡♥♦ ✺✺
①✐
✹✳✹ ◆❛♥♦✜t❛s ❩✐❣③❛❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✹✳✺ ▲❡✐ ❞❡ ❡s❝❛❧❛ ♣❛r❛ ♦s ❣❛♣s ❞❡ ♥❛♥♦✜t❛s ❞❡ ❢♦s❢♦r❡♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✹✳✻ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✹✳✼ ▼♦❞❡❧♦ t✐❣❤t✲❜✐♥❞✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✹✳✼✳✶ ▼♦♥♦❝❛♠❛❞❛ ❞❡ ❢♦s❢♦r❡♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✹✳✼✳✷ ❇✐❝❛♠❛❞❛ ❞❡ ❢♦s❢♦r❡♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✹✳✼✳✸ ◆ ❝❛♠❛❞❛s ❞❡ ❢♦s❢♦r❡♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✹✳✽ ❆♣r♦①✐♠❛çã♦ ❞♦ ❝♦♥tí♥✉♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✹✳✽✳✶ ▼♦♥♦❝❛♠❛❞❛ ❞❡ ❢♦s❢♦r❡♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✹✳✽✳✷ ❇✐❝❛♠❛❞❛ ❞❡ ❢♦s❢♦r❡♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✹✳✽✳✸ ◆ ❝❛♠❛❞❛s ❞❡ ❢♦s❢♦r❡♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✹✳✾ ◆í✈❡✐s ❞❡ ▲❛♥❞❛✉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺
✺ ❈♦♥❝❧✉sõ❡s ✽✽
❆♣ê♥❞✐❝❡ ❆
❋❛t♦r❡s ❞❡ ❊str✉t✉r❛ ❞♦ ♠♦❞❡❧♦ t✐❣❤t✲❜✐♥❞✐♥❣ ❞❡ ❞❡③✲❤♦♣♣✐♥❣s ✾✵ ❆♣ê♥❞✐❝❡ ❇
❚r❛♥s❢♦r♠❛çã♦ ✉♥✐tár✐❛ ♣❛r❛ ❛ ❜✐❝❛♠❛❞❛ ❞❡ ❋ós❢♦r♦ ♥❡❣r♦ ✾✸ ❆♣ê♥❞✐❝❡ ❈
P✉❜❧✐❝❛çõ❡s r❡❧❛❝✐♦♥❛❞❛s ✾✹
❆♣ê♥❞✐❝❡ ❉
❚r❛❜❛❧❤♦s ❡♠ ❛♥❞❛♠❡♥t♦ ✾✻
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✷✳✶ ■♠❛❣❡♥s ❞❛ ❡str✉t✉r❛ ❞❡ ♠✉❧t✐♣❧❛s ❝❛♠❛❞❛s ❞❡ ❢♦s❢♦r❡♥♦ ♦❜t✐❞❛s ❛tr❛✈és ❞❡ ♠✐❝r♦s❝♦♣✐❛ ❡❧❡trô♥✐❝❛ ❞❡ ✈❛rr❡❞✉r❛ ♣♦r tr❛♥s♠✐ssã♦ ✭❙❚❊▼✮✳ ✭❛✮ ❱✐st❛ s✉✲ ♣❡r✐♦r✱ ❛♦ ❧♦♥❣♦ ❞❛ ❞✐r❡çã♦ ❝r✐st❛❧♦❣rá✜❝❛ ❬✵✵✶❪✱ ❞♦ ❢ós❢♦r♦ ♥❡❣r♦ ❝♦♠♣❛r❛❞❛ ❝♦♠ ✉♠ ♠♦❞❡❧♦ ❞❛ ❡str✉t✉r❛✳ ✭❜✮ ❱✐st❛ ❛♦ ❧♦♥❣♦ ❞❛ ❞✐r❡çã♦ ❝r✐st❛❧♦❣rá✜❝❛ ❬✶✵✶❪✳ ✭❝✮ ■♠❛❣❡♠ ❞❡ ❙❚❊▼ ❝❛♣t✉r❛❞❛ ❞❛s ❜♦r❞❛s ❞❡ ✉♠❛ ❛♠♦str❛ ❞❡ ♠✉❧✲ t✐❝❛♠❛❞❛s ❞❡ ❢♦s❢♦r❡♥♦ ♠♦str❛♥❞♦ ♦ ❡♠♣✐❧❤❛♠❡♥t♦ ❞❛s ♠❡s♠❛s✱ ❛♦ ❧♦♥❣♦ ❞❛ ❞✐r❡çã♦ ❬✶✵✵❪✳ ✭❞✮ ❆♠♣❧✐❛çã♦ ❞❛ r❡❣✐ã♦ ❞❡st❛❝❛❞❛ ❡♠ ✭❝✮✳ ❆s ✐♠❛❣❡♥s ❢♦r❛♠ t✐r❛❞❛s ❞❛ ❘❡❢✳ ❬✸✽❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✷✳✷ ✭❛✮ ❊str✉t✉r❛ ❞❡ ✉♠❛ ♠♦♥♦❝❛♠❛❞❛ ❞❡ ❢ós❢♦r♦ ♥❡❣r♦ ✭❢♦s❢♦r❡♥♦✮✳ ❆s ❝♦♥s✲
t❛♥t❡s ❞❡ r❡❞❡ ❛♦ ❧♦♥❣♦ ❞❛s ❞✐r❡çõ❡s ❛r♠❝❤❛✐r ❡ ③✐❣③❛❣ sã♦ a ❡ b✱ r❡s♣❡❝✲
t✐✈❛♠❡♥t❡✳ ✭❜✮ ❊str✉t✉r❛ ❞❡ ♠✉❧t✐❝❛♠❛❞❛s ❞❡ ❢♦s❢♦r❡♥♦✳ ❆s ❝❛♠❛❞❛s sã♦ ❛❝♦♣❧❛❞❛s ❞❡✈✐❞♦ às ✐♥t❡r❛çõ❡s ❞❡ ✈❛♥ ❞❡r ❲❛❛❧ q✉❡✱ ♣❛r❛ ♦ ❝❛s♦ ♣❛rt✐❝✉❧❛r ❞♦ ❜✉❧❦ ✭✐♥✜♥✐t❛s ❝❛♠❛❞❛s ❡♠♣✐❧❤❛❞❛s✮✱ ❧❡✈❛ à ✉♠❛ ❝♦♥st❛♥t❡ ❞❡ r❡❞❡ ❛♦ ❧♦♥❣♦ ❞❛ ❞✐r❡çã♦ z ✐❣✉❛❧ ❛c✳ ❋✐❣✉r❛s ❛❞❛♣t❛❞❛s ❞❛ ❘❡❢✳ ❬✷✸❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼
①✐✐✐
✷✳✹ ❆ tr❛♥s✐çã♦ ❞❡ ❢❛s❡ t♦♣♦❧ó❣✐❝❛ q✉❡ ♦❝♦rr❡ ♥♦ ❝❛s♦ ❞❛ ❜✐❝❛♠❛❞❛ ❞❡ ❢♦s❢♦r❡♥♦ s♦❜ ❡❢❡✐t♦s ❞❡ ✉♠ ❝❛♠♣♦ ❡❧étr✐❝♦ ♣❡r♣❡♥❞✐❝✉❧❛r✳ ❊♠ ✭❛✮ ♦ ❝❛♠♣♦ ❡❧étr✐❝♦ ❛♣❧✐❝❛❞♦ é ♠❡♥♦r q✉❡ ♦ ✈❛❧♦r ❝rít✐❝♦ ♣❛r❛ ♦ q✉❛❧ ♦ ❣❛♣ ❛♥✉❧❛✲s❡✱ ❡♥q✉❛♥t♦ q✉❡ ❡♠ ✭❜✮ ♦ ❝❛♠♣♦ ❡❧étr✐❝♦ é ♠❛✐♦r q✉❡ ♦ ✈❛❧♦r ❝rít✐❝♦✳ ◆♦s s✉❜♣❛✐♥é✐s ❞❛s ✜❣✉r❛s ✭❛✮ ❡ ✭❜✮ sã♦ ❛♣r❡s❡♥t❛❞♦s r❡s✉❧t❛❞♦s ❛❜✲✐♥✐t✐♦ ♣❛r❛ ❛ ❡str✉t✉r❛ ❞❡ ❜❛♥❞❛s ❛♦ ❧♦♥❣♦ ❞❛s ❞✐r❡çõ❡s ✭✶✮ ③③ ❡ ✭✷✮ ❛❝✳ ✭❝✮ ❊str✉t✉r❛s ❞❡ ❜❛♥❞❛s ♦❜t✐❞❛s ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡ ♥❛s ♣r♦①✐♠✐❞❛❞❡s ❞♦ ♣♦♥t♦ Γ✱ ✭✶✮ ❛♥t❡s ❡ ✭✷✮
❞❡♣♦✐s ❞❛ ❛♣❧✐❝❛çã♦ ❞❡ ✉♠❛ ❜✐❛s✳ ❆ ❧✐♥❤❛ ❛♠❛r❡❧❛ ❡♠ ✭✶✮ ♠♦str❛ ❛ ❜❛♥❞❛ ❞❡ ❝♦♥❞✉çã♦ ♥ã♦ ♦❝✉♣❛❞❛ ❞❛ ❜✐❝❛♠❛❞❛✱ ♦❜t✐❞❛ ❞♦ ♠♦❞❡❧♦ t✐❣❤t✲❜✐♥❞✐♥❣✳ ❊♠ ✭✸✮ ♦❜s❡r✈❛✲s❡ ✉♠ ♠❛♣❛ ❞❡ ❡♥❡r❣✐❛ ❝♦♥st❛♥t❡ ❞❡st❛❝❛♥❞♦ ❛ ♣♦s✐çã♦ ❞❡ ❞♦✐s ❝♦♥❡s ❞❡ ❉✐r❛❝✳ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❛s ❘❡❢s✳ ❬✺✸✱ ✺✹❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✷✳✺ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♦s ✈❛❧♦r❡s ❞♦s ❣❛♣s ❞❡ ❡♥❡r❣✐❛ ♣❛r❛ ❞✐❢❡r❡♥t❡s s❡♠✐❝♦♥✲
❞✉t♦r❡s ✷❉ ❡ ❝♦♥✈❡♥❝✐♦♥❛✐s✳ ❆s ❜❛rr❛s ❤♦r✐③♦♥t❛✐s ✐♥❞✐❝❛♠ ♦ ✐♥t❡r✈❛❧♦ ❞❡ ✈❛❧♦r❡s ❞♦s ❣❛♣s ♣♦ssí✈❡✐s ❞❡ s❡r❡♠ ❛❧❝❛♥ç❛❞♦s ❛tr❛✈és ❞❡ ❢❛t♦r❡s ❡①t❡r♥♦s✱ t❛✐s ❝♦♠♦ ❝❛♠♣♦s ❡ t❡♥sõ❡s✱ ♦✉ ✐♥t❡r♥♦s✱ t❛✐s ❝♦♠♦ ♥ú♠❡r♦ ❞❡ ❝❛♠❛❞❛s ❡ ❞♦♣❛❣❡♠✳ ❖s ✐♥t❡r✈❛❧♦s ❞❡ ❣❛♣s r❡q✉❡r✐❞♦s ♣❛r❛ ❝❡rt❛s ❛♣❧✐❝❛çõ❡s sã♦ ✐♥❞✐❝❛❞♦s ♣❡❧❛s ❜❛rr❛s ♥❛ ♣❛rt❡ ❞❡ ❜❛✐①♦ ❞❛ ✜❣✉r❛✳ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❛ ❘❡❢✳ ❬✹✸❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✷✳✻ ❘❡♣r❡s❡♥t❛çã♦ ♣♦❧❛r ❞♦ ❝♦❡✜❝✐❡❛♥t❡ ❞❡ ❛❜s♦rçã♦ ❞❡ ♠✉❧t✐❝❛♠❛❞❛s ❞❡ ❢♦s❢♦✲
r❡♥♦ ♣❛r❛ ❧✉③ ♥♦r♠❛❧♠❡♥t❡ ✐♥❝✐❞❡♥t❡ ❝♦♠ ❡♥❡r❣✐❛s ❞❡ ❡①❝✐t❛çã♦ ♠❛✐♦r❡s q✉❡ ♦ ❣❛♣ ♦❜t✐❞❛ t❡♦r✐❝❛♠❡♥t❡ ✭❡sq✉❡r❞❛✮✳ ❘❡♣r❡s❡♥t❛çã♦ ♣♦❧❛r ❞♦ ❡s♣❡❝tr♦ ❞❡ ❡①t✐♥çã♦ ♦❜t✐❞♦ ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡ ♣❛r❛ ✉♠❛ ❛♠♦str❛ ❞❡ ♠✉❧t✐❝❛♠❛❞❛s ❞❡ ❢♦s❢♦r❡♥♦ s♦❜r❡ ✉♠ s✉❜str❛t♦ ❞❡ ❙✐❖2 ✭❞✐r❡✐t❛✮✳ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❛ ❘❡❢✳ ❬✹✽❪✳ ✸✷
✷✳✼ ✭❛✮ ❖ ♣❛✐♥❡❧ s✉♣❡r✐♦r ♠♦str❛ ✉♠ ❡sq✉❡♠❛ ❞❡ ✉♠ tr❛♥s✐st♦r ❞❡ ❡❢❡✐t♦ ❞❡ ❝❛♠♣♦ ❜❛s❡❛❞♦ ❡♠ ❢♦s❢♦r❡♥♦✱ ♦♥❞❡ ♦s ❝♦♥t❛t♦s ❢♦r❛♠ ❞❡♣♦s✐t❛❞♦s s♦❜r❡ ❛ ❛♠♦str❛ ❞❡ ❢♦s❢♦r❡♥♦ ❛tr❛✈és ❞♦s ♠ét♦❞♦s ❞✐s❝✉t✐❞♦s ♥❛ ❘❡❢✳ ❬✽❪✳ ❖ ♣❛✐♥❡❧ ✐♥❢❡r✐♦r ♠♦str❛ ♦ ✈❛❧♦r ❞❛ ❡s♣❡ss✉r❛ ❞❛ ❛♠♦str❛ ❞❡ ❢♦s❢♦r❡♥♦ ♦❜t✐❞♦ ❡①♣❡✲ r✐♠❡♥t❛❧♠❡♥t❡✳ ✭❜✮ ❈♦rr❡♥t❡ ❙♦✉r❝❡✲❉r❛✐♥ ❝♦♠♦ ❢✉♥çã♦ ❞❛ ✈♦❧t❛❣❡♠✱ Vg✱
✐♥❞✉③✐❞❛ ❛tr❛✈és ❞❡ ✉♠ s✉❜str❛t♦ ❞❡ ❙✐ ❞❡ ✺ ♥♠ ❞❡ ❡s♣❡ss✉r❛ ❛ t❡♠♣❡r❛t✉r❛ ❛♠❜✐❡♥t❡✳ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❛ ❘❡❢✳ ❬✽❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✷✳✽ ✭❛✮ ❊s❜♦ç♦ ❞♦ ❡s♣❡❝tr♦ ❡❧❡tr♦♠❛❣♥ét✐❝♦ ❞❡st❛❝❛♥❞♦ ❛s r❡❣✐õ❡s ❞♦ ✈✐sí✈❡❧ ❡
❞♦ ✐♥❢r❛✈❡r♠❡❧❤♦✳ ❖s ❚▼❉s✱ ❛ss✐♠ ❝♦♠♦ ♦ ▼♦❙2✱ ♣♦ss✉❡♠ ❣❛♣s ♥❛ ❢❛✐①❛ ❞♦
✈✐sí✈❡❧✱ ♦ ❢♦s❢♦r❡♥♦ ♥❛ ❢❛✐①❛ ❞♦ ✈✐sí✈❡❧ ❛♦ ✐♥❢r❛✈❡r♠❡❧❤♦ ♣ró①✐♠♦ ❡ ♦ ❣r❛❢❡♥♦ ♥❛ tr❛s✐çã♦ ❞♦ ✐♥❢r❛✈❡r♠❡❧❤♦ ✭❢❛r✲✐♥❢r❛r❡❞✮ ❛♦ t❡r❛❤❡rt③✳ ✭❜✮ ❡s❜♦ç♦ ❞❡ ✉♠ ❋❊❚ ❜❛s❡❛❞♦ ❡♠ ❢♦s❢♦r❡♥♦ s♦❜ ❡❢❡✐t♦s ❞❡ ✐❧✉♠✐♥❛çã♦✳ ✭❝✮ ❡ ✭❞✮ ♠♦str❛♠ ❛ ❢♦t♦❝♦rr❡♥t❡ ❡ ❛ r❡s♣♦♥s✐✈✐❞❛❞❡ ót✐❝❛ ♣❛r❛ ❝♦♠♣r✐♠❡♥t♦s ❞❡ ♦♥❞❛ ❞♦ ✈✐sí✈❡❧ ❛♦ ✐♥❢r❛✈❡r♠❡❧❤♦❬✻✻❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✷✳✾ ❊sq✉❡♠❛t✐③❛çã♦ ❞❡ ♠ét♦❞♦s ♣❛r❛ ❛ sí♥t❡s❡ ❞❡ ♠❛t❡r✐❛✐s ✷❉✳ ✭❛✮ ❈❧✐✈❛❣❡♠
①✐✈
✷✳✶✵ ✭❛✮ ■♠❛❣❡♠ ❞❡ ♠✐❝r♦s❝♦♣✐❛ ❡❧❡trô♥✐❝❛ ❞❡ ✈❛rr❡❞✉r❛ ✭❙❊▼✱ s✐♥❣❧❛ ❡♠ ✐♥❣❧ês ♣❛r❛ s❝❛♥♥✐♥❣ ❡❧❡❝tr♦♥ ♠✐❝r♦s❝♦♣②✮ ❞❡ ✉♠❛ ❛♠♦str❛ ❞❡ ✻✵✵ ♥♠ ❞❡ ❢ós❢♦r♦ ♥❡❣r♦✳ ✭❜✮ P❛❞rã♦ ❞❡ ❞✐❢r❛çã♦ ❞❡ ❡❧étr♦♥s ♥✉♠❛ ❞❛❞❛ ár❡❛ ❞❛s ❛♠♦str❛s ❞❡ ❢ós❢♦r♦ ♥❡❣r♦ ✭❙❆❊❉ ✲ ❙❡❧❡❝t❡❞ ❛r❡❛ ❡❧❡❝tr♦♥ ❞✐✛r❛❝t✐♦♥✮ ♠♦str❛♥❞♦ ❛ ❝r✐st❛❧✐♥✐❞❛❞❡ ❞❛ ❛♠♦str❛✳ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❛ ❘❡❢✳ ❬✻✾❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✷✳✶✶ ■♠❛❣❡♥s ❞❛ ❞❡❣r❛❞❛çã♦ ❞♦ ❢♦s❢♦r❡♥♦ ♥♦ ❛r ♦❜t✐❞❛s ❛tr❛✈és ❞❡ ✉♠ ♠✐❝r♦s❝ó✲
♣✐♦ ót✐❝♦ ✭❛✮ ❡ ❛tr❛✈és ❞❡ ✉♠ ♠✐❝r♦s❝ó♣✐♦ ❞❡ ❢♦rç❛ ❛tô♠✐❝❛ ✭❆❋▼✱ s✐♥❣❧❛ ❡♠ ✐♥❣❧ês ♣❛r❛ ❛t♦♠✐❝ ❢♦r❝❡ ♠✐❝r♦s❝♦♣②✮ ♥♦s t❡♠♣♦ ✐♥❞✐❝❛❞♦s ❛♣ós ❛ ❡s❢♦❧✐❛çã♦✳ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❛ ❘❡❢✳ ❬✼✸❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✸✳✶ ●❡♦♠❡tr✐❛ ❞❡ ✉♠❛ ♠♦♥♦❝❛♠❛❞❛ ❞❡ ❢ós❢♦r♦ ♥❡❣r♦✳ ✭❛✮ ❱✐st❛ ❧❛t❡r❛❧ ✭❡s✲
q✉❡r❞❛✮ ❡ ❞❡ ❝✐♠❛ ✭❞✐r❡✐t❛✮ ❞❛ ❡str✉t✉r❛ ❡♥rr✉❣❛❞❛ ❞♦ ❢♦s❢♦r❡♥♦✱ ❞❡st❛✲ ❝❛♥❞♦ ❛ ♦r✐❡♥t❛çã♦ ❞♦s ❡✐①♦s✱ ❛ ❝é❧✉❧❛ ✉♥✐tár✐❛ ✭r❡tâ♥❣✉❧♦ ❛③✉❧ ❝❧❛r♦✮✱ ❛ss✐♠ ❝♦♠♦ ❛s q✉❛tr♦ s✉❜r❡❞❡s ❞❡♥♦t❛❞❛s ♣♦r ❆✱ ❇✱ ❈ ❡ ❉✳ ❊♠ ✭❜✮ ❞❡st❛♠✲s❡ ❛s ♦s ♣❛râ♠❡tr♦s ❡str✉t✉r❛✐s ❞❛ ♠♦♥♦❝❛♠❛❞❛✿ ❛s ❞✐stâ♥❝✐❛s ❡♥tr❡ ♦s át♦♠♦s ✭❡sq✉❡r❞❛✮ ❡ ♦s â♥❣✉❧♦s ❞❡ ❧✐❣❛çã♦ ✭❞✐r❡✐t❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✸✳✷ ❉❡❝♦♠♣♦s✐çã♦ ♦r❜✐t❛❧ ❞❛s ❜❛♥❞❛s ❞❡ ❡♥❡r❣✐❛ ♠❛✐s ♣ró①✐♠❛s ❛♦ ♥í✈❡❧ ❞❡
❋❡r♠✐ ♣❛r❛ ❛ ♠♦♥♦❝❛♠❛❞❛ ❞❡ ❢♦s❢♦r❡♥♦✳ ❖ ♣❛✐♥❡❧ ❞✐r❡✐t♦ ♠♦str❛ ❛ ❞❡♥s✐✲ ❞❛❞❡ ❞❡ ❡st❛❞♦s ❝♦rr❡s♣♦♥❞❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✸✳✸ ❊s❜♦ç♦ ❞♦s ✈❡t♦r❡s ❝♦♥❡❝t❛♥❞♦ ♦s át♦♠♦s ❞❡ ❢ós❢♦r♦s ❞❡ ❞✐❢❡r❡♥t❡s s✉❜r❡❞❡s
❡♠ ✭❛✮ ❡ ♦s r❡s♣❡❝t✐✈♦s ❤♦♣♣✐♥❣s ❛ss♦❝✐❛❞♦s ❡♠ ✭❜✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✸✳✹ ❙✐♠❡tr✐❛s ❞❛s s✉❜r❡❞❡s ❞♦ ❢♦s❢♦r❡♥♦✳ ❆ ❡str✉t✉r❛s ❡♠ ✭❜✮ ❡ ✭❝✮ sã♦ ♦❜t✐✲
❞❛s ❛tr❛✈és ❞❛s tr❛♥s❢♦r♠❛çõ❡s y → −y ❡ z → −z ♥❛ ❡str✉t✉r❛ ❡♠ ✭❛✮✱
r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✸✳✺ ❘❡❧❛çã♦ ❞❡ ❞✐s♣❡rsã♦ ❞❡ ✉♠❛ ♠♦♥♦❝❛♠❛❞❛ ❞❡ ❢ós❢♦r♦ ♥❡❣r♦ ❛♦ ❧♦♥❣♦ ❞❛s
❞✐r❡çõ❡s ❞❡ ❛❧t❛ s✐♠❡tr✐❛ ❞❛ ③♦♥❛ ❞❡ ❇r✐❧❧♦✉✐♥✱ r❡♣r❡s❡♥t❛❞❛ ♣❡❧♦ r❡tâ♥❣✉❧♦ ✈❡r❞❡✳ ❆s ❝✉r✈❛s ❛③✉✐s sã♦ ♦s r❡s✉❧t❛❞♦s ❞♦ ♠♦❞❡❧♦ t✐❣❤t✲❜✐♥❞✐♥❣ ❞❡ ❝✐♥❝♦ ❤♦♣♣✐♥❣s q✉❡ ❡①✐❜❡ ❜♦❛ ❝♦♥❝♦r❞â♥❝✐❛ ❝♦♠ ♦s r❡s✉❧t❛❞♦s ❛❜✲✐♥✐t✐♦✱ ❝❛❧❝✉❧❛❞♦s ❛tr❛✈és ❞❛ ❛♣r♦①✐♠❛çã♦ ●❲✱ ✭❝✉r✈❛s ✈❡r♠❡❧❤❛s✮ ♣❛r❛ ❡♥❡r❣✐❛s ♣ró①✐♠❛s ❛♦ ♥í✈❡❧ ❞❡ ❋❡r♠✐✳ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❛ ❘❡❢✳ ❬✷✻❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✸✳✻ ❉✐s♣❡rsã♦ ❞❡ ❜❛✐①❛s ❡♥❡r❣✐❛s ❞♦ ❢♦s❢♦r❡♥♦ ✭❛✮ ♥ã♦ ❞♦♣❛❞♦ ✭✉♥❞♦♣❡❞✮✱ ✭❜✮
♥❡❣❛t✐✈❛♠❡♥t❡ ❞♦♣❛❞♦ ✭♥✲❞♦♣❡❞✮ ❡ ✭❝✮ ♣♦s✐t✐✈❛♠❡♥t❡ ❞♦♣❛❞♦ ✭♣✲❞♦♣❡❞✮✳ ❖ ❝♦♥tí♥✉♦ ❞❡ ❡st❛❞♦s ❛③✉✐s r❡♣r❡s❡♥t❛♠ ♦s ❜✉r❛❝♦✱ ❡♥q✉❛♥t♦ q✉❡ ♦s ✈❡r♠❡✲ ❧❤♦s r❡♣r❡s❡♥t❛♠ ❡❧étr♦♥s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✸✳✼ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ❛s ❜❛♥❞❛s ❞❡ ❡♥❡r❣✐❛s ♦❜t✐❞❛s ❞♦ ♠♦❞❡❧♦ t✐❣❤t✲❜✐♥❞✐♥❣
①✈
✸✳✽ ✭❛✮ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♦s ♥í✈❡✐s ❞❡ ▲❛♥❞❛✉ ❞♦ ❢♦s❢♦r❡♥♦ ❝❛❧❝✉❧❛❞♦ ❛tr❛✈és ❞♦ ♠♦❞❡❧♦ t✐❣❤t✲❜✐♥❞✐♥❣ ✭♣♦♥t♦s✮ ❡ ❞❛ ❛♣r♦①✐♠❛çã♦ ❞❡ ♠❛ss❛ ❡❢❡t✐✈❛ ✭❝✉r✈❛s ✈❡r♠❡❧❤❛s tr❛❝❡❥❛❞❛s✮✳ ❈♦♠♣❛r❛çõ❡s ❡♥tr❡ ❛s ❢✉♥çõ❡s ❞✐❡❧étr✐❝❛s ❡stát✐❝❛s ❞♦ ❢♦s❢♦r❡♥♦ ♦❜t✐❞❛s ♥ú♠❡r✐❝❛♠❡♥t❡ ✭sí♠❜♦❧♦s✮ ❡ ❛tr❛✈és ❞❛ ❛♣r♦①✐♠❛çã♦ ❞❛ ♠❛ss❛ ❡❢❡t✐✈❛ sã♦ ❛♣r❡s❡♥t❛❞❛s ♥♦s ♣❛✐♥❡✐s ✭❜✮ ✲ ✭❡✮ ♣❛r❛ ❞✐❢❡r❡♥t❡s t❡♠♣❡r❛t✉r❛s ❡ ❝♦♥❝❡♥tr❛çã♦ ❞❡ ♣♦rt❛❞♦r❡s ❞❡ ❝❛r❣❛✳ ❋✐❣✉r❛s ❛❞❛♣t❛❞❛s ❞❛s ❘❡❢✳ ❬✸✷✱ ✽✷❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✹✳✶ ✭❛✮ ♠♦♥♦❝❛♠❛❞❛ ❞❡ ❢♦s❢♦r❡♥♦✱ ❡♥❢❛t✐③❛♥❞♦ ❛ ♦r✐❡♥t❛çã♦ ❞♦ s✐st❡♠❛ ❡ ♦s
q✉❛tr♦ át♦♠♦s ❞❛ ❜❛s❡✳ ❆s s✉❜r❡❞❡s A ❡ B ✭C ❡ D✮ ❡stã♦ ♣❛rt❡ ✐♥❢❡r✐♦r
✭s✉♣❡r✐♦r✮ ❞❛ ♠♦♥♦❝❛♠❛❞❛✱ s❡♥❞♦ ❡ss❛s r❡♣r❡s❡♥t❛❞❛s ♣♦r át♦♠♦s ♣r❡t♦s ✭❝✐♥③❛s✮✱ r❡♣❡❝t✐✈❛♠❡♥t❡✳ t1,2,3,4,5 sã♦ ♦s ❝✐♥❝♦ ♣❛râ♠❡tr♦ ❞❡ ❤♦♣♣✐♥❣ ❞♦
♠♦❞❡❧♦ t✐❣❤t✲❜✐♥❞✐♥❣✳ ✭❜✮ ◆❛♥♦✜t❛s ❞❡ ❢♦s❢♦r❡♥♦ ❝♦♠ ❜♦r❞❛s ❛❝ ✭❝✐♠❛✮ ❡ ③③ ✭❜❛✐①♦✮✳ ❖s ♣❛râ♠❡tr♦ ❞❡ r❡❞❡ ❞❛s ♥❛♥♦✜t❛s ③③ ❡ ❛❝ sã♦ l1 = 3.31 ➴ ❡
l2 = 4.19➴✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼
✹✳✷ ❊str✉t✉r❛ ❞❡ ❜❛♥❞❛s ❞❡ ♥❛♥♦✜t❛s ❞❡ ❢♦s❢♦r❡♥♦ ❝♦♠ ❜♦r❞❛s ✭❛✱ ❝✮ ❛❝ ❡ ✭❜✱ ❞✮ ③③ ❝♦♠ W = 101 ➴✳ ❆s ❜❛♥❞❛s ❞❡ ❡♥❡r❣✐❛ ❡♠ ✭❛✮ ❡ ✭❜✮ ❢♦r❛♠ ♦❜t✐✲
❞❛s ❛tr❛✈és ❞♦ ♠♦❞❡❧♦ t✐❣❤t✲❜✐♥❞✐♥❣✳ ❯♠❛ ❝♦♠♣❛r❛çã♦ ❡♥tr❡ ❛s ❜❛♥❞❛s ❞❡ ❡♥❡r❣✐❛ ♦❜t✐❞❛s ✉❧t✐❧✐③❛♥❞♦ ♦ ♠♦❞❡❧♦ t✐❣❤t✲❜✐♥❞✐♥❣ ✭❝✉r✈❛s só❧✐❞❛s ❛③✉✐s✮ ❡ ❛ ❛♣r♦①✐♠❛çã♦ ❞♦ ❝♦♥tí♥✉♦ ✭❝✉r✈❛s tr❛❝❡❥❛❞❛s ♣r❡t❛s✮ é ❛♣r❡s❡♥t❛❞❛ ❡♠ ✭❝✮ ❡ ✭❞✮ ♣❛r❛ ♥❛♥♦✜t❛s ❛❝ ❡ ③③✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ♣❛r❛ ✈❛❧♦r❡s ❞❡ ❡♥❡r❣✐❛ ❞❡♥tr♦ ❞❛ r❡❣✐ã♦ ❛♠❛r❡❧❛ ❡♠ ✭❛✮ ❡ ✭❜✮ ❡♠ t♦r♥♦ ❞❡ E = 0 ❡❱✳ ❆ ❝✉r✈❛ ✈❡r♠❛❧❤❛
tr❛❝❡❥❛❞❛ ♥♦ ❡s♣❡❝tr♦ ❞❛ ♥❛♥♦✜t❛ ③③ r❡♣r❡s❡♥t❛ ❛ ❛♣r♦①✐♠❛çã♦ ❞❡ s❡❣✉♥❞❛ ♦r❞❡♠ ♣❛r❛ ♦ ❡st❛❞♦ ❞❡ ❜♦r❞❛ ♦❜t✐❞♦ ♥❛ ❘❡❢✳ ❬✼✼❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✹✳✸ ❉❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ♣❛r❛ ✭❛✮ ❛❝❇P◆ ❡ ✭❜✮ ③③❇P◆✱ ❝♦♠ ❡♥❡r❣✐❛s
E ≈ 0.39 ❡❱ ❡ E ≈ −0.3 ❡❱✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ♦❜t✐❞❛s ❞♦ ♠♦❞❡❧♦ t✐❣❤t✲
❜✐♥❞✐♥❣ ✭❝✐♠❛✮ ❡ ❞❛ ❛♣r♦①✐♠❛çã♦ ❞♦ ❝♦♥tí♥✉♦ ✭❜❛✐①♦✮✳ ❚❛✐s ❡♥❡r❣✐❛s ❝♦r✲ r❡s♣♦♥❞❡♠ ❛♦ ♠í♥✐♠♦ ❞♦ ❡st❛❞♦ ❞❡ ❜♦r❞❛s ♣❛r❛ ♦ ❝❛s♦ ③③✱ ❡ ♦ ♠í♥✐♠♦ ❞❛ ❜❛♥❞❛ ❞❡ ❝♦♥❞✉çã♦ ♣❛r❛ ♦ ❝❛s♦ ❛❝ ❝♦♥s✐❞❡r❛♥❞♦ ky = 0✳ ❖s ❞✐s❝♦s ❛③✉✐s ♥♦s r❡s✉❧t❛❞♦s ❞♦ ♠♦❞❡❧♦ t✐❣❤t✲❜✐♥❞✐♥❣ ❞❡♥♦t❛♠ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐✲ ❧✐❞❛❞❡ ❡♠ ❝❛❞❛ át♦♠♦✳ ❙✉❜r❡❞❡s A ❡ D ✭B ❡ C✮ sã♦ r❡♣r❡s❡♥t❛❞❛s ♣♦r
①✈✐
✹✳✹ ❈♦♠♣❛r❛çã♦ ❡♥tr❡ ♦s ❣❛♣✬s ❞❡ ❡♥❡r❣✐❛ ♦❜t✐❞♦s ✉❧t✐❧✐③❛♥❞♦ ♦ ♠♦❞❡❧♦ t✐❣❤t✲ ❜✐♥❞✐♥❣ ✭sí♠❜♦❧♦s✮ ❡ ❞❡r✐✈❛❞♦s ❞♦ ♠♦❞❡❧♦ ❞♦ ❝♦♥tí♥✉♦ ✭❝✉r✈❛s✮ ❝♦♠ ❢✉♥çã♦ ❞❛ ❡s♣❡ss✉r❛ ❞❛ ♥❛♥♦✜t❛W ♣❛r❛ ♦s ❝❛s♦s ❛❝ ✭q✉❛❞r❛❞♦s ❛③✉✐s ❡ ❝✉r✈❛ só❧✐❞❛
❛③✉❧✮ ❡ ③③ ✭❝✐r❝✉❧♦s ✈❡r♠❡❧❤♦s ❡ ❝✉r✈❛ ✈❡r♠❡❧❤❛ tr❛❝❡❥❛❞❛✮✳ ❖ ✐♥s❡t ♠♦str❛ ♦s ❣❛♣✬s ❞❡ ❡♥❡r❣✐❛ ❡♠ ❡s❝❛❧❛ ❧♦❣❛rít✐♠✐❝❛✱ ♦♥❞❡ ❛s ❝✉r✈❛s só❧✐❞❛s ♣r❡t❛s r❡♣r❡s❡♥t❛♠ ♦ ✜t ❧✐♥❡❛r ❞♦s r❡s✉❧t❛❞♦s t✐❣❤t✲❜✐♥❞✐♥❣✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✹✳✺ ❊s❜♦ç♦ ❞❛ ❡str✉t✉r❛ ❞❡ ✉♠ s✐st❡♠❛ ❞❡ ◆ ❝❛♠❛❞❛s ❞❡ ❢♦s❢♦r❡♥♦✱ ♦♥❞❡ ♦s
át♦♠♦s ❞❡ ❋ós❢♦r♦ ❡♠ ❞✐❢❡r❡♥t❡s s✉❜❝❛♠❛❞❛s sã♦ r❡♣r❡s❡♥t❛❞♦s ♣♦r ❝♦r❡s ❞✐❢❡r❡♥t❡s ❡♠ ❝❛❞❛ ♠♦♥♦❝❛❞❛✳ ✭❛✮ ❱✐st❛ s✉♣❡r✐♦r ❞❡ ✉♠ s✐st❡♠❛ ❞❡ ◆ ❝❛✲ ♠❛❞❛s✱ ❞❡st❛❝❛♥❞♦ ♦ st❛❝❦✐♥❣ ❆❇ ❡ ❛ ♦r✐❡♥t❛çã♦ ❞❛ r❡❞❡ ❝r✐st❛❧✐♥❛ ❛❞♦t❛❞❛ ♥❡st❡ tr❛❜❛❧❤♦✳ ✭❜✮ ❱✐st❛ ❧❛t❡r❛❧ ❞❡ ✉♠❛ ♠♦♥♦❝❛♠❛❞❛ ❞❡ ❢♦s❢♦r❡♥♦✱ ✐♥✲ ❞✐❝❛♥❞♦ ❛s q✉❛tr♦ s✉❜r❡❞❡s✿ A ❡ B ♥❛ s✉❜❝❛♠❛❞❛ ✐♥❢❡r✐♦r✱ ❡ C ❡ D ♥❛
s✉❜❝❛♠❛❞❛ s✉♣❡r✐♦r✳ ✭❝✮ ❱✐st❛ ❧❛t❡r❛❧ ❞❡ ✉♠ s✐st❡♠❛ ❞❡ ◆ ❝❛♠❛❞❛s✱ ♦♥❞❡
d = 10.69 ➴ é ♦ ♣❛râ♠❡tr♦ ❞❡ r❡❞❡ ♥❛ ❞✐r❡çã♦ ♣❡r♣❡♥❞✐❝✉❧❛r ❛♦ ♣❧❛♥♦
✭z✲❞✐r❡❝t✐♦♥✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵
✹✳✻ ❊str✉t✉r❛ ❞❡ ❜❛♥❞❛s ♣❛r❛ ❛ ✭❛✮ ♠♦♥♦❝❛♠❛❞❛✱ ✭❜✮ ❜✐❝❛♠❞❛✱ ✭❝✮ tr✐❝❛♠❛❞❛ ❡ ✭❞✮ t❡tr❛❝❛♠❛❞❛ ❞❡ ❢♦s❢♦r❡♥♦ ♦❜t✐❞❛s ❛tr❛✈és ❞❛s ❡①♣r❡ssõ❡s ❛♥❛❧ít✐❝❛s ❊qs✳ ✭✹✳✺✷✮ ❡ ✭✹✳✻✾✮ ♥♦ ❝♦♥t❡①t♦ ❞♦ ♠♦❞❡❧♦ t✐❣❤t✲❜✐♥❞✐♥❣ ✭❝✉r✈❛s só❧✐❞❛s ❛③✉✐s✮ ❡ ❞❛ ❛♣r♦①✐♠❛çã♦ ❞♦ ❝♦♥tí♥✉♦ ✭❝✉r✈❛s ✈❡r♠❡❧❤❛s tr❛❝❡❥❛❞❛s✮✱ r❡s✲ ♣❡❝t✐✈❛♠❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✹✳✼ ❉❡♥s✐❞❛❞❡ ❞❡ ❡st❛❞♦s ✭❉❖❙✮ ♣❛r❛ ❛ ✭❛✮ ♠♦♥♦❝❛♠❛❞❛✱ ✭❜✮ ❜✐❝❛♠❛❞❛✱ ✭❝✮
tr✐❝❛♠❛❞❛ ❡ ✭❞✮ t❡tr❛❝❛♠❛❞❛ ❡ ❢♦s❢♦r❡♥♦ ♦❜t✐❞❛ ❛tr❛✈és ❞♦ ♠♦❞❡❧♦ t✐❣❤t✲ ❜✐♥❞✐♥❣ ✭❝✉r✈❛s só❧✐❞❛s ❛③✉✐s✮ ❡ ❞❛ ❛♣r♦①✐♠❛çã♦ ❞♦ ❝♦♥tí♥✉♦ ✭❝✉r✈❛s tr❛✲ ❝❡❥❛❞❛s ✈❡r♠❡❧❤❛s✮✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ◆ós ✉❧t✐❧✐③❛♠♦s ❛ ❞❡✜♥✐çã♦ f(E) =
e−(E−E0)2/Γ2 ❝♦♠ ✉♠ ❢❛t♦r ❞❡ ❛❜❡rt✉r❛
Γ = 0.025 ♣❛r❛ s✉❛✈✐③❛r ♦s ♥í✈❡✐s
❞❡ ❡♥❡r❣✐❛s ❞✐s❝♦♥tí♥✉♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✹✳✽ ❈♦♥t♦r♥♦s ❞❡ ❡♥❡r❣✐❛ ❝♦♥st❛♥t❡s ♣❛r❛ ❛s ❜❛♥❞❛s ❞❡ ❝♦♥❞✉çã♦ ♠❛✐s ❜❛✐①❛s ♥♦
❡s♣❛ç♦ ❞♦s ♠♦♠❡♥t❛ ♣❛r❛ ✭❛✮ ♠♦♥♦❝❛♠❛❞❛✱ ✭❜✮ ❜✐❝❛♠❛❞❛✱ ✭❝✮ tr✐❝❛♠❛❞❛ ❡ ✭❞✮ t❡tr❛❝❛♠❛❞❛ ♦❜t✐❞♦s ❞♦ ♠♦❞❡❧♦ t✐❣❤t✲❜✐♥❞✐♥❣ ✭❝✉r✈❛s só❧✐❞❛s ❛③✉✐s✮ ❡ ❞❛ ❛♣r♦①✐♠❛çã♦ ❞♦ ❝♦♥tí♥✉♦ ✭❝✉r✈❛s ✈❡r♠❡❧❤❛s tr❛❝❡❥❛❞❛s✮✳ lx = 2a1sin(α1/2)
❡ ly = 2 [a1cos(α1/2) +a2cos(β)] sã♦ ♦s ♣❛râ♠❡tr♦s ❞❡ r❡❞❡ ❛♦ ❧♦♥❣♦ ❞❛s
❞✐r❡çõ❡s x ✭③③✮ ❡ y ✭❛❝✮✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻
✹✳✾ ●❛♣ ❞❡ ❡♥❡r❣✐❛ ❝♦♠♦ ❢✉♥çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ ❝❛♠❛❞❛s✳ ❖s sí♠❜♦❧♦s ❞❡st❛❝❛♠ ♦ ❝♦♠♣♦rt❛♠❡♥t❡ ❞❛ ❡①♣r❡ssã♦ ❛♥❛❧ít✐❝❛ ✭✹✳✺✹✮ ♣❛r❛ ✈❛❧♦r❡s ✐♥t❡✐r♦s ❞♦ ♥ú♠❡r♦ ❞❡ ❝❛♠❛❞❛s N✳ ❆s ❝✉r✈❛s tr❛❝❡❥❛❞❛s ✈❡r♠❡❧❤❛s sã♦ ♦s r❡s✉❧t❛❞♦s
①✈✐✐
✹✳✶✵ ▼❛ss❛s ❡❢❡t✐✈❛s ❡♠ ✉♥✐❞❛❞❡s ❞❛ ♠❛ss❛ ❞♦ ❡❧étr♦♥ ❧✐✈r❡ ✭m0✮ ❛♦ ❧♦♥❣♦ ❞❛s
❞✐r❡çõ❡s x ✭❝✉r✈❛s só❧✐❞❛s✮ ❡ y ✭❝✉r✈❛s tr❛❝❡❥❛❞❛s✮ ♣❛r❛ ✭❛✮ ❡❧étr♦♥s ❡ ✭❜✮
❜✉r❛❝♦s ❝♦♠♦ ❢✉♥çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ ❝❛♠❛❞❛s✳ ❖ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❛ ❡①✲ ♣r❡ssã♦ ❛♥❛❧ít✐❝❛ ✭✹✳✼✶✮ ♣❛r❛ ✈❛❧♦r❡s ✐♥t❡✐r♦s ❞❡ N sã♦ r❡♣r❡s❡♥t❛❞♦s ♣♦r
sí♠❜♦❧♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ✹✳✶✶ ◆í✈❡✐s ❞❡ ▲❛♥❞❛✉ ♣❛r❛ ❡❧étr♦♥s ✭❝✉r✈❛s ❛③✉✐s✮ ❡ ❜✉r❛❝♦s ✭❝✉r✈❛s ✈❡r♠❡❧❤❛s✮
❝♦♠♦ ❢✉♥çã♦ ❞♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ♣❛r❛ ❛ ✭❛✮ ♠♦♥♦❝❛♠❛❞❛✱ ✭❜✮ ❜✐❝❛♠❛❞❛✱ ✭❝✮ tr✐❝❛♠❛❞❛ ❡ ✭❞✮ t❡tr❛❝❛♠❛❞❛ ❞❡ ❢♦s❢♦r❡♥♦✳ ❖s ♣r✐♠❡✐r♦s ♦♥③❡ ♥í✈❡✐s ♠❡♥♦s ❡♥❡r❣ét✐❝♦s✭n= 0✱1✱ · · ·✱ 10✮ ♣❛r❛ ❝❛❞❛ s✉❜❜❛♥❞❛s sã♦ ❛♣r❡s❡♥t❛❞♦s✳ ✽✺
✹✳✶✷ ◆í✈❡✐s ❞❡ ▲❛♥❞❛✉ ♣❛r❛ ❡❧étr♦♥s ❡♠ t❡tr❛❝❛♠❛❞❛ ❞❡ ❢♦s❢♦r❡♥♦ ✭N = 4✮ ❝♦♠♦
❢✉♥çã♦ ❞❡ ✭❜✮ ✉♠ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ♣❡r♣❡♥❞✐❝✉❧❛r ❡ ✭❜✱ ❝✮ ❞♦ í♥❞✐❝❡ ❞♦ ♥í✈❡❧ ❞❡ ▲❛♥❞❛✉ n ❝♦♠ ❞✐❢❡r❡♥t❡s ❝❛♠♣♦s ♠❛❣♥ét✐❝♦s✳ ❯♠ ❝♦♠♣❛r❛çã♦ ❡♥tr❡ ❛s
❜❛♥❞❛s ❞❡ ❡♥❡r❣✐❛ ♦❜t✐❞❛s ✉t✐❧✐③❛♥❞♦ ❛ ❞✐s♣❡rsã♦ ❧✐♥❡❛r ❊q✳ ✭✹✳✼✷✮ ✭❝✉r✈❛s só❧✐❞❛s ❛③✉✐s✮ ❡ ❛tr❛✈és ❞❛ ❞✐❛❣♦♥❛❧✐③❛çã♦ ❞♦ ❍❛♠✐❧t♦♥✐❛♥♦ ✭✹✳✻✼✮ ❝♦♠ ♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ✭❝✉r✈❛ tr❛❝❡❥❛❞❛ ♣r❡t❛✮ é ❛♣r❡s❡♥t❛❞❛✳ ❙♦♠❡♥t❡ ♦s ♦♥③❡ ♣r✐♠❡✐r♦s ♥í✈❡✐s ❞❡ ▲❛♥❞❛✉ ♠❡♥♦s ❡♥❡r❣❡t✐❝♦s ❢♦r❛♠ ❝♦♥s✐❞❡r❛❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✽✻ ✺✳✶ ❊str✉t✉r❛ ❝r✐st❛❧✐♥❛ ❞❛s ♠✉❧t✐❝❛♠❛❞❛s ❞❡ ❋ós❢♦r♦ ♥❡❣r♦ ❝♦♠ ♦s ♣❛râ♠❡✲
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✸✳✶ ❈♦♠♣♦♥❡♥t❡s ❞♦s ✈❡t♦r❡s ❞❡ ❤♦♣♣✐♥❣ ♣r♦❥❡t❛❞❛s ♥♦ ♣❧❛♥♦ xy✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺
✹✳✶ ❈♦❡✜❝✐❡♥t❡s ❞♦s ❢❛t♦r❡s ❞❡ ❡str✉t✉r❛ ♣❛r❛ ❛s ❛♣r♦①✐♠❛çõ❡s ❞❡ ❝♦♥tí♥✉♦ ❜❛s❡❛❞❛s ♥♦s ♠♦❞❡❧♦s ❞❡ ❞❡③ ❡ ❞❡ ❝✐♥❝♦ ❤♦♣♣✐♥❣s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✺✳✶ ♣❛râ♠❡tr♦s ❞❡ ❤♦♣♣✐♥❣ ✐♥tr❛❝❛♠❛❞❛ ✭ti✮ ❡ ✐♥t❡r❝❛♠❛❞❛ ✭t⊥
1
■♥tr♦❞✉çã♦
❖ ❣r❛♥❞❡ ✐♥t❡r❡ss❡ ❣❡r❛❞♦ ♣❡❧❛ ♣r♦❞✉çã♦ ❞♦ ❣r❛❢❡♥♦✱ ❡♠ ✷✵✵✹✱ t❡♠ ❡st✐♠✉❧❛❞♦ ❛ ♣r♦❝✉r❛ ♣♦r ♠❛t❡r✐❛✐s ❛♥á❧♦❣♦s q✉❡ ❝♦♠♣❛rt✐❧❤❛♠ ❞❡ s✉❛s ✈❛♥t❛❣❡♥s✱ t❛✐s ❝♦♠♦ ✉♠❛ ❛❧t❛ ♠♦❜✐❧✐❞❛❞❡ ❡❧❡trô♥✐❝❛ ❡ ✉♠ ❣r❛♥❞❡ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ❝♦❡rê♥❝✐❛ ❞❡ ❢❛s❡✱ ♠❛s ♥ã♦ ❞❡ s✉❛s ❞❡✜❝✐ê♥❝✐❛s✱ t❛✐s ❝♦♠♦ ❛ ❛✉sê♥❝✐❛ ❞❡ ✉♠ ❣❛♣ ❞❡ ❡♥❡r❣✐❛ ❡ ❛ ❞✐✜❝✉❧❞❛❞❡ ❞♦ ❝♦♥✜♥❛✲ ♠❡♥t♦ ❞❡ ♣♦rt❛❞♦r❡s ❞❡ ❝❛r❣❛ ❛tr❛✈és ❞❡ ❜❛rr❡✐r❛s ❡❧❡tr♦stát✐❝❛s ❞❡✈✐❞♦ ❛♦ t✉♥❡❧❛♠❡♥t♦ ❞❡ ❑❧❡✐♥❬✶✱ ✷✱ ✸❪✳ ▼✉✐t♦s ❞♦s ♥♦✈♦s ❝r✐st❛✐s ❜✐❞✐♠❡♥s✐♦♥❛✐s ✭✷❉✮ ✐♥✈❡st✐❣❛❞♦s sã♦ ♦❜✲ t✐❞♦s ❞❡ ♠❛t❡r✐❛✐s ❧❛♠❡❧❛r❡s q✉❡✱ s✐♠✐❧❛r♠❡♥t❡ ❛♦ ❣r❛❢❡♥♦✱ ♣♦❞❡♠ s❡r ♠❡❝â♥✐❝❛♠❡♥t❡ ❡s❢♦❧✐❛❞♦s ♣❛r❛ ♦❜t❡r✲s❡ ❛♠♦str❛s ❝♦♠ ♣♦✉❝❛s ❝❛♠❛❞❛s ♦✉ ❛té ♠❡s♠♦ ✉♠❛ ú♥✐❝❛ ❝❛♠❛❞❛ ✭♠♦♥♦❝❛♠❛❞❛s✮❬✹❪✳ ❊ss❡ ♣r♦❝❡ss♦ r❡s✉❧t♦✉ ♥❛ ❞❡s❝♦❜❡rt❛ ❞❡ ♠♦♥♦❝❛♠❛❞❛s ❞❡ ❝r✐st❛✐s ❞❡ ❙✐❧í❝✐♦ ✭s✐❧✐❝❡♥♦✮❬✺❪✱ ●❡r♠â♥✐♦ ✭❣❡r♠❛♥❡♥♦✮❬✻❪✱ ❛ss✐♠ ❝♦♠♦ ❞❡ ✉♠❛ ❝❧❛ss❡ ❞❡ ♠❛t❡r✐❛✐s ❝♦♥❤❡❝✐❞♦s ❝♦♠♦ ❞✐❝❛❧❝♦❣❡♥❡t♦s ❞❡ ♠❡t❛✐s ❞❡ tr❛♥s✐çã♦❬✼❪✳
❯♠ ❞♦s ♠❛✐s ♣r♦♠✐ss♦r❡s ❞❡ss❛ ♥♦✈❛ s❛❢r❛ ❞❡ ♠❛t❡r✐❛✐s ✷❉ é ❛ ♠♦♥♦❝❛♠❛❞❛ ❞❡ ❋ós❢♦r♦ ♥❡❣r♦ ✭❇P✱ ❞♦ ✐♥❣❧ês ❇❧❛❝❦ P❤♦s♣❤♦r✉s✮❬✽✱✾✱✶✵✱✶✶✱✶✷✱✶✸✱✶✹❪ q✉❡ é ✉♠ s❡♠✐❝♦♥❞✉t♦r ❞❡ ❣❛♣ ♣❡q✉❡♥♦✶✱ t❛♠❜é♠ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ❢♦s❢♦r❡♥♦✱ q✉❡ ♣♦ss✉✐ ✉♠❛ ❛❧t❛ ♠♦❜✐❧✐❞❛❞❡ ❡❧❡trô✲
♥✐❝❛✱ ❞❛ ♦r❞❡♠ ❞❡≈1000 ❝♠2 ❱−1s−1✱ ❝♦♠♣❛rá✈❡❧ à ❞♦ ❣r❛❢❡♥♦✱ ♠❛s ❝♦♠ ✉♠❛ ❡str✉t✉r❛ ❞❡ ❜❛♥❞❛s ❛♥✐s♦tró♣✐❝❛✳ ❆❞✐❝✐♦♥❛❧♠❡♥t❡✱ ❛s ♠✉❧t✐❝❛♠❛❞❛s ❞❡ ❢♦s❢♦r❡♥♦ ❛♣r❡s❡♥t❛♠ ✉♠ ❣❛♣ ❞❡ ❡♥❡r❣✐❛ ❝♦♥tr♦❧á✈❡❧❬✾✱✶✷✱✶✺✱✶✻✱✶✼✱✶✽✱✶✾✱✷✵❪✱ ❝❛r❛❝t❡ríst✐❝❛ ❞❡ ❣r❛♥❞❡ r❡❧❡✈â♥❝✐❛ ♣❛r❛ ❛♣❧✐❝❛çõ❡s ❡♠ ❞✐s♣♦s✐t✐✈♦s✳ ❊♠ ♣❛rt✐❝✉❧❛r✱ ❡①♣❡r✐♠❡♥t♦s ♠♦str❛r❛♠ ❛ ❞❡♣❡♥❞ê♥❝✐❛ ❞♦ ❣❛♣ ❞❡ ❡♥❡r❣✐❛ ❝♦♠ ♦ ♥ú♠❡r♦ ❞❡ ❝❛♠❛❞❛s✱ ✈❛r✐❛♥❞♦ ❞❡ ≈✷✳✵ ❡❱ ♣❛r❛ ❛ ♠♦♥♦❝❛♠❛❞❛
❛té ≈ ✵✳✸ ❡❱ ♣❛r❛ ♦ ❜✉❧❦❬✷✶✱ ✷✷✱✷✸❪✳
❏á ❡①✐st❡ ✉♠❛ ❧✐t❡r❛t✉r❛ ❝r❡s❝❡♥t❡ s♦❜r❡ ❛s ♣r♦♣r✐❡❞❛❞❡s ❞♦ ❢♦s❢♦r❡♥♦✱ ❛ss✐♠ ❝♦♠♦ ❡st✉❞♦s ❞❡ ♣♦ssí✈❡✐s ❛♣❧✐❝❛çõ❡s t❡❝♥♦❧ó❣✐❝❛s❬✽✱✾✱✷✶✱✷✷❪✳ ❯♠❛ sér✐❡ ❞❡ ❡st✉❞♦s ♦❜t✐✈❡r❛♠ r❡❝❡♥t❡♠❡♥t❡ ❛ ❞✐s♣❡rsã♦ ❡❧❡trô♥✐❝❛ ❛tr❛✈és ❞❡ ❛♣r♦①✐♠❛çõ❡s t❛✐s ❝♦♠♦ àq✉❡❧❛s ❜❛s❡❛❞❛s ❡♠ ❝á❧❝✉❧♦s ❞❡ ♣r✐♠❡✐r♦s ♣r✐♥❝í♣✐♦s❬✶✺✱✶✼✱✷✸✱✷✹✱✷✺❪✱ ♥♦ ♠♦❞❡❧♦ t✐❣❤t✲❜✐♥❞✐♥❣❬✷✸✱✷✻❪✱ ❡♠ ♠ét♦❞♦sk·p❬✷✼✱✷✽❪✱ ❡ ♥❛ ❛♣r♦①✐♠❛çã♦ ❞❡ ❧♦♥❣♦s ❝♦♠♣r✐♠❡♥t♦s ❞❡ ♦♥❞❛❬✷✾❪✳ ❆♣❡s❛r ❞❛
❣r❛♥❞❡ ♣r❡❝✐sã♦ ❛♣r❡s❡♥t❛❞❛ ♣❡❧♦s r❡s✉❧t❛❞♦s ❜❛s❡❛❞♦s ❡♠ ❝á❧❝✉❧♦s ❛❜✲✐♥✐t✐♦✱ ♦❜s❡r✈❛✲s❡ q✉❡ ♣❛r❛ ❛ ♠❛✐♦r✐❛ ❞♦s ❝❛s♦s ❞❡ ✐♥t❡r❡ss❡✱ ♠♦❞❡❧♦s ♠❛✐s s✐♠♣❧❡s sã♦ s✉✜❝✐❡♥t❡s ♣❛r❛ ❛
✶❙ã♦ ❝♦♥s✐❞❡r❛❞♦s s❡♠✐❝♦♥❞✉t♦r❡s ❞❡ ❣❛♣ ♣❡q✉❡♥♦ ♠❛t❡r✐❛✐s s❡♠✐❝♦♥❞✉t♦r❡s q✉❡ ♣♦ss✉❡♠ ❣❛♣s ❝♦♠✲
✷✸
❞❡s❝r✐çã♦ q✉❛❧✐t❛t✐✈❛ ❞❛s ♣r♦♣r✐❡❞❛❞❡s ❡❧❡trô♥✐❝❛s ❞❡ ♠✉❧t✐❝❛♠❛❞❛s ❞❡ ❢♦s❢♦r❡♥♦❬✷✾✱ ✸✵❪✳ ❊♠❜♦r❛ s❡❥❛ ✉♠❛ ❛♣r♦①✐♠❛çã♦ ✈á❧✐❞❛ s♦♠❡♥t❡ ❞❡♥tr♦ ❞❡ ✉♠ ❝❡rt♦ ✐♥t❡r✈❛❧♦ ❞❡ ❡♥❡r❣✐❛s✱ ♦ ♠♦❞❡❧♦ t✐❣❤t✲❜✐♥❞✐♥❣ t❡♠ s✐❞♦ ❜❛st❛♥t❡ ✉t✐❧✐③❛❞♦ ❞❡✈✐❞♦ à s✉❛ s✐♠♣❧✐❝✐❞❛❞❡ ❡ ❛♦ ❢❛t♦ ❞❡ r❡q✉❡r❡r ♠❡♥♦s ♣♦❞❡r ❝♦♠♣✉t❛❝✐♦♥❛❧ ❡♠ r❡❧❛çã♦ ❛♦s ♠♦❞❡❧♦s ❛❜✲✐♥✐t✐♦✱ ♣❡r♠✐t✐♥❞♦ ❛ ♦❜t❡♥çã♦ ❞❡ r❡s✉❧t❛❞♦s ♣r❡❝✐s♦s ♣❛r❛ s✐st❡♠❛s ♠❛✐♦r❡s✱ ❝♦♠ ✉♠ ♠❛✐♦r ♥ú♠❡r♦ ❞❡ át♦♠♦s✱ ❡ ♠❛✐s ❝♦♠♣❧❡①♦s ❞❡ ✉♠❛ ❢♦r♠❛ ❝♦♠♣✉t❛❝✐♦♥❛❧♠❡♥t❡ ♠❛✐s ❜❛r❛t❛✳ ❆❞✐❝✐♦♥❛❧♠❡♥t❡✱ ❛ ❛♣r♦①✐♠❛çã♦ ❞❡ ❧♦♥❣♦s ❝♦♠♣r✐♠❡♥t♦s ❞❡ ♦♥❞❛ ❞❡r✐✈❛❞❛ ❞♦ ♠♦❞❡❧♦ t✐❣❤t✲❜✐♥❞✐♥❣✱ t❛♠❜é♠ ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ♠♦❞❡❧♦ ❞♦ ❝♦♥tí♥✉♦✱ é ✉♠❛ ót✐♠❛ ❛♣r♦①✐♠❛çã♦ ♣❛r❛ ❜❛✐①❛s ❡♥❡r❣✐❛s✳ ❚❛❧ ❛♣r♦①✐♠❛çã♦ t❡✈❡ ❣r❛♥❞❡ ✐♠♣♦rtâ♥❝✐❛ ♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ t❡ór✐❝♦ ❞❛s ♣r♦♣r✐❡❞❛❞❡s ❞♦ ❣r❛❢❡♥♦ ♠♦str❛♥❞♦ q✉❡ ♦s ♣♦rt❛❞♦r❡s ❞❡ ❝❛r❣❛ ❞❡ ❜❛✐①❛ ❡♥❡r❣✐❛ ♥♦ ♠❛t❡r✐❛❧ ❝♦♠♣♦rt❛♠✲ s❡ ❝♦♠♦ ❢❡r♠✐♦♥s ❞❡ ❉✐r❛❝ ❞❡ ♠❛ss❛ ♥✉❧❛❬✶✱✷❪✳ ❉❡ss❛ ❢♦r♠❛✱ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ♠♦❞❡❧♦s t❡ór✐❝♦s ♣❛r❛ ❛ ❞❡s❝r✐çã♦ ❞❛s ♣r♦♣r✐❡❞❛❞❡s ❡❧❡trô♥✐❝❛s ❞❡ ♠❛t❡r✐❛✐s ✷❉ t❡♠ ✐♠♣♦rtâ♥❝✐❛ ❢✉♥❞❛♠❡♥t❛❧ ♣❛r❛ ♦ ❝❛♠♣♦✱ ♣❡r♠✐t✐♥❞♦ ❛ ❡①♣❧♦r❛çã♦ ❡ ❛ ❛♥á❧✐s❡ ❞❛s ♣r♦♣r✐❡❞❛❞❡s ❞❡ss❡s ♠❛t❡r✐❛✐s ❞❡ ✉♠❛ ♠❛♥❡✐r❛ ♠❛✐s s✐♠♣❧❡s ❡ ❝♦♠♣✉t❛❝✐♦♥❛❧♠❡♥t❡ ❜❛r❛t❛✳
◆❡st❛ t❡s❡✱ ♣r♦♣♦♠♦s ♠♦❞❡❧♦s t❡ór✐❝♦s ❜❛s❡❛❞♦s ♥❛ ❛♣r♦①✐♠❛çã♦ t✐❣❤t✲❜✐♥❞✐♥❣ ❡ ♥♦ ♠♦❞❡❧♦ ❞♦ ❝♦♥tí♥✉♦ ♣❛r❛ ♦ ❡st✉❞♦ ❞❛s ♣r♦♣r✐❡❞❛❞❡s ❡❧❡trô♥✐❝❛s ❞❡ ♥❛♥♦❡str✉t✉r❛s ❞❡ ❢♦s❢♦r❡♥♦✳ ❊♠ r❡❧❛çã♦ à ❛♣r♦①✐♠❛çã♦ ❞❡ ❧♦♥❣♦s ❝♦♠♣r✐♠❡♥t♦s ❞❡ ♦♥❞❛✱ ❡♥❝♦♥tr❛♠♦s q✉❡ ❛ ❝♦♥❝♦r❞â♥❝✐❛ ❝♦♠ ♦ ♠♦❞❡❧♦ t✐❣❤t✲❜✐♥❞✐♥❣ é q✉❛♥t✐t❛t✐✈❛ ♣❛r❛ s✐st❡♠❛s ❡♠ ❡s❝❛❧❛ ♠❡s♦s❝ó♣✐❝❛✳ ❆❞✐❝✐♦♥❛❧♠❡♥t❡✱ ❡st❡♥❞❡♠♦s ♦s ♠♦❞❡❧♦s t✐❣❤t✲❜✐♥❞✐♥❣❬✷✻✱ ✸✶❪ ❡ ❝♦♥tí♥✉♦❬✸✷❪ ♣r♦♣♦st♦s ❛♥t❡r✐♦r♠❡♥t❡ ♣❛r❛ ❝♦♥s✐❞❡r❛r ✜❧♠❡s ❞❡ ❢♦s❢♦r❡♥♦ ❝♦♠ ✉♠ ♥ú♠❡r♦ ❛r❜✐trár✐♦ ❞❡ ❝❛♠❛❞❛s✳ ❚❛✐s ♠♦❞❡❧♦s sã♦ ✈á❧✐❞♦s ♣❛r❛ ✉♠ ❣r❛♥❞❡ ✐♥t❡r✈❛❧♦ ❞❡ ❡♥❡r❣✐❛s ❡ ♣♦❞❡♠ s❡r ❣❡♥❡r❛❧✐③❛❞♦s ♣❛r❛ ❞✐✈❡rs♦s t✐♣♦s ❞❡ ❡str✉t✉r❛s✱ t❛✐s ❝♦♠♦ ♥❛♥♦✜t❛s✱ ♣♦♥t♦s ❡ ❛♥é✐s q✉â♥t✐❝♦s✱ ❞✐s♣♦s✐t✐✈♦s ❡❧❡trô♥✐❝♦s ❡ ❡t❝✳
❆ ❚❡s❡ ❡stá ♦r❣❛♥✐③❛❞❛ ❞❛ s❡❣✉✐♥t❡ ♠❛♥❡✐r❛✿ ♥♦ ❈❛♣ít✉❧♦ ✷✱ ❢❛r❡♠♦s ✉♠❛ ❜r❡✈❡ r❡✈✐sã♦ s♦❜r❡ ❛s ♣r♦♣r✐❡❞❛❞❡s ❡❧❡trô♥✐❝❛s ❡ ót✐❝❛s ❞❛s ♠✉❧t✐❝❛♠❛❞❛s ❞❡ ❋ós❢♦r♦ ♥❡❣r♦✱ ❛ss✐♠ ❝♦♠♦ ❞❡ s✉❛s ❛♣❧✐❝❛çõ❡s ❡♠ ❞✐s♣♦s✐t✐✈♦s ❡❧❡trô♥✐❝♦s ❡ ♦♣t♦❡❧❡trô♥✐❝♦s✳ ❉✐s❝✉t✐r❡♠♦s t❛♠❜é♠ s♦❜r❡ ❛ sí♥t❡s❡ ❞❡ ❛♠♦str❛s ❡ s♦❜r❡ ♦s ❞❡s❛✜♦s r❡♠❛♥❡s❝❡♥t❡s r❡❧❛❝✐♦♥❛❞♦s✳ ❖ ❈❛♣ít✉❧♦ ✸ s❡rá ❞❡✈♦t❛❞♦ ❛♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ✉♠ ♠♦❞❡❧♦ t❡ór✐❝♦ ♣❛r❛ ❛ ❞❡s❝r✐çã♦ ❞❛s ♣r♦♣r✐❡❞❛✲ ❞❡s ❡❧❡trô♥✐❝❛s ❞♦ ❢♦s❢♦r❡♥♦✱ ♦♥❞❡ ✉♠ ♠♦❞❡❧♦ t✐❣❤t✲❜✐♥❞✐♥❣ ❜❛s❡❛❞♦ ❡♠ ❝á❧❝✉❧♦s ❛❜✲✐♥✐t✐♦ s❡rá ❞❡t❛❧❤❛❞❛♠❡♥t❡ ❞❡s❡♥✈♦❧✈✐❞♦✳ ❆s ❛♣r♦①✐♠❛çõ❡s ❞♦ ❝♦♥tí♥✉♦ ❡ ❞❛ ♠❛ss❛ ❡❢❡t✐✈❛ t❛♠✲ ❜é♠ s❡rã♦ ❞✐s❝✉t✐❞❛s✳ ◆♦ ❈❛♣ít✉❧♦ ✹✱ ✐♥✈❡st✐❣❛r❡♠♦s ❛ ❞✐s♣❡rsã♦ ❡❧❡trô♥✐❝❛ ❞❡ ♥❛♥♦✜t❛s ❞❡ ❢♦s❢♦r❡♥♦ ♥♦ ❝♦♥t❡①t♦ ❞♦ ♠♦❞❡❧♦ ❞♦ ❝♦♥tí♥✉♦ ❜❛s❡❛❞♦ ♥♦ ❍❛♠✐❧t♦♥✐❛♥♦ ♣❛r❛ ❧♦♥❣♦s ❝♦♠♣r✐♠❡♥t♦s ❞❡ ♦♥❞❛✳ ❉✐s❝✉t✐r❡♠♦s s♦❜r❡ ❛s ❝♦♥❞✐çõ❡s ❞❡ ❝♦♥t♦r♥♦ q✉❡ ❞❡s❝r❡✈❡♠ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❛ ❢✉♥çã♦ ❡♥✈❡❧♦♣❡ ❞♦ s✐st❡♠❛ ❡ ❝♦♥s✐❞❡r❛r❡♠♦s ♦ ❡❢❡✐t♦ ❞❛s ❞✐❢❡r❡♥t❡s ❜♦r❞❛s ♥♦ ❡s♣❡❝tr♦ ❞❡ ❡♥❡r❣✐❛s✳ ❆s ❜❛♥❞❛s ❞❡ ❡♥❡r❣✐❛s ♦❜t✐❞❛s ❛♥❛❧ít✐❝❛♠❡♥t❡ sã♦ ❝♦♠♣❛✲ r❛❞❛s ❝♦♠ àq✉❡❧❛s ♦❜t✐❞❛s ❛tr❛✈és ❞♦ ♠♦❞❡❧♦ t✐❣❤t✲❜✐♥❞✐♥❣ ❞❡ ✺ ♣❛râ♠❡tr♦s ❞❡ ❤♦♣♣✐♥❣✳ ◆♦ ❈❛♣ít✉❧♦ ✺✱ ✐r❡♠♦s ❞✐s❝✉t✐r ❞❡t❛❧❤❛❞❛♠❡♥t❡ ❛ ❡①t❡♥sã♦ ❞♦s ♠♦❞❡❧♦s t✐❣❤t✲❜✐♥❞✐♥❣ ❡ ❞♦ ❝♦♥tí♥✉♦ ♣❛r❛ ♦ s✐st❡♠❛ ❞❡ N ❝❛♠❛❞❛s ❞❡ ❢♦s❢♦r❡♥♦ ❛❝♦♣❧❛❞❛s✳ ▼♦str❛r❡♠♦s ❝♦♠♦ ❡ss❡
✷✹
2
❋♦s❢♦r❡♥♦
✷✳✶ ■♥tr♦❞✉çã♦
◆❡st❡ ❝❛♣ít✉❧♦✱ ❞✐s❝✉t✐r❡♠♦s ❛s ♣r♦♣r✐❡❞❛❞❡s ❢✉♥❞❛♠❡♥t❛✐s ❞♦ ❢♦s❢♦r❡♥♦ ❞❡st❛❝❛♥❞♦ s❡✉ ♣♦t❡♥❝✐❛❧ ♣❛r❛ ❛♣❧✐❝❛çõ❡s ❡♠ ❞✐s♣♦s✐t✐✈♦s ❡❧❡trô♥✐❝♦s ❡ ♦♣t❡❧❡trô♥✐❝♦s✳ ❉✐s❝✉t✐r❡♠♦s ❜r❡✈❡♠❡♥t❡ s♦❜r❡ ♦s ♣r♦❣r❡ss♦s r❡❝❡♥t❡s ❡♠ r❡❧❛çã♦ à s✉❛ ❢❛❜r✐❝❛çã♦ ❡ s♦❜r❡ ♦s ❞❡s❛✜♦s r❡♠❛♥❡s❝❡♥t❡s ❡♠ r❡❧❛çã♦ à ❡st❛❜✐❧✐❞❛❞❡ ❞❛s ❛♠♦str❛s✳
✷✳✷ ❊str✉t✉r❛ ❡ ♣r♦♣r✐❡❞❛❞❡s ❞♦ ♠❛t❡r✐❛❧
✷✳✷✳✶ ❊str✉t✉r❛ ❝r✐st❛❧✐♥❛
❖ ❢ós❢♦r♦ ♥❡❣r♦✱ s✐♠✐❧❛r♠❡♥t❡ ❛♦ ❣r❛✜t❡ ❡ ♦✉tr♦s ♠❛t❡✐r❛✐s ❧❛♠❡❧❛r❡s✱ é ❝♦♠♣♦st♦ ♣♦r ❝❛♠❛❞❛s ❜✐❞✐♠❡♥s✐♦♥❛✐s ❞❡ át♦♠♦s ✈❡rt✐❝❛❧♠❡♥t❡ ❡♠♣✐❧❤❛❞❛s ✉♠❛s s♦❜r❡ ❛s ♦✉tr❛s q✉❡ ✐♥t❡r❛❣❡♠ ❢r❛❝❛♠❡♥t❡ ❛tr❛✈és ❞❛ ✐♥t❡r❛çã♦ ❞❡ ✈❛♥ ✈❡r ❲❛❛❧s❬✸✺✱ ✸✻❪✳ ❖ ❝❛rát❡r ❢r❛❝♦ ❞❡ t❛✐s ❧✐❣❛çõ❡s✱ q✉❛♥❞♦ ❝♦♠♣❛r❛❞❛s às ❧✐❣❛çõ❡s ❡♥tr❡ ♦s át♦♠♦s ❡♠ ❝❛❞❛ ❝❛♠❛❞❛✱ ♣♦ss✐❜✐❧✐t❛ ❛ ♣r♦❞✉çã♦ ❞❡ ♠♦♥♦❝❛♠❛❞❛s ❞❡ ❢ós❢♦r♦ ♥❡❣r♦✱ ♠❛t❡r✐❛❧ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ❢♦s❢♦r❡♥♦✱ ❛tr❛✈és ❞❡ té❝♥✐❝❛s ♣❛r❡❝✐❞❛s ❝♦♠ àq✉❡❧❛s ✉t✐❧✐③❛❞❛s ♥❛ ♣r♦❞✉çã♦ ❞♦ ❣r❛❢❡♥♦❬✾✱✸✼❪✳
❆ ❋✐❣✷✳✶♠♦str❛ ❞❡t❛❧❤❡s ❞❛ ❡str✉t✉r❛ ❝r✐st❛❧✐♥❛ ❞❡ ♠✉❧t✐♣❧❛s ❝❛♠❛❞❛s ❞❡ ❢♦s❢♦r❡♥♦✳ ❆s ✐♠❛❣❡♥s ♦❜t✐❞❛s ❛tr❛✈és ❞❡ ♠✐❝r♦s❝♦♣✐❛ ❡❧❡trô♥✐❝❛ ❞❡ ✈❛rr❡❞✉r❛ ♣♦r tr❛♥s♠✐ssã♦ ✭❙❚❊▼✱ ❞♦ ✐♥❣❧ês s❝❛♥♥✐♥❣ tr❛♥s♠✐ss✐♦♥ ❡❧❡❝tr♦♥ ♠✐❝r♦s❝♦♣②✮ ♠♦str❛♠ ♥ã♦ s♦♠❡♥t❡ ❛ ❞✐s♣♦s✐çã♦ ❞♦s át♦♠♦s ❞❡ ❢ós❢♦r♦ ❞❡♥tr♦ ❞❡ ❝❛❞❛ ❝❛♠❛❞❛✱ ♠❛s t❛♠❜é♠ ❛ ♦r❞❡♠ ❞❡ ❡♠♣✐❧❤❛♠❡♥t♦ ❞❛s ♠❡s♠❛s❬✸✽❪✳ ◆❛s ❋✐❣s✳ ✷✳✶✭❛✮ ❡ ✷✳✶✭❜✮✱ ✉♠❛ ✈✐st❛ s✉♣❡r✐♦r ❞❛ ❡str✉t✉r❛✱ ❛♦ ❧♦♥❣♦ ❞❛ ❞✐r❡çã♦ ❝r✐st❛❧♦❣rá✜❝❛ ❬✵✵✶❪ ❡♠ ✭❛✮ ❡ ❬✶✵✶❪ ❡♠ ✭❜✮✱ ♠♦str❛ q✉❡ ❛s ♣♦s✐çõ❡s ❛tô♠✐❝❛s ❡♠ ❝❛❞❛ ❝❛♠❛❞❛ sã♦ ❝♦♠♣❛tí✈❡✐s ❝♦♠ ❛s ❞♦s ♠♦❞❡❧♦s ✉t✐❧✐③❛❞♦s ❡♠ ❝á❧❝✉❧♦s t❡ór✐❝♦s ♥❛ ❧✐t❡r❛t✉r❛✱ ❝♦♠♦ ❞❡st❛❝❛❞♦ ♥❛s ✜❣✉r❛s✳ ❆❞✐❝✐♦♥❛❧♠❡♥t❡✱ ❛s ❋✐❣s✳✷✳✶✭❝✮ ❡✷✳✶✭❞✮ ♠♦str❛♠ ♦ ❡♠♣✐❧❤❛♠❡♥t♦ ❞❛s ❝❛♠❛❞❛s ❞❡ ❢♦s❢♦r❡♥♦ ❛tr❛✈és ❞❡ ✉♠❛ ✈✐sã♦ ❧❛t❡r❛❧✱ ❛♦ ❧♦♥❣♦ ❞❛ ❞✐r❡çã♦ ❝r✐st❛❧♦❣rá✜❝❛ ❬✶✵✵❪✳
