■♥st✐t✉t♦ ❞❡ P❡sq✉✐s❛ ❊♥❡r❣ét✐❝❛s ❡ ◆✉❝❧❡❛r❡s
❆✉t❛rq✉✐❛ ❛ss♦❝✐❛❞❛ à ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦
❊st✉❞♦ ❞❛s ♣r♦♣r✐❡❞❛❞❡s ó♣t✐❝❛s ❞♦s ❛❡r♦ssó✐s ♥♦ ❊st❛❞♦
❞❡ ❙ã♦ P❛✉❧♦ ❝♦♠ ❛ té❝♥✐❝❛ ❞❡ ▲■❉❆❘ ❘❛♠❛♥
❘❡♥❛t❛ ❋❛❝✉♥❞❡s ❞❛ ❈♦st❛
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ ●r❛✉ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛s ♥❛ ➪r❡❛ ❞❡ ❚❡❝♥♦❧♦❣✐❛ ◆✉❝❧❡❛r ✲ ▼❛t❡r✐❛✐s✳
❖r✐❡♥t❛❞♦r✿
❉r✳ ❊❞✉❛r❞♦ ▲❛♥❞✉❧❢♦
■♥st✐t✉t♦ ❞❡ P❡sq✉✐s❛ ❊♥❡r❣ét✐❝❛s ❡ ◆✉❝❧❡❛r❡s
❆✉t❛rq✉✐❛ ❛ss♦❝✐❛❞❛ à ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦
❊st✉❞♦ ❞❛s ♣r♦♣r✐❡❞❛❞❡s ó♣t✐❝❛s ❞♦s ❛❡r♦ssó✐s ♥♦ ❊st❛❞♦
❞❡ ❙ã♦ P❛✉❧♦ ❝♦♠ ❛ té❝♥✐❝❛ ❞❡ ▲■❉❆❘ ❘❛♠❛♥
❘❡♥❛t❛ ❋❛❝✉♥❞❡s ❞❛ ❈♦st❛
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ ●r❛✉ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛s ♥❛ ➪r❡❛ ❞❡ ❚❡❝♥♦❧♦❣✐❛ ◆✉❝❧❡❛r ✲ ▼❛t❡r✐❛✐s✳
❖r✐❡♥t❛❞♦r✿
❉r✳ ❊❞✉❛r❞♦ ▲❛♥❞✉❧❢♦
❉❡❞✐❝♦ ❡st❡ tr❛❜❛❧❤♦ ❛♦s ♠❡✉s ♣❛✐s✱ ❊✈❛ ❡ ▼❛r❝♦s❀ ❛♦ ♠❡✉ ✐r♠ã♦✱ ❋á❜✐♦❀ à ♠✐♥❤❛ ❛✈ó✱ ▲❛✉r❛ ❡✱ ❡♠ ❡s♣❡❝✐❛❧✱ ❛♦ ♠❡✉ ❣r❛♥❞❡ ❛♠♦r✱ ●✐✉❧✐❛♥♦ ♣♦✐s✱ ❛❧é♠ ❞❡ t❡r❡♠ ♠❡ ❛❝♦❧❤✐❞♦ ❞✉r❛♥t❡ t♦❞♦ ♦ ♠❡str❛❞♦✱ ❝♦♠♣❛rt✐❧❤❛r❛♠ ❝♦♠✐❣♦ ♦s ♠♦♠❡♥t♦s ❞❡ tr✐st❡③❛s ❡ t❛♠❜é♠ ❞❡ ❛❧❡❣r✐❛s ❞❡st❛ ❡t❛♣❛ ❞❛ ♠✐♥❤❛ ✈✐❞❛✳
❆❣r❛❞❡❝✐♠❡♥t♦s
➚ ♠✐♥❤❛ ❣r❛♥❞❡ ❢❛♠í❧✐❛✱ t✐❛s ❡ t✐♦s✱ ♣r✐♠❛s ❡ ♣r✐♠♦s ❡ ❡♠ ❡s♣❡❝✐❛❧ à ♠✐♥❤❛ t✐❛ ❊❧✈✐r❛ ♣❡❧♦ ❛♣♦✐♦ ❡ ✐♥❝❡♥t✐✈♦ ♣❛r❛ ✐♥✐❝✐❛r ♦ ♣r♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡ ❛♦s ♠❡✉s t✐♦s ❙✉❡❧✐ ❡ ❘❛❢❛❡❧ ♣❡❧❛ ❡♥♦r♠❡ ♣❛❝✐ê♥❝✐❛ ❡♠ r❡✈✐s❛r ❡st❛ ❞✐ss❡rt❛çã♦ tã♦ ❝❤❡✐❛ ❞❡ ❡rr♦s ❣r❛♠❛t✐❝❛✐s✳
❆♦s ♠❡✉s ❛♠✐❣♦s ❞♦ ■P❊◆✱ ❋❛❜í♦❧❛✱ ●❡rs♦♥✱ ❍♦rá❝✐♦✱ ■✈❛♥✐❧❞♦✱ ❏❛✐r✱ ❏♦♥❛s ❡ ❚❤✐❛❣♦ ♣❡❧♦s ✐♥❡♥❛rrá✈❡✐s ❝❛❢és ❞❛ t❛r❞❡ ♥♦ ■P❊◆✳
❆♦s ❛♠✐❣♦s ❞♦ ■❋❯❙P✱ ❋❡❧✐s✱ ▲❡❛♥❞r♦ ✭▲▼✮✱ ▲❡❛♥❞r♦ ✭▲❡❧❛s✮✱ ◆❛t❤❛❧② ❡ ▼❡❧✐♥❛ ♣♦r ♠❡ s✉♣♦rt❛r❡♠ ♥❛s ♠❛❞r✉❣❛❞❛s ❞❡ ❡st✉❞♦s ❞❡ q✉â♥t✐❝❛ ❡ ♣❡❧❛s ❝♦♥✈❡rs❛s ♣r❡❝✐♦s❛s q✉❡ t✐✈❡♠♦s✳
❊♠ ❡s♣❡❝✐❛❧ ❛♦ ❛♠✐❣♦ ❋á❜✐♦ ♣❡❧❛s ✐♥ú♠❡r❛s ✈❡③❡s ❡♠ q✉❡ ♠❡ ❛❥✉❞♦✉ ❞✉r❛♥t❡ ♦ ♠❡str❛❞♦ ❞❛♥❞♦ s✉♣♦rt❡ té❝♥✐❝♦ ❡ ❛♣♦✐♦ ♠♦r❛❧✱ ❛❧é♠ ❞❛s ❜♦❛s r✐s❛❞❛s q✉❡ ♠❡ ♣r♦♣♦r❝✐♦♥♦✉✳
❆♦ ❉r✳ ❊❞✉❛r❞♦ ▲❛♥❞✉❧❢♦ ♣❡❧❛ ♠❛♥❡✐r❛ ❣❡♥t✐❧ ❡ ❞❡❧✐❝❛❞❛ q✉❡ ❝♦♥❞✉③✐✉ t♦❞♦s ♦s ♠♦♠❡♥✲ t♦s ❞❛ ♠✐♥❤❛ ♦r✐❡♥t❛çã♦ ❡ t❛♠❜é♠ ♣❡❧♦ ✐♥❝❛♥sá✈❡❧ ✐♥❝❡♥t✐✈♦ ❡ ♠♦t✐✈❛çã♦ ♥♦s ♠♦♠❡♥t♦s ♠❛✐s ár❞✉♦s ❡ ❞✐❢í❝❡✐s✳
❆ t♦❞❛ ❡q✉✐♣❡ ❞♦ ❈▲❆ ♣❡❧♦ ❛♣♦✐♦✳
❚♦❞❛ ❛ ❝♦♥❝❡♣çã♦ ♠♦❞❡r♥❛ ❞♦ ♠✉♥❞♦ t❡♠ ❝♦♠♦ ❢✉♥❞❛♠❡♥t♦ ❛ ✐❧✉sã♦ ❞❡ q✉❡ ❛s ❝❤❛♠❛❞❛s ❧❡✐s ❞❛ ♥❛t✉r❡③❛ s❡❥❛♠ ❛s ❡①♣❧✐❝❛çõ❡s ❞♦s ❢❡♥ô♠❡♥♦s ♥❛t✉r❛✐s✳
❊st✉❞♦ ❞❛s ♣r♦♣r✐❡❞❛❞❡s ó♣t✐❝❛s ❞♦s ❛❡r♦ssó✐s ♥♦ ❊st❛❞♦ ❞❡ ❙ã♦ P❛✉❧♦ ❝♦♠ ❛ té❝♥✐❝❛ ❞❡ ▲■❉❆❘ ❘❛♠❛♥
❘❡♥❛t❛ ❋❛❝✉♥❞❡s ❞❛ ❈♦st❛
❘❡s✉♠♦
❊st✉❞♦ ❞❛s ♣r♦♣r✐❡❞❛❞❡s ó♣t✐❝❛s ❞♦s ❛❡r♦ssó✐s ♥♦ ❊st❛❞♦ ❞❡ ❙ã♦ P❛✉❧♦ ❝♦♠ ❛ té❝♥✐❝❛ ❞❡ ▲■❉❆❘ ❘❛♠❛♥
❘❡♥❛t❛ ❋❛❝✉♥❞❡s ❞❛ ❈♦st❛
❆❜str❛❝t
❙✉♠ár✐♦
▲✐st❛ ❞❡ ❋✐❣✉r❛s ✾
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ✶✶
▲✐st❛ ❞❡ ❆❜r❡✈✐❛t✉r❛s ✶✷
■♥tr♦❞✉çã♦ ✶✸
❏✉st✐✜❝❛t✐✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ❖r❣❛♥✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸
❖❜❥❡t✐✈♦s ✶✽
✶ ❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛ ✶✾
✶✳✶ ❊s♣❛❧❤❛♠❡♥t♦ ❊❧ást✐❝♦ ❡ ■♥❡❧ást✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✶✳✷ ❊s♣❛❧❤❛♠❡♥t♦ ❘❛♠❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷
✷ ❚é❝♥✐❝❛ ▲■❉❆❘ ✷✼
✷✳✶ ❙✐st❡♠❛ ▲■❉❆❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✷✳✶✳✶ ❚r❛♥s♠✐ss♦r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✷✳✶✳✷ ❘❡❝❡♣t♦r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✷✳✶✳✸ ❉❡t❡❝t♦r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✷✳✷ ▲■❉❆❘ ❘❛♠❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✷✳✷✳✶ ▼❡❞✐❞❛s ❞❡ ❱❛♣♦r ❞✬➪❣✉❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✷✳✷✳✷ ▼❡❞✐❞❛s ❞❡ ❆❡r♦ss♦❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽
✸ P❛rt❡ ✶ ✲ ❈❛❧✐❜r❛çã♦ ❞❡ ✉♠ ▲❘❱❆ ✹✶
✸✳✶ ▼❡t♦❞♦❧♦❣✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✸✳✶✳✶ ❈á❧❝✉❧♦ ❞❛ ❘▼❱❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✸✳✶✳✷ ▼❛♣❡❛♠❡♥t♦ ❞♦ ❚❡❧❡s❝ó♣✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸
✸✳✶✳✸ ❋✉♥çã♦ ❘❡s♣♦st❛ ❞♦ ❙✐st❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✸✳✶✳✹ ❊✜❝✐ê♥❝✐❛ Ó♣t✐❝❛ ❞♦ ❙✐st❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✸✳✷ ❘❡s✉❧t❛❞♦s ❡ ❉✐s❝✉ssõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✸✳✷✳✶ ▲â♠♣❛❞❛ ❞❡ ❈❛❧✐❜r❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✸✳✷✳✷ ❈✉r✈❛s ❞❡ ❚r❛♥s♠✐ssã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✸✳✷✳✸ ▼❛♣❡❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✸✳✷✳✹ Pr✐♠❡✐r♦ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ✭▼❛rç♦ ❞❡ ✷✵✵✾✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✸✳✷✳✺ ❙❡❣✉♥❞♦ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ✭❏✉♥❤♦✴❏✉❧❤♦ ❞❡ ✷✵✵✾✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷
✹ P❛rt❡ ✷ ✲ ❆♥á❧✐s❡ ❞❛s ♣r♦♣r✐❡❞❛❞❡s ó♣t✐❝❛s ❞♦s ❛❡r♦ssó✐s ✺✽ ✹✳✶ ▼❡t♦❞♦❧♦❣✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✹✳✶✳✶ ❈❛r❛❝t❡ríst✐❝❛s ❞♦ s✐st❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✹✳✶✳✷ ❈á❧❝✉❧♦ ❞♦ ❝♦❡✜❝✐❡♥t❡ ❞❡ ❡①t✐♥çã♦ ❡ ❞❛ ❆❖❉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✹✳✶✳✸ ❈á❧❝✉❧♦ ❞♦ ❝♦❡✜❝✐❡♥t❡ ❞❡ r❡tr♦❡s♣❛❧❤❛♠❡♥t♦ ❡ ▲❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✹✳✶✳✹ ❈á❧❝✉❧♦ ❞❛ ❙❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✹✳✷ ❘❡s✉❧t❛❞♦s ❡ ❉✐s❝✉ssõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✹✳✷✳✶ ❙ã♦ P❛✉❧♦ ✲ ❆❜r✐❧ ❛ ❥✉♥❤♦ ❞❡ ✷✵✵✾ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✹✳✷✳✷ ❘✐♦ ❈❧❛r♦ ✲ ❏✉♥❤♦ ❛ ♦✉t✉❜r♦ ❞❡ ✷✵✵✾ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✹✳✷✳✸ ❈✉❜❛tã♦ ✲ ◆♦✈❡♠❜r♦ ❞❡ ✷✵✵✾ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✹✳✷✳✹ ❇❛✉r✉ ✲ ❋❡✈❡r❡✐r♦ ❞❡ ✷✵✶✵ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✹✳✷✳✺ ❈♦♥s✐❞❡r❛çõ❡s ✜♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼
❈♦♥❝❧✉sã♦ ✼✹
❆ ❊s♣❛❧❤❛♠❡♥t♦ ❘❛②❧❡✐❣❤ ❡ ▼✐❡ ✼✻
❆✳✶ ❊s♣❛❧❤❛♠❡♥t♦ ❘❛②❧❡✐❣❤ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ❆✳✷ ❊s♣❛❧❤❛♠❡♥t♦ ▼✐❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽
❇ ▲■❉❆❘ ❞❡ ❘❡tr♦❡s♣❛❧❤❛♠❡♥t♦ ❊❧ást✐❝♦ ✽✶
❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá✜❝❛s ✽✺
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✶✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞♦ ❡s♣❛❧❤❛♠❡♥t♦ ❘❛♠❛♥ ❙t♦❦❡s✳ ❆ tr❛♥s✐çã♦ ❛t✉❛❧ é ❞♦ ❡st❛❞♦|0 ♣❛r❛|f✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✶✳✷ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞♦ ❡s♣❛❧❤❛♠❡♥t♦ ❘❛♠❛♥ ❙t♦❦❡s ❡ ❆♥t✐✲❙t♦❦❡s
✭∆ν±1✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸
✶✳✸ ❉✐str✐❜✉✐çã♦ t❡ór✐❝❛ ❞♦ ❡s♣❡❝tr♦ ✈✐❜r❛❝✐♦♥❛❧✲r♦t❛❝✐♦♥❛❧ ❘❛♠❛♥ ❛ ✸✵✵ ❑✱ ♠♦s✲ tr❛♥❞♦ ❛s ❡str✉t✉r❛s ❞♦s r❛♠♦s O✱Q❡ S ♣❛r❛ ❛ ♠♦❧é❝✉❧❛ ❞❡ ♥✐tr♦❣ê♥✐♦✳ ✳ ✳ ✳ ✷✺
✷✳✶ ❚✐♣♦s ❞❡ ❝♦♥✜❣✉r❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✷✳✷ ❉✐❛❣r❛♠❛ ✐❧✉str❛t✐✈♦ ❞❡ ✉♠ s✐st❡♠❛ ▲■❉❆❘ ❝♦❛①✐❛❧ ❣❡♥ér✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵
✸✳✶ ❋♦t♦ ❞❛ ▲â♠♣❛❞❛ ❞❡ ❈❛❧✐❜r❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✸✳✷ ❉❛❞♦s ❢♦r♥❡❝✐❞♦s ♣❡❧♦ ❢❛❜r✐❝❛♥t❡✱ ❝✉r✈❛ ❛❥✉st❛❞❛ ❡ ❢✉♥çã♦ ❞❡ P❧❛♥❝❦✳ ✳ ✳ ✳ ✳ ✹✽ ✸✳✸ ❈✉r✈❛s ❞❡ tr❛♥s♠✐ssã♦ ❞♦s ✜❧tr♦s ❞❡ ❜❛♥❞❛ ❧❛r❣❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✸✳✹ ❋♦t♦s ❞♦ ❡①♣❡r✐♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✸✳✺ ❋♦t♦s ❞♦ ❡①♣❡r✐♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✸✳✻ ❋✐❣✉r❛s ❡♠ ✸❉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✸✳✼ ❱❛❧♦r❡s ❞❡ k∗ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺
✸✳✽ ❈♦♠♣♦rt❛♠❡♥t♦ ❞❛ t❛①❛ ❞❡ ❝♦♥t❛❣❡♠ ♠❡❞✐❞❛ ❡♠ r❡❧❛çã♦ à t❛①❛ ❞❡ ❝♦♥t❛❣❡♠ r❡❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✸✳✾ ❋✐❣✉r❛s ❡♠ ✸❉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✸✳✶✵ ❱❛❧♦r❡s ❞❡ k∗ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼
✹✳✶ ▲♦❝❛❧✐③❛çã♦ ❣❡♦❣rá✜❝❛ ❞❛s ❝✐❞❛❞❡s ♦♥❞❡ ❛ ❝❛♠♣❛♥❤❛ ❢♦✐ r❡❛❧✐③❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✹✳✷ ❋♦t♦s ❞♦ ▲■❉❆❘ ❘❛♠❛♥ ✉t✐❧✐③❛❞♦ ♥❛s ❝❛♠♣❛♥❤❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✹✳✸ ❉❛❞♦s r❡❢❡r❡♥t❡ ❛ ❛♥á❧✐s❡ ❞❛ ❙❘ ❡αaer ♣❛r❛ ❙ã♦ P❛✉❧♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸
✹✳✹ P❡r✜❧ ❛t♠♦s❢ér✐❝♦ ♣❛r❛ ❙ã♦ P❛✉❧♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹
✹✳✺ ❉❛❞♦s r❡❢❡r❡♥t❡ ❛ ❛♥á❧✐s❡ ❞❛ ❙❘ ❡αaer ♣❛r❛ ♦ ❞✐❛ ✵✻ ❡ ✶✹ ❞❡ ❥✉❧❤♦ ❞❡ ✷✵✵✾✳ ✳ ✻✺
✹✳✻ P❡r✜s ❛t♠♦s❢ér✐❝♦s r❡❢❡r❡♥t❡s ❛♦s ❞✐❛s ✵✻ ❡ ✶✹ ❞❡ ❥✉❧❤♦ ❞❡ ✷✵✵✾✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✹✳✼ ❉❛❞♦s r❡❢❡r❡♥t❡ ❛ ❛♥á❧✐s❡ ❞❛ ❙❘ ❡ αaer ♣❛r❛ ♦ ❞✐❛ ✵✶ ❡ ✶✽❞❡ ♥♦✈❡♠❜r♦ ❞❡ ✷✵✶✵✳ ✻✾
✹✳✽ P❡r✜s ❛t♠♦s❢ér✐❝♦s r❡❢❡r❡♥t❡s ❛♦s ❞✐❛s ✵✶ ❡ ✶✽❞❡ ♥♦✈❡♠❜r♦ ❞❡ ✷✵✵✾✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✹✳✾ ❉❛❞♦s r❡❢❡r❡♥t❡ ❛ ❛♥á❧✐s❡ ❞❛ ❙❘ ❡αaer ♣❛r❛ ♦ ❞✐❛ ✵✺ ❡ ✵✽❞❡ ❢❡✈❡r❡✐r♦ ❞❡ ✷✵✶✵✳ ✼✶
✹✳✶✵ P❡r✜s ❛t♠♦s❢ér✐❝♦s r❡❢❡r❡♥t❡s ❛♦s ❞✐❛s ✵✺ ❡ ✵✽❞❡ ❢❡✈❡r❡✐r♦ ❞❡ ✷✵✶✵✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✹✳✶✶ ❈♦♠♣❛r❛çã♦ ❞♦s ❞❛❞♦s ❡♥tr❡ ❛ r♦t✐♥❛ ❞❡s❡♥✈♦❧✈✐❞❛ ♥❡ss❛ ❞✐ss❡rt❛çã♦ ❡ ❞❛ ◆❆❙❆✳ ✼✸
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✶✳✶ ❉❡s✈✐♦ ❞♦ ♥ú♠❡r♦ ❞❡ ♦♥❞❛ ❡ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♦♥❞❛ ❘❛♠❛♥ ♣❛r❛ ♦ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♦♥❞❛ ❞❡ ✸✸✼✱✶ ♥♠ ❞❛ r❛❞✐❛çã♦ ✐♥❝✐❞❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻
✸✳✶ ❚❛❜❡❧❛ ❞❡ ✈❛❧♦r❡s ❞❡ ❝♦♥✈❡rsã♦ ❡♥tr❡ ❜❛♥❞❛s ♣❛ss❛♥t❡s ❡♠ ♥ú♠❡r♦ ❞❡ ♦♥❞❛ ❡ ❡♠ ❝♦♠♣r✐♠❡♥t♦s ❞❡ ♦♥❞❛ ♣❛r❛ ✸✺✹✱✼ ♥♠ ❡ ✺✸✷ ♥♠✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ✳ ✳ ✳ ✳ ✹✸ ✸✳✷ ❱❛❧♦r❡s ❞❛ r❛③ã♦ ❞❛ s❡❝çã♦ ❞❡ r❡tr♦❡s♣❛❧❤❛♠❡♥t♦ ❘❛♠❛♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✸✳✸ ◆♦✈♦s ✈❛❧♦r❡s ❞❛ r❛③ã♦ ❞❛ s❡❝çã♦ ❞❡ r❡tr♦❡s♣❛❧❤❛♠❡♥t♦ ❘❛♠❛♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸
✹✳✶ ❱❛❧♦r❡s ❞❡ ❆❖❉ ❡ ▲❘ ♣❛r❛ ❛s ❝✐❞❛❞❡s ♦♥❞❡ ❢♦✐ r❡❛❧✐③❛❞❛ ❛ ❝❛♠♣❛♥❤❛✳ ✳ ✳ ✳ ✳ ✻✼
▲✐st❛ ❞❡ ❆❜r❡✈✐❛t✉r❛s
ND ❋✐❧tr♦ ❞❡ ❞❡♥s✐❞❛❞❡ ♥❡✉tr❛
OD ❉❡♥s✐❞❛❞❡ Ó♣t✐❝❛
❆❖❉ ❊s♣❡ss✉r❛ Ó♣t✐❝❛ ❞♦ ❆❡r♦ss♦❧
❈❊❆P▲❆ ❈❡♥tr♦ ❞❡ ❆♥á❧✐s❡ ❡ P❧❛♥❡❥❛♠❡♥t♦ ❆♠❜✐❡♥t❛❧
❈❊P❊▼❆ ❈❡♥tr♦ ❞❡ P❡sq✉✐s❛ ❡ ❈❛♣❛❝✐t❛çã♦ ❡♠ ▼❡✐♦ ❆♠❜✐❡♥t❡
❈▲❆ ❈❡♥tr♦ ❞❡ ▲❛s❡rs ❡ ❆♣❧✐❝❛çõ❡s
❋❖❱❈❛♠♣♦ ❞❡ ✈✐sã♦
❋❲❍▼ ▲❛r❣✉r❛ ❛ ♠❡✐❛ ❛❧t✉r❛
■▼❍ ■♥t❡r✈❛❧♦s ❞❡ ♠é❞✐❛ ❤♦rár✐❛
■P❈❈ ■♥t❡r❣♦✈❡r♥♠❡♥t❛❧ P❛♥❡❧ ♦♥ ❈❧✐♠❛t❡ ❈❤❛♥❣❡
■P❊◆ ■♥st✐t✉t♦ ❞❡ P❡sq✉✐s❛s ❊♥❡r❣ét✐❝❛s ❡ ◆✉❝❧❡❛r❡s
■P▼❡t ■♥st✐t✉t♦ ❞❡ P❡sq✉✐s❛s ▼❡t❡♦r♦❧ó❣✐❝❛s
▲❆❆▲ ▲❛❜♦r❛tór✐♦ ❞❡ ❆♣❧✐❝❛çõ❡s ❆♠❜✐❡♥t❛✐s ❛ ▲❛s❡r
▲❘ ❘❛③ã♦ ▲■❉❆❘
▲❘❱❆ ▲■❉❆❘ ❘❛♠❛♥ ❞❡ ❱❛♣♦r ❞✬➪❣✉❛
P▼❚ ❋♦t♦♠✉❧t✐♣❧✐❝❛❞♦r❛s
❘▼❱❆ ❘❛③ã♦ ❞❡ ▼✐st✉r❛ ❞♦ ❱❛♣♦r ❞✬➪❣✉❛
❙❆❉▲ ❙✐st❡♠❛ ❞❡ ❆♥á❧✐s❡ ❞❡ ❉❛❞♦s ▲■❉❆❘
❙❘ ❘❛③ã♦ ❞❡ ❊s♣❛❧❤❛♠❡♥t♦
❚❘▲ ❚❛①❛ ❞❡ r❡♣❡t✐çã♦ ❞♦ ❧❛s❡r
❯◆❊❙P ❯♥✐✈❡rs✐❞❛❞❡ ❊st❛❞✉❛❧ P❛✉❧✐st❛
■♥tr♦❞✉çã♦
❏✉st✐✜❝❛t✐✈❛
❖ ❊st❛❞♦ ❞❡ ❙ã♦ P❛✉❧♦✱ ❧♦❝❛❧✐③❛❞♦ ♥❛ r❡❣✐ã♦ ❙✉❞❡st❡ ❞♦ ❇r❛s✐❧✱ ❝♦♥❝❡♥tr❛ ❝❡r❝❛ ❞❡
28,0% ❞❛ ♣♦♣✉❧❛çã♦ ❜r❛s✐❧❡✐r❛ ❡ 40,5% ❞♦ Pr♦❞✉t♦ ■♥t❡r♥♦ ❇r✉t♦ ❞❡ ✷✵✵✼❬✶❪✳❆❧é♠
❞✐ss♦✱ ♣♦ss✉✐ ♦ ♠❛✐♦r ❝❡♥tr♦ ✐♥❞✉str✐❛❧ ❞❛ ❆♠ér✐❝❛ ▲❛t✐♥❛✱ ❝❛r❛❝t❡r✐③❛♥❞♦✲s❡ ♣❡❧❛ ❛❧t❛ ♣r♦❞✉çã♦ ❞❡ ✈❡í❝✉❧♦s ❡ ♦ ♠❛✐♦r ❝❡♥tr♦ ❛❣r♦♣❡❝✉ár✐♦✱ ❝♦♠ ❜❛s❡✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡✱ ♥❛s ❝✉❧t✉r❛s ❞❡ ❝❛♥❛✲❞❡✲❛çú❝❛r✱ ❧❛r❛♥❥❛ ❡ ❝❛❢é❬✶❪✳❊ss❛s ♣❛rt✐❝✉❧❛r✐❞❛❞❡s ❢❛③❡♠ ❞♦ ❊st❛❞♦ ❞❡ ❙ã♦ P❛✉❧♦ ✉♠ ❞♦s ♠❛✐♦r❡s ❡♠✐ss♦r❡s ❞❡ ❣❛s❡s ♣♦❧✉❡♥t❡s ❡ ❛❡r♦ssó✐s ❞❡ ♦r✐❣❡♠ ❛♥✲ tr♦♣♦❣ê♥✐❝❛ ❞♦ ♣❛ís✳
P♦ré♠✱ ❛ ♣r❡♦❝✉♣❛çã♦ ❝♦♠ ♦s ♥í✈❡✐s ❞❡ ♣♦❧✉✐çã♦ ❛t♠♦s❢ér✐❝❛✱ ♥ã♦ s❡ r❡str✐♥❣❡ ❛♦ ❊st❛❞♦ ❞❡ ❙ã♦ P❛✉❧♦ ❡ ♥❡♠ tã♦ ♣♦✉❝♦ ❛♦ ❇r❛s✐❧✱ ♣♦✐s s❡❣✉♥❞♦ ♦ r❡❧❛tór✐♦ ❞♦ ■P❈❈ ✭■♥t❡r❣♦✈❡r♥♠❡♥t❛❧ P❛♥❡❧ ♦♥ ❈❧✐♠❛t❡ ❈❤❛♥❣❡ ✕ ❲♦r❦✐♥❣ ●r♦✉♣ ■ ✮ ❞✐✈✉❧❣❛❞♦ ❡♠ ✷✵✵✼✱ ♦♥③❡ ❞♦s ❞♦③❡ ú❧t✐♠♦s ❛♥♦s ✭✶✾✾✺✲✷✵✵✻✮ ❢♦r❛♠ ❝♦♥s✐❞❡r❛❞♦s ♦s ♠❛✐s q✉❡♥t❡s ❞❡ ❛❝♦r❞♦ ❝♦♠ r❡❣✐str♦s ❞❡ ♠❡❞✐❞❛s ❞❛ t❡♠♣❡r❛t✉r❛ ♠é❞✐❛ ❣❧♦❜❛❧ ❞❡s❞❡ ✶✽✺✵✳❊ss❡ r❡❧❛tór✐♦ t❛♠✲ ❜é♠ ❞❡st❛❝❛ q✉❡ ❛ ❛t✐✈✐❞❛❞❡ ❤✉♠❛♥❛ ❝♦♥tr✐❜✉✐✉✱ ❡ ❛✐♥❞❛ ❝♦♥tr✐❜✉✐✱ s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ♣❛r❛ ❡ss❛s ❛❧t❡r❛çõ❡s ❝❧✐♠át✐❝❛s ❝❛✉s❛❞❛s✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡✱ ♣♦r ♠✉❞❛♥ç❛s ♥❛ q✉❛♥t✐✲ ❞❛❞❡ ❞❡ ❛❡r♦ssó✐s ♣r♦✈♦❝❛❞❛s ♣❡❧❛s ❛❧t❛s t❛①❛s ❞❡ ❡♠✐ssã♦ ❞❡ ♣♦❧✉❡♥t❡s ✐♥❞✉str✐❛✐s✱ ✈❡✐❝✉❧❛r❡s✱ q✉❡✐♠❛ ❞❡ ❝♦♠❜✉stí✈❡✐s ❢óss❡✐s ❡ ❜✐♦♠❛ss❛✳
◆❡ss❡ ❝♦♥t❡①t♦✱ ♥✉♠❛ t❡♥t❛t✐✈❛ ❞❡ ❝♦♠♣r❡❡♥❞❡r ♠❡❧❤♦r ♦s ♣r♦❝❡ss♦s q✉❡ ❣♦✈❡r♥❛♠ ♦ ❝❧✐♠❛ ❞♦ ♥♦ss♦ ♣❧❛♥❡t❛✱ ❞✐✈❡rs❛s té❝♥✐❝❛s ❡ ✐♥str✉♠❡♥t♦s ❢♦r❛♠ ❞❡s❡♥✈♦❧✈✐❞♦s ♣❛r❛ ♦ ❡st✉❞♦ ❞❛s ♣r♦♣r✐❡❞❛❞❡s ❢ís✐❝❛s ❡ q✉í♠✐❝❛s ❞❛ ❛t♠♦s❢❡r❛✱ ❡st✉❞♦ ❡ss❡ q✉❡ ♣♦❞❡ s❡r r❡❛❧✐③❛❞♦ t❛♥t♦ ✐♥ s✐t✉✱ ✉t✐❧✐③❛♥❞♦ ✐♥str✉♠❡♥t♦s ❝♦♠♦ r❛❞✐♦s♦♥❞❛s ❡ ♥❡❢❡❧ô♠❡tr♦s❬✷❪✱ ❝♦♠♦ ♣♦r s❡♥s♦r✐❛♠❡♥t♦ r❡♠♦t♦✱ ✉t✐❧✐③❛♥❞♦ ✐♥str✉♠❡♥t♦s ❡♠ ❜❛s❡s ♥❛ s✉♣❡r❢í❝✐❡ ♦✉ ❛
❜♦r❞♦ ❞❡ s❛té❧✐t❡s❬✸❪✳
❆ té❝♥✐❝❛ ❞❡ s❡♥s♦r✐❛♠❡♥t♦ r❡♠♦t♦✱ q✉❡ ❢♦✐ ✉t✐❧✐③❛❞❛ ♥❡ss❛ ❞✐ss❡rt❛çã♦✱ ♣♦❞❡ s❡r ❞✐✈✐❞✐❞❛ ❡♠ ❞♦✐s t✐♣♦s✱ ♣❛ss✐✈♦ ❡ ❛t✐✈♦✳ ◆♦ ♣r✐♠❡✐r♦✱ ♦ s❡♥s♦r ❝❛♣t❛ ❛ r❛❞✐❛çã♦ ❡❧❡tr♦✲ ♠❛❣♥ét✐❝❛ r❡✢❡t✐❞❛ ♣♦r ✉♠ ❛❧✈♦✱ ♦ q✉❛❧ é ✐❧✉♠✐♥❛❞♦ ♣♦r ✉♠❛ ❢♦♥t❡ ❞❡ ❡♥❡r❣✐❛ ❡①t❡r♥❛❀ ♥♦ ❝❛s♦ ❞♦ ❛❧✈♦ s❡r ❛ ❛t♠♦s❢❡r❛✱ ❛ ❢♦♥t❡ ❞❡ ❡♥❡r❣✐❛ ❡①t❡r♥❛ é ♦ ❙♦❧✳ ◆♦ s❡❣✉♥❞♦✱ ♦ s❡♥s♦r ❝❛♣t❛ ❛ r❛❞✐❛çã♦ ❡s♣❛❧❤❛❞❛ ♦✉ r❡tr♦❡s♣❛❧❤❛❞❛ ♣❡❧♦ ❛❧✈♦ q✉❡ ❢♦✐ ✐rr❛❞✐❛❞♦ ♣♦r ✉♠❛ ❢♦♥t❡ ❛rt✐✜❝✐❛❧✱ s❡♥❞♦ ✉♠ ❣❡r❛❞♦r ❞❡ ♠✐❝r♦♦♥❞❛s ♥♦ ❝❛s♦ ❞♦ ❘❆❉❆❘ ♦✉ ✉♠ ❧❛s❡r ♥♦ ❝❛s♦ ❞❛ té❝♥✐❝❛ ▲■❉❆❘ ❛❝rô♥✐♠♦ ❞❡ ▲✐❣❤t ❉❡t❡❝t✐♦♥ ❛♥❞ ❘❛♥❣✐♥❣❬✸✕✺❪✳
❖ ▲■❉❆❘ é✱ ♣♦rt❛♥t♦✱ ✉♠❛ té❝♥✐❝❛ ❞❡ s❡♥s♦r✐❛♠❡♥t♦ r❡♠♦t♦ q✉❡ ❝♦♥s✐st❡ ♥❛ ❡♠✐s✲ sã♦ ❞❡ ✉♠ ❢❡✐①❡ ❞❡ r❛❞✐❛çã♦ ❡❧❡tr♦♠❛❣♥ét✐❝❛❬✻❪ q✉❡ ✐♥t❡r❛❣❡ ❝♦♠ ❛s ♣❛rtí❝✉❧❛s ❡✴♦✉ ♠♦❧é❝✉❧❛s ❞♦ ♠❡✐♦ s❡♥❞♦ ❡s♣❛❧❤❛❞♦ ❡✴♦✉ ❛❜s♦r✈✐❞♦✳ ➚ ♣❛r❝❡❧❛ ❞❛ r❛❞✐❛çã♦ q✉❡ é ❡s✲ ♣❛❧❤❛❞❛ ❡ r❡t♦r♥❛ ♣❛r❛ ♦ s✐st❡♠❛ ▲■❉❆❘ ❞á✲s❡ ♦ ♥♦♠❡ ❞❡ r❛❞✐❛çã♦ r❡tr♦❡s♣❛❧❤❛❞❛✳ ❊st❛ r❛❞✐❛çã♦ r❡tr♦❡s♣❛❧❤❛❞❛✱ ♠❡❞✐❞❛ ♣❡❧♦ r❡❝❡♣t♦r ❞♦ ▲■❉❆❘✱ é ✉s❛❞❛ ♣❛r❛ ❞❡t❡r✲ ♠✐♥❛r ♦s ❝♦❡✜❝✐❡♥t❡s ❞❡ r❡tr♦❡s♣❛❧❤❛♠❡♥t♦ ❡ ❡①t✐♥çã♦ ❞❛s ♣❛rtí❝✉❧❛s ❡✴♦✉ ♠♦❧é❝✉❧❛s ❞♦ ♠❡✐♦ ♥♦ q✉❛❧ ♦ ❢❡✐①❡ s❡ ♣r♦♣❛❣❛❬✼❪✳ ❊ss❛ té❝♥✐❝❛ ♣♦ss✉✐ ♦ ♠❡s♠♦ ♣r✐♥❝í♣✐♦ ❢ís✐❝♦ ❞♦ ❘❆❉❆❘✱ s❡♥❞♦ q✉❡ ❛ ♣r✐♥❝✐♣❛❧ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ❡❧❡s é ♦ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♦♥❞❛ ❞❛ r❛❞✐❛çã♦ ✉t✐❧✐③❛❞❛✳ ❖ ❘❆❉❆❘ tr❛❜❛❧❤❛ ❝♦♠ ❝♦♠♣r✐♠❡♥t♦s ❞❡ ♦♥❞❛ ♥❛ ❢❛✐①❛ ❤❡rt③✐❛♥❛✱ ❝♦♠ ❢r❡q✉ê♥❝✐❛s q✉❡ ✈❛r✐❛♠ ❞❡ ▼❍③ ❛ ●❍③✱ ❞♦ ❡s♣❡❝tr♦ ❡❧❡tr♦♠❛❣♥ét✐❝♦✱ ❡♥q✉❛♥t♦ ♦ ▲■❉❆❘ ✉t✐❧✐③❛ ❛ ❢❛✐①❛ ❞❡ r❛❞✐❛çã♦ q✉❡ ✈❛✐ ❞♦ ✐♥❢r❛✈❡r♠❡❧❤♦✱ ♣❛ss❛ ♣❡❧♦ ✈✐sí✈❡❧ ❡ ❝❤❡❣❛ ❛♦ ✉❧tr❛✈✐♦❧❡t❛✳ ❖ q✉❡ ❞❡t❡r♠✐♥❛ ♦ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♦♥❞❛ ♦✉ ♦s ❝♦♠♣r✐♠❡♥t♦s ❞❡ ♦♥❞❛ ❛ s❡r❡♠ ✉t✐❧✐③❛❞♦s ♣❡❧♦ ▲■❉❆❘ sã♦ ♦s ❞✐✈❡rs♦s ♦❜❥❡t♦s ❞❡ ❡st✉❞♦✳
❖ s✐st❡♠❛ ▲■❉❆❘ é ♠✉✐t♦ ❛tr❛t✐✈♦ ❞❡✈✐❞♦ ❛ ❛❧❣✉♠❛s ❝❛r❛❝t❡ríst✐❝❛s ❡s♣❡❝í✜❝❛s t❛✐s ❝♦♠♦✱ s✉❛ ❛❧t❛ r❡s♦❧✉çã♦ ❡s♣❛❝✐❛❧ ❡ t❡♠♣♦r❛❧ ❡ ❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ ♦❜s❡r✈❛çã♦ ❞♦ ♦❜❥❡t♦ ❞❡ ❡st✉❞♦ s❡♠ ✐♥t❡r❢❡rê♥❝✐❛ ❞✐r❡t❛ ❡ ❡♠ t❡♠♣♦ r❡❛❧✳ ◗✉❛♥❞♦ ♦ ♦❜❥❡t♦ ❞❡ ❡st✉❞♦ ❡♠ q✉❡stã♦ é ♦ ♠♦♥✐t♦r❛♠❡♥t♦ ❞❡ ♣♦❧✉❡♥t❡s ♥❛ ❛t♠♦s❢❡r❛✱ ♣♦r ❡①❡♠♣❧♦✱ ♦ ▲■❉❆❘ ♣♦❞❡ ❢♦r♥❡❝❡r✱ ❝♦♠ ✉♠❛ ❢♦♥t❡ ❧❛s❡r ❞❡ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♦♥❞❛ ❞❡ ❧❛r❣✉r❛ ❞❡ ❜❛♥❞❛ ❡str❡✐t❛✱ ✐♥❢♦r♠❛çõ❡s s♦❜r❡ ❛ ♣r❡s❡♥ç❛ ❡ ❞✐str✐❜✉✐çã♦ ❞❡ ♣❛rtí❝✉❧❛s ❞❡ ✵✱✶ ❛ ✶✵ µ♠ ❞❡ ❞✐â♠❡tr♦✱ ❡
s❡ ❢♦r ♦♣❡r❛❞♦ ❝♦♠ ❞♦✐s s✐♥❛✐s ❞✐st✐♥t♦s ❡♠ ❝♦♠♣r✐♠❡♥t♦s ❞❡ ♦♥❞❛✱ ♣♦❞❡ ♦❜t❡r ✐♥❢♦r♠❛✲ çã♦ ❞❛ ❝♦♥❝❡♥tr❛çã♦ ❡s♣❡❝í✜❝❛ ❞♦ ❝♦♥t❡ú❞♦ ❞❡ ❣❛s❡s ♥❛ ❛t♠♦s❢❡r❛✱ ❛t✐♥❣✐♥❞♦ ✉♠ ♥í✈❡❧ ❞❡ s❡♥s✐❜✐❧✐❞❛❞❡ ❞❡ ❛té ✵✱✶ ♣♣❜ ♥♦ ❝❛s♦ ❞❛s ❝♦♥❝❡♥tr❛çõ❡s ♠♦❧❡❝✉❧❛r❡s✳ ❚✉❞♦ ✐ss♦ ❝♦♠ ✉♠ ✐♥t❡r✈❛❧♦ ❞❡ ♠❛♣❡❛♠❡♥t♦ q✉❡ ✈❛✐ ❞❡s❞❡ ❞♦ s♦❧♦ ❛té ♠❛✐s ❞❡ ✶✵✵ ❦♠ ❞❡ ❛❧t✐t✉❞❡✳ ❆❧é♠ ❞✐ss♦✱ ♦ ▲■❉❆❘ t❛♠❜é♠ ♣♦❞❡ s❡r ♦♣❡r❛❞♦ ❡♠ ♣❧❛t❛❢♦r♠❛s ♠ó✈❡✐s ❝♦♠♦ ❜❛r❝♦s✱
❤❡❧✐❝ó♣t❡r♦s✱ ❛✈✐õ❡s ♦✉ s❛té❧✐t❡s✳
▲■❉❆❘ ❡❧ást✐❝♦✱ ❘❛♠❛♥✱ ❞❡ ❞❡♣♦❧❛r✐③❛çã♦✱ ❉■❆▲ sã♦ ❛❧❣✉♥s ❡①❡♠♣❧♦s ❞❡ s✐st❡♠❛s ▲■❉❆❘❬✸✱ ✺❪✳ ❊ss❡ tr❛❜❛❧❤♦ t❡♠ ❝♦♠♦ ❢♦❝♦ ♣r✐♥❝✐♣❛❧ ❛ té❝♥✐❝❛ ▲■❉❆❘ ❘❛♠❛♥✱ ♣♦✐s ❡❧❛ ♣♦ss✉✐ ❣r❛♥❞❡s ✈❛♥t❛❣❡♥s q✉❛♥❞♦ ❝♦♠♣❛r❛❞❛ ❝♦♠ ❛ té❝♥✐❝❛ ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ▲■❉❆❘ ❡❧ást✐❝♦❬✽❪✳ ◆♦ ▲■❉❆❘ ❡❧ást✐❝♦ ♦s ❝♦❡✜❝✐❡♥t❡s ❞❡ r❡tr♦❡s♣❛❧❤❛♠❡♥t♦ ❡ ❡①t✐♥çã♦ ❞♦ ❛❡r♦ss♦❧ ❞❡✈❡♠ s❡r ❞❡t❡r♠✐♥❛❞♦s ❛ ♣❛rt✐r ❞❡ ✉♠ ú♥✐❝♦ s✐♥❛❧ ♠❡❞✐❞♦ ❡ ♣❛r❛ ✐ss♦ é ♥❡❝❡ssár✐♦ ❢❛③❡r ❛❧❣✉♠❛s s✉♣♦s✐çõ❡s ❛ ♣r✐♦r✐❬✾❪✱ ❝♦♠♦ ❡stá ❞❡s❝r✐t♦ ♥♦ ❆♣ê♥❞✐❝❡ ❇ ❞❡st❛ ❞✐ss❡rt❛çã♦✳ P♦ré♠✱ ♦ ▲■❉❆❘ ❘❛♠❛♥ ♣❡r♠✐t❡ ❛ ❞❡t❡r♠✐♥❛çã♦ ❞♦ ♣❡r✜❧ ❞❡ ❡①t✐♥çã♦ ♣❛r❛ ♦s ❛❡r♦ssó✐s✱ ❞♦ ♣❡r✜❧ ❞❡ r❡tr♦❡s♣❛❧❤❛♠❡♥t♦ ❡ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ❞❛ ❘❛③ã♦ ▲■❉❆❘✶s❡♠
q✉❛❧q✉❡r t✐♣♦ ❞❡ s✉♣♦s✐çã♦ ❛ ♣r✐♦r✐❬✽❪✳
P❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦ ❢♦r❛♠ ✉t✐❧✐③❛❞♦s ❞♦✐s s✐st❡♠❛s ▲■❉❆❘ ❘❛✲ ♠❛♥✳ ❯♠ ❞❡❧❡s ❡stá ✐♥st❛❧❛❞♦ ❡♠ ❙ã♦ P❛✉❧♦ ♥♦ ▲❛❜♦r❛tór✐♦ ❞❡ ❆♣❧✐❝❛çõ❡s ❆♠❜✐❡♥t❛✐s ❛ ▲❛s❡r ✭▲❆❆▲✮✱ ❞❡♥tr♦ ❞♦ ❈❡♥tr♦ ❞❡ ▲❛s❡rs ❡ ❆♣❧✐❝❛çõ❡s ✭❈▲❆✮ ❞♦ ■♥st✐t✉t♦ ❞❡ P❡sq✉✐✲ s❛s ❊♥❡r❣ét✐❝❛s ❡ ◆✉❝❧❡❛r❡s ✭■P❊◆✮ ❡ s❡r✈✐✉ ♣❛r❛ ❛ r❡❛❧✐③❛çã♦ ❞❡ ✉♠❛ ❝❛❧✐❜r❛çã♦ ❛ ♣❛rt✐r ❞♦s ♣r✐♠❡✐r♦s ♣r✐♥❝í♣✐♦s✱ r❡♣❡t✐♥❞♦ ✉♠❛ ♠❡t♦❞♦❧♦❣✐❛ q✉❡ ❢♦✐ ✉t✐❧✐③❛❞❛ ♥❛ ❍♦✇❛r❞ ❯♥✐✲ ✈❡rs✐t②❬✶✵❪ ❡ ❡stá ❞❡s❝r✐t❛ ♥❛ ♣r✐♠❡✐r❛ ♣❛rt❡ ❞❡st❛ ❞✐ss❡rt❛çã♦✳ ❖ ♦✉tr♦✱ é ✉♠ s✐st❡♠❛ ▲■❉❆❘ ❘❛♠❛♥ ♠ó✈❡❧✱ ❞❡s❡♥✈♦❧✈✐❞♦ ♣❡❧❛ ❘❛②♠❡tr✐❝s ▲✐❞❛r ❙②st❡♠s q✉❡ ❢♦✐ ✉t✐❧✐③❛❞♦ ❡♠ ❝❛♠♣❛♥❤❛s r❡❛❧✐③❛❞❛s ❡♠ ❛❧❣✉♠❛s ❝✐❞❛❞❡s ❞♦ ❊st❛❞♦ ❞❡ ❙ã♦ P❛✉❧♦ ♣❛r❛ ❛q✉✐s✐çã♦ ❞❡ ❞❛❞♦s✱ ♦s q✉❛✐s ❢♦r❛♠ ❛♥❛❧✐s❛❞♦s ❡ ♦s r❡s✉❧t❛❞♦s ❡stã♦ ❛♣r❡s❡♥t❛❞♦s ♥❛ s❡❣✉♥❞❛ ♣❛rt❡ ❞♦ tr❛❜❛❧❤♦✳
❖r❣❛♥✐③❛çã♦
❆ ❞✐ss❡rt❛çã♦ ❡stá ❞✐✈✐❞✐❞❛ ❡♠ ♦✐t♦ ❝❛♣ít✉❧♦s✱ ❞♦✐s ❛♣ê♥❞✐❝❡s ❡ s✉❜❞✐✈✐❞✐❞❛ ❡♠ ❞✉❛s ♣❛rt❡s✱ ♥♦s q✉❛✐s sã♦ ❡①♣♦st❛s ❛s ❥✉st✐✜❝❛t✐✈❛s✱ ♦s ♦❜❥❡t✐✈♦s✱ ❛s t❡♦r✐❛s✱ ♦s r❡s✉❧t❛❞♦s ❡ ♦ q✉❡ ♠❛✐s ♣♦ss❛ ❢❛③❡r ♣❛rt❡ ❞❛ ❞❡s❝r✐çã♦ ❞♦ tr❛❜❛❧❤♦ r❡❛❧✐③❛❞♦ ♥❡st❡ ♠❡str❛❞♦✳
❖ ♣r✐♠❡✐r♦ ❝❛♣ít✉❧♦ ❝♦♠♣r❡❡♥❞❡ ❛ ❥✉st✐✜❝❛t✐✈❛ ❡ ❛ ♦r❣❛♥✐③❛çã♦ ❞❛ ❞✐ss❡rt❛çã♦✱ ♥♦ s❡❣✉♥❞♦ s❡rã♦ ❛♣r❡s❡♥t❛❞♦s ♦s ♦❜❥❡t✐✈♦s ♣r♦♣♦st♦s✱ ♦ t❡r❝❡✐r♦ tr❛t❛ ❞❡ ✉♠❛ r❡✈✐sã♦ ❞❛s t❡♦r✐❛s ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ ❡❧ást✐❝♦ ❡ ✐♥❡❧ást✐❝♦✱ t❡♥❞♦ ❝♦♠♦ ❡♥❢♦q✉❡ ♦ ❡s♣❛❧❤❛♠❡♥t♦ ❘❛♠❛♥✳ ❆ ❞❡s❝r✐çã♦ ❞♦ ❡s♣❛❧❤❛♠❡♥t♦ ❘❛②❧❡✐❣❤ ❡ ▼✐❡ s❡rá ♠❛✐s ❞❡t❛❧❤❛❞❛ ♥♦ ❛♣ê♥❞✐❝❡ ❆✳ ◆♦ q✉❛rt♦ ❝❛♣ít✉❧♦ s❡rá ❛♣r❡s❡♥t❛❞♦ ✉♠❛ ❞❡s❝r✐çã♦ ❞♦s ♣r✐♥❝✐♣❛✐s ❝♦♠♣♦♥❡♥t❡s ❞❡
✶r❛③ã♦ ❡♥tr❡ ♦s ❝♦❡✜❝✐❡♥t❡s ❞❡ ❡①t✐♥çã♦ ❡✱ r❡tr♦❡s♣❛❧❤❛♠❡♥t♦
✉♠ s✐st❡♠❛ ▲■❉❆❘ ❡ ❛ té❝♥✐❝❛ ▲■❉❆❘ ❘❛♠❛♥ ❡♠ ❞❡t❛❧❤❡✱ s❡♥❞♦ q✉❡ ❛ té❝♥✐❝❛ ▲■❉❆❘ ❊❧ást✐❝♦ s❡rá ❞❡s❝r✐t❛ ♥♦ ❛♣ê♥❞✐❝❡ ❇✳
❆ ♣❛rt✐r ❞♦ q✉✐♥t♦ ❝❛♣ít✉❧♦ ✜❝❛♠ ❡①♣♦st♦s ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♥❡st❡ tr❛❜❛❧❤♦ ❡✱ s❡♥❞♦ ❛ss✐♠✱ ❛ ❞✐ss❡rt❛çã♦ ♣❛ss❛ ❛ s❡r s✉❜❞✐✈✐❞✐❞❛ ❡♠ ❞✉❛s ♣❛rt❡s✳ ❖ q✉✐♥t♦ ❝❛♣ít✉❧♦✱ ♣r✐♠❡✐r❛ ♣❛rt❡ ❞♦ tr❛❜❛❧❤♦✱ tr❛t❛ ❞❛ ♠❡t♦❞♦❧♦❣✐❛ ✉t✐❧✐③❛❞❛ ♣❛r❛ ❛ ❝❛❧✐❜r❛çã♦ ❞♦ ▲■❉❆❘ ❘❛♠❛♥ ❞❡ ❱❛♣♦r ❞✬➪❣✉❛ ✭▲❘❱❆✮ ✐♥st❛❧❛❞♦ ♥♦ ▲❆❆▲ ❡ ❞♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♥❡ss❛ ❝❛❧✐❜r❛çã♦✳ ❆ s❡❣✉♥❞❛ ♣❛rt❡✱ ❛♣r❡s❡♥t❛❞❛ ♥♦ s❡①t♦ ❝❛♣ít✉❧♦✱ tr❛t❛ ❞❛ ♠❡t♦❞♦❧♦❣✐❛ ❡ r❡s✉❧t❛❞♦s ❞❛ ❛♥á❧✐s❡ ❞♦s ❞❛❞♦s ❞❡ ❛❡r♦ssó✐s ♦❜t✐❞♦s ❡♠ ✉♠❛ ❝❛♠♣❛♥❤❛ r❡❛❧✐③❛❞❛ ♥♦ ■♥st✐t✉t♦ ❞❡ P❡sq✉✐s❛s ▼❡t❡♦r♦❧ó❣✐❝❛s ✭■P▼❡t✮ ❞❛ ❯◆❊❙P ❞❡ ❇❛✉r✉✱ ♥♦ ❈❡♥tr♦ ❞❡ P❡sq✉✐s❛ ❡ ❈❛♣❛❝✐t❛çã♦ ❡♠ ▼❡✐♦ ❆♠❜✐❡♥t❡ ✭❈❊P❊▼❆✮ ❡♠ ❈✉❜❛tã♦✱ ♥♦ ❈❡♥tr♦ ❞❡ ❆♥á❧✐s❡ ❡ P❧❛♥❡❥❛♠❡♥t♦ ❆♠❜✐❡♥t❛❧ ✭❈❊❆P▲❆✮ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❊st❛❞✉❛❧ P❛✉❧✐st❛ ✭❯◆❊❙P✮ ❡♠ ❘✐♦ ❈❧❛r♦ ❡ ♥♦ ❈▲❆ ❡♠ ❙ã♦ P❛✉❧♦✳
❊♥❝❡rr❛♥❞♦✱ ♦ sét✐♠♦ ❝❛♣ít✉❧♦ ❛♣r❡s❡♥t❛ ✉♠❛ ❝♦♥❝❧✉sã♦ ❞♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♥❡st❡ ♠❡str❛❞♦ ❡ ♦ ♦✐t❛✈♦ ♠♦str❛ ❛s ♣❡rs♣❡❝t✐✈❛s ❞❡st❡ tr❛❜❛❧❤♦✳
❖❜❥❡t✐✈♦s
❖ ♦❜❥❡t✐✈♦ ♣r✐♥❝✐♣❛❧ ❞♦ tr❛❜❛❧❤♦ é ❛❞q✉✐r✐r ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ✐♥str✉♠❡♥t❛❧ ❞❡ ✉♠ s✐s✲ t❡♠❛ ▲■❉❆❘ ❘❛♠❛♥ ❡st✉❞❛♥❞♦ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ❝❛❞❛ ❝♦♠♣♦♥❡♥t❡ q✉❡ ♦ ❝♦♥st✐t✉✐ ❡✱ ❛ ♣❛rt✐r ❞❡ss❡ ❝♦♥❤❡❝✐♠❡♥t♦ ❛❞q✉✐r✐❞♦✱ ❝♦❧❡t❛r ❡ ❛♥❛❧✐s❛r ❞❛❞♦s ♦❜t✐❞♦s ❝♦♠ ❡ss❡ s✐st❡♠❛✳ P❛r❛ ✐ss♦✱ ❡st❛ ❞✐ss❡rt❛çã♦ ❡stá ❞✐✈✐❞✐❞❛ ❡♠ ❞✉❛s ♣❛rt❡s s❡♥❞♦ q✉❡ ❝❛❞❛ ♣❛rt❡ ♣♦ss✉✐ ✉♠ ♦❜❥❡t✐✈♦ ❡s♣❡❝í✜❝♦✳
❖ ♦❜❥❡t✐✈♦ ❡s♣❡❝í✜❝♦ ❞❛ ♣r✐♠❡✐r❛ ♣❛rt❡ ❞❛ ❞✐ss❡rt❛çã♦ é ❛ r❡❛❧✐③❛çã♦ ❞❡ ✉♠❛ ❝❛✲ ❧✐❜r❛çã♦ ✐♥❞❡♣❡♥❞❡♥t❡ ❞♦ s✐st❡♠❛ ▲■❉❆❘ ❘❛♠❛♥ ✐♥st❛❧❛❞♦ ♥♦ ❈▲❆ s❡❣✉✐♥❞♦ ✉♠❛ ♠❡t♦❞♦❧♦❣✐❛ q✉❡ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞❛ ♥❛ ❍♦✇❛r❞ ❯♥✐✈❡rs✐t②❬✶✵❪✳ ❊ss❛ ❝❛❧✐❜r❛çã♦ t❡♠ ❝♦♠♦ ♣r♦♣ós✐t♦ ❞❡t❡r♠✐♥❛r ❛ ❡✜❝✐ê♥❝✐❛ ó♣t✐❝❛ ❞♦ s✐st❡♠❛ ❡ ❛♣r❡s❡♥t❛r s✉❛ r❡s♣♦st❛ ❡s♣❡❝tr❛❧✳ ◆❛ s❡❣✉♥❞❛ ♣❛rt❡✱ ♦ ♦❜❥❡t✐✈♦ ❡s♣❡❝í✜❝♦ é ❡st✉❞❛r ❛s ♣r♦♣r✐❡❞❛❞❡s ó♣t✐❝❛s ❞♦s ❛❡✲ r♦ssó✐s ♥❛ tr♦♣♦s❢❡r❛ ♣♦r ♠❡✐♦ ❞❛ ❛✈❛❧✐❛çã♦ ❞❡ ❛❧❣✉♥s ♣❛râ♠❡tr♦s ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ♦s ♣❡r✜s ✈❡rt✐❝❛✐s ❞❡ ❡①t✐♥çã♦ ❞❡ss❡s ❛❡r♦ssó✐s✱ ❛ ▲❘ ❡ ❛ ❙❘✱ ✉t✐❧✐③❛♥❞♦ ✉♠ s✐st❡♠❛ ▲■✲ ❉❆❘ ❘❛♠❛♥ ♠ó✈❡❧ ❞❡s❡♥✈♦❧✈✐❞♦ ♣❡❧❛ ❘❛②♠❡tr✐❝s ▲✐❞❛r ❙②st❡♠s ❞✉r❛♥t❡ ❝❛♠♣❛♥❤❛s r❡❛❧✐③❛❞❛s ❡♠ ❛❧❣✉♥s ✐♥st✐t✉t♦s ❞❡ ♣❡sq✉✐s❛ ♥♦ ❊st❛❞♦ ❞❡ ❙ã♦ P❛✉❧♦✳
❈❛♣ít✉❧♦ ✶
❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛
◆❛ ❛t♠♦s❢❡r❛ é ♣♦ssí✈❡❧ ♦❜s❡r✈❛r ❞✐✈❡rs♦s ❡①❡♠♣❧♦s ❛ss♦❝✐❛❞♦s ❛♦ ❡s♣❛❧❤❛♠❡♥t♦ ❞❛ r❛❞✐❛çã♦ ❣❡r❛❞♦ ♣♦r ♠♦❧é❝✉❧❛s✱ ❛❡r♦ssó✐s ❡ ♥✉✈❡♥s ❝♦♥t❡♥❞♦ ❣♦tí❝✉❧❛s ❞❡ á❣✉❛ ❡ ❝r✐st❛✐s ❞❡ ❣❡❧♦✳ ❖ ❢❛t♦ ❞♦ ❝é✉ s❡r ❛③✉❧✱ ❛ ❝♦❧♦r❛çã♦ ❜r❛♥❝❛ ❞❛s ♥✉✈❡♥s✱ ❛ ❝♦r ❛③✉❧ ❡s✈❡r❞❡❛❞❛ ❞♦ ♠❛r ♠❡❞✐t❡rrâ♥❡♦ ❡ ♦✉tr♦s ❡❢❡✐t♦s✱ sã♦ ❞❡✈✐❞♦ ❛ ❢❡♥ô♠❡♥♦s ó♣t✐❝♦s ♣r♦❞✉③✐❞♦s ♣♦r ❡s♣❛✲ ❧❤❛♠❡♥t♦✱ q✉❡ é ✉♠ ♣r♦❝❡ss♦ ❢ís✐❝♦ ❞❡ ✐♥t❡r❛çã♦ ❞❛ ❧✉③ ❝♦♠ ❛ ♠❛tér✐❛❬✹❪✳ ❉❡ss❛ ❢♦r♠❛✱ ❡♥t❡♥❞❡r ♦s ♣r♦❝❡ss♦s ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ é ❢✉♥❞❛♠❡♥t❛❧ ♣❛r❛ ♦ ✉s♦ ❞♦ s❡♥s♦r✐❛♠❡♥t♦ r❡♠♦t♦ ♣❛r❛ ♦ ❡st✉❞♦ ❞❛ ❛t♠♦s❢❡r❛✳
❖ ❊s♣❛❧❤❛♠❡♥t♦ é ❞❡✜♥✐❞♦ ❝♦♠♦ ✉♠ ♣r♦❝❡ss♦ ♥♦ q✉❛❧ ✉♠❛ ♣❛rtí❝✉❧❛ ♦✉ ✉♠❛ ♣❡✲ q✉❡♥❛ q✉❛♥t✐❞❛❞❡ ❞❡ ♠❛tér✐❛✱ ♥♦ ❝❛♠✐♥❤♦ ❞❡ ♣r♦♣❛❣❛çã♦ ❞❡ ✉♠❛ ♦♥❞❛ ❡❧❡tr♦♠❛❣♥ét✐❝❛✱ ❛❜s♦r✈❡ ❡♥❡r❣✐❛ ❞❡ss❛ ♦♥❞❛ ✐♥❝✐❞❡♥t❡ ❡ ✐rr❛❞✐❛ ❡ss❛ ❡♥❡r❣✐❛ ❡♠ ✉♠ â♥❣✉❧♦ só❧✐❞♦ t♦t❛❧ ❝❡♥tr❛❞♦ ♥❛ ♣❛rtí❝✉❧❛❬✺❪✳ P❛r❛ q✉❡ ♦❝♦rr❛ ♦ ❡s♣❛❧❤❛♠❡♥t♦ é ♥❡❝❡ssár✐♦ q✉❡ ♦ í♥❞✐❝❡ ❞❡ r❡❢r❛çã♦ ❞❛ ♣❛rtí❝✉❧❛ s❡❥❛ ❞✐❢❡r❡♥t❡ ❞♦ í♥❞✐❝❡ ❞❡ r❡❢r❛çã♦ ❞♦ ♠❡✐♦✳
◆❛ t❡♦r✐❛ q✉â♥t✐❝❛ ❛ ❡♠✐ssã♦ ❡s♣♦♥tâ♥❡❛ ❞❡ ✉♠ ❢ót♦♥ ✐rr❛❞✐❛❞♦ ♣♦r ✉♠ át♦♠♦ ❡①✲ ❝✐t❛❞♦ é ❝♦♥s✐❞❡r❛❞♦ ✉♠ ♣r♦❝❡ss♦ r❛❞✐❛t✐✈♦ ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠✱ ❡♥q✉❛♥t♦ q✉❡ ❛ ❡♥❡r❣✐❛ ❡❧❡tr♦♠❛❣♥ét✐❝❛ ❡s♣❛❧❤❛❞❛ ♣♦r ✉♠❛ ♠♦❧é❝✉❧❛ ♦✉ ✉♠ át♦♠♦ é t✐❞♦ ❝♦♠♦ ✉♠❛ ✐♥t❡r❛çã♦ ❞❡ s❡❣✉♥❞❛ ♦r❞❡♠✱ ✉♠❛ ✈❡③ q✉❡ ❞♦✐s ❢ót♦♥s ❡stã♦ ❡♥✈♦❧✈✐❞♦s ♥♦ ♣r♦❝❡ss♦✱ ♦ ❢ót♦♥ ✐♥✲ ❝✐❞❡♥t❡ ❡ ♦ ❡s♣❛❧❤❛❞♦❬✺❪✳ ❯♠ ❢ót♦♥ ω ❞❛ r❛❞✐❛çã♦ ✐♥❝✐❞❡♥t❡ é ❛♥✐q✉✐❧❛❞♦ q✉❛♥❞♦ ✉♠ ❢ót♦♥ ωs ❞❛ r❛❞✐❛çã♦ ❡s♣❛❧❤❛❞❛ é ❝r✐❛❞♦✳ ❖ ❡s♣❛❧❤❛♠❡♥t♦ é ❞✐t♦ ❡❧ást✐❝♦ s❡ ❛ ❢r❡q✉ê♥✲ ❝✐❛ ωs ❞♦ ❢ót♦♥ ❡s♣❛❧❤❛❞♦ ❢♦r ❛ ♠❡s♠❛ ❢r❡q✉ê♥❝✐❛ ❞♦ ❢ót♦♥ ✐♥❝✐❞❡♥t❡ ω ❡ ❡ss❛ ❢♦r♠❛ ❞❡
❡s♣❛❧❤❛♠❡♥t♦ ♣♦r s✐st❡♠❛s q✉❛♥t✐③❛❞♦s r❡❝❡❜❡ ♦ ♥♦♠❡ ❞❡ ❊s♣❛❧❤❛♠❡♥t♦ ❘❛②❧❡✐❣❤✳ ❙❡ ❤á ✉♠❛ ♠✉❞❛♥ç❛ ♥❛ ❢r❡q✉ê♥❝✐❛✱ t❛❧ q✉❡ ωs s❡❥❛ ❞✐❢❡r❡♥t❡ ❞❡ ω✱ ❡♥tã♦ ♦ ❡s♣❛❧❤❛♠❡♥t♦
r❡❝❡❜❡ ♦ ♥♦♠❡ ❞❡ ❊s♣❛❧❤❛♠❡♥t♦ ❘❛♠❛♥ ❡ ❛ ❞✐❢❡r❡♥ç❛ ❞❡ ❡♥❡r❣✐❛ (ω−ωs) ❛ss♦❝✐❛❞❛ ❛ ❡ss❛ ❢♦r♠❛ ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ ✐♥❡❧ást✐❝♦ é r❡✢❡t✐❞♦ ❡♠ ✉♠❛ ♠✉❞❛♥ç❛ ♥♦ ❡st❛❞♦ q✉â♥t✐❝♦ ❞♦ ❡s♣❛❧❤❛❞♦r❬✺❪✳
✶✳✶ ❊s♣❛❧❤❛♠❡♥t♦ ❊❧ást✐❝♦ ❡ ■♥❡❧ást✐❝♦
❯♠❛ ♠❛♥❡✐r❛ út✐❧ ❞❡ ❝♦♠♣r❡❡♥❞❡r ♦ ❡s♣❛❧❤❛♠❡♥t♦ ❡❧ást✐❝♦ ❡ ♦ ✐♥❡❧ást✐❝♦ ♣♦❞❡ s❡r ♦❜t✐❞❛ ❝♦♥s✐❞❡r❛♥❞♦ ❛ ✐♥t❡r❛çã♦ ❞❡ ✉♠❛ ♦♥❞❛ ❡❧❡tr♦♠❛❣♥ét✐❝❛✱ E = E0cos ωt✱ ❝♦♠ ✉♠ s✐st❡♠❛ ❛tô♠✐❝♦ q✉❡ ♣♦ss✉✐ ♣♦❧❛r✐③❛❜✐❧✐❞❛❞❡ η = ηx= 0+
∂η ∂x
x= 0
x + ...✱ ♥❛
q✉❛❧ x é ♦ ❞❡s❧♦❝❛♠❡♥t♦ ❞❛ ❝❛r❣❛ ❡ x = 0 é ❛ ♣♦s✐çã♦ ❞❡ ❡q✉✐❧í❜r✐♦✱ ηx= 0 r❡♣r❡s❡♥t❛ ❛ ♣♦❧❛r✐③❛❜✐❧✐❞❛❞❡ ♥♦ ❡q✉✐❧í❜r✐♦ ❡
∂η ∂x
x= 0
❛ ♣♦❧❛r✐③❛❜✐❧✐❞❛❞❡ ❞♦ ❝❛♠♣♦ ✐♥❞✉③✐❞♦❬✶✶❪✳ ❙❡ ✉♠ s✐st❡♠❛ ❛tô♠✐❝♦ ♣♦❞❡ s❡r tr❛t❛❞♦ ❝♦♠♦ ✉♠ ♦s❝✐❧❛❞♦r ❤❛r♠ô♥✐❝♦ s✐♠♣❧❡s ❝♦♠ ❢r❡q✉ê♥❝✐❛ ❛♥❣✉❧❛r ω✱ ❡♥tã♦ t❡♠✲s❡ q✉❡ x =x0cos ωt ❡ ❛ ✐♥t❡♥s✐❞❛❞❡ ❞♦ ♠♦♠❡♥t♦ ❞❡ ❞✐♣♦❧♦ ❡❧étr✐❝♦ ✐♥❞✉③✐❞♦ ❞♦ s✐st❡♠❛ t♦r♥❛✲s❡
d =
ηx= 0+
∂η ∂x
x= 0
x
E0cos ωt ✭✶✳✶✳✶✮
=ηx= 0E0cos ωt+
1 2E0x0
∂η ∂x
x= 0
{cos(ω+ω1)t+ cos(ω−ω1)t}
❉❛ ❡q✉❛çã♦ ✭✶✳✶✳✶✮✱ s❡
∂η ∂x
x= 0
= 0✱ ❡♥tã♦ ♥ã♦ ❤á ❡s♣❛❧❤❛♠❡♥t♦ ✐♥❡❧ást✐❝♦✳ ❈♦♥s❡✲
q✉❡♥t❡♠❡♥t❡✱ é ❛ ♣♦❧❛r✐③❛❜✐❧✐❞❛❞❡ ♦s❝✐❧❛♥t❡ q✉❡ ♣♦❞❡ s❡r ♣❡♥s❛❞❛ ❝♦♠♦ ✉♠ ♠♦❞✉❧❛❞♦r ❞❛ r❛❞✐❛çã♦ ❡s♣❛❧❤❛❞❛ ❧❡✈❛♥❞♦✱ ❛ss✐♠✱ ❛♦ s✉r❣✐♠❡♥t♦ ❞❛s três ❢r❡q✉ê♥❝✐❛s ω✱ ω+ω1 ❡
ω−ω1✳ ❆ ♣r✐♠❡✐r❛ ❝♦rr❡s♣♦♥❞❡ ❛♦ ❡s♣❛❧❤❛♠❡♥t♦ ❘❛②❧❡✐❣❤ ✭❡❧ást✐❝♦✮✱ ❛ s❡❣✉♥❞❛ ❝♦rr❡s✲
♣♦♥❞❡ ❛♦ ❡s♣❛❧❤❛♠❡♥t♦ ❘❛♠❛♥ ❆♥t✐✲❙t♦❦❡s ❡ ❛ t❡r❝❡✐r❛ ❛♦ ❘❛♠❛♥ ❙t♦❦❡s ✭✐♥❡❧ást✐❝♦s✮✳ ❖❜s❡r✈❛✲s❡ q✉❡✱ ❡♠❜♦r❛ ❡ss❛ ❛❜♦r❞❛❣❡♠ ❝❧áss✐❝❛ ❞ê ❝♦♥t❛ ❞❡ ❡①♣❧✐❝❛r ❛ ❝r✐❛çã♦ ❞❛s ❝♦♠♣♦♥❡♥t❡s ω+ω1 ❡ ω−ω1 ❞♦ ❝❛♠♣♦ ❡❧❡tr♦♠❛❣♥ét✐❝♦ ❡s♣❛❧❤❛❞♦✱ ❡❧❛ s❡ ❛♣r❡s❡♥t❛ ✐♥❛❞❡q✉❛❞❛ ♣❛r❛ ❡s❝❧❛r❡❝❡r ❛ ❢♦rç❛ ❞❡ ✐♥t❡r❛çã♦❬✺❪✳
❯♠❛ ❛♥á❧✐s❡ ❞❛ t❡♦r✐❛ q✉â♥t✐❝❛ ❞❡ ♣❡rt✉r❜❛çõ❡s ❢♦r♥❡❝❡ ❛ ❡q✉❛çã♦ ❞✐❢❡r❡♥❝✐❛❧ ❞❛ s❡❝✲ çã♦ ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ ♣❛r❛ ✉♠❛ r❛❞✐❛çã♦ ❡❧❡tr♦♠❛❣♥ét✐❝❛ ♣❧❛♥♦✲♣♦❧❛r✐③❛❞❛ ❞❡ ❢r❡q✉ê♥✲ ❝✐❛ ❛♥❣✉❧❛r ✐♥❝✐❞❡♥t❡ ω s♦❜r❡ ✉♠❛ ♠♦❧é❝✉❧❛ ✭♦✉ át♦♠♦✮ ✐❞❡❛❧✐③❛❞❛ ❝♦♠ ❡st❛❞♦s ♥ã♦✲
❋✐❣✉r❛ ✶✳✶✿ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞♦ ❡s♣❛❧❤❛♠❡♥t♦ ❘❛♠❛♥ ❙t♦❦❡s✳ ❆ tr❛♥s✐çã♦ ❛t✉❛❧ é ❞♦ ❡st❛❞♦|0 ♣❛r❛|f✳
❞❡❣❡♥❡r❛❞♦s❬✶✶❪✳ dσ dΩ = ωf<ω f
ω(ω−ωf)3
(4πǫ0c2)2 i
f|ǫˆs·d|ii|ˆǫ·d|0
ωi0−ω ✭✶✳✶✳✷✮
+f|ˆǫ·d|ii|ǫˆs·d|0
ωif +ω
2
◆❛ ❡q✉❛çã♦ ✭✶✳✶✳✷✮ |0 r❡♣r❡s❡♥t❛ ♦ ❡st❛❞♦ q✉â♥t✐❝♦ ✐♥✐❝✐❛❧✱ |i ✉♠ ❡st❛❞♦ q✉â♥t✐❝♦ ✐♥t❡r♠❡❞✐ár✐♦ q✉❛❧q✉❡r ❡|f♦ ❡st❛❞♦ q✉â♥t✐❝♦ ✜♥❛❧✳ ωi0r❡♣r❡s❡♥t❛ ❛ ❢r❡q✉ê♥❝✐❛ ❛♥❣✉❧❛r ❝♦rr❡s♣♦♥❞❡♥t❡ à tr❛♥s✐çã♦ ❞♦ ❡st❛❞♦ ✐♥✐❝✐❛❧ ♣❛r❛ ♦ ❡st❛❞♦ ✈✐rt✉❛❧ ❡ ωif r❡♣r❡s❡♥t❛ ❛
❢r❡q✉ê♥❝✐❛ ❛♥❣✉❧❛r ❝♦rr❡s♣♦♥❞❡♥t❡ à tr❛♥s✐çã♦ ❞♦ ❡st❛❞♦ ✈✐rt✉❛❧ ♣❛r❛ ♦ ❡st❛❞♦ ✜♥❛❧✳ ❆ ❢r❡q✉ê♥❝✐❛ ❛♥❣✉❧❛r ❡s♣❛❧❤❛❞❛ é ωs ≡ ω − ωf✳ ❆❧é♠ ❞✐ss♦✱ ǫˆ ❡ ǫˆs r❡♣r❡s❡♥t❛♠✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ♦s ✈❡t♦r❡s ✉♥✐tár✐♦s ❞❛ ♣♦❧❛r✐③❛çã♦ ❞♦ ❝❛♠♣♦ ❡❧étr✐❝♦ ❞❛ r❛❞✐❛çã♦ ✐♥❝✐❞❡♥t❡ ❡ ❡s♣❛❧❤❛❞❛✳ ❋✐♥❛❧♠❡♥t❡✱ d r❡♣r❡s❡♥t❛ ♦ ♦♣❡r❛❞♦r ❞♦ ♠♦♠❡♥t♦ ❞❡ ❞✐♣♦❧♦
❡❧étr✐❝♦❬✺❪✳ ❆ ✜❣✉r❛ ✶✳✶ ♠♦str❛ ✉♠❛ r❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❛s ✐♥t❡r❛çõ❡s ❞❡s❝r✐t❛s ❛❝✐♠❛✳ ❆ s♦♠❛tór✐❛ s♦❜r❡ ♦s ❡st❛❞♦s ✐♥t❡r♠❡❞✐ár✐♦s✱|i✱ ♥❛ ❡q✉❛çã♦ ✭✶✳✶✳✷✮ t❡♠ ❛ ❢✉♥çã♦ ❞❡ ✐♥t❡❣r❛r ♦ ❝♦♥tí♥✉♦ ❞♦s ❡st❛❞♦s ❞❡ ❡♥❡r❣✐❛ ♣♦s✐t✐✈♦s ✭❞✐ss♦❝✐❛❞♦s ❡ ✐♦♥✐③❛❞♦s✮✳ ❏á ❛ s♦♠❛tór✐❛ s♦❜r❡ ♦s ❡st❛❞♦s ✜♥❛✐s |f ❡stá r❡str✐t❛ ❛♦s ❡st❛❞♦s q✉❡ ❝♦♥tr✐❜✉❡♠ ♣❛r❛ ❛ ❢r❡q✉ê♥❝✐❛ ♦❜s❡r✈❛❞❛✳
❉❡✈❡✲s❡ t❡r ❡♠ ♠❡♥t❡ q✉❡ ❛ ❡q✉❛çã♦ ✭✶✳✶✳✷✮ é ❞❡r✐✈❛❞❛ ❞❛ t❡♦r✐❛ q✉â♥t✐❝❛ ❞❡ ♣❡r✲
t✉r❜❛çõ❡s ❡✱ ♣♦rt❛♥t♦✱ ❛ s♦♠❛tór✐❛ s✉r❣❡ ❝♦♠♦ ✉♠❛ ❝♦♥s❡q✉ê♥❝✐❛ ♠❛t❡♠át✐❝❛ ❞❛ ❡①✲ ♣❛♥sã♦ ❞❛ ❢✉♥çã♦ ❞❡ ♦♥❞❛ ♣❡rt✉r❜❛❞❛ ❡♠ t❡r♠♦s ❞❡ ✉♠❛ sér✐❡ ✐♥✜♥✐t❛ ❞❡ ❢✉♥çõ❡s ❞❡ ♦♥❞❛ ♥ã♦✲♣❡rt✉r❜❛❞❛✳ ❊♠❜♦r❛ ❛ ❡q✉❛çã♦ ✭✶✳✶✳✷✮ t❡♥❤❛ s✐❞♦ ✉s❛❞❛ ♣❛r❛ ♦ ❝❛s♦ ❞♦ H2✱
♣♦r ❡①❡♠♣❧♦✱ é ❞✐❢í❝✐❧ ❢❛③❡r ✉♠❛ ❛♣❧✐❝❛çã♦ ♠❛✐s ❣❡r❛❧ ❞❡ss❛ ❡q✉❛çã♦✱ ♣♦✐s ❡①✐st❡ ✉♠❛ ❝❡rt❛ ❝❛rê♥❝✐❛ ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦ ❡♠ r❡❧❛çã♦ à ♠❛❣♥✐t✉❞❡ ❡ ❛♦ s✐♥❛❧ ❞❡ t♦❞♦s ♦s ♣♦ssí✈❡✐s t❡r♠♦s q✉❡ ♣♦ss❛♠ ✈✐r ❛ ❝♦♥tr✐❜✉✐r ❡ ❡♠ r❡❧❛çã♦✱ t❛♠❜é♠✱ ❛ ✉♠❛ ♣♦ssí✈❡❧ ✐♥t❡r❢❡rê♥❝✐❛ ❞❡ t❡r♠♦s q✉❡ ♣♦ss❛♠ t❡r ❞✐❢❡r❡♥t❡s ❢❛s❡s❬✶✷✱ ✶✸❪✳
❆ ❡q✉❛çã♦ ❞✐❢❡r❡♥❝✐❛❧ ❞❛ s❡❝çã♦ ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ ❞❡✜♥✐❞❛ ❡♠ ✭✶✳✶✳✷✮ ✐♥❝❧✉✐ t❛♥t♦ ♦ ❡s♣❛❧❤❛♠❡♥t♦ ❡❧ást✐❝♦ ❘❛②❧❡✐❣❤✱ ♥♦ q✉❛❧|f❡|0❝♦✐♥❝✐❞❡♠ ❡✱ ♣♦rt❛♥t♦✱ωf = 0✱ q✉❛♥t♦
♦ ❡s♣❛❧❤❛♠❡♥t♦ ✐♥❡❧ást✐❝♦ ❘❛♠❛♥ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛♦s ❞❡♠❛✐s t❡r♠♦s ❞❛ s♦♠❛tór✐❛ s♦❜r❡
f✳ P❛r❛ ♦ ❡s♣❛❧❤❛♠❡♥t♦ ❡❧ást✐❝♦✱ ❛ ♠♦❧é❝✉❧❛ ✭♦✉ át♦♠♦✮ ✈♦❧t❛ ❛♦ s❡✉ ❡st❛❞♦ ♦r✐❣✐♥❛❧
|0 ♥♦ ✜♥❛❧ ❞♦ ❡s♣❛❧❤❛♠❡♥t♦ ❡ ❛ ❡q✉❛çã♦ ❞✐❢❡r❡♥❝✐❛❧ ❞❛ s❡❝çã♦ ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ ♣❛r❛ ❡ss❡ ❝❛s♦ ♣♦❞❡ s❡r ❡s❝r✐t❛ ❝♦♠♦
dσ
dΩ =
ω4
16π2ǫ2 02c4
i 0|ǫˆ
s·d|ii|ˆǫ·d|0
ωi0−ω ✭✶✳✶✳✸✮
+0|ˆǫ·d|ii|ǫˆs·d|0
ωi0+ω
2
◆♦ ❧✐♠✐t❡ ω ≪ωi0 ❡ss❛ ❡q✉❛çã♦ ♣♦❞❡ s❡r r❡❞✉③✐❞❛❬✶✶❪✱ ♥♦ ❝❛s♦ ❞♦ ❤✐❞r♦❣ê♥✐♦✱ ♣❛r❛ ❛ ❢♦r♠❛ dσ dΩ = 81 64r 2 e ω ωH 4
{cos2φcos2θ+ sen2φ} ✭✶✳✶✳✹✮
♥♦ q✉❛❧ é ❜❡♠ ♣ró①✐♠♦ ❞♦ ✈❛❧♦r ❝❧áss✐❝♦ s❡ ωH✱ ❛ ❢r❡q✉ê♥❝✐❛ ❛♥❣✉❧❛r ❝♦rr❡s♣♦♥❞❡♥t❡ à
❡♥❡r❣✐❛ ❞❡ ❧✐❣❛çã♦ ♥♦ ❡st❛❞♦ ❢✉♥❞❛♠❡♥t❛❧ ❞♦ ❤✐❞r♦❣ê♥✐♦✱ ❢♦r ✐❣✉❛❧ à ❢r❡q✉ê♥❝✐❛ ♥❛t✉r❛❧ ❞❡ ♦s❝✐❧❛çã♦ ❞♦ ♦s❝✐❧❛❞♦r ❤❛r♠ô♥✐❝♦✱ ω0✳
✶✳✷ ❊s♣❛❧❤❛♠❡♥t♦ ❘❛♠❛♥
◆♦ ❡s♣❛❧❤❛♠❡♥t♦ ❘❛♠❛♥✱ ❛ s❡❝çã♦ ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ é ❝❡r❝❛ ❞❡ três ♦r❞❡♥s ❞❡ ❣r❛♥✲
❋✐❣✉r❛ ✶✳✷✿ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞♦ ❡s♣❛❧❤❛♠❡♥t♦ ❘❛♠❛♥ ❙t♦❦❡s ❡ ❆♥t✐✲❙t♦❦❡s ✭∆ν±
1✮✳
❞❡③❛ ♠❡♥♦r ❞♦ q✉❡ ❛ s❡❝çã♦ ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ ❝♦rr❡s♣♦♥❞❡♥t❡ ❘❛②❧❡✐❣❤ ❡ ♦ s✐♥❛❧ ❡s♣❛✲ ❧❤❛❞♦ ❝♦♥s✐st❡ ♥❛ r❛❞✐❛çã♦ q✉❡ s♦❢r❡✉ ✉♠ ❞❡s✈✐♦ ♥❛ ❢r❡q✉ê♥❝✐❛ ❛ q✉❛❧ é❝❛r❛❝t❡ríst✐❝❛ ❞♦s ❡st❛❞♦s ❡st❛❝✐♦♥ár✐♦s ❞❡ ❡♥❡r❣✐❛ ❞❛ ♠♦❧é❝✉❧❛ ✐rr❛❞✐❛❞❛✳ ❆ ❡s♣❡❝tr♦s❝♦♣✐❛ ❘❛♠❛♥ r❡♣r❡s❡♥t❛ ✉♠❛ ♣♦❞❡r♦s❛ ❢❡rr❛♠❡♥t❛ ♣❛r❛ ♦ s❡♥s♦r✐❛♠❡♥t♦ r❡♠♦t♦ ❛ ❧❛s❡r✱ ♣♦✐s ♣❡r♠✐t❡ q✉❡ ❝♦♥st✐t✉✐♥t❡s tr❛ç♦s ❞❡ ✉♠❛ ♠✐st✉r❛ s❡❥❛♠ ✐❞❡♥t✐✜❝❛❞♦s ❡ q✉❛♥t✐✜❝❛❞♦s ❡♠ r❡❧❛çã♦ ❛♦ ❝♦♥st✐t✉✐♥t❡ ♠❛❥♦r✐tár✐♦ ❞❡ss❛ ♠❡s♠❛ ♠✐st✉r❛❬✺❪✳
❙❡ ✉♠❛ ♠♦❧é❝✉❧❛ ❛❜s♦r✈❡ ❡♥❡r❣✐❛✱ ✉♠ ❞♦s ♥í✈❡✐s ♠❛✐s ❛❧t♦s é ❡①❝✐t❛❞♦✱ ❛ ❢r❡q✉ê♥❝✐❛ ❞♦ ❢ót♦♥ ❡s♣❛❧❤❛❞♦ ❞✐♠✐♥✉✐ ❡ ♦ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♦♥❞❛ é❞❡s❧♦❝❛❞♦ ♣❛r❛ ♦ ✈❡r♠❡❧❤♦ ✭r❡❞✲s❤✐❢t✮✳ ❊st❡ ♣r♦❝❡ss♦ ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ ✐♥❡❧ást✐❝♦ é❝❤❛♠❛❞♦ ❞❡ ❘❛♠❛♥ ❙t♦❦❡s✳ ❙❡ ❛ ♠♦❧é❝✉❧❛ tr❛♥s❢❡r❡ ❡♥❡r❣✐❛ ♣❛r❛ ♦ ❢ót♦♥ ❡s♣❛❧❤❛❞♦ ❞✐♠✐♥✉✐♥❞♦ ♦ ♥í✈❡❧ ❞❡ ❡♥❡r❣✐❛ ❞❛ ♠♦❧é❝✉❧❛✱ ❛ ❢r❡q✉ê♥❝✐❛ ❞♦ ❢ót♦♥ ❡s♣❛❧❤❛❞♦ ❛✉♠❡♥t❛ ❡ ♦ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♦♥❞❛ é ❞❡s❧♦❝❛❞♦ ♣❛r❛ ♦ ❛③✉❧ ✭❜❧✉❡✲s❤✐❢t✮✳ ❆ ❡st❡ ♣r♦❝❡ss♦ ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ é❞❛❞♦ ♦ ♥♦♠❡ ❞❡ ❘❛♠❛♥ ❆♥t✐✲❙t♦❦❡s❬✸❪✳ ❆♠❜♦s ♦s ♣r♦❝❡ss♦s ❡stã♦ ✐❧✉str❛❞♦s ❞❡ ❢♦r♠❛ ❡sq✉❡♠át✐❝❛ ♥❛ ❋✐❣✉r❛ ✶✳✷✳
❆ ❡str✉t✉r❛ ❞♦ ❡s♣❡❝tr♦ ❘❛♠❛♥ é❜❡♠ ♠❛✐s ❝♦♠♣❧❡①❛✱ ♠❡s♠♦ ♣❛r❛ ♠♦❧é❝✉❧❛s ❞✐✲ ❛tô♠✐❝❛s✳ ◆♦ ❝❛s♦ ♣❛rt✐❝✉❧❛r ❞❡ ♠♦❧é❝✉❧❛s ❞✐❛tô♠✐❝❛s ♣♦ss✉ír❡♠ ♠♦♠❡♥t♦ ❛♥❣✉❧❛r ❡❧❡trô♥✐❝♦ ❡♠ t♦r♥♦ ❞♦ ❡✐①♦ ✐♥t❡r♥✉❝❧❡❛r✶ ✐❣✉❛❧ ❛ ③❡r♦✱ ❛s r❡❣r❛s ❞❡ s❡❧❡çã♦ ♣❡r♠✐t❡♠
tr❛♥s✐çõ❡s ✈✐❜r❛❝✐♦♥❛✐s✲r♦t❛❝✐♦♥❛✐s ♣❛r❛ q✉❡ ❛ ♠✉❞❛♥ç❛ ♥♦ ♥ú♠❡r♦ q✉â♥t✐❝♦ r♦t❛❝✐♦✲ ♥❛❧✱ J✱ ❞❛ ♠♦❧é❝✉❧❛ ♣♦ss❛♠ s❡r s♦♠❡♥t❡ 0 ♦✉ ±2 ❡ ❛ ♠✉❞❛♥ç❛ ♥♦ ♥ú♠❡r♦ q✉â♥t✐❝♦
✈✐❜r❛❝✐♦♥❛❧✱ ν✱ ♣♦ss❛ s❡r s♦♠❡♥t❡ 0 ♦✉ ±1✱ t❛❧ q✉❡
✶❡✐①♦ ❝❛rt❡s✐❛♥♦ q✉❡ ✉♥❡ ♦s ❞♦✐s át♦♠♦s✳
∆ν = 0,±1 ✭✶✳✷✳✶✮
∆J = 0,±2
◆❡ss❛s ❝✐r❝✉♥stâ♥❝✐❛s ♦ ❡s♣❡❝tr♦ ❘❛♠❛♥ ❝♦♥s✐st❡ ❞❡ três r❛♠♦s✿ S ♣❛r❛ ∆J = +2✱
Q♣❛r❛∆J = 0❡O♣❛r❛∆J =−2✱ ❛❧é♠ ❞❛ ❡str✉t✉r❛ ♣✉r♦ r♦t❛❝✐♦♥❛❧ ❝❡♥tr❛❞❛ s♦❜r❡ ♦
❝♦♠♣r✐♠❡♥t♦ ❞❡ ♦♥❞❛ ❞❛ ♠♦❧é❝✉❧❛ ❡①❝✐t❛❞❛ ♣❛r❛ ∆ν = 0✳ ■♥❛❜❛ ❡ ❑♦❜❛②❛s✐ ❝❛❧❝✉❧❛r❛♠
❛ ❞✐str✐❜✉✐çã♦ t❡ór✐❝❛ ❞❛s ❧✐♥❤❛s ✈✐❜r❛❝✐♦♥❛❧✲r♦t❛❝✐♦♥❛❧ ❘❛♠❛♥ ❝♦rr❡s♣♦♥❞❡♥t❡s ❛ ∆ν = +1✭❘❛♠❛♥ ❙t♦❦❡s✮ ❞♦ ❡s♣❡❝tr♦ ❞❛ ♠♦❧é❝✉❧❛ ❞❡N2 ❛ ✸✵✵ ❑❬✶✹❪✳ ❆ ❋✐❣✉r❛ ✶✳✸ ❛♣r❡s❡♥t❛ ♦s r❡s✉❧t❛❞♦ q✉❡ ❡❧❡s ♦❜t✐✈❡r❛♠✳ ❆ ♦r❞❡♥❛❞❛ ❢♦r♥❡❝❡ ♦ ✈❛❧♦r ❞❛ ❞✐❢❡r❡♥❝✐❛❧ ❞❛ s❡❝çã♦ ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ ♣❛r❛ ❝❛❞❛ ✉♠ ❞♦s ❝♦♠♣♦♥❡♥t❡s ❘❛♠❛♥ ❝♦rr❡s♣♦♥❞❡♥t❡s à tr❛♥s✐çã♦ ✈✐❜r❛❝✐♦♥❛❧ ν = 0→1✳ ❈♦♠♦ ♣♦❞❡ s❡r ✈✐st♦ ♥❛ ✜❣✉r❛ ✶✳✸✱ t♦❞❛s ❛s ❧✐♥❤❛s ❞♦ r❛♠♦ Q
✭∆J = 0✮ ❡stã♦ ♠✉✐t♦ ♣ró①✐♠❛s ✉♠❛s ❞❛s ♦✉tr❛s ❡✱ ♥♦r♠❛❧♠❡♥t❡✱ ♥ã♦ sã♦ r❡s♦❧✈✐❞❛s✳
❖s r❛♠♦s S ❡ O ✭∆J = ±2✮ sã♦ ❜❡♠ s❡♣❛r❛❞❛s ❡ ❛♣❛r❡❝❡♠ ❝♦♠♦ ❢❛✐①❛s ❞❛ ❧✐♥❤❛ ❞❡
✐♥t❡♥s✐❞❛❞❡∆J = 0✳ ❉❡✈❡✲s❡ ♥♦t❛r q✉❡✱ ❛♣❡s❛r ❞❛ ✈❛r✐❛çã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ✐♥✢✉❡♥❝✐❛r
♦s r❛♠♦s S ❡O✱ ♥♦ r❛♠♦ Q ❡ss❡ ❡❢❡✐t♦ ♣♦❞❡ s❡r ♥❡❣❧✐❣❡♥❝✐❛❞♦❬✺❪✳
❯♠ ♣r♦❜❧❡♠❛ q✉❡ ♣♦❞❡ s✉r❣✐r ♥♦ ♠♦♥✐t♦r❛♠❡♥t♦ ❞❛ ♣♦❧✉✐çã♦ ❛t♠♦s❢ér✐❝❛ ♣♦r s❡♥✲ s♦r✐❛♠❡♥t♦ r❡♠♦t♦ ✉s❛♥❞♦ ❡s♣❡❝tr♦s❝♦♣✐❛ ❘❛♠❛♥ é ♦ ❢❛t♦ ❞❡ q✉❡ ❛s ❢❛✐①❛s ❘❛♠❛♥ ❞♦s r❛♠♦s S ❡ O ❞❡ ✉♠ ❡s♣❛❧❤❛♠❡♥t♦ ♠❛✐s ✐♥t❡♥s♦ ♣r♦✈♦❝❛❞♦ ♣♦r ❡s♣é❝✐❡s ❞❡ ♠❛✐♦r
❝♦♥❝❡♥tr❛çã♦ ♣♦❞❡♠ s♦❜r❡♣♦r ❡ ♠❛s❝❛r❛r ✉♠ r❛♠♦ Q ❞❡ ✉♠ ❡s♣❛❧❤❛♠❡♥t♦ ♠❛✐s ❢r❛❝♦
♣r♦✈♦❝❛❞♦ ♣♦r ✉♠ ❝♦♥st✐t✉✐♥t❡ tr❛ç♦ ❞❛ ❛t♠♦s❢❡r❛❬✶✹❪✳
❆ ❚❛❜❡❧❛ ✶✳✷ ♠♦str❛ ♦s ❞❡s✈✐♦s ❞❛ ❢r❡q✉ê♥❝✐❛ ❞♦ r❛♠♦ Q ❞♦ ❡s♣❡❝tr♦ ✈✐❜r❛❝✐♦♥❛❧✲
r♦t❛❝✐♦♥❛❧ ❘❛♠❛♥ ♣❛r❛ ❛❧❣✉♠❛s ♠♦❧é❝✉❧❛s ❞❡ ✐♥t❡r❡ss❡ ♥♦ ♠♦♥✐t♦r❛♠❡♥t♦ ❞❡ ♣♦❧✉✐çã♦ ❛t♠♦s❢ér✐❝❛ ❡✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡✱ ❞♦ ✐♥t❡r❡ss❡ ❞❡ss❡ tr❛❜❛❧❤♦✱ ❡♥✈♦❧✈❡♥❞♦ s❡♥s♦r✐❛♠❡♥t♦ r❡♠♦t♦ ❛ ❧❛s❡r ♥✉♠ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♦♥❞❛ ❞❡ ❡①❝✐t❛çã♦ ❞❡ ✸✸✼✱✶ ♥♠✳
❆ ❡q✉❛çã♦ ❞✐❢❡r❡♥❝✐❛❧ ❞❛ s❡❝çã♦ ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ ❘❛♠❛♥ é ❞❛❞❛ ♣❡❧♦ t❡r♠♦ ✐♥❡❧ás✲ t✐❝♦✷ ❞❡ ✭✶✳✶✳✷✮ ❞❡s❞❡ q✉❡ ❛ ❢r❡q✉ê♥❝✐❛ ✐♥❝✐❞❡♥t❡✱ ω✱ s❡❥❛ s✉♣❡r✐♦r à ♠❡♥♦r ❢r❡q✉ê♥❝✐❛
❞❡ ❡①❝✐t❛çã♦ ❞❛ ♠♦❧é❝✉❧❛✳ ❊♠ ❣❡r❛❧✱ ❛ r❛❞✐❛çã♦ ❡s♣❛❧❤❛❞❛ t❡♠ t❛♥t♦s ❝♦♠♣♦♥❡♥t❡s ❞❡ ❢r❡q✉ê♥❝✐❛ ❛♥❣✉❧❛r ωs q✉❛♥t♦s ❡st❛❞♦s ❞❡ ❡♥❡r❣✐❛ ❝♦♠ ❢r❡q✉ê♥❝✐❛ ωf ♠❡♥♦r❡s ❞♦ q✉❡
✷q✉❛♥❞♦|fé ❞✐❢❡r❡♥t❡ ❞❡|0
❋✐❣✉r❛ ✶✳✸✿ ❉✐str✐❜✉✐çã♦ t❡ór✐❝❛ ❞♦ ❡s♣❡❝tr♦ ✈✐❜r❛❝✐♦♥❛❧✲r♦t❛❝✐♦♥❛❧ ❘❛♠❛♥ ❛ ✸✵✵ ❑✱ ♠♦s✲ tr❛♥❞♦ ❛s ❡str✉t✉r❛s ❞♦s r❛♠♦sO✱Q❡ S ♣❛r❛ ❛ ♠♦❧é❝✉❧❛ ❞❡ ♥✐tr♦❣ê♥✐♦✳
ω❬✺❪✳ ❆❧é♠ ❞✐ss♦✱ ❡ss❛ r❡❧❛çã♦ só ❢♦r♥❡❝❡ ✉♠❛ s❡❝çã♦ ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ ❘❛♠❛♥ ♣r❡❝✐s❛
♣❛r❛ ♠♦❧é❝✉❧❛s ❝♦♠ ❡st❛❞♦s ♥ã♦✲❞❡❣❡♥❡r❛❞♦s ❝♦♠♦ ♦ H2 ❡ ♦ D2✳
❯♠❛ ❡①♣r❡ssã♦ ❛❧t❡r♥❛t✐✈❛ ♣❛r❛ ❛ ❡q✉❛çã♦ ❞✐❢❡r❡♥❝✐❛❧ ❞❛ s❡❝çã♦ ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ ❘❛♠❛♥ ♣♦❞❡ s❡r ♦❜t✐❞❛ ❛ ♣❛rt✐r ❞❡ ✉♠ tr❛t❛♠❡♥t♦ t❡ór✐❝♦ ❞❛ ♣♦❧❛r✐③❛❜✐❧✐❞❛❞❡ ❞❛s ♠♦❧é✲ ❝✉❧❛s ❡①♣♦st❛s ❛ ✉♠ ❝❛♠♣♦ ❡❧❡tr♦♠❛❣♥ét✐❝♦❬✺❪✳ ❉❡ ❛❝♦r❞♦ ❝♦♠ P❧❛❝③❡❦❬✶✺❪ ❡ ■♥❛❜❛❬✶✻❪✱ q✉❛♥❞♦ ♦ ❡s♣❛❧❤❛♠❡♥t♦ ❘❛♠❛♥ é ♦❜s❡r✈❛❞♦ ❡♠ ✉♠❛ ❞✐r❡çã♦ ♣❡r♣❡♥❞✐❝✉❧❛r à ❞✐r❡çã♦ ❞❡ ♣♦❧❛r✐③❛çã♦ ❞❡ ✉♠❛ ❧✉③ ❧✐♥❡❛r♠❡♥t❡ ♣♦❧❛r✐③❛❞❛✱ ❛ s❡❝çã♦ ❞❡ r❡tr♦❡s♣❛❧❤❛♠❡♥t♦ ✈✐✲ ❜r❛❝✐♦♥❛❧ ❘❛♠❛♥ ♣❛r❛ ♦ r❛♠♦ Q ✭∆ν = 1,∆J = 0✮ é
dσj
dΩ
Q
= b
2
j(ω−ωj)4gj c4[1−e−ωj/kT]{
◦
α2j +
7 180
◦
γ2j} ✭✶✳✷✳✷✮
❡♥q✉❛♥t♦ q✉❡ ❛ s❡❝çã♦ ❞❡ r❡tr♦❡s♣❛❧❤❛♠❡♥t♦ ✈✐❜r❛❝✐♦♥❛❧ ❘❛♠❛♥ ♣❛r❛ ♦s r❛♠♦s O ❡ S
✭∆ν = 1,∆J =−2❡ ∆ν= 1,∆J = 2 r❡s♣❡❝t✐✈❛♠❡♥t❡✮ é
dσj
dΩ
O+S
= b
2
j(ω−ωj)4gj c4[1−e−ωj/kT
]· 7 60
◦
γ2j ✭✶✳✷✳✸✮
▼♦❧é❝✉❧❛ ❉❡s✈✐♦ ❘❛♠❛♥ ✭cm−1✮
λ ❘❛♠❛♥ ✭♥♠✮
N2 ✷✸✸✵✱✼ ✸✻✺✱✾
H2 ✹✶✻✵✱✷ ✸✾✷✱✷
O2 ✶✺✺✻ ✸✺✺✱✾
H2O ✸✻✺✶✱✼ ✸✽✹✱✹
CO2 ✶✸✽✽ ✸✺✸✱✼
SO2 ✶✶✺✶✱✺ ✸✺✵✱✽
❚❛❜❡❧❛ ✶✳✶✿ ❉❡s✈✐♦ ❞♦ ♥ú♠❡r♦ ❞❡ ♦♥❞❛ ❡ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♦♥❞❛ ❘❛♠❛♥ ♣❛r❛ ♦ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♦♥❞❛ ❞❡ ✸✸✼✱✶ ♥♠ ❞❛ r❛❞✐❛çã♦ ✐♥❝✐❞❡♥t❡✳
P♦r ✜♠✱ ❛ s❡❝çã♦ ❞❡ r❡tr♦❡s♣❛❧❤❛♠❡♥t♦ ✈✐❜r❛❝✐♦♥❛❧ ❘❛♠❛♥ t♦t❛❧ ♦❜t✐❞♦ s♦♠❛♥❞♦✲s❡ ❛s ❡q✉❛çõ❡s ✭✶✳✷✳✷✮ ❡ ✭✶✳✷✳✸✮ é
dσj
dΩ =
b2
j(ω−ωj)4gj c4[1−e−ωj/kT]{
◦
α2j + 7 45
◦
γ2j} ✭✶✳✷✳✹✮
♥♦ q✉❛❧ω❡ωj r❡♣r❡s❡♥t❛♠✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❛ ❢r❡q✉ê♥❝✐❛ ❛♥❣✉❧❛r ❞❛ r❛❞✐❛çã♦ ✐♥❝✐❞❡♥t❡
❡ ❞♦ j✲és✐♠♦ ♠♦❞♦ ✈✐❜r❛❝✐♦♥❛❧ ❞❛ ♠♦❧é❝✉❧❛✱ bj = (/2ωj)1/2 r❡♣r❡s❡♥t❛ ❛ ❛♠♣❧✐t✉❞❡ ✈✐❜r❛❝✐♦♥❛❧ ❞❡ ♣♦♥t♦ ③❡r♦ ❞❡ss❡ ♠♦❞♦ ❡ gj s✉❛ ❞❡❣❡♥❡r❡s❝ê♥❝✐❛✱ 3αj◦ ❡ γ◦2j ❝♦rr❡s♣♦♥✲
❞❡♠✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ à ❝♦♠♣♦♥❡♥t❡ tr❛ç♦ ❡ ❛♥✐s♦tró♣✐❝❛ ❞♦ t❡♥s♦r ♣♦❧❛r✐③❛❜✐❧✐❞❛❞❡ ❛ss♦❝✐❛❞♦ à ❝♦♦r❞❡♥❛❞❛ ♥♦r♠❛❧✱ T é ❛ t❡♠♣❡r❛t✉r❛ ❞❡ ✈✐❜r❛çã♦ ❞❛s ♠♦❧é❝✉❧❛s ❡ c é ❛
✈❡❧♦❝✐❞❛❞❡ ❞❛ ❧✉③ ♥♦ ✈á❝✉♦❬✺❪✳
❈❛♣ít✉❧♦ ✷
❚é❝♥✐❝❛ ▲■❉❆❘
✷✳✶ ❙✐st❡♠❛ ▲■❉❆❘
❆s ♣r✐♠❡✐r❛s t❡♥t❛t✐✈❛s ❞❡ ♠❡❞✐r ♣❡r✜s ❞❡ ❞❡♥s✐❞❛❞❡ ❛t♠♦s❢ér✐❝❛ ♥❛ ❛❧t❛ ❛t♠♦s❢❡r❛ ♣♦r ❞❡t❡r♠✐♥❛çã♦ ❞❛ ✐♥t❡♥s✐❞❛❞❡ ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ ❞❛ ❧✉③ ❝♦♠ ❛ ✉t✐❧✐③❛çã♦ ❞❡ ❤♦❧♦❢♦t❡s ❢♦r❛♠ ❢❡✐t❛s ♥♦s ❛♥♦s ✸✵❬✶✼✕✷✵❪✳
❙②♥❣❡✱ ❡♠ ✶✾✸✵✱ ♣r♦♣ôs ♦ ♣r✐♠❡✐r♦ ♠ét♦❞♦ ❞❡ ❞❡t❡r♠✐♥❛çã♦ ❞❡ ♣❡r✜s ❛t♠♦s❢ér✐❝♦s✱ ♥♦ q✉❛❧ ✉♠ ❤♦❧♦❢♦t❡ s❡r✐❛ ✉s❛❞♦ ❝♦♠♦ ✉♠❛ ❢♦♥t❡ ❞❡ ❧✉③ ❡ ✉♠ ❣r❛♥❞❡ t❡❧❡s❝ó♣✐♦ ❝♦♠♦ ✉♠ r❡❝❡♣t♦r ❡ ❛ ✈❛rr❡❞✉r❛ s❡r✐❛ r❡❛❧✐③❛❞❛ ❝♦♠ ♦ s✐st❡♠❛ ♦♣❡r❛♥❞♦ ❡♠ ✉♠❛ ❝♦♥✜❣✉r❛çã♦ ❜✐❡stát✐❝❛❬✶✼❪✳❖ ❢❡✐①❡ ❞❡ ❧✉③ s❡r✐❛ ❞❡t❡❝t❛❞♦ ✉t✐❧✐③❛♥❞♦✲s❡ ✉♠ ❛♣❛r❛t♦ ❢♦t♦❡❧étr✐❝♦ ❡ ♦ ❝❛♠♣♦ ❞❡ ✈✐sã♦ ❞♦ r❡❝❡♣t♦r s❡r✐❛ ✈❛rr✐❞♦ ♣❡❧♦ ❢❡✐①❡ ❞♦ ❤♦❧♦❢♦t❡ ♦❜t❡♥❞♦✲s❡ ✉♠ ♣❡r✜❧ ❞❡ ❛❧t✐t✉❞❡ ❞❛ ✐♥t❡♥s✐❞❛❞❡ ❞❛ ❧✉③ ❡s♣❛❧❤❛❞❛ ♣♦r ♠❡✐♦ ❞❡ ❝♦♥s✐❞❡r❛çõ❡s ❣❡♦♠étr✐❝❛s s✐♠♣❧❡s✳
❖s ♣r✐♠❡✐r♦s r❡s✉❧t❛❞♦s r❡♣♦rt❛❞♦s✱ ♦❜t✐❞♦s ✉t✐❧✐③❛♥❞♦ ❡ss❡ ♠ét♦❞♦✱ ❢♦r❛♠ ❞❡ ❉✉✲ ❝❧❛✉①❬✷✶❪✱ ♦ q✉❛❧ ❢❡③ ✉♠ r❡❣✐str♦ ❢♦t♦❣rá✜❝♦ ❞❛ ❧✉③ ❡s♣❛❧❤❛❞❛ ♣❡❧♦ ❢❡✐①❡ ❞♦ ❤♦❧♦❢♦t❡✳ ❆ ❢♦t♦❣r❛✜❛ ❢♦✐ t✐r❛❞❛ ❛ ✉♠❛ ❞✐stâ♥❝✐❛ ❞❡ ✷✱✹ ❦♠ ❞♦ ❤♦❧♦❢♦t❡ ✉s❛♥❞♦ ✉♠❛ ❧❡♥t❡ ❢✴✶✱✺ ❞✉r❛♥t❡ ✉♠❛ ❡①♣♦s✐çã♦ ❞❡ ✶✱✺ ❤♦r❛s s❡♥❞♦ q✉❡✱ ❝♦♠ ❡ss❛s ❝♦♥✜❣✉r❛çõ❡s✱ ♦ ❢❡✐①❡ ❡r❛ ✈✐sí✈❡❧ ♥❛ ❢♦t♦❣r❛✜❛ ❛ ✉♠❛ ❛❧t✐t✉❞❡ ❞❡ ✸✱✹ ❦♠✳❍✉❧❜✉rt✱ ❡♠ ✶✾✸✼✱ r❡♣♦rt♦✉ r❡s✉❧t❛❞♦s ♥♦ q✉❛❧ ❢♦t♦❣r❛❢♦✉ ✉♠ ❢❡✐①❡ ❛ ✉♠❛ ❛❧t✐t✉❞❡ ❞❡ ✷✽ ❦♠ r❡❛❧✐③❛♥❞♦✱ ❛ss✐♠✱ ❝á❧❝✉❧♦s ❞❡ ♣❡r✜s ❞❡ ❞❡♥s✐❞❛❞❡ ❛t♠♦s❢ér✐❝❛❬✶✾❪✳
❖s s✐st❡♠❛s ▲■❉❆❘ ♠❛✐s ♠♦❞❡r♥♦s ♣♦ss✉❡♠ ✉♠❛ ❝♦♥✜❣✉r❛çã♦ ♠♦♥♦❡stát✐❝❛✳❖s s✐st❡♠❛s ♠♦♥♦❡stát✐❝♦s ♣♦❞❡♠ s❡r s✉❜❞✐✈✐❞✐❞♦s ❡♠ ❞✉❛s ❝❛t❡❣♦r✐❛s✿ s✐st❡♠❛s ❝♦❛①✐❛✐s✱
