❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❛ P❛r❛í❜❛
❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❡ ❞❛ ◆❛t✉r❡③❛
Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❙tr✐❝t♦ ❙❡♥s✉ ❡♠ ❋ís✐❝❛
❆♥❞❡rs♦♥ ❆❧❡①❛♥❞r❡ ❱✐❡✐r❛ ●♦♠❡s
❚r❛♥s♣♦rt❡ ◗✉â♥t✐❝♦ ❞❡ ❈❛r❣❛✱ ❙♣✐♥ ❡ ❈❛❧♦r ❡♠
◆❛♥♦❡str✉t✉r❛s ❈❛ót✐❝❛s
❏♦ã♦ P❡ss♦❛ ✶✽ ❞❡ ♠❛rç♦ ❞❡ ✷✵✶✻
❆♥❞❡rs♦♥ ❆❧❡①❛♥❞r❡ ❱✐❡✐r❛ ●♦♠❡s
❚r❛♥s♣♦rt❡ ◗✉â♥t✐❝♦ ❞❡ ❈❛r❣❛✱ ❙♣✐♥ ❡ ❈❛❧♦r ❡♠ ◆❛♥♦❡str✉t✉r❛s
❈❛ót✐❝❛s
❉✐ss❡rt❛çã♦ ❞❡ ♠❡str❛❞♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ ❞❡♣❛r✲ t❛♠❡♥t♦ ❞❡ ❢ís✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❛ P❛r❛í❜❛ ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ♠❡str❡ ❡♠ ❢ís✐❝❛
➪r❡❛ ❞❡ ❝♦♥❝❡♥tr❛çã♦✿ ▼❛tér✐❛ ❈♦♥❞❡♥s❛❞❛
❖r✐❡♥t❛❞♦r✿ ❏♦r❣❡ ●❛❜r✐❡❧ ●♦♠❡s ❞❡ ❙♦✉③❛ ❘❛♠♦s✳
❆❣r❛❞❡❝✐♠❡♥t♦s
❆ ♠✐♥❤❛ ❡s♣♦s❛✱ P❛trí❝✐❛✱ ♣♦r t❛♥t♦ t♦r❝❡r ❡ ♠❡ ♣r♦♣♦r❝✐♦♥❛r tr❛♥q✉✐❧✐❞❛❞❡ ♣❛r❛ ❝♦♥❝❧✉✐r ❡st❛ ❡t❛♣❛✳ P❛r❛ ✈♦❝ê ❛ ♠❡t❛❞❡ ❞❡ t♦❞♦ ♠❡✉ ❛♠♦r✳
❆♦ ♠❡✉ ✜❧❤♦✱ P❡rs❡✉✱ ♣♦r t❛♥t♦ t♦r❝❡r ❡ ♠❡ ♣r♦♣♦r❝✐♦♥❛r tr❛♥q✉✐❧✐❞❛❞❡ ♣❛r❛ ❝♦♥❝❧✉✐r ❡st❛ ❡t❛♣❛✳ P❛r❛ ✈♦❝ê ❛ ♦✉tr❛ ♠❡t❛❞❡ ❞❡ t♦❞♦ ♠❡✉ ❛♠♦r✳
❆♦ ♠❡✉ ♦r✐❡♥t❛❞♦r✱ ❏♦r❣❡ ●❛❜r✐❡❧✱ ♣♦r q✉❡♠ ❣✉❛r❞♦ ✉♠❛ ♣r♦❢✉♥❞❛ ❛❞♠✐r❛çã♦✳
❆♦ ♠❡✉ ♣r✐♠❡✐r♦ ♦r✐❡♥t❛❞♦r✱ ❆❞❡❧s✐♥❞♦ ▲✐❜❡r❛t♦ ❞❡ ❇r✐t♦ ✭✐♥ ♠❡♠♦r✐❛♠✮✱ ♣♦r t✉❞♦ q✉❡ ❡❧❡ r❡♣r❡s❡♥t❛ ♣❛r❛ ♠✐♠✳
❆ ♠✐♥❤❛ ♠ã❡✱ ♣♦r sê✲❧❛✳
❆♦ ♠❡✉ ♣❛✐✱ ♣♦r sê✲❧♦✳
❆♦ Pr♦❢❡ss♦r ❡ ❛♠✐❣♦✱ ❈❛r❧♦s P✐r❡s✱ ♣♦r s❡♠♣r❡ t❡r ♠❡ ✐♥❝❡♥t✐✈❛❞♦ à r❡t♦♠❛❞❛ ❞❡ ♠✐♥❤❛ ❝❛rr❡✐r❛ ❛❝❛❞ê♠✐❝❛✳
❆♦ ♠❡✉ ❛♠✐❣♦ ❊r✐❝❦✱ ♣❡❧♦ ❛♣♦✐♦ ❡ ♣♦r s✉❛ ❛♠✐③❛❞❡✳
❆♦s ♠❡✉s ❛♠✐❣♦s✱ ▼❛t❤❡✉s ❡ ❘♦❞♦❧❢♦✱ ♣❡❧❛ ❛♠✐③❛❞❡ ❡ ♣❛❝✐ê♥❝✐❛ ❡♠ ❞✐✈✐❞✐r ♦ ❛♠❜✐❡♥t❡ ❞❡ ❡st✉❞♦ ❝♦♠✐❣♦✳
❆ ❙❡✉ ▼❛r✐❛♥♦✱ ♣❡❧❛s ♣❛❧❛✈r❛s ❞❡ ✐♥❝❡♥t✐✈♦ ❡ ♣❡❧♦s ♠♦♠❡♥t♦s ❞❡ ❞❡s❝♦♥tr❛çã♦ ❡ ❛❧❡❣r✐❛ ♣r♦♣♦r❝✐♦♥❛❞♦s ♣♦r ❡❧❡ s❡♠♣r❡ q✉❡ ✈♦✉ t♦♠❛r ✉♠ ❝❛❢é✳
❆ t♦❞♦s ♦s ❢✉♥❝✐♦♥ár✐♦s ❡ ♣r♦❢❡ss♦r❡s ❞❛ ❯❋P❇✳
◗✉❡ ♠❡✉s ✐❞❡❛✐s s❡❥❛♠ t❛♥t♦ ♠❛✐s ❢♦rt❡s q✉❛♥t♦ ♠❛✐♦r❡s ❢♦r❡♠ ♦s ❞❡s❛❢✐♦s✱ ♠❡s♠♦ q✉❡ ♣r❡❝✐s❡ tr❛♥s♣♦r ♦❜stá❝✉❧♦s ❛♣❛r❡♥t❡♠❡♥t❡ ✐♥tr❛♥s♣♦♥í✈❡✐s✳ P♦rq✉❡ ♠❡t❛❞❡ ❞❡ ♠✐♠ é ❢❡✐t❛ ❞❡ s♦♥❤♦s ❡ ❛ ♦✉tr❛ ♠❡t❛❞❡ ❞❡ ❧✉t❛s✳
❘❡s✉♠♦
❆ ❢♦r♠✉❧❛çã♦ ♠❛tr✐❝✐❛❧ ❞❡ ▲❛♥❞❛✉❡r✲❇ütt✐❦❡r é ✉♠❛ ❞❛s ♣r✐♥❝✐♣❛✐s ❢❡rr❛♠❡♥t❛s ✉t✐❧✐✲ ③❛❞❛s ♥❛ ❢ís✐❝❛ ♠❡s♦s❝ó♣✐❝❛ ♣❛r❛ ❞❡s❝r❡✈❡r s✐st❡♠❛s q✉❡ ❣✉❛r❞❛♠ ❝♦♥s✐❣♦ s❡♠❡❧❤❛♥ç❛s ❝♦♠ ♦s s✐st❡♠❛s ♥✉❝❧❡❛r❡s✱ ♥♦ q✉❡ ❞✐③ r❡s♣❡✐t♦ às ♣♦ssí✈❡✐s r❡ss♦♥â♥❝✐❛s ❛♣r❡s❡♥t❛❞❛s ♥♦s ❞❡✲ ❝❛✐♠❡♥t♦s ❞❡ss❡s s✐st❡♠❛s q✉❛♥❞♦ ❜♦♠❜❛r❞❡❛❞♦s✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ❡st✉❞❛♠♦s ❛ t❡♦r✐❛ ❞❡ ♠❛tr✐③❡s ❛❧❡❛tór✐❛s ❝♦♠♦ ❢♦r♠❛ ❞❡ ❥✉st✐✜❝❛r ❛s ❝♦♥❞✐çõ❡s ❞❡ ❝♦♥t✐♥✉✐❞❛❞❡ ❡ ❞❡ ❝♦♥t♦r♥♦ q✉❡ ♦s s✐st❡♠❛s ♠❡s♦s❝ó♣✐❝♦s ❛♣r❡s❡♥t❛♠ ♥♦ tr❛♥s♣♦rt❡ ❞❡ ❝❛r❣❛ ❡❧étr✐❝❛✳ ❆ s❡❣✉✐r✱ ❧❡✈❛♠♦s ❛s ❝♦♥❞✐çõ❡s ❞♦ s✐st❡♠❛ à ❡s❝❛❧❛ ❛❞❡q✉❛❞❛ ❡ ❛♣❧✐❝❛♠♦s ❛s ✐❞❡✐❛s ❞❛ ❢♦r♠✉❧❛çã♦ ♠❛tr✐❝✐❛❧ ❞♦ ❡s♣❛❧❤❛♠❡♥t♦ ♣❛r❛ ❞❡❞✉③✐r ❛ ❢ór♠✉❧❛ ❞❡ ▼❛❤❛✉①✲❲❡✐♥❞❡r♠ü❧❧❡r ❡ ❡♥❝♦♥tr❛r ❛ ❡str✉t✉r❛ ❞❛ ♠❛tr✐③ ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ ❞❡ s✐st❡♠❛s q✉❡ s❡ ❡♥❝♦♥tr❛♠ ♥❛ ❡s❝❛❧❛ ❞❡ ❝♦♠♣r✐♠❡♥t♦ ❡♠ q✉❡s✲ tã♦✳ ❉❡ ♣♦ss❡ ❞❛ ♠❛tr✐③ ❞❡ ❡s♣❛❧❤❛♠❡♥t♦✱ ❛♥❛❧✐s❛♠♦s ❛s ❝♦♥❞✐çõ❡s ❞♦ tr❛♥s♣♦rt❡ q✉â♥t✐❝♦ ❞❛ ❝❛r❣❛ ❡❧étr✐❝❛ ♣❛r❛ s✐st❡♠❛s à t❡♠♣❡r❛t✉r❛ ♥✉❧❛✳ ❆ s❡❣✉✐r✱ ♣♦❞❡♠♦s ❛♠♣❧✐❛r ♦ ❛❧❝❛♥❝❡ ❞❡ ♥♦ss❛ ❛♥á❧✐s❡ ✐♥✈❡st✐❣❛♥❞♦ ♦s s✐st❡♠❛s ♦♥❞❡ ❛ t❡♠♣❡r❛t✉r❛ ❞❡✐①❛ ❞❡ s❡r ♥✉❧❛✱ ❛❝❛rr❡t❛♥❞♦ ♦ s✉r❣✐♠❡♥t♦ ❞❡ ❡❢❡✐t♦s ♥ã♦ ❝♦♥✈❡♥❝✐♦♥❛✐s ❞❡ tr❛♥s♣♦rt❡✱ ❝♦♠♦ ♦ q✉❡ ❛❝♦♥t❡❝❡ ♥♦ ❡❢❡✐t♦ ❙❡✲ ❡❜❡❡❝❦ ❞❡ s♣✐♥s✱ ♣♦r ❡①❡♠♣❧♦✳ ◆❛ s❡q✉ê♥❝✐❛✱ ✉t✐❧✐③❛♠♦s ✉♠❛ ✐♠♣❧❡♠❡♥t❛çã♦ ♥✉♠ér✐❝❛ ❞❡ ♠❛tr✐③❡s ❛❧❡❛tór✐❛s q✉❡ r❡♣r❡s❡♥t❛♠ ♦s ❡♥s❡♠❜❧❡s ❞❡ ❲✐❣♥❡r ♣❛r❛ r❡❝✉♣❡r❛r r❡s✉❧t❛❞♦s ❡s♣❡✲ ❝í✜❝♦s ❞❡ r❡❢❡rê♥❝✐❛s q✉❡ ❛♣r❡s❡♥t❛♠ r❡s✉❧t❛❞♦s r❡❧❛❝✐♦♥❛❞♦s ❝♦♠ ❡st❡ tr❛❜❛❧❤♦✳ ❊st❛ ❢♦✐ ❛ ❢♦r♠❛ ❞❡ t❡st❛r ♦ ♠ét♦❞♦ ❛q✉✐ ✉t✐❧✐③❛❞♦ ❡ ❞❡♠♦♥str❛r ❛ ❡✜❝á❝✐❛ ❞♦ ♠❡s♠♦✳ P♦r ✜♠✱ t❛♠❜é♠ ♣♦r ♠❡✐♦ ❞❡ ✐♠♣❧❡♠❡♥t❛çõ❡s ♥✉♠ér✐❝❛s✱ ♦♥❞❡ ❢♦✐ ✉t✐❧✐③❛❞♦ ✉♠ ❡♥s❡♠❜❧❡ ❞❡ ✹✾✾✽ ♠❛tr✐③❡s ❛❧❡❛tór✐❛s✱ ❛♥❛❧✐s❛♠♦s ♦ tr❛♥s♣♦rt❡ q✉â♥t✐❝♦ ❞❡ ❝❛♥❛✐s ❞❡ s♣✐♥s✱ ❢❛③❡♥❞♦ ❛ ❝♦rr❡❧❛çã♦ ❞♦s ♠❡s♠♦s✱ ♣❛r❛ ❝♦♥st❛t❛r q✉❡✱ ❛ ♣❛rt✐r ❞❡ ✉♠❛ ❢✉♥çã♦ ❣❡r❛tr✐③✱ é ♣♦ssí✈❡❧ ❡♥❝♦♥tr❛r ♦s ❝✉♠✉✲ ❧❛♥t❡s ❡st❛tíst✐❝♦s q✉❡ ♥♦s ♣❡r♠✐t❡♠ ❛♥❛❧✐s❛r ♦s ♦❜s❡r✈á✈❡✐s ❞❡ tr❛♥s♣♦rt❡✱ t❛♥t♦ ♥♦ r❡❣✐♠❡ s❡♠✐✲❝❧áss✐❝♦ ✭♣❛r❛ ♦ q✉❛❧ ❤á ✉♠ ♥ú♠❡r♦ ❣r❛♥❞❡ ❞❡ ❝❛♥❛✐s ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ ❛❜❡rt♦s✮✱ q✉❛♥t♦ ♥♦ r❡❣✐♠❡ q✉â♥t✐❝♦ ❡①tr❡♠♦ ✭♦♥❞❡ ♥ú♠❡r♦ ❞❡ ❝❛♥❛✐s ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ ❛❜❡rt♦s é ♣❡q✉❡♥♦✮✳
❆❜str❛❝t
❚❤❡ ▲❛♥❞❛✉❡r✲❇ütt✐❦❡r ♠❛tr✐① ❢♦r♠✉❧❛t✐♦♥ ✐s ♦♥❡ ♦❢ t❤❡ ♠❛✐♥ t♦♦❧s ✉s❡❞ ♦♥ t❤❡ ♠❡s♦s❝♦✲ ♣✐❝ ♣❤②s✐❝s t♦ ❞❡s❝r✐❜❡ s②st❡♠s ✇❤♦s❡ ❜❡❤❛✈✐♦r ✐s t❤❡ s❛♠❡ ❧✐❦❡ t❤❡ ♥✉❝❧❡❛r ♦♥❡s✱ s♣❡❝✐❛❧❧② ❝♦♥❝❡r♥s t♦ t❤❡ r❡ss♦♥❛♥❝❡s ♣r❡s❡♥t❡s ♦♥ t❤❡ ❞❡❝❛②s ♣r♦❝❡ss❡s ✇❤❡♥ t❤❡② ❛r❡ ❜♦♠❜❛r❞❡❞✳ ■♥ t❤✐s ✇♦r❦✱ ✇❡ st✉❞② t❤❡ r❛♥❞♦♠ ♠❛tr✐① t❤❡♦r② t♦ ❥✉st✐❢② ❝♦♥t✐♥✉✐t② ❝♦♥❞✐t✐♦♥s ♣r❡s❡♥ts ♦♥ t❤❡ ♠❡s♦s❝♦♣✐❝ s②st❡♠s ✐♥ ❝❤❛r❣❡ tr❛♥s♣♦rt ♣❤❡♥♦♠❡♥❛✳ ◆❡①t✱ ✇❡ ❛r❡ t❛❦❡ t❤❡ s②st❡♠s ❜♦✉♥❞❛r② ❝♦♥❞✐t✐♦♥s ✐♥ ❛♣r♦♣r✐❛t❡ s❝❛❧❡ ❛♥❞ ✇❡ ✉s❡ t❤❡ ✐❞❡❛s ♦❢ ♠❛tr✐❝✐❛❧ s❝❛tt❡r✐♥❣ ❢♦r♠✉✲ ❧❛t✐♦♥ t♦ ❞❡r✐✈❡ t❤❡ ▼❛❤❛✉①✲❲❡✐♥❞❡r♠ü❧❧❡r ❢♦r♠✉❧❛ ❛♥❞ ✜♥❞ t❤❡ str✉❝t✉r❡ ♦❢ t❤❡ s❝❛tt❡r✐♥❣ ♠❛tr✐① t♦ s②st❡♠s ✐♥ t❤❡ ❧❡♥❣❤t s❝❛❧❡ ✉♥❞❡r ❝♦♥s✐❞❡r❛t✐♦♥✳ ❲✐t❤ ♣♦ss❡ss✐♦♥ ♦❢ t❤✐s s❝❛tt❡r✐♥❣ ♠❛tr✐①✱ ✇❡ ❤❛✈❡ ❛♥❛❧②③❡❞ t❤❡ q✉❛♥t✉♠ tr❛♥s♣♦rt ❝♦♥❞✐t✐♦♥s ♦❢ ❡❧❡tr✐❝ ❝❤❛r❣❡ ❢♦r s②st❡♠s ❛t ♥✉❧❧ t❡♠♣❡r❛t✉r❡✳ ◆❡①t✱ ✇❡ ❤❛✈❡ ❡①♣❛♥❞ ♦✉r ❛♥❛❧②s✐s ✐♥✈❡st✐❣❛t✐♥❣ t❤✐s s②st❡♠s ❛t ♥♦t ♥✉❧❧ t❡♠♣❡r❛t✉r❡✱ ❧❡❛❞✐♥❣ t♦ ❡♠❡r❣❡♥❝❡ ♦❢ ✉♥❝♦♥✈❡♥t✐♦♥❛❧ ❡✛❡❝ts✱ ❛s ❤❛♣♣❡♥s ✐♥ t❤❡ s♣✐♥s ❙❡❡❜❡❝❦ ❡✛❡❝t✱ ❢♦r ✐♥st❛♥❝❡✳ ▲❛t❡r✱ ✇❡ ✉s❡ ❛ r❛♥❞♦♠ ♠❛tr✐① ♥✉♠❡r✐❝❛❧ ✐♠♣❧❡♠❡♥t❛t✐♦♥ t♦ r❡♣r❡s❡♥ts t❤❡ ❲✐❣♥❡r✬s ❡♥s❡♠❜❧❡s t♦ t❛❦❡ ❜❛❝❦ s♣❡❝✐✜❝s r❡s✉❧ts ♦❢ t❤❡ s❛♠❡ ♣❛♣❡rs t❤❛t ♣r❡s❡♥ts r❡s✉❧ts r❡❧❛t❡❞ t♦ t❤✐s ✇♦r❦✳ ❚❤✐s ✇❛s t❤❡ ✇❛② t♦ t❡st t❤❡ ♠❡t❤♦❞ ❛♥❞ ❞❡♠♦♥str❛t❡ t❤❡✐r ❡✛❡❝t✐✈❡✲ ♥❡ss✳ ❋✐♥❛❧❧②✱ ❛❧s♦ t❤r♦✉❣❤ ♥✉♠❡r✐❝❛❧ ✐♠♣❧❡♠❡♥t❛t✐♦♥ ✇❤❡r❡ ✇❡ ✉s❡❞ ❛♥ ❡♥s❡♠❜❧❡ ✇✐t❤ ✹✾✾✽ r❛♥❞♦♠ ♠❛tr✐①✱ ✇❡ ❤❛✈❡ ❛♥❛❧②③❡❞ t❤❡ ❝❤❛♥♥❡❧s q✉❛♥t✉♠ tr❛♥s♣♦rt ❢♦r s♣✐♥s✱ ✐♥✈❡st✐❣❛t✐♥❣ t❤❡✐r ❝♦rr❡❧❛t✐♦♥s t♦ ♥♦t❡ t❤❛t✱ st❛rt✐♥❣ ♦❢ t❤❡ ❣❡♥❡r❛t✐♥❣ ❢✉♥❝t✐♦♥s✱ ✐t ✐s ♣♦ss✐❜❧❡ t♦ ✜♥❞ t❤❡ st❛t✐st✐❝❛❧ ❝✉♠✉❧❛♥ts t❤❛t ❛❧❧♦✇ ✉s ❛♥❛❧②③❡ tr❛♥s♣♦rt ♦❜s❡r✈❛❜❧❡s✱ ❜♦t❤ ✐♥ t❤❡ s❡♠✐ ❝❧❛ss✐❝❛❧ r❡❣✐♠❡ ✭✇❤❡r❡ t❤❡r❡ ❛r❡ ❧❛r❣❡r ♥✉♠❜❡r ♦❢ t❤❡ ♦♣❡♥ s❝❛tt❡r✐♥❣ ❝❤❛♥♥❡❧s✮✱ ❛s ✐♥ t❤❡ ❡①tr❡♠❡ q✉❛♥t✉♠ r❡❣✐♠❡ ✭✇❤❡r❡ t❤❡ ♥✉♠❜❡r ♦❢ t❤❡ ♦♣❡♥ s❝❛tt❡r✐♥❣ ❝❤❛♥♥❡❧s ✐s s♠❛❧❧✮✳
❙✉♠ár✐♦
✶ ■◆❚❘❖❉❯➬➹❖ ✶✺
✶✳✶ ❉❊❙❈❘■➬➹❖ ❉❖ ❈❊◆➪❘■❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✶✳✷ ❊❙❈❆▲❆❙ ❉❊ ❈❖▼P❘■▼❊◆❚❖ ❊ ❉❊ ❚❊▼P❖ ❊▼ ❈❖◆❉❯❚❖❘❊❙ ▼❊✲
❙❖❙❈ÓP■❈❖❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✶✳✷✳✶ ❈❛✈✐❞❛❞❡s ❜❛❧íst✐❝❛s ♠❡s♦s❝ó♣✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✶✳✷✳✷ ❈♦♥❞✉t♦r❡s ♠❡s♦s❝ó♣✐❝♦s ❞✐❢✉s✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✶✳✸ ❆P❘❖❳■▼❆➬Õ❊❙ ❊❙❚❆❚❮❙❚■❈❆❙ P❆❘❆ ❋▲❯❚❯❆➬Õ❊❙ ▼❊❙❖❙❈ÓP■❈❆❙ ✶✾ ✶✳✹ ❖ P❖◆❚❖ ◗❯➶◆❚■❈❖ ❊ ❆ ❈❖◆❉❯❚➶◆❈■❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶
✷ ❯▼❆ ❇❘❊❱❊ ❉■❙❈❯❙❙➹❖ ❙❖❇❘❊ ❈❖◆❉❯❚➶◆❈■❆ ❊▼ ❙■❙❚❊▼❆❙
❈▲➪❙❙■❈❖❙ ✷✹
✷✳✶ ◆❆❚❯❘❊❩❆ ❉❊ ❯▼❆ ❈❖❘❘❊◆❚❊ ❊▲➱❚❘■❈❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹
✷✳✷ ❉❊◆❙■❉❆❉❊ ❉❊ ❈❖❘❘❊◆❚❊ ❊ ❊◗❯❆➬➹❖ ❉❊ ❈❖◆❚■◆❯■❉❆❉❊ ✳ ✳ ✳ ✳ ✷✹
✷✳✸ ▲❊■ ❉❊ ❖❍▼ ❊ ❈❖◆❉❯❚■❱■❉❆❉❊ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻
✸ ❆ ❚❊❖❘■❆ ❉❊ ▼❆❚❘■❩❊❙ ❆▲❊❆❚Ó❘■❆❙ ✷✽
✸✳✶ ❊◆❙❊▼❇▲❊❙ ❉❊ ❲■●◆❊❘✲❉❨❙❖◆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✸✳✷ ❆ ❚❊❖❘■❆ ❉❊ ▲❆◆❉❆❯❊❘ ✲ ❇Ü❚❚■❑❊❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✸✳✸ ❋❖❘▼❯▲❆➬➹❖ ❉❆ ▼❆❚❘■❩ ❉❊ ❊❙P❆▲❍❆▼❊◆❚❖ P❆❘❆ ❆ ❋Ó❘▼❯▲❆
❉❊ ▲❆◆❉❆❯❊❘✲❇Ü❚❚■❑❊❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✸✳✹ ❋❖❘▼❯▲❆➬➹❖ ▼❆❚❘■❈■❆▲ ❉❖ ❊❙P❆▲❍❆▼❊◆❚❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺
✸✳✺ ❆ ▼❆❚❘■❩ ❉❊ ❊❙P❆▲❍❆▼❊◆❚❖(S)❊ ❆ ❉❊❉❯➬➹❖ ❉❆ ❋Ó❘▼❯▲❆ ❉❊
▼❆❍❆❯❳✲❲❊■◆❉❊❘▼Ü▲▲❊❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼
✹ ❖ ❊❋❊■❚❖ ❙❊❊❇❊❈❑ ❊ ❖ ❚❘❆◆❙P❖❘❚❊ ❉❊ ❙P■◆❙ ✹✼
✹✳✶ ❊❋❊■❚❖❙ ❚❊❘▼❖❊▲➱❚❘■❈❖❙✿ P❊▲❚■❊❘✱ ❙❊❊❇❊❈❑ ❊ ❚❍❖▼❙❖◆ ✳ ✳ ✳ ✹✽
✹✳✷ ❖ ❊❋❊■❚❖ ❙❊❊❇❊❈❑ ❉❊ ❙P■◆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✹✳✷✳✶ ❖ ❊❢❡✐t♦ ❙♣✐♥✲❍❛❧❧ ■♥✈❡rs♦ ✭❊❙❍■✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✹✳✸ ❈❆▲❖❘■❚❘Ô◆■❈❆ ❉❊ ❙P■◆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✹✳✸✳✶ ❚❡r♠♦❡❧❡tr✐❝✐❞❛❞❡✿ ✉♠ ♣❡q✉❡♥♦ r❡s✉♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✹✳✸✳✷ ❉❡♣❡♥❞ê♥❝✐❛ t❡r♠♦❡❧étr✐❝❛ ❡♠ ✉♠❛ ❤❡t❡r♦ ❡str✉t✉r❛ ♠❡tá❧✐❝❛
♠❛❣♥ét✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✹✳✹ ❘❡❧❛çõ❡s ❞❡ ❖♥s❛❣❡r ♥♦s ❛❝♦♣❧❛♠❡♥t♦s ❡❧étr✐❝♦s✱ t❡r♠♦❡❧étr✐❝♦s ❡
tr❛♥s♣♦rt❡ ❞❡ s♣✐♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✹✳✹✳✶ ❆s ❞❡③ ❝❧❛ss❡s ❞❡ s✐♠❡tr✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽
✹✳✹✳✷ ❆ ♠❛tr✐③ ❙✿ s✐♠❡tr✐❛s ❡ r❡❝✐♣r♦❝✐❞❛❞❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✹✳✹✳✸ ❋♦r♠✉❧❛çã♦ ❣❡r❛❧ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ tr❛♥s♣♦rt❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✹✳✺ ■▼P▲❊▼❊◆❚❆➬Õ❊❙ ◆❯▼➱❘■❈❆❙✿ ❚❊❙❚❊ ❉❆ ■▼P▲❊▼❊◆❚❆➬➹❖ ◆❯✲
▼➱❘■❈❆ P❆❘❆ ❆ ❋❖❘▼❯▲❆➬➹❖ ❉❊ ▼❆❍❆❯❳✲❲❊■◆❉❊◆▼Ü▲▲❊❘ ✳ ✻✸
✹✳✺✳✶ ❉✐str✐❜✉✐çã♦ ❞❡ ❝✉♠✉❧❛♥t❡s ❞❡ ❝❛r❣❛ ❞❡ ✉♠ ♣♦♥t♦ q✉â♥t✐❝♦ ❝❛ót✐❝♦ ❝♦♠ ❝♦♥t❛t♦s ♥ã♦ ✐❞❡❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✹✳✺✳✷ P✐❝♦s ❞❡ ❝♦♥❞✉tâ♥❝✐❛ ❡♠ ♣♦♥t♦s q✉â♥t✐❝♦s ❛❜❡rt♦s ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✹✳✺✳✸ ❋✉♥çã♦ ❞❡ ❝♦rr❡❧❛çã♦ ❣❡♥❡r❛❧✐③❛❞❛ ♣❛r❛ ✢✉t✉❛çõ❡s ❞❛ ❝♦♥❞✉✲
tâ♥❝✐❛ ❡ ♦ ❡❢❡✐t♦ s♣✐♥ ❤❛❧❧❧ ♠❡s♦s❝ó♣✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✹✳✺✳✹ ❋✉♥çã♦ ❞❡ ❝♦rr❡❧❛çã♦ ❞❛s ✢✉t✉❛çõ❡s ❞❛ ❝♦♥❞✉tâ♥❝✐❛ ❝♦♠ ♦s
♣♦ssí✈❡✐s ❝❛♥❛✐s ❞❡ s♣✐♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✶ ▼♦❞❡❧♦ ❣❡♥ér✐❝♦ ❞❡ ✉♠ ♣♦♥t♦ q✉â♥t✐❝♦ ❝♦♥❡❝t❛❞♦ ❛ ❞♦✐s ❣✉✐❛s✳ ❋✐✲ ❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ❬✸✻❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷ ❙✐♠✉❧❛çã♦ ❞❛s ❋❧✉t✉❛çõ❡s ❞❡ ❝♦♥❞✉tâ♥❝✐❛ ♣❛r❛ ♣♦♥t♦s q✉â♥t✐❝♦s ❝♦✲
♥❡❝t❛❞♦s ❛ ❞♦✐s ❣✉✐❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✸ ❱❛r✐â♥❝✐❛ ❞❛ t❛①❛ ❞❡ tr❛♥s♠✐ssã♦ ❚ ❡♠ ❢✉♥çã♦ ❞♦ í♥❞✐❝❡ ❞❡ tr❛♥s✲
♠✐ssã♦ ❞❛ ❜❛rr❡✐r❛ ❞❡ t✉♥❡❧❛♠❡♥t♦ Γ✱ r❡s❣❛t❛❞♦ ❞♦ t❡①t♦ ♦r✐❣✐♥❛❧
❞♦s ❛✉t♦r❡s ❞❛ r❡❢❡rê♥❝✐❛ ❬✶✽❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✹ ❙✐st❡♠❛ ❝❧áss✐❝♦ ♣❛r❛ ♦ ♥ú❝❧❡♦ ❛tô♠✐❝♦ ♥♦ q✉❛❧ ❡❧❡ é ✈✐st♦ ❝♦♠♦ ✉♠
❜✐❧❤❛r ❝♦♠ ✉♠❛ ❝r❛t❡r❛ ❞❡ ❢♦r♠❛t♦ q✉❛❧q✉❡r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✺ ◆❡st❛ ✜❣✉r❛ ❡stã♦ ♣❧♦t❛❞♦s ❞❡③ ✈❛❧♦r❡s ❞❛s ❝♦♥❞✉tâ♥❝✐❛s ♠é❞✐❛s ❡♠
❢✉♥çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ ❝❛♥❛✐s ♣r❡s❡♥t❡s ♥♦s ❣✉✐❛s✳ ◆❡st❛ ✐♠♣❧❡♠❡♥✲ t❛çã♦ ✉t✐❧✐③❛♠♦s ✶✺✵✵ r❡❛❧✐③❛çõ❡s ❞❡ ✉♠ ❡♥s❡♠❜❧❡ ❝♦♥t❡♥❞♦ ✹✾✾✽ ♠❛tr✐③❡s✳ ❈♦♥s✐❞❡r❛♠♦s✱ t❛♠❜é♠✱ ✷✵✵ r❡ss♦♥â♥❝✐❛s ♣♦ssí✈❡✐s✳ P♦r ✉♠❛ q✉❡stã♦ ❞❡ s✐♠❡tr✐❛✱ ❝♦♥s✐❞❡r❛♠♦s ♦ ❝❛s♦ ✐❞❡❛❧ ✲ t❛①❛ ❞❡ tr❛♥s✲ ♠✐ssã♦ ✶ ✲ ❡ ♦ ♠❡s♠♦ ♥ú♠❡r♦ ❞❡ ❝❛♥❛✐s ❡♠ ❝❛❞❛ ❣✉✐❛ (N1 = N2)✳ ❱ê✲s❡ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❧✐♥❡❛r ♣❛r❛ ❛ ❝♦♥❞✉tâ♥❝✐❛ ♠é❞✐❛ ❡♠ ❢✉♥çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ ❝❛♥❛✐s ♥♦s ❣✉✐❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✻ ❍✐st♦❣r❛♠❛ ❞❡ ❢r❡q✉ê♥❝✐❛s✿ P♦♥t♦ ◗✉â♥t✐❝♦ ❝♦♠ ❞♦✐s ❣✉✐❛s✳ ❙✐♠✉✲
❧❛çã♦ r❡❛❧✐③❛❞❛ ❝♦♠ ✶✵ ❝❛♥❛✐s ❡♠ ❝❛❞❛ ❣✉✐❛✱ ✹✾✾✽ r❡❛❧✐③❛çõ❡s ❡ ✸✵✵ r❡ss♦♥â♥❝✐❛s✳ ❚❡♠✲s❡ ❛♣r♦①✐♠❛çã♦ ❞❡ ✉♠❛ ❞✐str✐❜✉✐çã♦ ●❛✉ss✐❛♥❛✳ ✸✵ ✼ ❍✐st♦❣r❛♠❛ ❞❡ ❢r❡q✉ê♥❝✐❛s ♣❛r❛ ❛ ❝♦♥❞✉tâ♥❝✐❛ ❞❡ ✉♠ ♣♦♥t♦ q✉â♥t✐❝♦
❝♦♥❡❝t❛❞♦s ❛ ❞♦✐s ❣✉✐❛s ❞❡ ❢♦r♠❛ ♥ã♦ ✐❞❡❛❧ ❡ ❝♦♠ t❛①❞❡ tr❛♥♠✐ssã♦
Γ = 2/3✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶
✽ ❉✐str✐❜✉✐çã♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡s ❛tr❛✈és ❞❡ ✉♠ ♣♦♥t♦ q✉â♥t✐❝♦ ❝♦✲ ♥❡❝t❛❞♦s ❛ ❞♦✐s ❣✉✐❛s ❞❡ ❢♦r♠❛ ♥ã♦ ✐❞❡❛❧ ❡ ❝♦♠ t❛①❞❡ tr❛♥♠✐ssã♦
Γ = 2/3✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷
✾ ❙✐st❡♠❛ ♠❡s♦s❝ó♣✐❝♦ ✐❞❡❛❧✐③❛❞♦ ♣♦r ▲❛♥❞❛✉❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✶✵ P♦t❡♥❝✐❛✐s ♥♦s r❡s❡r✈❛tór✐♦s ❝♦♥❡❝t❛❞♦s ❛♦s ❣✉✐❛s ❧✐❣❛❞♦s ❛♦ ♣♦♥t♦
q✉â♥t✐❝♦ ❬✷❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✶✶ ❘❡❣✐ã♦ ❞❡ ✐♥t❡r❛çã♦ ❝♦♠ ❢♦r♠❛ ❛r❜✐trár✐❛ ❡ r❡❣✐ã♦ ❞❡s♣❛❤❛♠❡♥t♦ ❞❡
❧❛r❣✉r❛ d ♣♦r ♦♥❞❡ ✧✈✐❛❥❛♠✧♦s ♠♦❞♦s ♣r♦♣❛❣❛♥t❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼
✶✷ ❱❛r✐â♥❝✐❛ ❞❛ t❛①❛ ❞❡ tr❛♥s♠✐ssã♦ ❚ ❡♠ ❢✉♥çã♦ ❞♦ í♥❞✐❝❡ ❞❡ tr❛♥s✲ ♠✐ssã♦ ❞❛ ❜❛rr❡✐r❛ ❞❡ t✉♥❡❧❛♠❡♥t♦ Γ✱ r❡s❣❛t❛❞♦ ❞♦ t❡①t♦ ♦r✐❣✐♥❛❧
❞♦s ❛✉t♦r❡s ❞❛ r❡❢❡rê♥❝✐❛ ❬✶✽❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✶✸ ❱❛r✐â♥❝✐❛ ❞❛ t❛①❛ ❞❡ tr❛♥s♠✐ssã♦ ❚ ❡♠ ❢✉♥çã♦ ❞❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡
tr❛♥s♠✐ssã♦ Γ✳ ❘❡s✉❧t❛❞♦ r❡s❣❛t❛❞♦ ✈✐❛ s✐♠✉❧❛çã♦ ♥✉♠ér✐❝❛ ✳ ✳ ✳ ✳ ✳ ✹✻
✶✹ ❊❢❡✐t♦ ❍❛❧❧ s♦❜r❡ ❡❧étr♦♥s q✉❛♥❞♦ ✐♠❡rs♦s ❡♠ ✉♠ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ♣❡r♣❡♥❞✐❝✉❧❛r à s✉❛ ❞✐r❡çã♦ ❞❡ ♣r♦♣❛❣❛çã♦✳ ❆ ✜❣✉r❛ ❢♦✐ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ❬✷✵❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼
✶✺ ❯♠❛ ❝♦rr❡♥t❡ ❡❧étr✐❝❛ é ❢♦rç❛❞❛ ❛ ♣❛ss❛r ♣♦r ❥✉♥çõ❡s ❞❡ ♠❡t❛✐s ❞✐❢❡r❡♥t❡s✱ r❡s✉❧t❛♥❞♦ ❡♠ ❛q✉❡❝✐♠❡♥t♦ ❞❡ ✉♠❛ ❡ r❡s❢r✐❛♠❡♥t♦ ❞❡ ♦✉tr❛✳ ❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ❬✷✺❪ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✶✻ ❆♦ s❡ ❝♦♥❡❝t❛r ❞♦✐s ♠❡t❛✐s ❞✐❢❡r❡♥t❡s ✭♦✉ ❧✐❣❛s ♠❡tá❧✐❝❛s✮✱ tê♠✲s❡
✉♠ ❝✐r❝✉✐t♦ t❛❧ q✉❡✱ s❡ ❛s ❥✉♥çõ❡s ❢♦r❡♠ ♠❛♥t✐❞❛s ❡♠ t❡♠♣❡r❛t✉r❛s ❞✐❢❡r❡♥t❡s✱ s✉r❣✐rá ✉♠❛ ❢✳❡✳♠✳ t❡r♠♦❡❧étr✐❝❛ ❡ ✉♠❛ ❝♦rr❡♥t❡ ❡❧é✲ tr✐❝❛ ✧✐✧❝✐r❝✉❧❛rá ♣❡❧♦ ❝❤❛♠❛❞♦ ✧♣❛r t❡r♠♦❡❧étr✐❝♦✧♦✉ ✧t❡r♠♦♣❛r✧✳ ❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ❬✷✻❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✶✼ ■❧✉str❛çã♦ ❞♦ t❡r♠♦♣❛r s♦❜ ✉♠❛ t❡♥sã♦ ❡❧étr✐❝❛ ❣❡r❛❞❛ ❛ ♣❛rt✐r ❞❡
✉♠ ❣r❛❞✐❡♥t❡ ❞❡ t❡♠♣❡r❛t✉r❛ ❡ ♦ ♠❛❣♥❡t♦ ♠❡tá❧✐❝♦ s♦❜ ✉♠❛ t❡♥sã♦ ❞❡ s♣✐♥ ❣❡r❛❞❛✱ t❛♠❜é♠✱ ♣♦r ✉♠ ❣r❛❞✐❡♥t❡ ❞❡ t❡♠♣❡r❛t✉r❛✳ ❆ ✜❣✉r❛ ❢♦✐ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ❬✷✸❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✶✽ ❉✐str✐❜✉✐çã♦ ❞❡ ♣♦t❡♥❝✐❛✐s ❞❡ s♣✐♥ ❛♦ ❧♦♥❣♦ ❞♦ ♠❛❣♥❡t♦ s✉❜♠❡t✐❞♦
❛ ✉♠ ❣r❛❞✐❡♥t❡ ❞❡ t❡♠♣❡r❛t✉r❛✳ ❆ ✜❣✉r❛ ❢♦✐ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ❬✷✸❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✶✾ ▼♦✈✐♠❡♥t❛çã♦ ❞❛ ❝♦rr❡♥t❡ ❞❡ s♣✐♥✳ ❊st❡ ✢✉①♦ ❞❡ ❝♦rr❡♥t❡ ❞❡ s♣✐♥
❣❡r❛ ♦ ■❙❍❊✳ ❆ ✜❣✉r❛ ❢♦✐ ❡①tr❛í❞❛ ❞❛ s✐t❛çã♦ ❬✷✹❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✷✵ ❈♦rr❡♥t❡ ❞❡ ❝❛❧♦r ✐♥❞✉③✐♥❞♦ ✉♠❛ ❝♦rr❡♥t❡ ❞❡ ❝❛r❣❛ ❡❧étr✐❝❛ ❛♦ ❧♦♥❣♦
❞❛ ❞✐r❡çã♦ ❧♦♥❣✐t✉❞✐♥❛❧ ❞♦ ❣r❛❞✐❡♥t❡ ❞❡ t❡♠♣❡r❛t✉r❛✳ ❆ ✜❣✉r❛ ❢♦✐ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ❬✷✼❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✷✶ ❉✐str✐❜✉✐çã♦ ❞❛ ❝♦♥❞✉tâ♥❝✐❛ ❞❡ ✉♠ ♣♦♥t♦ q✉â♥t✐❝♦ ❝♦♠ ❝♦♥t❛t♦s
✐❞❡❛✐s✳ ◆❛ ✜❣✉r❛✱ ♦ ♥ú♠❡r♦ ✶ ❛♦ ❧❛❞♦ ❞❛ ❝✉r✈❛ ♦❜t✐❞❛ r❡♣r❡s❡♥t❛ ♦ ✈❛❧♦r ❞♦ ♥ú♠❡r♦ ❞❡ ❝❛♥❛✐s ♣r♦✈❡♥✐❡♥t❡s ❞♦ r❡s❡r✈❛tór✐♦ ✷✱ ❡♥q✉❛♥t♦ q✉❡ ♦ N1 = 4✳ ❆ ✜❣✉r❛ ❢♦✐ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ❬✸✻❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✷✷ ❚❡♠✲s❡ ♥❡st❛ s✐♠✉❧❛çã♦ N1 = 4 ❡ N2 = 1✱ ♣❛r❛ ♦ ❝❛s♦ ♦rt♦❣♦♥❛❧ ♦♥❞❡
β = 1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻
✷✸ ❚❡♠✲s❡ ♥❡st❛ s✐♠✉❧❛çã♦ N1 = 4 ❡ N2 = 2✱ ♣❛r❛ ♦ ❝❛s♦ ♦rt♦❣♦♥❛❧ ♦♥❞❡
β = 1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻
✷✹ ❚❡♠✲s❡ ♥❡st❛ s✐♠✉❧❛çã♦ N1 = 4 ❡ N2 = 4✱ ♣❛r❛ ♦ ❝❛s♦ ♦rt♦❣♦♥❛❧ ♦♥❞❡
β = 1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻
✷✺ ❚❡♠✲s❡ ♥❡st❛ s✐♠✉❧❛çã♦ N1 = 4 ❡ N2 = 9✱ ♣❛r❛ ♦ ❝❛s♦ ♦rt♦❣♦♥❛❧ ♦♥❞❡
β = 1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻
✷✻ ❉❡♣❡♥❞ê♥❝✐❛ ❧✐♥❡❛r ❞❛ ❞✐str✐❜✉✐çã♦ ❞❡ ❝♦♥❞✉tâ♥❝✐❛s ♣❛r❛ ♦ ♥ú♠❡r♦ ♣❡q✉❡♥♦ ❞❡ ❝❛♥❛✐s N1 = 4 ❡ N2 = 1✱ ♥♦ ❝❛s♦ ♦rt♦❣♦♥❛❧ ♦♥❞❡ β = 1✳ ❱ê✲s❡ ❛ ❝♦♥✈❡r❣ê♥❝✐❛ ❞♦s ♣♦♥t♦s ♦❜t✐❞♦s ♥❛ s✐♠✉❧❛çã♦ ❝♦♠ ♦ ✜tt✐♥❣✳ ✻✼ ✷✼ ❉❡♣❡♥❞ê♥❝✐❛ ❞❛ ❞✐str✐❜✉✐çã♦ ❞❡ ❝♦♥❞✉tâ♥❝✐❛s ♣❛r❛ ♦ ♥ú♠❡r♦ ❞❡ ❝❛✲
♥❛✐s N1 = 4 ❡ N2 = 2✱ ♥♦ ❝❛s♦ ♦rt♦❣♦♥❛❧ ♦♥❞❡ β = 1✳ P❡r❝❡❜❡✲s❡ ❛q✉✐ ✉♠❛ ❞✐str✐❜✉✐çã♦ ●❛✉ss✐❛♥❛ ❡♥✈♦❧✈❡♥❞♦ ♦s ♣♦r♥t♦s ♦❜t✐❞♦s ♥❛ s✐♠✉❧❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼
✷✽ ❉❡♣❡♥❞ê♥❝✐❛ ❞❛ ❞✐str✐❜✉✐çã♦ ❞❡ ❝♦♥❞✉tâ♥❝✐❛s ♣❛r❛ ♦ ♥ú♠❡r♦ ❞❡ ❝❛✲ ♥❛✐s N1 = 4 ❡ N2 = 4✱ ♥♦ ❝❛s♦ ♦rt♦❣♦♥❛❧ ♦♥❞❡ β = 1✳ P❡r❝❡❜❡✲s❡ ❛q✉✐ ✉♠❛ ❞✐str✐❜✉✐çã♦ ●❛✉ss✐❛♥❛ ❡♥✈♦❧✈❡♥❞♦ ♦s ♣♦r♥t♦s ♦❜t✐❞♦s ♥❛ s✐♠✉❧❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✷✾ ❉❡♣❡♥❞ê♥❝✐❛ ❞❛ ❞✐str✐❜✉✐çã♦ ❞❡ ❝♦♥❞✉tâ♥❝✐❛s ♣❛r❛ ♦ ♥ú♠❡r♦ ❞❡ ❝❛✲
♥❛✐s N1 = 4 ❡ N2 = 9✱ ♥♦ ❝❛s♦ ♦rt♦❣♦♥❛❧ ♦♥❞❡ β = 1✳ P❡r❝❡❜❡✲s❡ ❛q✉✐ ✉♠❛ ❞✐str✐❜✉✐çã♦ ●❛✉ss✐❛♥❛ ❡♥✈♦❧✈❡♥❞♦ ♦s ♣♦r♥t♦s ♦❜t✐❞♦s ♥❛ s✐♠✉❧❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✸✵ ❢✉♥çã♦ ❞❡ tr❛♥s♠✐ssã♦ ❞❛ ❛✉t♦❝♦rr❡❧❛çã♦ ♥♦r♠❛❧✐③❛❞❛Ceε(δε)❡♠ ❢✉♥✲
çã♦ ❞❛ ❡♥❡r❣✐❛ δε ♣❡❧❛ t❛①❛ ❞❡ tr❛♥s♠✐ssã♦ Γ ♦❜t✐❞❛ ♥❛ r❡❢❡rê♥❝✐❛
❬✸✻❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✸✶ ❢✉♥çã♦ ❞❡ tr❛♥s♠✐ssã♦ ❞❛ ❛✉t♦❝♦rr❡❧❛çã♦ ♥♦r♠❛❧✐③❛❞❛Ceε(δε)❡♠ ❢✉♥✲
çã♦ ❞❛ ❡♥❡r❣✐❛ δε♣❡❧❛ t❛①❛ ❞❡ tr❛♥s♠✐ssã♦ Γ ♦❜t✐❞❛ ❝♦♠ ✐♠♣❧❡♠❡♥✲
t❛çã♦ ❞❡ ✹✷✵✵ r❡❛❧✐③❛çõ❡s ❡ ✸✵✵ r❡ss♦♥â♥❝✐❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✸✷ ◗✉❛t✉♠ ❞♦t ❜❛❧íst✐❝♦ ❝♦♥❡❝t❛❞♦ ❞❡ ❢♦r♠❛ ✐❞❡❛❧ ❛ q✉❛tr♦ ❡❧❡tr♦❞♦s✱
t❡♥❞♦ ✉♠❛ ❞✐❢❡r❡♥ç❛ ❞❡ ✈♦❧t❛❣❡♠ ❡♥tr❡ ♦s ❣✉❛✐s ✶ ❡ ✷✱ ❡♥q✉❛♥t♦ q✉❡ ♦ ❛❥✉st❡ ❢❡✐t♦ ♣❛r❛ ✸ ❡ ✹ ❢❛③ ❝♦♠ q✉❡ ❛ ❞✐❢❡r❡♥ç❛ ❞❡ ♣♦t❡♥❝✐❛❧ tr❛♥s✈❡rs❛❧ s❡❥❛ ♥✉❧❛✳ ❆ ✜❣✉r❛ ❢♦✐ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ❬✸✽❪✳ ✳ ✳ ✳ ✳ ✼✷ ✸✸ ❈♦✈❛r✐â♥❝✐❛ ❞♦s ❝♦❡✜❝✐❡♥t❡s ❞❡ tr❛♥s♠✐ssã♦ ❡♠ ❢✉♥çã♦ ❞❛ ❞✐❢❡r❡♥ç❛
❞❡ ❡♥❡r❣✐❛✳ ❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ❬✶✵❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✸✹ ❈♦✈❛r✐â♥❝✐❛ ❞♦s ❝♦❡✜❝✐❡♥t❡s ❞❡ tr❛♥s♠✐ssã♦ ❡♠ ❢✉♥çã♦ ❞❛ ❞✐❢❡r❡♥ç❛
❞❡ ❡♥❡r❣✐❛✳ ❋✐❣✉r❛ ♦❜t✐❞❛ ❛ ♣❛rt✐r ❞❡ ✉♠❛ ✐♠♣❧❡♠❡♥t❛çã♦ ♥✉♠ér✐❝❛ ❝♦♠ ✹✾✾✽ r❡❛❧✐③❛çõ❡s ❡ ✹✵✵ r❡ss♦♥â♥❝✐❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✸✺ ❈♦♠♣♦rt❛♠❡♥t♦ ❞❛ ❢✉♥çã♦ ❞❡ ❋❡r♠✐ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛✳ ❆
❢✉♥çã♦ ❞❡❣r❛✉ t❡♥❞❡ ❛ ✉♠❛ ❝✉r✈❛ ▲♦r❡♥t③✐❛♥❛ ❝♦♠ ♦ ❛✉♠❡♥t♦ ❞❛ t❡♠♣❡r❛t✉r❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✸✻ ❈♦✈❛r✐â♥❝✐❛ ❞♦s ❝♦❡✜❝✐❡♥t❡s ❞❡ tr❛♥s♠✐ssã♦ ❡♠ ❢✉♥çã♦ ❞❛ ❞✐❢❡r❡♥ç❛
❞❡ ❡♥❡r❣✐❛ ♣❛r❛ ❞✐❢❡r❡♥t❡s ♣r♦❥❡çõ❡s ❞❡ s♣✐♥✳ ❋✐❣✉r❛ ♦❜t✐❞❛ ❛ ♣❛rt✐r ❞❡ ✉♠❛ ✐♠♣❧❡♠❡♥t❛çã♦ ♥✉♠ér✐❝❛ ❝♦♠ ✹✾✾✽ r❡❛❧✐③❛çõ❡s ❡ ✹✵✵ r❡ss♦✲ ♥â♥❝✐❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼ ✸✼ ❈♦♠♣♦rt❛♠❡♥t♦ ❞❛ ❝♦♥❞✉tâ♥❝✐❛ ❡♠ ❢✉♥çã♦ ❞♦ ❝❛♠♣♦ ♣❛r❛ ♦ ♣♦♥t♦
q✉â♥t✐❝♦ ❛❝♦♣❧❛❞♦ ❛♦s r❡s❡r✈❛tór✐♦s ✶ ❡ ✷ ❛tr❛✈és ❞♦s ❣✉✐❛s ✶ ❡ ✷✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❖s r❡s❡r✈❛tór✐♦s sã♦ ♠❛♥t✐❞♦s à t❡♠♣❡r❛t✉r❛ ♥ã♦ ♥✉❧❛ T ❡ ♠❛♥t✐❞♦s ♥♦s ♣♦t❡♥❝✐❛✐s q✉í♠✐❝♦s µ1 ❡ µ2✳ ▼♦str❛♠♦s ❡ss❡ ❝♦♠♣♦rt❛♠❡♥t♦ ♣❛r❛ q✉❛tr♦ ✈❛❧♦r❡s ♣♦ssí✈❡✐s ❞❛ t❡♠♣❡r❛t✉r❛✳ ✳ ✳ ✳ ✼✾ ✸✽ ❈♦♠♣♦rt❛♠❡♥t♦ ❞❛ ❝♦♥❞✉tâ♥❝✐❛ ❡♠ ❢✉♥çã♦ ❞❡ ✐♥❝r❡♠❡♥t♦s ❞♦ ❝❛♠♣♦
♣❛r❛ ♦ ♣♦♥t♦ q✉â♥t✐❝♦ ❛❝♦♣❧❛❞♦ ❛♦s r❡s❡r✈❛tór✐♦s ✶ ❡ ✷ ❛tr❛✈és ❞♦s ❣✉✐❛s ✶ ❡ ✷✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❖s r❡s❡r✈❛tór✐♦s sã♦ ♠❛♥t✐❞♦s à t❡♠✲ ♣❡r❛t✉r❛ ♥ã♦ ♥✉❧❛ T ❡ ♠❛♥t✐❞♦s ♥♦s ♣♦t❡♥❝✐❛✐s q✉í♠✐❝♦s µ1 ❡ µ2✳ ▼♦str❛♠♦s ❡ss❡ ❝♦♠♣♦rt❛♠❡♥t♦ ♣❛r❛ q✉❛tr♦ ✈❛❧♦r❡s ♣♦ssí✈❡✐s ❞❛ t❡♠♣❡r❛t✉r❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾
✸✾ ❈♦♠♣♦rt❛♠❡♥t♦ ❞❛ ❝♦♥❞✉tâ♥❝✐❛ ❡♠ ❢✉♥çã♦ ❞❛ t❛①❛ ❞❡ tr❛♥s♠✐s✲ sã♦ ♣❛r❛ ♦ ♣♦♥t♦ q✉â♥t✐❝♦ ❛❝♦♣❧❛❞♦ ❛♦s r❡s❡r✈❛tór✐♦s ✶ ❡ ✷ ❛tr❛✈és ❞♦s ❣✉✐❛s ✶ ❡ ✷✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❖s r❡s❡r✈❛tór✐♦s sã♦ ♠❛♥t✐❞♦s à t❡♠♣❡r❛t✉r❛ ♥ã♦ ♥✉❧❛ T ❡ ♠❛♥t✐❞♦s ♥♦s ♣♦t❡♥❝✐❛✐s q✉í♠✐❝♦s µ1 ❡
µ2✳ ▼♦str❛♠♦s ❡ss❡ ❝♦♠♣♦rt❛♠❡♥t♦ ♣❛r❛ q✉❛tr♦ ✈❛❧♦r❡s ♣♦ssí✈❡✐s
❞❡ ❝❛♠♣♦ ❡♠ q✉❡stã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✹✵ ❈♦♠♣♦rt❛♠❡♥t♦ ❞❛ ❝♦♥❞✉tâ♥❝✐❛ ❡♠ ❢✉♥çã♦ ❞❛ t❛①❛ ❞❡ tr❛♥s♠✐s✲
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✶ ❈❧❛ss✐✐❝❛çã♦ ❞❛s ❝❧❛ss❡s ❞❡ ❡♥s❡♠❜❧❡s s❡❣✉♥❞♦ s✉❛s s✐♠❡tr✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✷ ❈❧❛ss✐✜❝❛çã♦ ❞❛s ❞❡③ ❝❧❛ss❡s ❞❡ s✐♠❡tr✐❛s ♣❛r❛ ♦s ❍❛♠✐❧t♦♥✐❛♥♦s✱ s❡❣✉✐♥❞♦ ❛
♥♦♠❡❝❧❛t✉r❛ ❞❡ ❈❛rt❛♥✳ ❖s í♥❞✐❝❡s0❡±1r❡♣r❡s❡♥t❛♠ ❛s s✐♠❡tr✐❛s q✉❡❜r❛❞❛s
✶ ■◆❚❘❖❉❯➬➹❖
✶✳✶ ❉❊❙❈❘■➬➹❖ ❉❖ ❈❊◆➪❘■❖
❖ ✐♥í❝✐♦ ❞❡ss❛ ❞✐s❝✉ssã♦ s❡ ❞á ❛ ♣❛rt✐r ❞♦ s✐❣♥✐✜❝❛❞♦ ❞♦ ♣r❡✜①♦ ♠❡s♦✳ ❉♦ ❣r❡❣♦✱ ♦ ♣r❡✜①♦ ♠❡s♦ s✐❣♥✐✜❝❛ ❛q✉✐❧♦ q✉❡ ❡stá ♥♦ ♠❡✐♦✱ ♦ q✉❡ é ✐♥t❡r♠❡❞✐ár✐♦✳ ❚r❛③❡♥❞♦ ♦ s✐❣♥✐✜❝❛❞♦ ♣❛r❛ ♦s ♣r♦♣ós✐t♦s ❞❡st❡ tr❛❜❛❧❤♦✱ ❞✐③✲s❡ q✉❡ ✉♠ s✐st❡♠❛ ❢ís✐❝♦ é ♠❡s♦s❝ó♣✐❝♦ q✉❛♥❞♦ s✉❛ ❡s❝❛❧❛ ❞❡ ❝♦♠♣r✐♠❡♥t♦ s❡ s✐t✉❛ ❡♥tr❡ ♦ q✉❡ s❡ ❝❧❛ss✐✜❝❛ ❝♦♠♦ ♠✐❝r♦s❝ó♣✐❝♦ ❡ ♠❛❝r♦s❝ó♣✐❝♦✳ ❊ss❛ ❢♦✐ ❛ ❞❡s✐❣♥❛çã♦ ❝r✐❛❞❛ ♣♦r ❑❛♠♣❡♥ (1981)✳ ➱ ♣♦r ✐ss♦ q✉❡✱ ❛♦ s❡ ❛♥❛❧✐s❛r t❛✐s s✐st❡♠❛s
t❡♥❞♦ ❡♠ ✈✐st❛ s❡✉ ❝❛rát❡r ♠✐❝r♦s❝ó♣✐❝♦✱ é ♥❡❝❡ssár✐♦ r❡s❣❛t❛r ♦s ❛s♣❡❝t♦s ❝❛r❛❝t❡ríst✐❝♦s ❞❛ t❡♦r✐❛ q✉â♥t✐❝❛✱ ❛♦ ♠❡s♠♦ t❡♠♣♦ ❡♠ q✉❡✱ ❛♦ s❡ ❝♦♥s✐❞❡r❛r ✉♠❛ q✉❛♥t✐❞❛❞❡ s✉✜❝✐❡♥t❡♠❡♥t❡ ❣r❛♥❞❡ ❞❡ át♦♠♦s✱ ❛♦ ♣♦♥t♦ ❞❡ t❡r♠♦s q✉❡ r❡❝♦rr❡r ❛ ❢❡rr❛♠❡♥t❛s ❞❛ ♠❡❝â♥✐❝❛ ❡st❛tíst✐❝❛ ♣❛r❛ ❝♦♠♣r❡❡♥❞ê✲❧♦✳ ❆ ❛♥á❧✐s❡ ❡st❛tíst✐❝❛ ❞♦ tr❛♥s♣♦rt❡ ❞❡ ❡❧étr♦♥s✱ ♣♦r ❡①❡♠♣❧♦✱ ♠❡s♠♦ ✉t✐❧✐③❛♥❞♦ ✉♠ ❝❛rát❡r q✉â♥t✐❝♦✱ ♥♦s ♣❡r♠✐t❡ ❧❡✈á✲❧♦ à ❡s❝❛❧❛ ♠❡s♦s❝ó♣✐❝❛ ❡ r❡❛❧✐③❛r ♠❡❞✐❞❛s ❞❡ q✉❛♥t✐❞❛❞❡s ❢ís✐❝❛s ❝♦♠✉♠❡♥t❡ tr❛t❛❞❛s ❞♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❝❧áss✐❝♦ ❡ q✉❡ sã♦ ❢✉♥❞❛♠❡♥t❛✐s à s✉❛ ❞❡s❝r✐çã♦✳ ➱ ✐♠♣♦rt❛♥t❡ ❞✐③❡r q✉❡ ❛❧❣✉♠❛s ♣r♦♣r✐❡❞❛❞❡s ❞❡ss❡s s✐st❡♠❛s ♥ã♦ ❞❡♣❡♥❞❡♠ ❞❡ ♠❛♥❡✐r❛ ❡ss❡♥❝✐❛❧ ❞❡ s✉❛ ❡str✉t✉r❛ ❛tô♠✐❝❛✱ ♦✉ t✐♣♦ ❞❡ ♠❛t❡r✐❛❧ q✉❡ ❝♦♥st✐t✉✐ ♦ s✐st❡♠❛✳ ❊ss❛s ♣r♦♣r✐❡❞❛❞❡s sã♦ ❝♦♥❤❡❝✐❞❛s ❝♦♠♦ ♣r♦♣r✐❡❞❛❞❡s ✉♥✐✈❡rs❛✐s ❞❡ tr❛♥s♣♦rt❡ q✉â♥t✐❝♦ ❡ ❞❡♣❡♥❞❡♠ ❛♣❡♥❛s ❞❛s s✐♠❡tr✐❛s q✉❡ sã♦ ❝❛r❛❝t❡r✐③❛♠ ♦ s✐st❡♠❛ ❡♠ q✉❡stã♦✳
◆♦s t❡♠♣♦s ❛t✉❛✐s✱ ❛ ❢ís✐❝❛ ❞❛ ♠❛tér✐❛ ❝♦♥❞❡♥s❛❞❛ ✈❡♠ ❣❛♥❤❛♥❞♦ ✉♠❛ ✈❛r✐❡❞❛❞❡ ♠✉✐t♦ ❣r❛♥❞❡ ❞❡ ♦❜s❡r✈❛çõ❡s ❞❡ ♥♦✈♦s ❡❢❡✐t♦s q✉â♥t✐❝♦s ❛ ♣❛rt✐r ❞❛ ❛♥á❧✐s❡ ❡ ❞❡s❝r✐çã♦ ❞❡ s✐st❡♠❛s ♥❡ss❛ ❡s❝❛❧❛ ❞❡ ❝♦♠♣r✐♠❡♥t♦✳ ❉❛í ❛ ✐♠♣♦rtâ♥❝✐❛ ❞❡ ❡st✉❞á✲❧♦s ❞❡ ♠❛♥❡✐r❛ ♠❛✐s ✐♥❝✐s✐✈❛✳ P♦r✲ t❛♥t♦✱ ♣❛r❛ ❞❡s❝r❡✈❡r ✉♠ s✐st❡♠❛ ♥❛ ❡s❝❛❧❛ ♠❡s♦s❝ó♣✐❝❛ é ♥❡❝❡ssár✐❛ ❛ ❛❞♦çã♦ ❞❡ ♣❛râ♠❡tr♦s q✉❡ ♦ ❝❛r❛❝t❡r✐③❡♠ ❜❡♠✳ P♦ré♠✱ ❞❡✈✐❞♦ ❛♦s ❧✐♠✐t❡s q✉❡ s❡♣❛r❛♠ s❡✉ ❝❛rát❡r ♠✐❝r♦s❝ó♣✐❝♦ ❞♦ ♠❛❝r♦s❝ó♣✐❝♦✱ é ♣r❡❝✐s♦ q✉❡ t❡♥❤❛♠♦s ✉♠ ♦❧❤❛r ♠❛✐s ❝❛✉t❡❧♦s♦ ♥♦ q✉❡ s❡ r❡❢❡r❡ às ❝♦♥❝❧✉sõ❡s q✉❡ s❡ ♣♦❞❡ t✐r❛r ❝♦♠ r❡s♣❡✐t♦ ❛♦s ❢❡♥ô♠❡♥♦s q✉❡ ♥❡❧❡s ♦❝♦rr❡♠ ❡ q✉❡ s❡ ❞❡s❡❥❛ ❛♥❛❧✐s❛r✳
❯♠❛ ❞❛s té❝♥✐❝❛s q✉❡ s❡ ♣♦❞❡ ❛❞♦t❛r à ❞❡s❝r✐çã♦ ❞❡ ✉♠ s✐st❡♠❛ ♠❡s♦s❝ó♣✐❝♦ é ❝♦♥s✐❞❡r❛r ♦ ❝❛♠✐♥❤♦ ❧✐✈r❡ ♠é❞✐♦ ❞❡ ✉♠ ❡❧étr♦♥✱ le✱ ❡♠ ✉♠ ♠❡✐♦ ❝✉❥❛ ❡s❝❛❧❛ ❡♥❝♦♥tr❛✲s❡ ❞❡♥tr♦ ❞♦s
❧✐♠✐t❡s ❥á ❝✐t❛❞♦s ❡ ❝♦♠♣❛rá✲❧♦ ❝♦♠ ♦ ❝♦♠♣r✐♠❡♥t♦ ❝❛r❛❝t❡ríst✐❝♦✱ ▲✱ ❞♦ s✐st❡♠❛✳ ❙❛❜❡✲s❡ q✉❡ ♦ ❡s♣❛❧❤❛♠❡♥t♦ ❞❡ ✉♠ ❡❧étr♦♥ s❡ ❞á ❛ ♣❛rt✐r ❞❡ s✉❛ ✐♥t❡r❛çã♦ ❝♦♠ ♦✉tr♦ ❡❧étr♦♥✱ ❝♦♠ ❢r♦♥t❡✐r❛s ❞❡ ✉♠❛ r❡❣✐ã♦ ♦♥❞❡ ❡❧❡ ❡stá ❧♦❝❛❧✐③❛❞♦ ♦✉ ❝♦♠ ❢r❡♥t❡s ❞❡ ♦♥❞❛s ❡♠✐t✐❞❛s ♣♦r ❛❣❡♥t❡s ❡①t❡r♥♦s à r❡❣✐ã♦ ♦♥❞❡ ♦ ♠❡s♠♦ s❡ ❡♥❝♦♥tr❛✳ ❚❛✐s ✐♥t❡r❛çõ❡s sã♦ ❝❛♣❛③❡s ❞❡ ♠♦❞✐✜❝❛r ♦ s❡✉ s❡♥t✐❞♦ ❞❡ ♣r♦♣❛❣❛çã♦✳ ❈♦♥s✐❞❡r❛♥❞♦ q✉❡ le é ❛ ❞✐stâ♥❝✐❛ q✉❡ ♦ ❡❧étr♦♥ ♣❡r❝♦rr❡ ❡♥tr❡ ❞♦✐s
❡s♣❛❧❤❛♠❡♥t♦s ❝♦♥s❡❝✉t✐✈♦s✱ s❡♠ q✉❡ ❤❛❥❛ ❛❧t❡r❛çõ❡s ❡♠ s✉❛ ❡♥❡r❣✐❛ ❝✐♥ét✐❝❛✱ ♦s s✐st❡♠❛s ♦♥❞❡ ♦❝♦rr❡ ❞❡ le > L s❡rã♦ ❝❤❛♠❛❞♦s ❞❡ ❜❛❧íst✐❝♦s✳ ❈❛s♦ ❝♦♥trár✐♦✱ q✉❛♥❞♦ ♦❝♦rr❡r ❞❡
le < L✱ ♦ s✐st❡♠❛ s❡rá ❝❤❛♠❛❞♦ ❞❡ ❞✐❢✉s✐✈♦✳ ❇♦♥s ❡①❡♠♣❧♦s ❞❡ ❡s♣❛❧❤❛♠❡♥t♦s q✉â♥t✐❝♦s
♣♦r s✐st❡♠❛s ❞❡ ♠✉✐t♦s ❝♦r♣♦s ♣♦❞❡♠ s❡r ❡♥❝♦♥tr❛❞♦s ♥❛ ❢ís✐❝❛ ♥✉❝❧❡❛r✱ ♦♥❞❡ ❛s r❡❣✐õ❡s ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ s❡ s✐t✉❛♠ ❡♠ ❡s❝❛❧❛s ❞❡ ❝♦♠♣r✐♠❡♥t♦ ❞❛ ♦r❞❡♠ ❞❡ ♣♦✉❝♦s ❋❡r♠✐s(10−15m)✳ ❖s ❡st✉❞♦s ❞❡♥tr♦ ❞❛ ár❡❛ q✉❡ r❡s✉❧t❛r❛♠ ♥❛ ❞❡s❝♦❜❡rt❛ ❞❡ r❡ss♦♥â♥❝✐❛s ❞❡ ♥ú❝❧❡♦s ❝♦♠♣♦st♦s ❢♦r❛♠ r❡❛❧✐③❛❞♦s ❛♥t❡s ❞♦s ❛♥♦s ✸✵ ❞♦ sé❝✉❧♦ ♣❛ss❛❞♦ ❬✶❪✳
❆❧❣✉♥s s✐st❡♠❛s q✉â♥t✐❝♦s s✐♠♣❧❡s ❣✉❛r❞❛♠ ❝❛r❛❝t❡ríst✐❝❛s s❡♠❡❧❤❛♥t❡s ❝♦♠ ♣r♦❜❧❡♠á✲ t✐❝❛ ❛❜♦r❞❛❞❛ ♥❛ ❢ís✐❝❛ ♥✉❝❧❡❛r ❞❡ s✐st❡♠❛s ❞❡ ♠✉✐t♦s ❝♦r♣♦s ❬✶✹❪✳ P♦rt❛♥t♦✱ ❛ ♣❛rt✐r ❞❡ r❡s✉❧t❛❞♦s ❥á ❝♦♥❤❡❝✐❞♦s ♥❛q✉❡❧❡ ❝❛♠♣♦✱ ❢♦✐ ♣♦ssí✈❡❧ s❡ ❝♦♥str✉✐r ✉♠❛ ❛❞❛♣t❛çã♦ ♣❛r❛ ♦s s✐st❡♠❛s ♠❡s♦s❝ó♣✐❝♦s ❞❡ ❢♦r♠❛ q✉❡ s❡ ♣✉❞❡ss❡ ❝♦♠♣r❡❡♥❞❡r ❛ s✉❛ ❞✐♥â♠✐❝❛ ♣♦r s✐♠♣❧❡s
❛♥❛❧♦❣✐❛ ❝♦♠ ♦s ♣r♦❝❡❞✐♠❡♥t♦s ❛❞♦t❛❞♦s à ❢ís✐❝❛ ♥✉❝❧❡❛r✳ P♦ré♠✱ ❛♦ ❝♦♥trár✐♦ ❞♦s s✐st❡♠❛s ♥❛q✉❡❧❡ ❝❛♠♣♦✱ ♦s s✐st❡♠❛s ♠❡s♦s❝ó♣✐❝♦s sã♦ ♠❛✐s ❣❡r❛✐s ✉♠❛ ✈❡③ q✉❡ ♥♦s ♦❢❡r❡❝❡ ❛ ♣♦s✲ s✐❜✐❧✐❞❛❞❡ ❞❡ ❝♦♥tr♦❧❡ ❞♦s ❢❡♥ô♠❡♥♦s ❛❜♦r❞❛❞♦s ❡♠ s✉❛ ✉t✐❧✐③❛çã♦✳ ❙❡♥❞♦ ❛ss✐♠✱ ❛ q✉❡stã♦ ❢✉♥❞❛♠❡♥t❛❧ é ❡♥t❡♥❞❡r ❝♦♠♦ ❛ ❞✐♥â♠✐❝❛ ❝❧áss✐❝❛ ♣♦❞❡ ✐♥✢✉❡♥❝✐❛r ♥❛s ♣r♦♣r✐❡❞❛❞❡s q✉â♥✲ t✐❝❛s ❞❡st❡s ✏♥♦✈♦s✑ s✐st❡♠❛s✳ ❊♥tr❡t❛♥t♦✱ ❛♦ ❝♦♥trár✐♦ ❞♦ q✉❡ ♦❝♦rr❡ ♥❛ ❢ís✐❝❛ ♥✉❝❧❡❛r✱ é ♣♦ssí✈❡❧ r❡❛❧✐③❛r s✐♠✉❧❛çõ❡s ♥✉♠ér✐❝❛s ♣❛r❛ ♦s t❛✐s s✐st❡♠❛s ❡ ✲ ♣❛r❛ q✉❡ s❡ ♣♦ss❛ ❢❛③❡r ✉♠❛ ❧❡✐t✉r❛ ❡st❛tíst✐❝❛ ❞♦s r❡s✉❧t❛❞♦s ❞♦s r❡s✉❧t❛❞♦s ♦❜s❡r✈❛❞♦s ✲ ❝♦♥st❛t❛r q✉❡ ❡❧❡s ❡stã♦ ✐♥t✐♠❛✲ ♠❡♥t❡ r❡❧❛❝✐♦♥❛❞♦s ❛♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♥♦s ❡st✉❞♦s ❞❡ ❞❡❝❛✐♠❡♥t♦ ❞❡ ♥ú❝❧❡♦s ❡♠ s✐st❡♠❛s ♥✉❝❧❡❛r❡s✳ ❖ ♣r♦❜❧❡♠❛ ❢✉♥❞❛♠❡♥t❛❧ ❛ s❡r tr❛t❛❞♦✱ ♣♦rt❛♥t♦✱ é ♦ ❡s♣❛❧❤❛♠❡♥t♦ ❞♦s ♥✉❝❧❡♦♥s✳ ❊♠ ♣❛rt✐❝✉❧❛r✱ ❞♦✐s t✐♣♦s ❞❡ ❡s♣❛❧❤❛♠❡♥t♦s ♣♦❞❡♠ s❡r ❡st✉❞❛❞♦s ❛ ♣❛rt✐r ❞❛ ❝r✐❛çã♦ ❞❡ ❡♥✲ s❡♠❜❧❡s ❞❡ s✐st❡♠❛s s❡♠❡❧❤❛♥t❡s ❝r✐❛❞♦s ❛rt✐✜❝✐❛❧♠❡♥t❡✳ ❆ s❛❜❡r✱ ♦ tr❛♥s♣♦rt❡ ❞❡ ❡❧étr♦♥s ❛tr❛✈és ❞❡ ♠✐❝r♦❡str✉t✉r❛s ❝♦♥❤❡❝✐❞❛s ❝♦♠♦ ♣♦♥t♦s q✉â♥t✐❝♦s ❜❛❧íst✐❝♦s ❞❡ ❝♦♠♣r✐♠❡♥t♦s ❞❛ ♦r❞❡♠ ❞❡ 1µm ❡ ♦ ❡s♣❛❧❤❛♠❡♥t♦ ❞❡ ♠✐❝r♦ ♦♥❞❛s ❛tr❛✈és ❞❡ ❝❛✈✐❞❛❞❡s ♠❡tá❧✐❝❛s✱ ❝♦♠
❞✐♠❡♥sõ❡s ❞❛ ♦r❞❡♠ ❞❡ 0,1m✳
◆♦s ❛♥♦s 50 ❞♦ sé❝✉❧♦ ♣❛ss❛❞♦✱ ❋❡s❤❜❛❝❤✱ P♦rt❡r ❛♥❞ ❲❡✐ss❦♦♣❢ ❬✶❪ ❝r✐❛r❛♠ ✉♠ ♠♦❞❡❧♦
❝❤❛♠❛❞♦ ❞❡ ♠♦❞❡❧♦ ó♣t✐❝♦ ❞♦ ♥ú❝❧❡♦ q✉❡ ❢✉♥❝✐♦♥❛ ❜❡♠ ♣❛r❛ ✉♠ ❝♦♥❥✉♥t♦ ♠✉✐t♦ ❣r❛♥❞❡ ❞❡ ❡♥❡r❣✐❛s✳ ❊ss❡ ♠♦❞❡❧♦ t❛♠❜é♠ ❞❡s❝r❡✈❡ ♣r♦❝❡ss♦s ❞❡ r❡❛çõ❡s q✉í♠✐❝❛s ❞❡ ♠❛♥❡✐r❛ ❡✜❝✐❡♥t❡✱ ♦ q✉❡ ♥♦s ♣❡r♠✐t❡ tr❛③❡r ♦ tr❛t❛♠❡♥t♦ ❞❛❞♦ ♣♦r ❝♦♥str✉çã♦ à ❡s❝❛❧❛ ♥✉❝❧❡❛r ♣❛r❛ ✉♠❛ ❡s❝❛❧❛ ❞❡ ❝♦♠♣r✐♠❡♥t♦ ❝♦♠♣❛tí✈❡❧ ❝♦♠ ♦ t❛♠❛♥❤♦ ❞❡ ✉♠❛ ♠♦❧é❝✉❧❛✳ ◆❛ ❛❜♦r❞❛❣❡♠ ❞❛❞❛ ♣❡❧♦s ❛✉t♦r❡s ❞❡st❡ tr❛❜❛❧❤♦✱ ♦ ❡s♣❛❧❤❛♠❡♥t♦ ❞❡ ✉♠ ♥✉❝❧❡♦♥ é ❞❡s❝r✐t♦ ❡♠ ❢✉♥çã♦ ❞❛s s❡❣✉✐♥t❡s ❡s❝❛❧❛s ❞❡ t❡♠♣♦✿
❛✮ ✉♠❛ r❡s♣♦st❛ ❞❡ ♣r♦♠♣t ♣r♦✈❡♥✐❡♥t❡ ❞❡ ✉♠ ♣r♦❝❡ss♦ ❞✐r❡t♦✱ ♥♦ q✉❛❧ ✉♠❛ ♣❛rtí❝✉❧❛ ✐♥✲ ❝✐❞❡♥t❡ ✜❝❛ s♦❜ ❛ ❛çã♦ ❞♦ ❝❛♠♣♦ ❡❧❡tr♦♠❛❣♥ét✐❝♦ ♣r♦❞✉③✐❞♦ ♣♦r ♦✉tr❛s ♣❛rtí❝✉❧❛s✳ ❚❛❧ r❡s♣♦st❛ é ❞❡s❝r✐t❛ ♠❛t❡♠❛t✐❝❛♠❡♥t❡ ❡♠ t❡r♠♦s ❞♦ ❡s♣❛❧❤❛♠❡♥t♦ ♠é❞✐♦ ❞❛s ❛♠♣❧✐t✉❞❡s ❡♠ ✉♠ ✐♥t❡r✈❛❧♦ ❞❡ ❡♥❡r❣✐❛ s✐t✉❛❞♦ ❡♠ t♦r♥♦ ❞❡ ✉♠❛ ❡♥❡r❣✐❛ E✳ ❊ss❛ ♠é❞✐❛ ❞❡ ❛♠♣❧✐✲
t✉❞❡s é ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ❛♠♣❧✐t✉❞❡ ó♣t✐❝❛ ❡ ♠♦str❛ ✉♠❛ ✈❛r✐❛çã♦ ♠❛✐s ❧❡♥t❛ ❞❡ q✉❡ ❛ ✈❛r✐❛çã♦ s♦❜r❡ ❛ ❡♥❡r❣✐❛ ♦r✐❣✐♥❛❧❀
❜✮ ✉♠❛ r❡s♣♦st❛ ❞❡ ❛tr❛s♦ q✉❡ ❝♦rr❡s♣♦♥❞❡ à ❢♦r♠❛çã♦ ❡ ❞❡❝❛✐♠❡♥t♦ ❞❡ ♥ú❝❧❡♦s ❝♦♠♣♦st♦s✳ ❊st❛ r❡s♣♦st❛ é ❞❡s❝r✐t❛ ♣❡❧❛ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ❛s ❛♠♣❧✐t✉❞❡s ❞❡ ❡s♣❛❧❤❛♠❡♥t♦ ó♣t✐❝❛ ❡ ❡①❛t❛✳ ❊❧❛ ✈❛r✐❛ ❛♣r❡❝✐❛✈❡❧♠❡♥t❡ ❝♦♠ ❛ ❡♥❡r❣✐❛✱ E✱ ❡ ♣♦❞❡ s❡r ❡①♣❧✐❝❛❞❛ ✉t✐❧✐③❛♥❞♦ ❛
t❡♦r✐❛ ❞❡ ♠❛tr✐③❡s ❛❧❡❛tór✐❛s q✉❡ s❡rá ❝♦♠❡♥t❛❞❛ ♠❛✐s ❛ ❞✐❛♥t❡✳
❯♠❛ q✉❡stã♦ té❝♥✐❝❛ q✉❡ ❡♥✈♦❧✈❡ ♦s s✐st❡♠❛s ♠❡s♦s❝ó♣✐❝♦s é ❛ q✉❡ s❡ r❡❢❡r❡ à ♠♦♥t❛✲ ❣❡♠ ❞❡ ❞✐s♣♦s✐t✐✈♦s q✉❡ ❛♣r❡s❡♥t❡♠ ❛s ❝❛r❛❝t❡ríst✐❝❛s s✉♣r❛❝✐t❛❞❛s✳ ▼❛s✱ s❡ ♣♦r ✉♠ ❧❛❞♦ ♦s ❞✐✈❡rs♦s ♥♦✈♦s ❢❡♥ô♠❡♥♦s ♣r❡✈✐st♦s ❡♠ ❛♥á❧✐s❡s t❡ór✐❝❛s s❡ ❛♣r❡s❡♥t❛♠ ♥❛t✉r❛❧♠❡♥t❡ ♥❛ ❛♥á❧✐s❡ ❞❡ss❡s s✐st❡♠❛s✱ ♣♦r ♦✉tr♦✱ ❛ ❛♥á❧✐s❡ ❡①♣❡r✐♠❡♥t❛❧ ❡①✐❣❡ ❛ ❝♦♥❢❡❝çã♦ ❞❡ ❞✐s♣♦s✐t✐✈♦s ❡①tr❡♠❛♠❡♥t❡ s❡♥sí✈❡✐s ❡ q✉❡ ♥ã♦ sã♦ ❢á❝❡✐s ❞❡ s❡r❡♠ ❡♥❝♦♥tr❛❞♦s ♥❛ ♥❛t✉r❡③❛✱ ❡①✐❣✐♥❞♦ ❛ss✐♠ ✉♠❛ ❡♥❣❡♥❤❛r✐❛ ❡s♣❡❝í✜❝❛ à s✉❛ ❝♦♥❢❡❝çã♦✳ ❚❛✐s ❞✐s♣♦s✐t✐✈♦s sã♦ ❝❤❛♠❛❞♦s ❞❡ ❛♠♦s✲ tr❛s ♠❡s♦s❝ó♣✐❝❛s ♦✉ ♠❡s♠♦ át♦♠♦s ❛rt✐✜❝✐❛✐s ✉♠❛ ✈❡③ q✉❡ ♥❛ ♦❜s❡r✈❛çã♦ ❞❛ ❝♦♥❞✉tâ♥❝✐❛ ❞❡ ❡❧étr♦♥s ♣♦r ❡st❛s ❡str✉t✉r❛s✱ ♣❡r❝❡❜❡✲s❡ ♦ ♠❡s♠♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ ✉♠ át♦♠♦ ♣❡s❛❞♦ q✉❛♥❞♦ s✉❜♠❡t✐❞♦s ❛ ♣r♦❝❡ss♦s ❞❡ ❜♦♠❜❛r❞❡❛♠❡♥t♦ ❞❡ s❡✉s ♥ú❝❧❡♦s✳ P❛r❛ s❡r❡♠ ❝♦♥str✉í❞♦s s❡❣✉❡♠ ♦s s❡❣✉✐♥t❡s ♣r♦❝❡ss♦s✿
• ❖ ❝r❡s❝✐♠❡♥t♦ ❞❡ ✉♠ ❝r✐st❛❧ ❡s♣❡❝í✜❝♦❀
• ❆ ❡♣✐t❛①✐❛✶ ♣❛r❛ ❛❞✐❝✐♦♥❛r ❝❛♠❛❞❛s ❞✐❢❡r❡♥t❡s ❞❡ ♠❛t❡r✐❛✐s❀
• ❯♠❛ ♣❡ç❛ ♣❛r❛ ❛ ❧❛t❡r❛❧ ❞❛ ❛♠♦str❛❀
• ❖ ♣r♦❝❡ss♦ ❞❡ ❧✐t♦❣r❛✜❛✷✳
❙❡❣✉✐♥❞♦ ❡ss❡s ♣r♦❝❡ss♦s✱ ❝♦♥✜♥❛♠♦s ❡❧étr♦♥s ❡♠ ✉♠❛ ♣❡q✉❡♥❛ r❡❣✐ã♦ ❞❡ ❢♦r♠❛ q✉❡ s❡ ❝♦♠♣♦rt❡♠ ❝♦♠♦ ✉♠ ❣ás ❜✐❞✐♠❡♥s✐♦♥❛❧ ❡♠ ❝♦♥✜♥❛♠❡♥t♦ tr❛♥s✈❡rs❛❧ ❛♦ ❧♦♥❣♦ ❞❛ ❛♠♦str❛✳ ❖ ❣ás✱ ♣♦r s✉❛ ✈❡③✱ ✜❝❛ r❡str✐t♦ ❛ ✉♠❛ ♠❡s❛ ❝♦♠ ❣❡♦♠❡tr✐❛ ❡s♣❡❝í✜❝❛ ❡ ❝♦♠ ❝♦♥t❛t♦s ô❤✲ ♠✐❝♦s✱ ❛❧é♠ ❞❡ ♣♦rtõ❡s ❞❡ ❡❧étr♦♥s✳ ❚❛❧ ❡str✉t✉r❛✱ ♥❛ ❧✐t❡r❛t✉r❛ ♠♦❞❡r♥❛ ✜❝♦✉ ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ♣♦♥t♦s q✉â♥t✐❝♦s ✭♦✉ q✉❛♥t✉♠ ❞♦ts✱ ❞♦ t❡r♠♦ ♦r✐❣✐♥❛❧✮ ❡ ❝♦♠ ❡❧❛s é ♣♦ssí✈❡❧ ❝♦♥✜♥❛r ❛❧❣✉♥s ♠✐❧❤❛r❡s ❞❡ ❡❧étr♦♥s ❡♠ ✉♠❛ r❡❣✐ã♦ ❞❡ ❞✐♠❡♥sõ❡s ❛♣r♦①✐♠❛❞❛s ❞❡ 0,1µm ❛ 1µm✳
❈♦♥s✐❞❡r❛♥❞♦ q✉❡ ♥❛t✉r❛❧♠❡♥t❡ ♦s ❡❧étr♦♥s s❡ ♠♦✈❡♠ ❡♠ três ❞✐♠❡♥sõ❡s✱ ♦ ♣♦♥t♦ q✉â♥t✐❝♦ é t❛♠❜é♠ ❝❤❛♠❛❞♦ ❞❡ s✐st❡♠❛ ③❡r♦ ❞✐♠❡♥s✐♦♥❛❧✳
❆s ❡str✉t✉r❛s ♦♥❞❡ s❡ ❢♦r♠❛♠ ♦ ❣ás ❜✐❞✐♠❡♥s✐♦♥❛❧✱ ❡♥tr❡t❛♥t♦✱ ♣♦❞❡♠ s❡r ❝♦♥str✉í❞❛s ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡ ❛❧t❡r♥❛♥❞♦ ❝❛♠❛❞❛s ✜♥❛s ❞❡ ●❛❆s ✭❆rs❡♥❡t♦ ❞❡ ●á❧✐♦✮ ❡ ❆s❆❧●❛ ✭❆r✲ s❡♥❡t♦ ❞❡ ●á❧✐♦ ❞♦♣❛❞♦ ❝♦♠ ❛❧✉♠í♥✐♦✮❬✹❪✳ P♦r ❝♦♥t❛ ❞❡ss❛ ❞♦♣❛❣❡♠✱ ❝r✐❛✲s❡✱ ♥❛ ✐♥t❡r❢❛❝❡ ❞❛s ❞✉❛s ❝❛♠❛❞❛s ✜♥❛s✱ ♦ ❣ás q✉❡ ♣❡r♠❛♥❡❝❡rá ❡♥tr❡ ❡❧❛s ❢♦rt❡♠❡♥t❡ ❝♦♥✜♥❛❞♦✳ ❆ ❛♠♦str❛ ♦❜t✐❞❛ ♦❢❡r❡❝❡ ♦s ♣r✐♥❝í♣✐♦s ♠❛✐s ❢✉♥❞❛♠❡♥t❛✐s ❞❛ ♠❡❝â♥✐❝❛ q✉â♥t✐❝❛✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦✱ t✉♥❡❧❛♠❡♥t♦ q✉â♥t✐❝♦ ❞❡✈✐❞♦ à ♣ró♣r✐❛ ❡str✉t✉r❛ ❢ís✐❝❛ ❞❛ ❛♠♦str❛ q✉❡ s❡ ❞á ❞❡✈✐❞♦ ❛♦ ❝♦♥✲ t❛t♦ ô❤♠✐❝♦ ❡ ❞♦s ♣♦rtõ❡s ❞❡ ❡❧étr♦♥s❬✶✷❪❀ ✐♥t❡r❢❡rê♥❝✐❛ q✉â♥t✐❝❛✱ ♠❛♥t❡♥❞♦✲s❡ ❛ ❝♦❡rê♥❝✐❛ ❞❡ ❢❛s❡✱ ❞❡✈✐❞♦ à q✉❛♥t✐❞❛❞❡ ❝♦♥tr♦❧❛❞❛ ❞❡ ✐♠♣✉r❡③❛s ♥❛ ❛♠♦str❛ ❡ t❛♠❜é♠ ❞❡✈✐❞♦ ❛♦ ♣ró♣r✐♦ ❝♦♥✜♥❛♠❡♥t♦ ❞♦s ❡❧étr♦♥s ♥❛ ❡str✉t✉r❛❬✹❪❀ ♠❡❞✐çõ❡s ❞✐s❝r❡t❛s ❞❡ ❝♦rr❡♥t❡s ❞❡s❝r✐t❛s ♣❡❧♦s ❝✉♠✉❧❛♥t❡s ❡st❛tíst✐❝♦s❬✶✺✱ ✶✻❪❀ ❡ ♦ ❡♠❛r❛♥❤❛♠❡♥t♦ q✉â♥t✐❝♦ ❡♥tr❡ ♦ ✢✉①♦ ❞❡ss❛s ❝♦rr❡♥t❡s ♥♦s t❡r♠✐♥❛✐s ✐❞❡❛✐s❬✶✼❪✳
❆ ✜❣✉r❛ ❬✶❪ ❛❜❛✐①♦ ♠♦str❛ ✉♠ ❡sq✉❡♠❛ ❞❡st❛ ❡str✉t✉r❛✳
❋✐❣✉r❛ ✶✿ ▼♦❞❡❧♦ ❣❡♥ér✐❝♦ ❞❡ ✉♠ ♣♦♥t♦ q✉â♥t✐❝♦ ❝♦♥❡❝t❛❞♦ ❛ ❞♦✐s ❣✉✐❛s✳ ❋✐❣✉r❛ ❡①tr❛í❞❛ ❞❛ r❡❢❡rê♥❝✐❛ ❬✸✻❪✳
❆s ♣r♦♣r✐❡❞❛❞❡s ❞❡ tr❛♥s♣♦rt❡s ❞❡ss❛s ❡str✉t✉r❛s sã♦ ❛✈❛❧✐❛❞❛s ❛ ♣❛rt✐r ❞❛ ♣❛ss❛❣❡♠ ❞❡ ❝♦rr❡♥t❡ ❛tr❛✈és ❞❡ s✉❛ ❝♦♠♣♦s✐çã♦✳ ❊ss❛ ♣❛ss❛❣❡♠ ❞❡ ❝♦rr❡♥t❡ s❡ ♦❜té♠ ❝♦♠ ❛ ❛♣❧✐❝❛çã♦ ❞❡ ✉♠❛ ❞✐❢❡r❡♥ç❛ ❞❡ ♣♦t❡♥❝✐❛❧ ❡♥tr❡ s❡✉s t❡r♠✐♥❛✐s ❡ ✐♥❞❡①❛ r❡s✉❧t❛❞♦s ✐♠♣♦rt❛♥t❡s ❡♠ s✉❛ ❛♥á❧✐s❡ q✉❡ ❝❛rr❡❣❛♠ ✐♥tr✐♥s❡❝❛♠❡♥t❡ ♣r♦♣r✐❡❞❛❞❡s ❞❡ ❝❛rát❡r q✉â♥t✐❝♦✱ ✈✐❛ ❝♦♥❝❡✐t♦s q✉❡ tr❛❞✐❝✐♦♥❛❧♠❡♥t❡ sã♦ ❛♣❧✐❝❛❞♦s ❛ s✐st❡♠❛s ❞❡ ❝❛r❛❝t❡ríst✐❝❛s ❝❧áss✐❝❛s✱ ❝♦♠♦ ♥❛ ❛♥á❧✐s❡ ❞❛ ❝♦♥❞✉tâ♥❝✐❛ ❞♦ ♣♦♥t♦ ❛ ♣❛rt✐r ❞❛ ♠é❞✐❛ ❞❡ tr❛♥s♠✐ssã♦ ❞♦s ❝❛♥❛✐s ♣r♦♣❛❣❛♥t❡s ♥♦s ❣✉✐❛s ❞❛ ❡str✉t✉r❛✳
P❛r❛ s❡ ♦❜s❡r✈❛r ❛ q✉❛♥t✐③❛çã♦ ❞♦s ♣♦♥t♦s q✉â♥t✐❝♦s é ♣r❡❝✐s♦ q✉❡ ❞✉❛s ❝♦♥❞✐çõ❡s s❡❥❛♠ s❛t✐s❢❡✐t❛s✳ ❊♠ ♣r✐♠❡✐r♦ ❧✉❣❛r✱ ❛s ❜❛rr❡✐r❛s ♣♦❞❡♠ s❡r ❧❛r❣❛s ♦ ❜❛st❛♥t❡ ❛♦ ♣♦♥t♦ ❞❡ t♦r♥❛r
✶Pr♦❝❡ss♦ ❞❡ ❝r❡s❝✐♠❡♥t♦ ❞❡ ❝r✐st❛❧✱ ❡♠ q✉❡ ❛s ❝❛♠❛❞❛s ❞❡♣♦s✐t❛❞❛s ❛❝♦♠♣❛♥❤❛♠ ❛ ♦r✐❡♥t❛çã♦ ❞♦ ❝r✐st❛❧
❞❡ s✉❜str❛t♦✳
✷❆rt❡ ❞❡ r❡♣r♦❞✉③✐r ♣❡❧❛ ✐♠♣r❡ssã♦ ❞❡ ❞❡s❡♥❤♦s✳
❛ tr❛♥s♠✐ssã♦ ♠✉✐t♦ ♣❡q✉❡♥❛✳ ■st♦ ♥♦s ❧❡✈❛ ❛ ❝♦♥❞✐çã♦ ❞❡ q✉❡ G≪e2
h✱ ♦ q✉❡ t♦r♥❛ ♦ ♣♦♥t♦
q✉â♥t✐❝♦ ♣r❛t✐❝❛♠❡♥t❡ ✐s♦❧❛❞♦✳ ❊♠ s❡❣✉♥❞♦ ❧✉❣❛r✱ ❛ t❡♠♣❡r❛t✉r❛ ❞❡✈❡ s❡r ❜❛✐①❛ ♦ ❜❛st❛♥t❡ ♣❛r❛ q✉❡ ♦s ❡❢❡✐t♦s tér♠✐❝♦s ♥ã♦ s❡ s♦❜r❡♣♦♥❤❛♠ ❛♦s ❡❢❡✐t♦s q✉â♥t✐❝♦s✳
❈♦♠♦ ❢♦r♠❛ ❞❡ ❡st✐♠❛r ♦ r❡❣✐♠❡ ❞❡ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞❡ ✉♠ ♣♦♥t♦ q✉â♥t✐❝♦✱ ✈❛♠♦s ♦❧❤❛r ♣❛r❛ ✉♠❛ ❣r❛♥❞❡③❛ ❜❛st❛♥t❡ út✐❧ ♥❡st❛ ❞❡s❝r✐çã♦✿ ❝❛♣❛❝✐tâ♥❝✐❛ ❝❧áss✐❝❛ ♠é❞✐❛C✳ ❉❡s❞❡ q✉❡
❛ ❡♥❡r❣✐❛ ♣❛r❛ s❡ ❛❞✐❝✐♦♥❛r ✉♠ ú♥✐❝♦ ❡❧étr♦♥ ♥♦ ♣♦♥t♦ q✉â♥t✐❝♦ é ≈ e2
C✱ t❡♠♦s ❛ ❝♦♥❞✐çã♦
❞❡ q✉❡ KT≪e2
C✳ P❛r❛ t❡r♠♦s ✐❞❡✐❛ ❞❛ ♦r❞❡♠ ❞❡ ❣r❛♥❞❡③❛✱ ✉♠❛ ❡♥❡r❣✐❛ tí♣✐❝❛ ♣❛r❛ ♦ ❞✐s❝♦
❝❛rr❡❣❛❞♦ ❞❡ ●❛❆s ❞❡ r❛✐♦ tí♣✐❝♦ 0.2µm é EC ≪ e
2
C ∼ 1000µeV✱ ❞❡ss❛ ❢♦r♠❛ ❛ ❝♦♥❞✐çã♦
KT≪e2
C s❡rá s❡♠♣r❡ s❛t✐s❢❡✐t❛ q✉❛♥❞♦ ❛ t❡♠♣❡r❛t✉r❛ ✉s❛❞❛ ♥♦ ❡①♣❡r✐♠❡♥t♦ ❢♦r ❜❛✐①❛ ♦
s✉✜❝✐❡♥t❡ ♣❛r❛ ❛t❡♥❞❡r ❛♦s r❡q✉✐s✐t♦s s✉♣r❛❝✐t❛❞♦s❬✹❪✳
✶✳✷ ❊❙❈❆▲❆❙ ❉❊ ❈❖▼P❘■▼❊◆❚❖ ❊ ❉❊ ❚❊▼P❖ ❊▼ ❈❖◆❉❯✲
❚❖❘❊❙ ▼❊❙❖❙❈ÓP■❈❖❙
❖ t❡r♠♦ s✐st❡♠❛ ♠❡s♦s❝ó♣✐❝♦ r❡❢❡r❡✲s❡ ❛ s✐st❡♠❛s ♦♥❞❡ ♦s ❢❡♥ô♠❡♥♦s ❞❡ tr❛♥s♣♦rt❡s ❛❝♦♥✲ t❡❝❡♠ ♠❛♥t❡♥❞♦ ❛ ❝♦❡rê♥❝✐❛ ❞❡ ❢❛s❡✳ ❚❛✐s s✐st❡♠❛s ♣♦❞❡♠ s❡r tr❛t❛❞♦s ❝♦♠♦ ♠✐❝r♦❡str✉t✉r❛s ♥❛s q✉❛✐s ❛ ❢✉♥çã♦ ❞❡ ♦♥❞❛ ❞❡ ✉♠ ❡❧étr♦♥ t❡♠ s✉❛ ❢❛s❡ ♠❛♥t✐❞❛ ❡♥q✉❛♥t♦ ♦ ♠❡s♠♦ ✐♥t❡r❛❣❡ ❝♦♠ ❡st❛ ♠✐❝r♦❡str✉t✉r❛❬✷❪✳ ■st♦ s✐❣♥✐✜❝❛ q✉❡ ♦ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ❝♦❡rê♥❝✐❛ ❞❡ ❢❛s❡ q✉❛♥❞♦ ❛ss♦❝✐❛❞♦s ❛ ♣r♦❝❡ss♦s q✉❡ ♣♦❞❡♠ ♠✉❞❛r ♦ ❛♠❜✐❡♥t❡ ♣♦r ♦♥❞❡ ♣❛ss❛ ♦ ❡❧étr♦♥ ♣❛r❛ ✉♠ ❡st❛❞♦ ♦rt♦❣♦♥❛❧ é ♠❛✐♦r q✉❡ ♦ t❛♠❛♥❤♦ ❞♦ ♣ró♣r✐♦ s✐st❡♠❛✳ ❖❜✈✐❛♠❡♥t❡✱ ♣❛r❛ q✉❡ ❡st❛ ❝♦♥❞✐çã♦ s❡❥❛ ♠❛♥t✐❞❛✱ ❛ ♠✐❝r♦❡str✉t✉r❛ ❞❡✈❡ ❛t❡♥❞❡r ❛ ❛❧❣✉♠❛s ❝♦♥❞✐çõ❡s ❡s♣❡❝í✜❝❛s q✉❡ ♥♦s ♣❡r♠✐t❡ ❞❡✜♥✐✲❧❛s ❝♦♠♦ t❛❧✳
❯♠ ❡①❡♠♣❧♦ ❝❛♥ô♥✐❝♦ ❞❡ ✉♠ s✐st❡♠❛ ♠❡s♦s❝ó♣✐❝♦ é ✉♠❛ ❛♠♦str❛ ♠❡tá❧✐❝❛ ❞❡ ❝♦♠♣r✐✲ ♠❡♥t♦ ▲✱ ♠❛♥t✐❞❛ ❛ t❡♠♣❡r❛t✉r❛ s✉✜❝✐❡♥t❡♠❡♥t❡ ❜❛✐①❛✳ ❈♦♠ ❡st❡ s✐st❡♠❛ tí♣✐❝♦✱ ♣♦❞❡♠♦s ❛♥❛❧✐s❛r ❛s ❝♦♥❞✐çõ❡s ❞❡ ❡s❝❛❧❛ ❡s♣❛ç♦✲t❡♠♣♦r❛❧ q✉❡ ❞❡✜♥❡♠ ❡ ❝❛r❛❝t❡r✐③❛♠ ♦s ❞✐❢❡r❡♥t❡s r❡✲ ❣✐♠❡s ❞❡ tr❛♥s♣♦rt❡ q✉â♥t✐❝♦ ❡ ❛ ❡st❛tíst✐❝❛ ❞❛s ✢✉t✉❛çõ❡s ❛ss♦❝✐❛❞❛s q✉❡ ❞❡✜♥❡♠ ♦ s✐st❡♠❛ ♠❡s♦s❝ó♣✐❝♦ ♣r♦♣r✐❛♠❡♥t❡ ❞✐t♦✳
❆ ♣r✐♥❝✐♣❛❧ ❡s❝❛❧❛ ❞❡ ❝♦♠♣r✐♠❡♥t♦ ❝♦♥s✐❞❡r❛❞❛ ❡♠ ✉♠ s✐st❡♠❛ ♠❡s♦s❝ó♣✐❝♦ é ♦ ❝❛♠✐♥❤♦ ❧✐✈r❡ ♠é❞✐♦ ❞❡ ✉♠ ❡❧étr♦♥ ♣❛r❛ ♦ ❡s♣❛❧❤❛♠❡♥t♦ ❡❧ást✐❝♦ ❞❡ ✉♠ ♣♦t❡♥❝✐❛❧ ❛❧❡❛tór✐♦✳ ❊st❡✱ ❡♠ ❝♦♥❥✉♥t♦ ❝♦♠ ♦ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♦♥❞❛ ❞❡ ❋❡r♠✐✱ λF = 2kFπ✱ ♣❛r❛ ✉♠ s✐st❡♠❛ ♠❡tá❧✐❝♦
r❛♥❞ô♠✐❝♦ ❡ ❝♦♠ ♦ ✈❡t♦r ❞❡ ♦♥❞❛ ❞❡ ❋❡r♠✐ ❞❡ ❛♠♣❧✐t✉❞❡ ❞❛❞❛ ♣♦rkF✱ ❞❡✜♥❡♠ ✉♠❛ ❣r❛♥❞❡③❛
❢ís✐❝❛ ❛❞✐♠❡♥s✐♦♥❛❧ q✉❡ ♠❡❞❡ ♦ ❣r❛✉ ❞❡ ❛❧❡❛t♦r✐❡❞❛❞❡ ❞♦ s✐st❡♠❛✿ (k1
Fle)❬✶❪✳ ❉❛ ♠❡s♠❛ ❢♦r♠❛✱
t❡♠♦s ♦ ❝❛♠✐♥❤♦ ❧✐✈r❡ ♠é❞✐♦ ✐♥❡❧ást✐❝♦✱lin✱ ❞❡✈✐❞♦ à ✐♥✢✉ê♥❝✐❛ ❞❡ ♦✉r♦s ❡❧étr♦♥s✱ ❢ô♥♦♥s ❡✴♦✉
♦✉tr♦s ❛s♣❡❝t♦s ❞♦ s✐st❡♠❛✳ ❆♦ ♣❡r❝♦rr❡r ❡st❡ ❝❛♠✐♥❤♦✱ ♦ ❡❧étr♦♥ ♣❡r❞❡ s✉❛ ❝♦❡rê♥❝✐❛ ❞❡ ❢❛s❡✳ ❖ t❡♠♣♦ ❣❛st♦ ❛té ♣❡r❞ê✲❧❛ ❞❡✜♥❡ ❛ ❡s❝❛❧❛ ❞❡ t❡♠♣♦ τin(lin)❬✶❪✳ ▲❡✈❛♥❞♦✲s❡ ❡♠ ❝♦♥t❛
❡ss❛s ❡s❝❛❧❛s✱ ❡ ❛s ❣r❛♥❞❡③❛s ❞❡st❛ ❛♥á❧✐s❡✱ ♣♦❞❡✲s❡ ❞❡✜♥✐r ✉♠ ♦✉tr♦ ♣❛râ♠❡tr♦ ❝❤❛♠❛❞♦ ❞❡ ❝♦♥st❛♥t❡ ❞❡ ❞✐❢✉sã♦ q✉❡ s❡ r❡❧❛❝✐♦♥❛ ❝♦♠ ♦ t❡♠♣♦ τin✱ ♣❛r❛ q✉❡ ♣♦ss❛♠♦s ❞❡✜♥✐r ✉♠
❝♦♠♣r✐♠❡♥t♦ ❝❛r❛❝t❡ríst✐❝♦✱ ❝❤❛♠❛❞♦ ❞❡ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ❚❤♦✉❧❡ss✱ LT =
q 1
3linle ❬✶❪✱ q✉❡ ♥♦s ✐♥❢♦r♠❛ ❛ ❞✐stâ♥❝✐❛ ♥❛ q✉❛❧ ❛ ♣❛rtí❝✉❧❛ é ❡s♣❛❧❤❛❞❛ s❡♠ ♣❡r❞❡r s✉❛ ❝♦❡rê♥❝✐❛ ❞❡ ❢❛s❡✳ ➱ ✐♠♣♦rt❛♥t❡ ♥♦t❛r q✉❡ ❧❡✈❛♠♦s ❡♠ ❝♦♥s✐❞❡r❛çã♦ ❜❛✐①❛s t❡♠♣❡r❛t✉r❛s✱ ♣❛r❛ q✉❡ ♦s ❡❢❡✐t♦s tér♠✐❝♦s ♥ã♦ s❡❥❛♠ ❛ ♣r✐♥❝✐♣❛❧ ❝❛✉s❛ ❞❡ss❡s ❡s♣❛❧❤❛♠❡♥t♦s✳ ◆❡st❡ ❝❛s♦✱ le < LT < lin✳
✶✳✷✳✶ ❈❛✈✐❞❛❞❡s ❜❛❧íst✐❝❛s ♠❡s♦s❝ó♣✐❝❛s
❈❛✈✐❞❛❞❡s ❜❛❧íst✐❝❛s ♦✉ ♣♦♥t♦s q✉â♥t✐❝♦s✱ ♦✉ ❛✐♥❞❛ át♦♠♦s ❛rt✐✜❝✐❛✐s✱ sã♦ ❛q✉❡❧❛s ♦♥❞❡ ♦ ♠♦✈✐♠❡♥t♦ ❞♦s ❡❧étr♦♥s é ♣r❛t✐❝❛♠❡♥t❡ ❜❛❧íst✐❝♦✱ ❡①❝❡t♦ ♣❡❧❛s r❡✢❡①õ❡s q✉❡ ♦❝♦rr❡♠ ♥❛s ♣❛r❡❞❡s ❞❛ ♠❡s♠❛✳ ❙❡♥❞♦ ❛ss✐♠ ❛s ♣ró♣r✐❛s ♣❛r❡❞❡s ❞❛ ❡str✉t✉r❛ ♣❛ss❛♠ ❛ t❡r ✉♠ ♣❛♣❡❧ ❢✉❞❛♠❡♥t❛❧ s♦❜ ❛ ❞✐str✐❜✉✐çã♦ ❞❡ ❝♦♥❞✉çã♦ ❞❛ ♠❡s♠❛✳ ◆❡st❛s ❡str✉t✉r❛s✱ ♦ t❛♠❛♥❤♦ ❡ ❛ ❢♦r♠❛ ♣♦❞❡♠ s❡r ❝♦♥tr♦❧❛❞♦s ♣♦r t❡♥sõ❡s ❞❡ ❡♥tr❛❞❛s✱ ❝♦♠♦ é ♦ ❝❛s♦ ❞♦ ▼❖❙❋❊❚ ✭♠❡t❛❧ ♦①✐❞❡ s❡♠✐❝♦♥❞✉❝t♦r ✜❡❧❞ ❡✛❡❝t tr❛♥s✐st♦r✮✳
❊①♣❡r✐♠❡♥t❛❧♠❡♥t❡✱ ✉♠❛ ❝♦rr❡♥t❡ ❡❧étr✐❝❛ é ❝♦♥❞✉③✐❞❛ ❛tr❛✈és ❞❡ ✉♠ ❞♦s ❣✉✐❛s ❝♦♥❡❝✲ t❛❞♦s à ❝❛✈✐❞❛❞❡✱ ❝♦♠♦ ♥❛ ✜❣✉r❛ ✶✱ ♦♥❞❡ s❡ ♣r♦❞✉③ ✉♠❛ q✉❡❞❛ ❞❡ ♣♦t❡♥❝✐❛❧ ♣❛r❛ ❛ q✉❛❧ ❛ ❝♦♥❞✉tâ♥❝✐❛ é ❝❛❧❝✉❧❛❞❛✳ ❈♦♥s✐❞❡r❛♥❞♦ ♦ ♠♦❞❡❧♦ ❞❡ ❛♣❡♥❛s ✉♠ ❡❧étr♦♥ ♥❛ ❝❛✈✐❞❛❞❡✱ ✈ê✲s❡ q✉❡ ❤á ✉♠ ♦ ❡s♣❛❧❤❛♠❡♥t♦ ❞❡st❡ ❡❧étr♦♥ ❞❡✈✐❞♦ ❛ s✉❛ ✐♥t❡r❛çã♦ ❝♦♠ ❛s ♣❛r❡❞❡s ❞❛ ❝❛✈✐❞❛❞❡✳ ❈♦♥s✐❞❡r❛♥❞♦✲s❡ ♠❛✐s ❞❡ ✉♠ ❡❧étr♦♥ ♥❡st❡ ♣r♦❝❡ss♦ ❞❡ ❝♦♥❞✉çã♦ ❡ ❡s♣❛❧❤❛♠❡♥t♦✱ t❡♠✲s❡ ✉♠ ❢❡♥ô♠❡♥♦ ❞❡ ✐♥t❡r❢❡rê♥❝✐❛ ❞❛s ♦♥❞❛s r❡✢❡t✐❞❛s ♣❡❧❛ ❝❛✈✐❞❛❞❡✳ ❙❡♥❞♦ ❛ss✐♠✱ ♣♦❞❡♠♦s r❡❧❛❝✐♦✲ ♥❛r ❛ ❝♦♥❞✉tâ♥❝✐❛ ❝♦♠ ♦ ♣❛❞rã♦ ❞❡ ✐♥t❡r❢❡rê♥❝✐❛ ❞♦s ❡❧étr♦♥s ♥❛ ❝❛✈✐❞❛❞❡✳ ❊①✐st✐♥❞♦ r❛③õ❡s q✉❡ ♣r♦♣♦r❝✐♦♥❡♠ ❛ ♠✉❞❛♥ç❛ ♥♦ ♣❛❞rã♦ ❞❡ ✐♥t❡r❢❡rê♥❝✐❛✱ ♣♦❞❡ s❡ ❛♥❛❧✐s❛r ❝♦♠♦ ❝♦♥s❡q✉ê♥❝✐❛ ✢✉t✉❛çõ❡s ♥❛ ♠❡❞✐❞❛ ❞❛ ❝♦♥❞✉tâ♥❝✐❛ ❞♦ s✐st❡♠❛✳
✶✳✷✳✷ ❈♦♥❞✉t♦r❡s ♠❡s♦s❝ó♣✐❝♦s ❞✐❢✉s✐✈♦s
❙❛❜❡✲s❡ q✉❡ q✉❛❧q✉❡r ❛♠♦str❛ ❝♦♥té♠ ✉♠ ♥ú♠❡r♦ ❞❡ ✐♠♣✉r❡③❛s ♣♦r ✉♥✐❞❛❞❡ ❞❡ ✈♦❧✉♠❡ q✉❡ ❞ã♦ ♦r✐❣❡♠ ❛♦s ❡s♣❛❧❤❛♠❡♥t♦s ♠ú❧t✐♣❧♦s r❡s♣♦♥sá✈❡✐s ♣❡❧♦ s✉r❣✐♠❡♥t♦ ❞♦ ♣❛❞rã♦ ❞❡ ✐♥t❡r❢❡rê♥❝✐❛ ♥♦ ♣r♦❝❡ss♦ ❞❡ ❝♦♥❞✉çã♦ ❞❡ ❡❧étr♦♥s ❛tr❛✈és ❞❡❧❛✳ ❉✐❛♥t❡ ❞✐st♦✱ é r❛③♦á✈❡❧ ♣❡♥s❛r q✉❡ ❡①✐st❡ ♥ã♦ só ✉♠❛ ❝♦♥❞✉tâ♥❝✐❛ ♠é❞✐❛ à ❛♠♦str❛✱ ♠❛s✱ s♦❜r❡t✉❞♦✱ q✉❡ ❡①✐st❡♠ ✢✉t✉❛çõ❡s ❛❧❡❛tór✐❛s s♦❜r❡ ❛ ♣ró♣r✐❛ ♠é❞✐❛✳ ❖ q✉❡ s❡ ✈ê ❞❡ ❢❛t♦ é q✉❡ ❛s ✢✉t✉❛çõ❡s s♦❜r❡ ❛ ❝♦♥❞✉tâ♥❝✐❛ ♥ã♦ só ♥ã♦ ❡①❝❡❞❡♠ ♦ ✈❛❧♦r ❝❧áss✐❝♦✱ ♠❛s t❛♠❜é♠ sã♦ ✉♥✐✈❡rs❛✐s ❡ q✉❡ sã♦ ❞♦♠✐♥❛❞❛s ♣❡❧❛s ✐♥t❡r❢❡rê♥❝✐❛s ❡♥tr❡ ❛s ♦♥❞❛s ❞❡✈✐❞♦ ❛♦s ❡s♣❛❧❤❛♠❡♥t♦s q✉❡ ♦❝♦rr❡♠ ❞❡♥tr♦ ❞❛ ❝❛✈✐❞❛❞❡✳ ❆ ✜❣✉r❛ ❬✷❪ ❛❜❛✐①♦ ♠♦str❛ ❛ s✐♠✉❧❛çã♦ ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ss❛s ✢✉t✉❛çõ❡s ♣❛r❛ ❞✐✈❡rs❛s r❡❛❧✐③❛çõ❡s✳ ◆♦t❡ q✉❡ ♦ ✈❛❧♦r ♠á①✐♠♦ ❞❡ss❛s ✢✉t✉❛çõ❡s ♥ã♦ ❡①❝❡❞❡ ❛ ✉♥✐❞❛❞❡✳
✶✳✸ ❆P❘❖❳■▼❆➬Õ❊❙ ❊❙❚❆❚❮❙❚■❈❆❙ P❆❘❆ ❋▲❯❚❯❆➬Õ❊❙ ▼❊✲
❙❖❙❈ÓP■❈❆❙
❱✐♠♦s q✉❡ ❝♦♥tr♦❧❛r ❛ ❝♦❡rê♥❝✐❛ ❞❛s ♦♥❞❛s ❞❡♥tr♦ ❞❛ ❝❛✈✐❞❛❞❡ é ✉♠ ♣r♦❝❡ss♦ ♠✉✐t♦ ❝♦♠♣❧✐❝❛❞♦ ❡ ❡①♣❧✐❝✐t❛♠❡♥t❡ ❞❡s♦r❞❡♥❛❞♦ ♦✉ ❞✐♥❛♠✐❝❛♠❡♥t❡ ❝❛ót✐❝♦✱ ❡①✐❣✐♥❞♦✱ ♣♦rt❛♥t♦✱ ✉♠ tr❛t❛♠❡♥t♦ ❡st❛tíst✐❝♦ s♦❜r❡ ❛s ♠❡❞✐❞❛s✳ P♦ré♠✱ ❡ss❛ ❞✐♥â♠✐❝❛✱ q✉❡ ❞❡♣❡♥❞❡ ❞❡ ❝❛r❛❝t❡rís✲ t✐❝❛s ♠✐❝r♦s❝ó♣✐❝❛s ❞♦ s✐st❡♠❛✱ ♥♦s ❝♦♥❞✉③ ❛ ❝❡rt❛s ❣❡♥❡r❛❧✐❞❛❞❡s ❡♠ s❡✉ ❝♦♠♣♦rt❛♠❡♥t♦ ♠❛❝r♦s❝ó♣✐❝♦✳ ❚❛❧ ❝♦♠♣♦rt❛♠❡♥t♦ ♣♦❞❡ s❡r ❡①♣r❡ss♦ ❡♠ ✉♠❛ ❧❡✐ ❡st❛tíst✐❝❛ ♣❛r❛ ❛s ✢✉t✉❛çõ❡s q✉❡ ♣❡rt❡♥❝❡♠ ❛ ✉♠❛ ❝❧❛ss❡ ❞❡ ✉♥✐✈❡rs❛❧✐❞❛❞❡s t❛✐s ❝♦♠♦ s✐♠❡tr✐❛s ❞♦ s✐st❡♠❛ ❡♠ q✉❡stã♦✱ ♥ú♠❡r♦ ❞❡ ♣❛râ♠❡tr♦s r❡❧❡✈❛♥t❡s ♥♦ ♠❡s♠♦✱ ❡♥tr❡ ♦✉tr♦s ❞❡t❛❧❤❡s q✉❡ s❡ ❧❤❡ r❡❧❛❝✐♦♥❛♠✳
❖ ♣✐♦♥❡✐r♦ ❛ ❞❛r ❡st❡ tr❛t❛♠❡♥t♦ ❡st❛tíst✐❝♦ ❛♦s s✐st❡♠❛s ♥✉❝❧❡❛r❡s ❢♦✐ ❲✐❣♥❡r✸✳ ◆♦s
✸❊✉❣❡♥❡ P❛✉❧ ❲✐❣♥❡r✭✶✾✵✷✲✶✾✾✺✮✱ ❤ú♥❣❛r♦✱ r❡❝❡❜❡✉ ♦ ♣rê♠✐♦ ◆♦❜❡❧ ❞❡ ❋ís✐❝❛ ❡♠ ✶✾✻✸ ✭❥✉♥t♦ ❝♦♠ ❏✳
❍❛♥s ❉✳ ❏❡♥s❡♥ ❡ ▼❛r✐❛ ●♦❡♣♣❡rt✲▼❛②❡r✮✱ ♣♦r s❡✉ tr❛❜❛❧❤♦ ♥❛ t❡♦r✐❛ ❞♦ ♥ú❝❧❡♦ ❛tô♠✐❝♦ ❡ ❞❛s ♣❛rtí❝✉❧❛s
