UNIVERSIDADE DE BRASÍLIA INSTITUTO DE FÍSICA Dissertação de Mestrado

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❯◆■❱❊❘❙■❉❆❉❊ ❉❊ ❇❘❆❙❮▲■❆

■◆❙❚■❚❯❚❖ ❉❊ ❋❮❙■❈❆

❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦

❊❋❊■❚❖❙ ❉❊ ❚❊▼P❊❘❆❚❯❘❆ ❙❖❇❘❊ ❆

❊❙❚❆❇■▲■❉❆❉❊ ❉❊ ◗❯❆❙■✲P❆❘❚❮❈❯▲❆❙ ❊▼

P❖▲❮▼❊❘❖❙ ❈❖◆❉❯❚❖❘❊❙

▲❯■❩ ❆◆❚Ô◆■❖ ❘■❇❊■❘❖ ❏❯◆■❖❘

❖r✐❡♥t❛❞♦r✿

●❊❘❆▲❉❖ ▼❆●❊▲❆ ❊ ❙■▲❱❆

❈♦✲♦r✐❡♥t❛❞♦r✿

P❊❉❘❖ ❍❊◆❘■◗❯❊ ❉❊ ❖▲■❱❊■❘❆ ◆❊❚❖

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✏❙❡❣✉♥❞♦ ✉♠ ✈❡❧❤♦ ❞✐t❛❞♦✱ é ♠❡❧❤♦r ✈✐❛✲ ❥❛r ❝♦♠ ❡s♣❡r❛♥ç❛ ❞♦ q✉❡ ❝❤❡❣❛r✳ ◆♦ss❛ ❜✉s❝❛ ♣❡❧❛ ❞❡s❝♦❜❡rt❛ ❛❧✐♠❡♥t❛ ♥♦ss❛ ❝r✐❛✲ t✐✈✐❞❛❞❡✱ ❡♠ t♦❞♦s ♦s ❝❛♠♣♦s✱ ♥ã♦ ❛♣❡♥❛s ♥❛ ❝✐ê♥❝✐❛✳ ❙❡ ❝❤❡❣áss❡♠♦s ❛♦ ✜♠ ❞❛ ❧✐♥❤❛ ♦ ❡s♣ír✐t♦ ❤✉♠❛♥♦ ❞❡✜♥❤❛r✐❛ ❡ ♠♦rr❡r✐❛✳✑

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❆❣r❛❞❡❝✐♠❡♥t♦s

❉❡✈♦✱ ♥ã♦ só ❡st❡ tr❛❜❛❧❤♦✱ ♠❛s t✉❞♦ ♦ q✉❡ s♦✉ ❛♦s ♠❡✉s ♣❛✐s ▲✉✐③ ❆♥tô♥✐♦ ❡ ❩✐❧❞❛ q✉❡ ❝♦♠ ♠✉✐t♦ ❝❛r✐♥❤♦ ❡ s❛❜❡❞♦r✐❛ ❣✉✐❛♠ ♠❡✉s ♣❛ss♦s ❛té ❤♦❥❡✳ ❆❣r❛❞❡ç♦ ❛ ♠✐♥❤❛ ❡s♣♦s❛ ❇ár❜❛r❛✱ ❢♦♥t❡ ❞❡ ❛♠♦r ❡ ❡stí♠✉❧♦✱ ♣♦r ❡st❛r s❡♠♣r❡ ❛♦ ♠❡✉ ❧♦❞♦ ❡♠ t♦❞❛s ❛s ❥♦r♥❛❞❛s✳ ❆♦s ♠❡✉s ✜❧❤♦s ▲✉❝❛s ●❛❜r✐❡❧✱ ▲✉✐③ ❊❞✉❛r❞♦ ❡ ▲✉í③❛ ❇❡❛tr✐③ ♣♦r ♠❡ ❢❛③❡r❡♠ ✉♠❛ ♣❡ss♦❛ ♠❡❧❤♦r ❝♦♠ s❡✉s s♦rr✐s♦s✳ ❆♦s ♠❡✉s t✐♦s ❋á❜✐♦ ❡ ❩❡♥✐❧❞❛ ♣♦r t♦❞♦ ❛♠♦r ❡ ✐♥❝❡♥t✐✈♦✳ ▼❡ s✐♥t♦ ❤♦♥r❛❞♦ ❡♠ ♣♦❞❡r ❢❛③❡r ♣❛rt❡ ❞❛ ✈✐❞❛ ❞❡ ✈♦❝ês✳ ❆❣r❛❞❡ç♦ ❛♦ ♠❡✉ ✐r♠ã♦ ▲✉✐③ ❍❡♥r✐q✉❡ ❡ ❛♦ ♠❡✉ ♣r✐♠♦ ❉❛♥✐❧♦ ♣♦r t♦❞❛ ❛♠✐③❛❞❡ ❝♦♠♣❛rt✐❧❤❛❞❛ ❛♦ ❧♦♥❣♦ ❞♦s ❛♥♦s✳ ❆♦s ♠❡✉s t✐♦s ❱❛❣♥❡r ❡ ❊❧✐❛♥❡ ♣❡❧♦ ❡①❡♠♣❧♦ ❞❡ ❝❛rát❡r ❡ ❝♦♠♣❛♥❤❡✐r✐s♠♦ ❡✱ t❛♠❜é♠✱ ❛♦s ♠❡✉s t✐♦s ❈❧❡✉❜❡r ❡ ❏♦s❡ ❡ ❛♦ ♠❡✉ ❣r❛♥❞❡ ❛♠✐❣♦ ❆♥❞r❡✐ ♣♦r ❢❛③❡r❡♠ ♣❛rt❡ ❞❛ ♠✐♥❤❛ ✈✐❞❛✳ ❆ ♠✐♥❤❛ ❛✈ó ▼❛r✐❛ ♣♦r t♦❞❛s ❛s ♦r❛çõ❡s ❡♠ q✉❡ ❡st✐✈❡ ✐♥❝❧✉í❞♦✳ ❆ ♠✐♥❤❛ s♦❣r❛ ❘♦s❛ ♣❡❧❛ ❝♦♠♣r❡❡♥sã♦ ❡ ❝❛r✐♥❤♦ ❡♠ t♦❞♦s ♦s ♠♦♠❡♥t♦s✳ ◆ã♦ ❡①✐st❡ ✉♠ só ❞✐❛ ❡♠ q✉❡ ❡✉ ♥ã♦ ♣❡♥s❡ ❡♠ ♦r❣✉❧❤á✲❧♦s✳

❆❣r❛❞❡ç♦ ❛♦s ♣r♦❢❡ss♦r❡s ●❡r❛❧❞♦ ▼❛❣❡❧❛ ❡ P❡❞r♦ ❍❡♥r✐q✉❡ ♣♦r t♦❞❛ ❝♦♠✲ ♣❡tê♥❝✐❛ ❡ ❛♠✐③❛❞❡ ❡♠♣r❡❣❛❞❛s ♥❛ t❛r❡❢❛ ❞❡ ♠❡ ♦r✐❡♥t❛r ♥❡ss❡ tr❛❜❛❧❤♦✳ ❆♦s ♣r♦✲ ❢❡ss♦r❡s ❡ ❛♠✐❣♦s ❘✐❝❛r❞♦ ●❛r❣❛♥♦✱ ▲✉✐③ ❘♦♥❝❛r❛tt✐ ❡ ❲✐❧✐❛♠ ♣♦r t♦❞❛ ❛❥✉❞❛ ❡ ✐♥❝❡♥t✐✈♦✳ ❆♦s ♣r♦❢❡ss♦r❡s ❉❡♠étr✐♦ ❋✐❧❤♦ ❡ ❋❡❧❧✐♣❡ ❇❡❛❦❧✐♥❡ ♣❡❧❛s ♣r❛③❡r♦s❛s ❤♦✲ r❛s ❞❡ tr❛❜❛❧❤♦✳ ❆♦s ♣r♦❢❡ss♦r❡s ▼❛r❝♦ ❈é③❛r✱ ❈❛r❧♦s ●❛❧✈ã♦✱ P❛✉❧♦ ❇r✐t♦✱ P❛✉❧♦ ❍❡♥r✐q✉❡✱ ❆r❛❦❡♥ ❲❡r♥❡❦✱ ❆r♠❛♥❞♦ ▼❛r♦❥❛✱ ❆❞❡♠✐r ❙❛♥t❛♥❛✱ ❚❛r❝ís✐♦ ▼❛r❝✐❛♥♦ ❡ ❈áss✐♦ ▲❛r❛♥❥❡✐r❛s ♣❡❧❛ ❢♦r♠❛çã♦✿ ♣❡ss♦❛s q✉❡ t❡♥❤♦ ❝♦♠♦ ❡①❡♠♣❧♦ ❞❡ ❡①❝❡❧❡♥t❡s ♣r♦✜ss✐♦♥❛✐s✳

❆♦s ❣r❛♥❞❡s ❛♠✐❣♦s ▼❛r❝❡❧♦✱ ▼❛❦s✇❡❧✱ ❘❛❢❛❡❧✱ ❇r✉♥♦✱ ▲❡♦♥❛r❞♦✱ ▲❡❛♥❞❡r✱ ❏❡❢❡rs♦♥✱ ▲✉❝✐❛♥♦✱ ❍❡♥r✐q✉❡ ❡ ●✐♦✈❛♥♥✐ ♣♦r t♦❞♦ ❝♦♠♣❛♥❤❡✐r✐s♠♦ ✐♥❝♦♥❞✐❝✐♦♥❛❧ ❡ ♣❡❧♦s ♠♦♠❡♥t♦s ❞❡ ❞❡s❝♦♥tr❛çã♦✳ ❆♦s ❝♦❧❡❣❛s ❞♦ ✐♥st✐t✉t♦ ❉❛♥✐❡❧✱ ❇r✉♥♦ ✫ ◆❛tá❧✐❛✱ ▼❛r❝♦s ✏●❛ú❝❤♦✑✱ ■❣♦✱ ❊r✐♥❛❧❞♦✱ ❊❞s♦♥✱ ❏♦♥❛t❛♥✱ ❋á❜✐♦✱ ❊❞♥❛r❞♦✱ ▼❛r❝♦s ✏▼❡♥t✐r❛✑ ❡ ❊✈❛♥❞r♦ ♣❡❧❛s ❝♦♥✈❡rs❛s ♣r❛③❡r♦s❛s ❡ ♣♦r t♦❞❛ ❛❥✉❞❛✳ ❖ q✉❡ ♠❛✐s ♠❡ ✐♠♣r❡ss✐♦♥❛ ❡♠ t♦❞♦s é q✉❡ ✈♦❝ês s❡♠♣r❡ s❡ ♠♦str❛♠ ♠❡❧❤♦r❡s ❞♦ q✉❡ ❡✉ ♣♦❞❡r✐❛ ✐♠❛❣✐♥❛r✳

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❘❡s✉♠♦

❖ ❣r❛♥❞❡ ♣♦t❡♥❝✐❛❧ ❞♦s ♣♦❧í♠❡r♦s ❝♦♥❞✉t♦r❡s ♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ♥♦✈❛s t❡❝♥♦❧♦❣✐❛s ♣❛r❛ ❞✐s♣♦s✐t✐✈♦s ♦♣t♦❡❧❡trô♥✐❝♦s ✈❡♠ ❛tr❛✐♥❞♦✱ ❞❡ ❢♦r♠❛ ❝r❡s❝❡♥t❡✱ ♦ ✐♥t❡r❡ss❡ ❞❛ ❝♦♠✉♥✐❞❛❞❡ ❝✐❡♥tí✜❝❛ ♥♦s ú❧t✐♠♦s ❛♥♦s✳ ❆s ❛♣❧✐❝❛çõ❡s ❞❡ss❡s ♠❛t❡r✐❛✐s ✐♥❝❧✉❡♠ ❞✐♦❞♦s ❡♠✐ss♦r❡s ❞❡ ❧✉③ ♦r❣â♥✐❝♦s ✭❖▲❊❉s✮✱ tr❛♥s✐st♦r❡s ❞❡ ✜❧♠❡ ✜♥♦ ✭❖❚✲ ❋❊❚s✮✱ ❢♦t♦❞✐♦❞♦s ❡ ❢♦t♦✈♦❧t❛✐❝♦s ♦r❣â♥✐❝♦s ✭❖P❱s✮✳ ❊♠ ❡s♣❡❝✐❛❧✱ ♦s ❢♦t♦✈♦❧t❛✐❝♦s ♦r❣â♥✐❝♦s sã♦ ♠✉✐t♦ ❛tr❛t✐✈♦s ♣♦r ❛♣r❡s❡♥t❛r❡♠ ✈❛♥t❛❣❡♥s ❝♦♠♦ ❝♦♥❞✉t✐✈✐❞❛❞❡ ❝♦♥✲ tr♦❧❛❞❛✱ ❛❧t❛ ♠❛❧❡❛❜✐❧✐❞❛❞❡ ❡ ❜❛✐①♦ ❝✉st♦ ❞❡ ♣r♦❞✉çã♦✳ ❖ tr❛♥s♣♦rt❡ ❞❡ ❝❛r❣❛ ♥❡ss❡s ♠❛t❡r✐❛✐s t❡♠ s✐❞♦ ✐❞❡♥t✐✜❝❛❞♦ ❝♦♠♦ ✉♠ ♣r♦❝❡ss♦ ✐♠♣♦rt❛♥t❡ ❡♠ t♦❞❛s ❛s ❛♣❧✐❝❛çõ❡s ❡ ❛ ❡st❛❜✐❧✐❞❛❞❡ ❞♦s ♣♦rt❛❞♦r❡s ❞❡ ❝❛r❣❛ ❡stá ❞✐r❡t❛♠❡♥t❡ r❡❧❛❝✐♦♥❛❞❛ ❝♦♠ ❛ ♣❡r❢♦r✲ ♠❛♥❝❡ ❞♦ ❞✐s♣♦s✐t✐✈♦✳ ❯♠ ❞♦s ❞❡s❛✜♦s s✐❣♥✐✜❝❛t✐✈♦s ♥❛ ❝✐ê♥❝✐❛ ❞❡ss❡s ♠❛t❡r✐❛✐s é ❛ ❝❛r❛❝t❡r✐③❛çã♦ ❞♦ ❡❢❡✐t♦ ❞❛ t❡♠♣❡r❛t✉r❛ s♦❜r❡ ♦ tr❛♥s♣♦rt❡ ❞❡ ❝❛r❣❛✳ ❈♦♠ ✐ss♦✱ ❡♥t❡♥❞❡r ❡❢❡✐t♦s ❞❛ t❡♠♣❡r❛t✉r❛ s♦❜r❡ ❛ ❡st❛❜✐❧✐❞❛❞❡ ❞♦s ♣♦rt❛❞♦r❡s ❞❡ ❝❛r❣❛ é ❢✉♥✲ ❞❛♠❡♥t❛❧ ♣❛r❛ ❛ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ ❝✐ê♥❝✐❛ ❡ t❡❝♥♦❧♦❣✐❛ ❞♦s ♣♦❧í♠❡r♦s ❝♦♥❞✉t♦r❡s✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ❛ ❡st❛❜✐❧✐❞❛❞❡ ❞♦s ♣♦rt❛❞♦r❡s ❞❡ ❝❛r❣❛ ❡♠ ♣♦❧í♠❡r♦s ❝♦♥❥✉❣❛❞♦s ❢♦✐ ✐♥✈❡st✐❣❛❞❛ ♥✉♠❡r✐❝❛♠❡♥t❡✱ s♦❜ ❞✐❢❡r❡♥t❡s r❡❣✐♠❡s ❞❡ t❡♠♣❡r❛t✉r❛ ❡ ❝❛♠♣♦s ❡❧étr✐✲ ❝♦s ❡①t❡r♥♦s✳ ◆❛s s✐♠✉❧❛çõ❡s ❢♦r❛♠ ✉t✐❧✐③❛❞♦s ♦s ♣♦rt❛❞♦r❡s ❞❡ ❝❛r❣❛ ♠❛✐s ❝♦♠✉♥s ♥❡ss❡s ♠❛t❡r✐❛✐s✿ ♦ só❧✐t♦♥✱ ♦ ♣ó❧❛r♦♥ ❡ ♦ ❜✐♣ó❧❛r♦♥✳ ❖ ♦❜❥❡t✐✈♦ ♣r✐♥❝✐♣❛❧ é ✐♥✈❡st✐✲ ❣❛r ❛ ❡st❛❜✐❧✐❞❛❞❡ ❞❡ss❡s ♣♦rt❛❞♦r❡s ❡♠ ❝❛❞❡✐❛s ❞❡ ♣♦❧✐❛❝❡t✐❧❡♥♦ s♦❜ ❛ ❢♦r♠❛ ❞❡ s❡✉s ✐sô♠❡r♦s tr❛♥s ❡ ❝✐s✳ P❛r❛ ✐ss♦✱ ✉♠❛ ✈❡rsã♦ ♠♦❞✐✜❝❛❞❛ ❞♦ ♠♦❞❡❧♦ ❙✉✲❙❝❤r✐❡✛❡r✲ ❍❡❡❣❡r ✭❙❙❍✮ ❢♦✐ ✉t✐❧✐③❛❞❛ ♣❛r❛ ✐♥❝❧✉✐r ❡❢❡✐t♦s ❞❡ ❝❛♠♣♦ ❡❧étr✐❝♦ ❡①t❡r♥♦ ❡ ♦ t❡r♠♦ ❞❡ q✉❡❜r❛ ❞❡ s✐♠❡tr✐❛ ❞❡ ❇r❛③♦✈✐s❦✐✐✲❑✐r♦✈❛✳ ❖s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ♥❛s s✐♠✉❧❛çõ❡s s✉❣❡r❡♠ q✉❡ ❛ ❡st❛❜✐❧✐❞❛❞❡ ❞♦s ♣♦rt❛❞♦r❡s ❞❡ ❝❛r❣❛ ❞✐♠✐♥✉✐ ❞❡✈✐❞♦ ❛♦ ❛✉♠❡♥t♦ ❞❛ t❡♠♣❡r❛t✉r❛✳ ❚❛♠❜é♠ ❢♦✐ ❛♥❛❧✐s❛❞❛ ❛ ❞✐♥â♠✐❝❛ ❞♦s ♣♦rt❛❞♦r❡s ❞❡ ❝❛r❣❛ q✉❛♥❞♦ ♦s ❡❢❡✐t♦s ❞❡ t❡♠♣❡r❛t✉r❛ ❢♦r❛♠ ❧❡✈❛❞♦s ❡♠ ❝♦♥s✐❞❡r❛çã♦✳

(6)

❆❜str❛❝t

❚❤❡ ❣r❡❛t ♣♦t❡♥t✐❛❧ ♦❢ ❝♦♥❞✉❝t✐♥❣ ♣♦❧②♠❡rs t♦ t❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ ♥❡✇ ♦♣✲ t♦❡❧❡❝tr♦♥✐❝ ❞❡✈✐❝❡s ❤❛s ❛ttr❛❝t❡❞ t❤❡ ✐♥t❡r❡st ♦❢ t❤❡ s❝✐❡♥t✐✜❝ ❝♦♠♠✉♥✐t② ✐♥ r❡❝❡♥t ②❡❛rs✳ ❚❤❡ ❛♣♣❧✐❝❛t✐♦♥s ♦❢ t❤❡s❡ ♠❛t❡r✐❛❧s ✐♥❝❧✉❞❡ ♦r❣❛♥✐❝ ❧✐❣❤t ❡♠✐tt✐♥❣ ❞✐♦❞❡s ✭❖▲❊❉s✮✱ t❤✐♥ ✜❧♠ tr❛♥s✐st♦rs ✭❖❚❋❊❚s✮✱ ♦r❣❛♥✐❝ ♣❤♦t♦❞✐♦❞❡s ❛♥❞ ♣❤♦t♦✈♦❧t❛✐❝s ✭❖P❱s✮✳ ❊s♣❡❝✐❛❧❧②✱ ♦r❣❛♥✐❝ ♣❤♦t♦✈♦❧t❛✐❝s ❛r❡ ❛ttr❛❝t✐✈❡ ❜❡❝❛✉s❡ t❤❡② ❤❛✈❡ ❛❞✈❛♥✲ t❛❣❡s s✉❝❤ ❛s ❝♦♥tr♦❧❧❡❞ ❝♦♥❞✉❝t✐✈✐t②✱ ❤✐❣❤ ✢❡①✐❜✐❧✐t② ❛♥❞ ❧♦✇ ❝♦st ♦❢ ♣r♦❞✉❝t✐♦♥✳ ❚❤❡ ❝❤❛r❣❡ tr❛♥s♣♦rt ✐♥ t❤❡s❡ ♠❛t❡r✐❛❧s ❤❛✈❡ ❜❡❡♥ ✐❞❡♥t✐✜❡❞ ❛s ❛♥ ✐♠♣♦rt❛♥t ♣r♦❝❡ss ✐♥ ❛❧❧ ❛♣♣❧✐❝❛t✐♦♥s ❛♥❞ t❤❡ ❝❤❛r❣❡ ❝❛rr✐❡rs st❛❜✐❧✐t② ❤❛s ❜❡❡♥ s❤♦✇♥ t♦ ❜❡ ❞✐r❡❝t❧② r❡✲ ❧❛t❡❞ t♦ ❞❡✈✐❝❡ ♣❡r❢♦r♠❛♥❝❡✳ ❖♥❡ ♦❢ t❤❡ s✐❣♥✐✜❝❛♥t ❝❤❛❧❧❡♥❣❡s ✐♥ t❤❡ s❝✐❡♥❝❡ ♦❢ t❤❡s❡ ♠❛t❡r✐❛❧s ✐s t❤❡ ❝❤❛r❛❝t❡r✐③❛t✐♦♥ ♦❢ t❤❡ t❡♠♣❡r❛t✉r❡ ❡✛❡❝ts ♦♥ ❝❤❛r❣❡ tr❛♥s♣♦rt✳ ❚❤✉s✱ ✉♥❞❡rst❛♥❞✐♥❣ t❤❡ t❡♠♣❡r❛t✉r❡ ❡✛❡❝ts ♦♥ t❤❡ st❛❜✐❧✐t② ♦❢ t❤❡ ❝❤❛r❣❡ ❝❛rr✐❡rs ✐s ❝r✉❝✐❛❧ ❢♦r t❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ s❝✐❡♥❝❡ ❛♥❞ t❡❝❤♥♦❧♦❣② ♦❢ ❝♦♥❞✉❝t✐♥❣ ♣♦❧②♠❡rs✳ ■♥ t❤✐s ✇♦r❦✱ t❤❡ st❛❜✐❧✐t② ♦❢ ❝❤❛r❣❡ ❝❛rr✐❡rs ✐♥ ❝♦♥❥✉❣❛t❡❞ ♣♦❧②♠❡rs ✇❛s ♥✉♠❡r✐❝❛❧❧② ✐♥✈❡st✐❣❛t❡❞ ✉♥❞❡r ❞✐✛❡r❡♥t t❡♠♣❡r❛t✉r❡ r❡❣✐♠❡s ❛♥❞ ❡①t❡r♥❛❧ ❡❧❡❝tr✐❝ ✜❡❧❞s✳ ■♥ t❤❡ s✐♠✉❧❛t✐♦♥s✱ t❤❡ ♠♦st ❝♦♠♠♦♥ ❝❤❛r❣❡ ❝❛rr✐❡rs ✐♥ t❤❡s❡ ♠❛t❡r✐❛❧s ✇❡r❡ s✐♠✉❧❛t❡❞✿ s♦❧✐t♦♥s✱ ♣♦❧❛r♦♥s ❛♥❞ ❜✐♣♦❧❛r♦♥s✳ ❚❤❡ ♠❛✐♥ ♦❜❥❡❝t✐✈❡ ✐s ✐♥✈❡st✐❣❛t❡ t❤❡ st❛❜✐❧✐t② ♦❢ t❤❡s❡ ❝❤❛r❣❡ ❝❛rr✐❡rs ✐♥ ♣♦❧②❛❝❡t②❧❡♥❡ ❝❤❛✐♥s ♦♥ ❜♦t❤ ✐s♦♠❡rs tr❛♥s ❛♥❞ ❝✐s✳ ❋♦r t❤✐s✱ ❛ ♠♦❞✐✜❡❞ ✈❡rs✐♦♥ ♦❢ t❤❡ ❙❙❍ ♠♦❞❡❧ ✇❛s ✉s❡❞ t♦ ✐♥❝❧✉❞❡ ❡①t❡r♥❛❧ ❡❧❡❝tr✐❝ ✜❡❧❞ ❡✛❡❝ts ❛♥❞ t❤❡ ❇r❛③♦✈✐s❦✐✐✲❑✐r♦✈❛ s②♠♠❡tr② ❜r❡❛❦✐♥❣ t❡r♠✳ ❚❤❡ s✐♠✉❧❛t✐♦♥ r❡s✉❧ts s✉❣❣❡st t❤❛t t❤❡ ❝❤❛r❣❡ ❝❛rr✐❡rs st❛❜✐❧✐t② ❞❡❝r❡❛s❡s ❞✉❡ t♦ t❤❡ ✐♥❝r❡❛s❡ ✐♥ t❤❡ t❡♠✲ ♣❡r❛t✉r❡✳ ■t ✇❛s ❛❧s♦ ❛♥❛❧②③❡❞ t❤❡ ❝❤❛r❣❡ ❝❛rr✐❡rs ❞②♥❛♠✐❝s ✇❤❡♥ t❤❡ t❡♠♣❡r❛t✉r❡ ❡✛❡❝ts ✇❡r❡ t❛❦❡♥ ✐♥t♦ ❛❝❝♦✉♥t✳

(7)

❙✉♠ár✐♦

✶ ■♥tr♦❞✉❝ã♦ ✶

✶✳✶ ❆ ❉❡s❝♦❜❡rt❛ ❞♦s P♦❧í♠❡r♦s ❈♦♥❞✉t♦r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶ ✶✳✷ ❖ P♦❧✐❛❝❡t✐❧❡♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸ ✶✳✸ P♦rt❛❞♦r❡s ❞❡ ❈❛r❣❛✿ ❙ó❧✐t♦♥s✱ Pó❧❛r♦♥s ❡ ❇✐♣ó❧❛r♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✶✳✹ ❊st❛❜✐❧✐❞❛❞❡ ❡ ❊❢❡✐t♦s ❞❡ ❚❡♠♣❡r❛t✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶

✷ ▼♦❞❡❧❛♠❡♥t♦ ❚❡ór✐❝♦ ✶✹

✷✳✶ ❖ Pr♦❜❧❡♠❛ ❞❡ ▼✉✐t♦s ❈♦r♣♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ✷✳✷ ❆♥t✐✲s✐♠❡tr✐❛ ❞❛ ❋✉♥çã♦ ❞❡ ❖♥❞❛ ❡ ♦s ❉❡t❡r♠✐♥❛♥t❡s ❞❡ ❙❧❛t❡r ✳ ✳ ✳ ✳ ✶✻ ✷✳✸ ❙❡❣✉♥❞❛ ◗✉❛♥t✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✷✳✹ ❆ ❆♣r♦①✐♠❛çã♦ ❞❡ ❚✐❣❤t✲❇✐♥❜✐♥❣ ❡ ❛ ■♥✈❛r✐â♥❝✐❛ ❚r❛♥s❧❛❝✐♦♥❛❧ ✳ ✳ ✳ ✳ ✷✸ ✷✳✺ ❆ ❊q✉❛çã♦ ❞❡ ▲❛♥❣❡✈✐♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼

✸ ❖ ▼♦❞❡❧♦ ❙✉✲❙❝❤❡r✐❡✛❡r✲❍❡❡❣❡r ✭❙❙❍✮ ✸✶

✸✳✶ ❖ ❍❛♠✐❧t♦♥✐❛♥♦ ❙❙❍ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✸✳✷ ❆ ❈❛❞❡✐❛ ❉✐♠❡r✐③❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✸✳✸ ■♥❝❧✉sã♦ ❞♦ ❈❛♠♣♦ ❊❧étr✐❝♦ ❡ ♦ ❚❡r♠♦ ❞❡ ◗✉❡❜r❛ ❞❡ ❙✐♠❡tr✐❛ ✳ ✳ ✳ ✳ ✹✵ ✸✳✹ ❉✐♥â♠✐❝❛ ▼♦❧❡❝✉❧❛r✿ ❆s ❊q✉❛çõ❡s ❞❡ ▼♦✈✐♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✸✳✺ ❆ ■♥❝❧✉sã♦ ❞❛ ❚❡♠♣❡r❛t✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹

✹ ❊❢❡✐t♦s tér♠✐❝♦s s♦❜r❡ ❛ ❊st❛❜✐❧✐❞❛❞❡ ❞❡ ◗✉❛s✐✲P❛rtí❝✉❧❛s ✹✻ ✹✳✶ P❛râ♠❡tr♦s ❯t✐❧✐③❛❞♦s ♥❛s ❙✐♠✉❧❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼

(8)

✹✳✷ ■♠♣❧❡♠❡♥t❛çã♦ ❞♦ ❈❛♠♣♦ ❊❧étr✐❝♦ ❡ ❞❛ ❚❡♠♣❡r❛t✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✹✳✸ ❊st❛❜✐❧✐❞❛❞❡ ❞❡ ◗✉❛s✐✲P❛rtí❝✉❧❛s ❡♠ ❙✐♠❡tr✐❛ ❚r❛♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✹✳✸✳✶ ❙ó❧✐t♦♥ ❈❛rr❡❣❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✹✳✸✳✷ Pó❧❛r♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✹✳✹ ❊st❛❜✐❧✐❞❛❞❡ ❞❡ ◗✉❛s✐✲P❛rtí❝✉❧❛s ❡♠ ❙✐♠❡tr✐❛ ❈✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✹✳✹✳✶ Pó❧❛r♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✹✳✹✳✷ ❇✐♣ó❧❛r♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾

✺ ❈♦♥❝❧✉sõ❡s ❡ P❡rs♣❡❝t✐✈❛s ✼✹

❘❡❢❡rê♥❝✐❛s ✽✶

❆♣ê♥❞✐❝❡ ❆ ✾✶

(9)

▲✐st❛ ❞❡ ❋✐❣✉r❛s

✶✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❛ ❝♦♥✜❣✉r❛çã♦ ❞❡ ❡q✉✐❧í❜r✐♦ ❞♦ tr❛♥s✲ P♦❧✐❛❝❡t✐❧❡♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹

✶✳✷ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❛ ❝♦♥✜❣✉r❛çã♦ ❞❡ ❡q✉✐❧í❜r✐♦ ❞♦ ❝✐s✲P♦❧✐❛❝❡t✐❧❡♥♦ ✺

✶✳✸ ❊①❡♠♣❧♦s ❞❡ ♣♦❧í♠❡r♦s ❝♦♥❥✉❣❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻

✶✳✹ ❆s ❞✉❛s ❞✐❢❡r❡♥t❡s ❞✐s♣♦s✐çõ❡s ❞❡ ✉♠❛ ❝❛❞❡✐❛ ❞❡ tr❛♥s✲♣♦❧✐❛❝❡t✐❧❡♥♦✳ ✳ ✳ ✼

✶✳✺ ❊str✉t✉r❛ ❞❡ ❜❛♥❞❛s ❞❡ ❡♥❡r❣✐❛ ❛ss♦❝✐❛❞❛s ❛ ♣r❡s❡♥ç❛ ❞❡ só❧✐t♦♥s ✳ ✳ ✳ ✽

✶✳✻ ❊str✉t✉r❛ ❞❡ ❜❛♥❞❛s ❞❡ ❡♥❡r❣✐❛ ❛ss♦❝✐❛❞❛s ❛ ♣r❡s❡♥ç❛ ❞❡ ♣ó❧❛r♦♥s ✳ ✳ ✳ ✾

✶✳✼ ❊str✉t✉r❛ ❞❡ ❜❛♥❞❛s ❞❡ ❡♥❡r❣✐❛ ❛ss♦❝✐❛❞❛s ❛ ♣r❡s❡♥ç❛ ❞❡ ❜✐♣ó❧❛r♦♥s ✳ ✳ ✶✵

✷✳✶ ❙✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ♠♦❧❡❝✉❧❛r❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ ♠✉✐t♦s ❝♦r♣♦s✳ ✶✺

✷✳✷ ❘❡♣r❡s❡♥t❛çã♦ ❞♦ ♣♦t❡♥❝✐❛❧ ♣❡r✐ó❞✐❝♦ ❞❛ ❝❛❞❡✐❛ ❝♦♠ ✉♠❛ ❜❛rr❡✐r❛ ❞❡ ♣♦t❡♥❝✐❛❧ ✜♥✐t❛ ❡♥tr❡ ♦s sít✐♦s ✭❛✮✳ ❊♠ ✭❜✮ ❡st❛ r❡♣r❡s❡♥t❛❞♦ ♦ ♣♦t❡♥❝✐❛❧

♣❡r✐ó❞✐❝♦ ❞❛ ❝❛❞❡✐❛ ❝♦♠ ✉♠❛ ❜❛rr❡✐r❛ ❞❡ ♣♦t❡♥❝✐❛❧ ✐♥✜♥✐t❛ ❡♥tr❡ ♦s sít✐♦s✳ ✷✹

✸✳✶ ❈♦♦r❞❡♥❛❞❛ ❞❡ ❞❡s❧♦❝❛♠❡♥t♦✿ ❊str✉t✉r❛ ❞✐♠❡r✐③❛❞❛ ❞♦ ♣♦❧✐❛❝❡t✐❧❡♥♦✳ ✳ ✸✷

✸✳✷ ■♥t❡❣r❛❧ ❞❡ r❡ss♦♥â♥❝✐❛ ❡ s✉❛ ❛♣r♦①✐♠❛çã♦ ❡♠ ♣r✐♠❡✐r❛ ♦r❞❡♠ ❡ t♦r♥♦ ❞❡ ✉♠ ♣♦♥t♦ ❞❡ ❞✐♠❡r✐③❛çã♦ ♥✉❧♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹

✸✳✸ ❊♥❡r❣✐❛ t♦t❛❧ ❞❡ ✉♠❛ ❝❛❞❡✐❛ ❞❡ ♣♦❧✐❛❝❡t✐❧❡♥♦ ❞✐♠❡r✐③❛❞❛✿ ❡♥❡r❣✐❛ ❞♦ ❣r✉♣♦CH ❡♠ ❢✉♥çã♦ ❞❛ ❝♦♦r❞❡♥❛❞❛u✳ ◆♦t❡ ♦s ❞♦✐s ♠í♥✐♠♦s ❛ss♦❝✐❛❞♦s

à q✉❡❜r❛ ❡s♣♦♥tâ♥❡❛ ❞❡ s✐♠❡tr✐❛ ❡ ♦ ❡st❛❞♦ ❢✉♥❞❛♠❡♥t❛❧ ❞✉♣❧❛♠❡♥t❡

❞❡❣❡♥❡r❛❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾

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✹✳✶ ❚♦❞♦s ♦s ✈❛❧♦r❡s ❞❡ ❝❛♠♣♦ ❡❧étr✐❝♦ s✐♠✉❧❛❞♦ ❧✐❣❛❞♦s ❞❡ ♠❛♥❡✐r❛ ❛❞✐❛✲ ❜át✐❝❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵

✹✳✷ ✭❛✮ P❛râ♠❡tr♦ ❞❡ ♦r❞❡♠ ♣❛r❛ ♦ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ❧✐❣❛çã♦ ❡ ✭❜✮ ♣❛râ♠❡tr♦ ❞❡ ♦r❞❡♠ ♣❛r❛ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝❛r❣❛ ❞❡ ✉♠ só❧✐t♦♥ ❝❛rr❡❣❛❞♦✳ ✳ ✳ ✳ ✳ ✳ ✺✶

✹✳✸ ❊✈♦❧✉çã♦ t❡♠♣♦r❛❧ ♣❛r❛ yn ❞❡ ✉♠ só❧✐t♦♥ ❝❛rr❡❣❛❞♦ ♣❛r❛ ✭❛✮ 0K ✭❜✮

50_K ❡ ✭❝✮300_K✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸

✹✳✹ ❊✈♦❧✉çã♦ t❡♠♣♦r❛❧ ❞❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝❛r❣❛ ❞❡ ✉♠ só❧✐t♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹

✹✳✺ ❊✈♦❧✉çã♦ t❡♠♣♦r❛❧ ❞♦s ♥í✈❡✐s ❞❡ ❡♥❡r❣✐❛ ♣❛r❛ ✭❛✮ 0_K ❡ ✭❜✮ 300_K✳ ✳ ✳ ✳ ✳ ✺✺

✹✳✻ ❚r❛❥❡tór✐❛ ❞♦ só❧✐t♦♥ ♣❛r❛ ✭❛✮ 3_,9_{mV /}_A˚❡ ✭❜✮ 1_,95_{mV /}_A˚✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻

✹✳✼ ❱❡❧♦❝✐❞❛❞❡ ♠é❞✐❛ ❞♦ só❧✐t♦♥ ✭❛✮ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ❡ ✭❜✮ ❡♠ ❢✉♥çã♦ ❞♦ ❝❛♠♣♦ ❡❧étr✐❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼

✹✳✽ ✭❛✮ P❛râ♠❡tr♦ ❞❡ ♦r❞❡♠ ♣❛r❛ ♦ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ❧✐❣❛çã♦ ❡ ✭❜✮ ♣❛râ♠❡tr♦ ❞❡ ♦r❞❡♠ ♣❛r❛ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝❛r❣❛ ❞❡ ✉♠ ♣♦❧❛r♦♥ ❝❛rr❡❣❛❞♦✳ ✳ ✳ ✳ ✳ ✳ ✺✾

✹✳✾ ❊✈♦❧✉çã♦ t❡♠♣♦r❛❧ ♣❛r❛ yn ❞❡ ✉♠ ♣ó❧❛r♦♥ ♣❛r❛ ✭❛✮0K ❡ ✭❜✮ 100K✳ ✳ ✳ ✳ ✻✵ ✹✳✶✵ ❊✈♦❧✉çã♦ t❡♠♣♦r❛❧ ❞❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝❛r❣❛ ♣❛r❛ ♦ ♣ó❧❛r♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵

✹✳✶✶ ❊✈♦❧✉çã♦ t❡♠♣♦r❛❧ ❞♦s ♥í✈❡✐s ❞❡ ❡♥❡r❣✐❛ ♣❛r❛ ✭❛✮ 0_K ❡ ✭❜✮ 200_K✳ ✳ ✳ ✳ ✳ ✻✶

✹✳✶✷ ❚r❛❥❡tór✐❛ ❞♦ ♣ó❧❛r♦♥ ♣❛r❛ ✭❛✮ 1_,3_{mV /}_A˚❡ ✭❜✮ 2_,6_{mV /}_A˚✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸

✹✳✶✸ ❱❡❧♦❝✐❞❛❞❡ ♠é❞✐❛ ❞♦ ♣ó❧❛r♦♥ ❡♠ s✐♠❡tr✐❛ tr❛♥s ✭❛✮ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠✲ ♣❡r❛t✉r❛ ❡ ✭❜✮ ❡♠ ❢✉♥çã♦ ❞♦ ❝❛♠♣♦ ❡❧étr✐❝♦✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹

✹✳✶✹ ✭❛✮ ❊✈♦❧✉çã♦ t❡♠♣♦r❛❧ ❞❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝❛r❣❛ ♣❛r❛ ♦ ♣ó❧❛r♦♥✳ ✭❜✮ ❊✈♦❧✉çã♦ t❡♠♣♦r❛❧ ❞♦s ♥í✈❡✐s ❞❡ ❡♥❡r❣✐❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻

✹✳✶✺ ❚r❛❥❡tór✐❛ ❞♦ ♣ó❧❛r♦♥ ❡♠ s✐♠❡tr✐❛ ❝✐s ♣❛r❛ ✭❛✮ 1_,3_{mV /}_A˚❡ ✭❜✮ 2_,6_{mV /}_A˚✳ ✻✼

✹✳✶✻ ❱❡❧♦❝✐❞❛❞❡ ♠é❞✐❛ ❞♦ ♣ó❧❛r♦♥ ❡♠ s✐♠❡tr✐❛ ❝✐s ✭❛✮ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠✲ ♣❡r❛t✉r❛ ❡ ✭❜✮ ❡♠ ❢✉♥çã♦ ❞♦ ❝❛♠♣♦ ❡❧étr✐❝♦✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽

✹✳✶✼ ✭❛✮ P❛râ♠❡tr♦ ❞❡ ♦r❞❡♠ ♣❛r❛ ♦ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ❧✐❣❛çã♦ ❡ ✭❜✮ ♣❛râ♠❡tr♦ ❞❡ ♦r❞❡♠ ♣❛r❛ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝❛r❣❛ ❞❡ ✉♠ ❜✐♣♦❧❛r♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾

✹✳✶✽ ❊✈♦❧✉çã♦ t❡♠♣♦r❛❧ ♣❛r❛ yn ❞❡ ✉♠ ❜✐♣ó❧❛r♦♥ ♣❛r❛ ✭❛✮ 0K ❡ ✭❜✮ 300K✳✳ ✳ ✼✵ ✹✳✶✾ ❊✈♦❧✉çã♦ t❡♠♣♦r❛❧ ❞❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❝❛r❣❛ ❞❡ ✉♠ ❜✐♣ó❧❛r♦♥ ❛ t❡♠♣❡r✲

❛t✉r❛ 300_K✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶

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✹✳✷✵ ❊✈♦❧✉çã♦ t❡♠♣♦r❛❧ ❞♦s ♥í✈❡✐s ❞❡ ❡♥❡r❣✐❛ ❞❡ ✉♠❛ ❝❛❞❡✐❛ ❞❡ ❝✐s✲♣♦❧✐❛❝❡t✐❧❡♥♦ ❝♦♥t❡♥❞♦ ✉♠ ❜✐♣ó❧❛r♦♥ ❛ t❡♠♣❡r❛t✉r❛ 300_K✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶

✹✳✷✶ ❚r❛❥❡tór✐❛ ❞♦ ❜✐♣ó❧❛r♦♥ ❡♠ s✐♠❡tr✐❛ ♣❛r❛ ✭❛✮ 1_,95_{mV /}_A˚❡ ✭❜✮ 3_,9_{mV /}_A˚✳ ✼✷

✹✳✷✷ ❱❡❧♦❝✐❞❛❞❡ ♠é❞✐❛ ❞♦ ❜✐♣ó❧❛r♦♥ ✭❛✮ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ❡ ✭❜✮ ❡♠ ❢✉♥çã♦ ❞♦ ❝❛♠♣♦ ❡❧étr✐❝♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸

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❈❛♣ít✉❧♦ ✶

■♥tr♦❞✉❝ã♦

◆❡st❡ ❝❛♣ít✉❧♦ é ❛♣r❡s❡♥t❛❞♦ ✉♠ ❜r❡✈❡ ❤✐stór✐❝♦ s♦❜r❡ ❛ ❞❡s❝♦❜❡rt❛ ❞♦s ♣♦❧í♠❡r♦s ❝♦♥❞✉t♦r❡s✳ P❛rt✐❝✉❧❛r♠❡♥t❡✱ ❝❛r❛❝t❡r✐③❛✲s❡ ♦ ♦❜❥❡t♦ ❞❡ ❡st✉❞♦ ❞❡st❡ tr❛❜❛❧❤♦✿ ♦ P♦❧✐❛❝❡t✐❧❡♥♦✳ ❆❧é♠ ❞✐ss♦✱ ♣❛r❛ ❛ ❝♦♠♣r❡❡♥sã♦ ❞❛ ❝♦♥❞✉t✐✈✐❞❛❞❡ ❡♠ ♣♦❧í♠❡r♦s ❝♦♥❥✉❣❛❞♦s✱ é ❢♦r♥❡❝✐❞❛ ✉♠❛ ✈✐sã♦ ❣❡r❛❧ s♦❜r❡ ♦s ♣♦rt❛❞♦r❡s ❞❡ ❝❛r❣❛ ♥❡ss❡s ♠❛t❡r✐❛✐s✳ ❋✐♥❛❧♠❡♥t❡✱ ❥✉st✐✜❝❛✲s❡ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ✐♥❝❧✉sã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ♣❛r❛ ❛ ❛♥á❧✐s❡ ❞❛ ❡st❛❜✐❧✐❞❛❞❡ ❞❡ ♣♦rt❛❞♦r❡s ❞❡ ❝❛r❣❛ ♥❡ss❡s s✐st❡♠❛s✳

✶✳✶ ❆ ❉❡s❝♦❜❡rt❛ ❞♦s P♦❧í♠❡r♦s ❈♦♥❞✉t♦r❡s

❉✉r❛♥t❡ ❛ ❞é❝❛❞❛ ❞❡ ✶✾✼✵✱ ❛ ❤✐♣ót❡s❡ ❞❡ q✉❡ ❛❧❣✉♥s ❝♦♠♣♦st♦s ♦r❣â♥✐❝♦s ♣♦❞❡r✐❛♠ s❡r ❝❛r❛❝t❡r✐③❛❞♦s ❝♦♠♦ s✉♣❡r❝♦♥❞✉t♦r❡s ✈❡♥❤♦ à t♦♥❛✳ ❆té ❡ss❡ ♠♦✲ ♠❡♥t♦ ♦s ❝♦♠♣♦st♦s ♦r❣â♥✐❝♦s✱ ❢♦r♠❛❞♦s ❡ss❡♥❝✐❛❧♠❡♥t❡ ♣♦r át♦♠♦s ❞❡ ❝❛r❜♦♥♦ ❡ ❤✐❞r♦❣ê♥✐♦✱ ❡r❛♠ ❡①❡♠♣❧♦s tí♣✐❝♦s ❞❡ ♠❛t❡r✐❛✐s ✐s♦❧❛♥t❡s✳ ❆s ♣❡sq✉✐s❛s ❝♦♠ r❡❧❛çã♦ ❛ ❝✐ê♥❝✐❛ ❡ t❡❝♥♦❧♦❣✐❛ ❞❡ss❡s ♠❛t❡r✐❛✐s ❝r❡s❝❡r❛♠ r❛♣✐❞❛♠❡♥t❡ ❛ ♣❛rt✐r ❞❡ss❡ ♠♦♠❡♥t♦✳ ❉♦✐s ❢❛t♦r❡s ❢♦r❛♠ ❞❡t❡r♠✐♥❛♥t❡s ♣❛r❛ ❡ss❡ ❝r❡s❝✐♠❡♥t♦✳ ❖ ♣r✐♠❡✐r♦ ❢♦✐ ♦ ❣r❛♥❞❡ ✐♥t❡r❡ss❡ t❡❝♥♦❧ó❣✐❝♦✱ ♣♦✐s ♦s ♣♦❧í♠❡r♦s ❝♦♥❞✉t♦r❡s ♠❛t❡r✐❛✐s ♣♦❞❡r✐❛♠ s✉❜st✐t✉✐r ♦s ♠❡t❛✐s ❡♠ s✐st❡♠❛s ❞❡ ❝♦♥❞✉çã♦ ❞❡ ❡❧❡tr✐❝✐❞❛❞❡✳ ❆❧é♠ ❞✐ss♦✱ ♣❡❧♦ ❢❛t♦ ❞❡ ♦s ❝♦♠♣♦s✲ t♦s ♦r❣â♥✐❝♦s s❡r❡♠ ❢♦r♠❛❞♦s ❜❛s✐❝❛♠❡♥t❡ ♣♦r ❞♦✐s ❞♦s ❡❧❡♠❡♥t♦s ♠❛✐s ❛❜✉♥❞❛♥t❡s ❞❛ ♥❛t✉r❡③❛✱ ♦ ✈❛❧♦r ❡❝♦♥ô♠✐❝♦ ❞❡ss❡s ♠❛t❡r✐❛✐s ❛❞q✉✐r❡ ❣r❛♥❞❡ ✐♠♣♦rtâ♥❝✐❛ ♥♦s

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✷

♣r♦❝❡ss♦s ❞❡ ❢❛❜r✐❝❛çã♦ ❞❡ ❞✐s♣♦s✐t✐✈♦s ❡❧❡trô♥✐❝♦s✳

❖ ♣r✐♠❡✐r♦ ❝♦♠♣♦st♦ ♦r❣â♥✐❝♦ ❞♦❛❞♦r ❞❡ ❡❧étr♦♥s✱ ♦ t❡tr❛t✐♦❢✉❧✈❛❧❡♥♦ ✭❚❚❋✮✱ ❢♦✐ s✐♥t❡t✐③❛❞♦ ♣❡❧❛ ♣r✐♠❡✐r❛ ✈❡③ ♣♦r ❋r❡❞ ❲✉❞❧ ♥❛ ❞é❝❛❞❛ ✶✾✻✵ ❬✶❪✳ ❆té ❡♥tã♦✱ ❛s ❛♠♦str❛s ♦❜t✐❞❛s ♥ã♦ ❡r❛♠ ❞❡ ❜♦❛ q✉❛❧✐❞❛❞❡✳ ❆♣❡♥❛s ❝♦♠ ♦ ❛❞✈❡♥t♦ ❞♦s ❝❛t❛❧✐③❛✲ ❞♦r❡s ❞❡ ❩✐❡❣❧❡r✲◆❛tt❛✱ ❞❡s❡♥✈♦❧✈✐❞♦s ♥❛ ♠❡s♠❛ ❞é❝❛❞❛✱ é q✉❡ ❛s ❛♠♦str❛s ♦❜t✐❞❛s ♣❛ss❛r❛♠ ❛ t❡r q✉❛❧✐❞❛❞❡ ❡❧❡✈❛❞❛✳ ❊ss❡s ❝❛t❛❧✐③❛❞♦r❡s ❡r❛♠ ❢♦r♠❛❞♦s ♣♦r ♠❡t❛✐s ❞❡ tr❛♥s✐çã♦ ❝♦♠ ❛ ♣r♦♣r✐❡❞❛❞❡ ❞❡ ❛❝❡❧❡r❛r ❛❧❣✉♥s t✐♣♦s ❞❡ r❡❛çã♦ ❞❡ ♣♦❧✐♠❡r✐③❛çã♦ ❛♦ ♦r✐❡♥t❛r❡♠ ❝♦♥✈❡♥✐❡♥t❡♠❡♥t❡ ❛s ♠♦❧é❝✉❧❛s q✉❡ s❡ ❛❣r❡❣❛♠ ❛ ❝❛❞❡✐❛ ♣♦❧✐♠ér✐❝❛✳ ❈♦♠ ✐ss♦✱ ❛ ♣❛rt✐r ❞❛ ❞é❝❛❞❛ ❞❡ ✼✵✱ ❛ ❝♦♥❞✉t✐✈✐❞❛❞❡ ♦r❣â♥✐❝❛ ❝♦♠❡ç♦✉ ❛tr❛✐r ❛ ❛t❡♥çã♦ ❞❛ ❝♦♠✉♥✐❞❛❞❡ ❝✐❡♥tí✜❝❛✳

❊♠ ✶✾✼✸✱ ✈ár✐♦s ❣r✉♣♦s ❞❡ ♣❡sq✉✐s❛ ♦❜t✐✈❡r❛♠ s✐♠✉❧t❛♥❡❛♠❡♥t❡ ✉♠ ❝r✐st❛❧ ♦r❣â♥✐❝♦ ❞❡ ❛❧t❛ ❝♦♥❞✉t✐✈✐❞❛❞❡ ❝♦♠❜✐♥❛❞♦ ♦ ❚❚❋ ❝♦♠ ♦ t❡tr❛❝✐❛♥♦q✉✐♥♦❞✐♠❡t❛♥♦ ✭❚❈◆◗✮ ❬✶❪✱ ✉♠❛ ♠♦❧é❝✉❧❛ ♦r❣â♥✐❝❛ ❛❝❡✐t❛❞♦r❛ ❞❡ ❡❧étr♦♥s✳ ❖ ❝r✐st❛❧ ♦❜t✐❞♦ ♣♦ss✉í❛ ♠♦❞❡❧♦ ❞❡ ❝♦♥❞✉t✐✈✐❞❛❞❡ ✉♥✐❞✐♠❡♥s✐♦♥❛❧ ♣❡❧♦ ❢❛t♦ ❞❛s ♠♦❧é❝✉❧❛s ❞❡ ❚❚❋ ❡ ❚❈◆◗ ♣♦ss✉ír❡♠ ❣❡♦♠❡tr✐❛ ♣❧❛♥❛✱ ❞✐s♣♦♥❞♦✲s❡ ♥♦ ❝r✐st❛❧ ❡♠ ❝♦❧✉♥❛s ❛❧t❡r♥❛❞❛s ❡ ♣❛r❛❧❡✲ ❧❛s✳ ❆ss✐♠✱ ❛ ✐♥t❡r❛çã♦ ❡♥tr❡ ❛s ❝♦❧✉♥❛s ♦❝♦rr❡ ♣❡❧❛ tr❛♥s❢❡rê♥❝✐❛ ❞❡ ❡❧étr♦♥s ❡♥tr❡ ❛s ♠♦❧é❝✉❧❛s ❞❡ ❝❛❞❛ ♣❛r ❞❡ ❚❚❋ ❡ ❚❈◆◗✳ ❆ ❝♦♥❞✉t✐✈✐❞❛❞❡ ❡♥tã♦ é ❞✐t❛ ✉♥✐❞✐✲ ♠❡♥s✐♦♥❛❧ ♣♦r s❡r ♠✉✐t♦ ♠❛✐♦r ❛♦ ❧♦♥❣♦ ❞♦ ❡✐①♦ ❞❛s ❝♦❧✉♥❛s ❞♦ q✉❡ ♥❛s ❞✐r❡çõ❡s ♣❡r♣❡♥❞✐❝✉❧❛r❡s✳ ❖✉tr♦s ❝r✐st❛✐s ♦r❣â♥✐❝♦s ❢♦r❛♠ ❡♥tã♦ ♦❜t✐❞♦s ♣❡❧❛ ❝♦♠❜✐♥❛çã♦ ❞❡ ♠♦❧é❝✉❧❛s ❞♦❛❞♦r❛s ❡ ❛❝❡✐t❛❞♦r❛s ❛♣r❡s❡♥t❛♥❞♦ ❡str✉t✉r❛ ❞❡ ❝♦♥❞✉çã♦ ✉♥✐❞✐♠❡♥✲ s✐♦♥❛❧✳ ❊ss❡s ♠❛t❡r✐❛✐s ♣❛ss❛r❛♠ ❛ ❢♦r♠❛r ✉♠❛ ❝❧❛ss❡ ❞❡ ❝♦♥❞✉t♦r❡s ♦r❣â♥✐❝♦s q✉❡ r❡❝❡❜❡✉ ♦ ♥♦♠❡ ❞❡ ❝r✐st❛✐s ❝♦♥❞✉t♦r❡s ♣♦r tr❛♥s❢❡rê♥❝✐❛ ❞❡ ❝❛r❣❛✳

❈♦♠ ❛ ❞❡s❝♦❜❡rt❛ ❞❛ ❝♦♥❞✉t✐✈✐❞❛❞❡ ♥♦s ❝r✐st❛✐s ❞❡ tr❛♥s❢❡rê♥❝✐❛ ❞❡ ❝❛r❣❛✱ ✈ár✐♦s ❡st✉❞♦s ❢♦r❛♠ ❢❡✐t♦s ❛❝❡r❝❛ ❞❡ss❡s ♠❛t❡r✐❛✐s ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ❝♦♠♣r❡❡♥✲ ❞❡r ♦s ♠❡❝❛♥✐s♠♦s ❞❡ ❝♦♥❞✉çã♦✱ ❛❧é♠ ❞❡ s❡ ♦❜t❡r ✉♠❛ ♥♦✈❛ ❝❧❛ss❡ ❞❡ ❝♦♥❞✉t♦r❡s ♦r❣â♥✐❝♦s✳ ◆♦ ❛♥♦ ❞❡ ✶✾✼✶✱ ♦ ❣r✉♣♦ ❞❡ ♣r♦❢❡ss♦r ❍✐❞❡❦✐ ❙❤✐r❛❦❛✇❛ s✐♥t❡t✐③♦✉ ♦ P♦❧✐✲ ❛❝❡t✐❧❡♥♦(CH)X ❛ ♣❛rt✐r ❞❡ ✉♠ ❣ás ❞❡ ❛❝❡t✐❧❡♥♦(CH)x❬✷✱ ✸❪✳ ◆❛ ❜✉s❝❛ ♣❡❧❛ sí♥t❡s❡

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✸

✉♠ ✜❧♠❡ ♠❡tá❧✐❝♦ ❜r✐❧❤❛♥t❡✱ ♠❛s ❝♦♠ ❡❧❛st✐❝✐❞❛❞❡ ♣❛r❡❝✐❞❛ ❝♦♠ ✉♠❛ ❢♦❧❤❛ ✜♥❛ ❞❡ ♣❧ást✐❝♦✳ ❖s tr❛❜❛❧❤♦s ❞❡ ❙❤✐r❛❦❛✇❛ ❧❡✈❛r❛♠ ❛ ✉♠❛ ♥♦✈❛ ❣❡r❛çã♦ ❞❡ ♣♦❧í♠❡r♦s ❝♦♥✲ ❞✉t♦r❡s✱ ❝♦♥❤❡❝✐❞♦s ❝♦♠♦ ♣♦❧í♠❡r♦s ❝♦♥❥✉❣❛❞♦s ❬✹✱ ✺❪✳ P♦st❡r✐♦r♠❡♥t❡ ❙❤✐r❛❦❛✇❛ ❡ ♦s ♣r♦❢❡ss♦r❡s ❆❧❛♥ ●✳ ▼❛❝❉✐❛r♠✐❞ ❡ ❆❧❛♥ ❏✳ ❍❡❡❣❡r✱ r❡❛❧✐③❛r❛♠ ❡st✉❞♦s s♦❜r❡ ❛ ❝♦♥❞✉t✐✈✐❞❛❞❡ ❞♦s ✜❧♠❡s ❞❡ ♣♦❧✐❛❝❡t✐❧❡♥♦ ❛✉♠❡♥t❛♥❞♦ ❛ ♠❡s♠❛ s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ♣♦r ❞♦♣❛❣❡♠ ❝♦♠ ✐♦❞♦ ❬✻❪✳ ❉❡✈✐❞♦ ❛s ❞❡s❝♦❜❡rt❛s r❡❛❧✐③❛❞❛s ❡ ❛✈❛♥ç♦s ♦❜t✐❞♦s ♥♦ ❝❛♠♣♦ ❞♦s ♣♦❧í♠❡r♦s ❝♦♥❞✉t♦r❡s ❡st❡s ♣r♦❢❡ss♦r❡s ❢♦r❛♠ ❧❛✉r❡❛❞♦s ❝♦♠ ♦ Prê♠✐♦ ◆♦❜❡❧ ❞❡ ◗✉í♠✐❝❛ ♥♦ ❛♥♦ ✷✵✵✵✳

✶✳✷ ❖ P♦❧✐❛❝❡t✐❧❡♥♦

❖ ♣♦❧✐❛❝❡t✐❧❡♥♦ é ♦ ♠❛✐s s✐♠♣❧❡s ♣♦❧í♠❡r♦s ❝♦♥❥✉❣❛❞♦s ❝♦♠ ❡str✉t✉r❛ ❧✐♥✲ ❡❛r✱ s❡♥❞♦ ❢♦r♠❛❞♦ ♣♦r ✉♠❛ ❧♦♥❣❛ ❝❛❞❡✐❛ ❞❡ át♦♠♦s ❞❡ ❝❛r❜♦♥♦✳ ❊♥t❡♥❞❡✲s❡ ♣♦r ❝♦♥❥✉❣❛çã♦ ❛ ❛❧t❡r♥â♥❝✐❛ ❡♥tr❡ ❧✐❣❛çõ❡s ❞✉♣❧❛s ❡ s✐♠♣❧❡s ❡♥tr❡ ♦s át♦♠♦s ❞❡ ❝❛r❜♦♥♦ q✉❡ ❝♦♥st✐t✉❡♠ ❛ ❝❛❞❡✐❛ ♣r✐♥❝✐♣❛❧✳ ❈❛❞❛ ❝❛r❜♦♥♦ ❢❛③ ✉♠❛ ❧✐❣❛çã♦ ❝♦♠ ✉♠ át♦♠♦ ❞❡ ❤✐❞r♦❣ê♥✐♦✱ ❛❧é♠ ❞❡ s❡r ❧✐❣❛❞♦ ❧❛t❡r❛❧♠❡♥t❡ ❛ ❞♦✐s ♦✉tr♦s át♦♠♦s ❞❡ ❝❛r❜♦♥♦ ❡♠ ✉♠ ❛rr❛♥❥♦ t✐♣✐❝❛♠❡♥t❡ ❧✐♥❡❛r ❬✼✱ ✽❪✳

❉✉r❛♥t❡ ❛s ❞é❝❛❞❛s ❞❡ ✸✵ ❡ ✹✵✱ ❡st❡ ♣♦❧í♠❡r♦ ❢♦✐ t❡♠❛ ❞❡ ✈ár✐❛s ❞✐s❝✉ssõ❡s t❡ór✐❝❛s ❝♦♥tr♦✈❡rs❛s ♥♦ q✉❡ ❞✐③ r❡s♣❡✐t♦ ❛ ❢✉♥çã♦ ❞❡s❡♠♣❡♥❤❛❞❛ ♣❡❧♦s ❡❧étr♦♥s π✳

P♦r ✉♠ ❧❛❞♦✱ ❝♦♥s✐❞❡r❛✈❛✲s❡ q✉❡✱ ♣♦r r❛③õ❡s ❞❡ s✐♠❡tr✐❛✱ s❡ ❛ ❝❛❞❡✐❛ ♣♦❧✐♠ér✐❝❛ ❢♦ss❡ ❝♦♥❥✉❣❛❞❛✱ ❤❛✈❡r✐❛ ✉♠❛ s❡♣❛r❛çã♦ ❡♥tr❡ ♦ ú❧t✐♠♦ ❡st❛❞♦ ❡❧❡trô♥✐❝♦ ♦❝✉♣❛❞♦ ❡ ♦ ♣r✐♠❡✐r♦ ✈❛③✐♦✳ ❈♦♠ ✐ss♦✱ ♦ ♠❛t❡r✐❛❧ t❡r✐❛ ♣r♦♣r✐❡❞❛❞❡s s❡♠✐❝♦♥❞✉t♦r❛s ❬✽❪✳ P❡♥s❛✈❛✲s❡ t❛♠❜é♠ q✉❡✱ s❡ ❛ ♥✉✈❡♠ ❡❧❡trô♥✐❝❛ ❢♦ss❡ ❞❡s❧♦❝❛❧✐③❛ ♣♦r t♦❞♦ s✐st❡♠❛✱ ♦s ❝♦♠♣r✐♠❡♥t♦s ❞❡ ❧✐❣❛çõ❡s t❡♥❞❡r✐❛♠ ❛ ♣♦ss✉✐r ♦ ♠❡s♠♦ t❛♠❛♥❤♦✳ ❆ss✐♠✱ ❛ s✐♠❡tr✐❛ ❞♦ s✐st❡♠❛ ❧❡✈❛r✐❛ ❛ ✉♠❛ ❝♦♥✜❣✉r❛çã♦ ❞❡ ❡str✉t✉r❛ ❞❡ ❜❛♥❞❛s ❡q✉✐✈❛❧❡♥t❡ ❛ ❞♦s ♠❡t❛✐s✱ ✐st♦ é✱ ❝♦♠ ❛ ú♥✐❝❛ ❜❛♥❞❛ r❡s✉❧t❛♥t❡ s❡♠✐♣r❡❡♥❝❤✐❞❛✳

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✹

❬✾❪✿ q✉❛❧q✉❡r ❝♦♥❞✉t♦r ✉♥✐❞✐♠❡♥s✐♦♥❛❧ é ✐♥stá✈❡❧✱ s✉❥❡✐t♦ ❛ tr❛♥s❢♦r♠❛çõ❡s ❡str✉t✉✲ r❛✐s q✉❡ ♣♦❞❡♠ t♦r♥á✲❧♦ s❡♠✐❝♦♥❞✉t♦r✳ P♦rt❛♥t♦✱ ❡st❡ t❡♦r❡♠❛ ❢❛✈♦r❡❝❡✉ ♦ ♣♦♥t♦ ❞❡ ✈✐st❛ q✉❡ ❞❡❢❡♥❞✐❛ ❛ ❝❛❞❡✐❛ ♣♦❧✐♠ér✐❝❛ ❝♦♥❥✉❣❛❞❛ ❝♦♠♦ ❡str✉t✉r❛ ♠❛✐s ❡stá✈❡❧✱ ❝♦♠♦ ♠♦str❛❞♦ ♥❛ ❋✐❣✉r❛ ✶✳✶✳ ◆❡st❛ ❡str✉t✉r❛ ♦ ♣♦❧✐❛❝❡t✐❧❡♥♦ ❛❝♦♣❧❛✲s❡ ❢r❛❝❛♠❡♥t❡ ❝♦♠ ❛ ❝❛❞❡✐❛ ✈✐③✐♥❤❛✳ ❈♦♠♦ ❝♦♥s❡q✉ê♥❝✐❛✱ ♦ ♠❛t❡r✐❛❧ r❡s✉❧t❛♥t❡ é ✢❡①í✈❡❧✳ ❆ ❝♦♥❥✉❣❛çã♦ ♣r♦❞✉③ ❞✐stâ♥❝✐❛s ❞✐❢❡r❡♥t❡s ❡str❡ ♦s ❣r✉♣♦sCH✱ ♦s ❝❛r❜♦♥♦s ✉♥✐❞♦s ♣♦r ❧✐❣❛çõ❡s ❞♦

t✐♣♦π❡stã♦ ❛ ✉♠❛ ❞✐stâ♥❝✐❛ ♠❡♥♦r ❡♥tr❡ ❡❧❡s ❞♦ q✉❡ ❛q✉❡❧❡s ✉♥✐❞♦s ♣♦r ❧✐❣❛çõ❡s ❞♦

t✐♣♦σ✳ ❊ss❡ ♣r♦❝❡ss♦ r❡❝❡❜❡ ♦ ♥♦♠❡ ❞❡ ❞✐♠❡r✐③❛çã♦✳

C H C H C H C H C H C H C H C H C H C H C H C H C H C H

❋✐❣✉r❛ ✶✳✶✿ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❛ ❝♦♥✜❣✉r❛çã♦ ❞❡ ❡q✉✐❧í❜r✐♦ ❞♦ tr❛♥s✲ P♦❧✐❛❝❡t✐❧❡♥♦

(16)

✺ C H C H C H C H C H C H C H C H C H C H C H C H

❋✐❣✉r❛ ✶✳✷✿ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❛ ❝♦♥✜❣✉r❛çã♦ ❞❡ ❡q✉✐❧í❜r✐♦ ❞♦ ❝✐s✲ P♦❧✐❛❝❡t✐❧❡♥♦

❆♣ós ❛ ♦❜t❡♥çã♦ ❞♦ ♣♦❧✐❛❝❡t✐❧❡♥♦ ♣❡❧♦ ❣r✉♣♦ ❞♦ ♣r♦❢❡ss♦r ❙❤✐r❛❦❛✇❛✱ ❞✐✲ ✈❡rs♦s ♣♦❧í♠❡r♦s ❝♦♥❞✉t♦r❡s ♦r❣â♥✐❝♦s✱ ❝♦♠ ❡str✉t✉r❛s ♠❛✐s ❝♦♠♣❧❡①❛s✱ ❢♦r❛♠ s✐♥✲ t❡t✐③❛❞♦s✳ P♦ré♠✱ ✉♠❛ ❝❛r❛❝t❡ríst✐❝❛ ❡r❛ ❝♦♠✉♠ ❛ t♦❞♦s✿ ❤❛✈✐❛ ❛❧t❡r♥â♥❝✐❛ ❡♥tr❡ ❛s ❧✐❣❛çõ❡s s✐♠♣❧❡s ❡ ❞✉♣❧❛s✱ ✐st♦ é✱ ❡st❛s ❡str✉t✉r❛s ♠❛✐s ❝♦♠♣❧❡①❛s t❛♠❜é♠ ❡r❛♠ ♣♦❧í♠❡r♦s ❝♦♥❞✉t♦r❡s ❝♦♥❥✉❣❛❞♦s✳ ❆❧❣✉♥s ❡①❡♠♣❧♦s ❞❡ss❡s ❝♦♠♣♦st♦s ❡stã♦ r❡♣r❡✲ s❡♥t❛❞♦s ♥❛ ✜❣✉r❛ ✶✳✸✳

✶✳✸ P♦rt❛❞♦r❡s ❞❡ ❈❛r❣❛✿ ❙ó❧✐t♦♥s✱ Pó❧❛r♦♥s ❡ ❇✐♣ó❧❛r♦♥s

❉❡✈✐❞♦ ❛ ❞✐✈❡rs✐❞❛❞❡ ❞❡ r❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s✱ ❝♦♠ r❡❧❛çã♦ ❛ ❝♦♥❞✉✲ t✐✈✐❞❛❞❡ ❡♠ ♣♦❧í♠❡r♦s ❝♦♥❥✉❣❛❞♦s✱ s✉r❣✐✉ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ♣r♦♣♦r ♠❡❝❛♥✐s♠♦s ❞❡ ❝♦♥❞✉çã♦ ❞✐❢❡r❡♥t❡s ❞❛q✉❡❧❡s ✉t✐❧✐③❛❞♦s ♣❛r❛ ❝❛r❛❝t❡r✐③❛r ❡st❡ ❢❡♥ô♠❡♥♦ ♥♦s ♠❡t❛✐s✳ ❊♠ ✶✾✼✾ ♦s ❣r✉♣♦s ❞❡ ♣❡sq✉✐s❛ ❞♦s ♣r♦❢❡ss♦r❡s ❘✐❝❡ ❡ ❙✉ ❡ ❞❡ ❙❝❤r✐❡✛❡r ❡ ❍❡❡❣❡r✱ ♣r♦♣✉s❡r❛♠ ✐♥❞❡♣❡♥❞❡♥t❡♠❡♥t❡ ✉♠ ♥♦✈♦ ♠♦❞❡❧♦ ♣❛r❛ ♦ ♠❡❝❛♥✐s♠♦ ❞❡ ❝♦♥❞✉çã♦ ❡♠ ♣♦❧í♠❡r♦s ♦r❣â♥✐❝♦s✱ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ♠♦❞❡❧♦ ❙❙❍ ❬✶✸✱ ✶✹❪✳ ◆❡st❡ ♠♦❞❡❧♦ ♦ ❝♦♥❞✉t♦r ♦❣â♥✐❝♦ é ❝♦♥st✐t✉í❞♦ ❞❡ ❝❛❞❡✐❛s ✜♥✐t❛s✱ t♦r♥❛♥❞♦✲s❡ ♥❛t✉r❛❧ ❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ ♦❝♦r✲ rê♥❝✐❛ ❞❡ ❞❡❢❡✐t♦s t♦♣♦❧ó❣✐❝♦s ♥♦ ♣r♦❝❡ss♦ ❞❡ ♣♦❧✐♠❡r✐③❛çã♦✱ ✐st♦ é✱ ❡st❡s ❞❡❢❡✐t♦s ❡str✉t✉r❛✐s ♣♦❞❡r✐❛♠ s❡r ❝r✐❛❞♦s ♣♦r ♣r♦❝❡ss♦s ❞❡ ❞♦♣❛❣❡♠ ♦✉ ❢♦t♦❡①❝✐t❛çã♦✱ ❢♦r✲ ♠❛♥❞♦ r❛❞✐❝❛✐s✳ ❚❛✐s ❞❡❢❡✐t♦s ❛❧t❡r❛♠ ♦ ♣❡r✜❧ ❞❡ ❞✐♠❡r✐③❛çã♦ ❞❛ ❝❛❞❡✐❛ ♣♦❧✐♠ér✐❝❛ ❣❡r❛♥❞♦ ❢♦r♠❛s ❡s♣❡❝í✜❝❛s ❝♦♥✜❣✉r❛çã♦ ❞♦s ❣r✉♣♦s CH✳ ❆ ❛❧t❛ ❝♦♥❞✉t✐✈✐❞❛❞❡ ❞♦s

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✻

P♦❧✐❢❡♥✐❧❡♥♦

N H

N H P♦❧✐❛♥✐❧✐♥❛

N H P♦❧✐♣✐rr♦❧

S P♦❧✐t✐♦❢❡♥♦

❋✐❣✉r❛ ✶✳✸✿ ❊①❡♠♣❧♦s ❞❡ ♣♦❧í♠❡r♦s ❝♦♥❥✉❣❛❞♦s

❝♦♥✈❡♥❝✐♦♥❛✐s✳ P♦r ❡ss❛ r❛③ã♦ r❡❝❡❜❡♠ ♦ ♥♦♠❡ ❞❡ q✉❛s✐✲♣❛rtí❝✉❧❛s✳

(18)

✼

♠✉✐t♦ ♣❡q✉❡♥❛✱ ♠❛s ❞❛ ♦r❞❡♠ ❞❛q✉❡❧❛ ❞♦s ♣♦rt❛❞♦r❡s ✉s✉❛✐s✱ ❧❡✈❛♥❞♦ ❡ss❛ ♣❛r❡❞❡ ❞❡ ❞♦♠í♥✐♦ ❛ s❡r ❝❛r❛❝t❡r✐③❛❞❛ ❝♦♠♦ ✉♠ ♦❜❥❡t♦ q✉â♥t✐❝♦✳ ❉❡ss❛ ♠❛♥❡✐r❛✱ ❛ ♣❛r❡❞❡ ❞❡ ❞♦♠í♥✐♦ s❡r✐❛ ♠ó✈❡❧ ❛♦ ❧♦♥❣♦ ❞❛ ❝❛❞❡✐❛✳ ❊ss❛s ♣❛r❡❞❡s ❞❡ ❞♦♠í♥✐♦ sã♦ ❡str✉t✉r❛s ♥ã♦ ❧✐♥❡❛r❡s q✉❡ ♣r❡s❡r✈❛♠ s❡✉ ♣❡r✜❧ ❛♦ s❡ ♣r♦♣❛❣❛r❡♠✳ ❚❛✐s ❡str✉t✉r❛s r❡❝❡❜❡r❛♠ ♦ ♥♦♠❡ ❞❡ ✏só❧✐t♦♥✑✱ ❡♠ ❛♥❛❧♦❣✐❛ ❛♦ ♥♦♠❡ ❞❛❞♦✱ ❡♠ ♦✉tr❛s ár❡❛s ❞❛ ❢ís✐❝❛✱ ❛ ✉♠❛ ♦♥❞❛ q✉❡ s❡ ♣r♦♣❛❣❛ s❡♠ ❞✐s♣❡rsã♦ ❡♠ ✉♠ ♠❡✐♦✳ ❉❡ ❢❛t♦✱ só❧✐t♦♥s t♦♣♦❧ó❣✐❝♦s ✐❞❡❛✐s sã♦ ♦❜t✐❞♦s q✉❛♥❞♦ s❡ ❝♦♥s✐❞❡r❛♠ ❝❛❞❡✐❛s ♠✉✐t♦ ❧♦♥❣❛s✱ ❡ ♣♦ss✉❡♠ ♣r♦♣r✐❡❞❛❞❡ ❞❡ ♥ã♦ ❞❡❢♦r♠❛çã♦✳

❈♦♥s✐❞❡r❡ ✉♠❛ ❝❛❞❡✐❛ ❞❡ ♣♦❧✐❛❝❡t✐❧❡♥♦ ❝♦♠♦ ❛ ❞❛ ✜❣✉r❛ ✶✳✹ ♦♥❞❡ s❡✉s ♠♦♥ô♠❡r♦s sã♦ ✐♥❞❡①❛❞♦s ♣♦r 1,2,3, ...✳ ❖ ♣♦❧✐❛❝❡t✐❧❡♥♦ s❡ ❛♣r❡s❡♥t❛ ❞✐♠❡r✐③❛❞♦

♦♥❞❡ ❛ ❧✐❣❛çã♦ ♠❛✐s ❝✉rt❛ é r❡♣r❡s❡♥t❛❞❛ ♣♦r ❡♥q✉❛♥t♦ ❛ ♠❛✐s ❧♦♥❣❛ é r❡♣r❡✲ s❡♥t❛❞❛ ♣♦r ✳ ❆s ❝❛❞❡✐❛s ♣♦❞❡♠ s❡ ❞✐♠❡r✐③❛r s♦❜ ♦s ❞♦✐s ❛rr❛♥❥♦s ♣♦ssí✈❡✐s ❞❛ ✜❣✉r❛ ✶✳✹✳ ◆♦ ♣♦❧✐❛❝❡t✐❧❡♥♦✱ ✉♠ só❧✐t♦♥ ❝♦rr❡s♣♦♥❞❡ ❛ ✉♠❛ ♠✉❞❛♥ç❛ ♥♦ ♣❛❞rã♦ ❞❡

· · ·1 2 3 4 5 6_{· · ·}

❋❆❙❊ ❆

· · ·1 2 3 4 5 6_{· · ·}

❋❆❙❊ ❇

❋✐❣✉r❛ ✶✳✹✿ ❆s ❞✉❛s ❞✐❢❡r❡♥t❡s ❞✐s♣♦s✐çõ❡s ❞❡ ✉♠❛ ❝❛❞❡✐❛ ❞❡ tr❛♥s✲♣♦❧✐❛❝❡t✐❧❡♥♦✳

❧✐❣❛çõ❡s ❞✉♣❧❛s ❡ s✐♠♣❧❡s✳ ■st♦ é ❝❛r❛❝t❡r✐③❛❞♦ ♣♦r ✉♠❛ ❞✐♠✐♥✉✐çã♦ ♥♦ ❝♦♠♣r✐♠❡♥t♦ ❞❛s ❧✐❣❛çõ❡s ❡ ✉♠ ❛✉♠❡♥t♦ ♥♦ ❝♦♠♣r✐♠❡♥t♦ ❞❛s ❧✐❣❛çõ❡s ✳ ❖ r❡s✉❧t❛❞♦ é ✉♠❛ ♠✉❞❛♥ç❛ ❡♥tr❡ ❛s ❢❛s❡s ❞❡ ❞✐♠❡r✐③❛çã♦ ❆ ❡ ❇ ❞❛ ✜r❣✉r❛ ✶✳✹✳ ◆♦ tr❛♥s✲♣♦❧✐❛❝❡t✐❧❡♥♦ ❛ ❝❛❞❡✐❛ ♣♦❞❡ s❡r ❞✐♠❡r✐③❛❞❛ s♦❜ ❛s ❞✉❛s ❢♦r♠❛s ♣♦ssí✈❡✐s ❝♦♠♦ ♠♦str❛ ❛ ✜r❣✉r❛ ✶✳✹✳ ❈♦♠♦ ❛s ❧✐❣❛çõ❡s ❝♦♠ ♦s ❣r✉♣♦s CH sã♦ ✐❞ê♥t✐❝❛s ♥❛s ❞✉❛s ❢❛s❡s✱ ♠✉❞❛♥❞♦

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✽

❣✐❛s ❞❛s ❞✉❛s ❢❛s❡s sã♦ ✐❣✉❛✐s ❬✶✺✱ ✶✻❪✳ ❉✐③❡♠♦s ❡♥tã♦ q✉❡ ♦ ❡st❛❞♦ ❞✐♠❡r✐③❛❞♦ ❞♦ tr❛♥s✲♣♦❧✐❛❝❡t✐❧❡♥♦ é ❞✉♣❧❛♠❡♥t❡ ❞❡❣❡♥❡r❛❞♦✱ s❡♥❞♦ ♦ só❧✐t♦♥ ✉♠❛ s♦❧✉çã♦ ♥❛t✉r❛❧ ❞❡ss❛ ❞❡❣❡♥❡r❡s❝ê♥❝✐❛✳ ❊st❛ s♦❧✉çã♦ ❢♦✐ ♣r♦♣♦st❛ ♣♦r ❙✉✱ ❙❝❤r✐❡✛❡r ❡ ❍❡❡❣❡r ❝♦♠ ❛ ❢♦r♠✉❧❛çã♦ ❞♦ ♠♦❞❡❧♦ ❙❙❍ ❬✶✹❪✳

❊♠ r❡❧❛çã♦ ❛ ❡str✉t✉r❛ ❡❧❡trô♥✐❝❛ ❞♦ ♠❛t❡r✐❛❧✱ ♦ ❞❡❢❡✐t♦ r❡♣r❡s❡♥t❛ ✉♠❛ q✉❡❜r❛ ❞❡ s✐♠❡tr✐❛ ❞❛ ❝❛❞❡✐❛✳ ■ss♦ ♣r♦✈♦❝❛ ♦ s✉r❣✐♠❡♥t♦ ❞❡ ✉♠ ❡st❛❞♦ ❡❧❡trô♥✐❝♦ ❧♦❝❛❧✐③❛❞♦ ♥❛ r❡❣✐ã♦ ❞❡ ❡♥❡r❣✐❛ ❢♦r❛ ❞❛s ❜❛♥❞❛s✳ ❉❡✈✐❞♦ ♦ ❛❧t♦ ❣r❛✉ ❞❡ s✐♠❡tr✐❛ ❞♦ ♣♦❧✐❛❝❡t✐❧❡♥♦✱ ♦ só❧✐t♦♥ é ❡♥❡r❣❡t✐❝❛♠❡♥t❡ ❝❛r❛❝t❡r✐③❛❞♦ ♣❡❧❛ ♣r❡s❡♥ç❛ ❞❡ ✉♠ ❡st❛❞♦ ♣ró①✐♠♦ ❛♦ ❝❡♥tr♦ ❞♦ ❣❛♣✳ ◆♦ ❝❛s♦ ❞❡ ✉♠ só❧✐t♦♥ ♥❡✉tr♦✱ ❡ss❡ ❡st❛❞♦ é ♦❝✉♣❛❞♦ ♣♦r ✉♠ ú♥✐❝♦ ❡❧étr♦♥ ❡✱ ❛❧t❡r♥❛t✐✈❛♠❡♥t❡✱ s❡ ♦ só❧✐t♦♥ ❢♦r ♥❡❣❛t✐✈❛♠❡♥t❡ ❝❛rr❡❣❛❞♦✱ ❞♦✐s ❡❧étr♦♥s s❡ ❡♠♣❛r❡❧❤❛♠ ♣❛r❛ ♦❝✉♣❛r ❡ss❡ ❡st❛❞♦✳ ❈♦♠♦ t♦❞♦s ♦✉tr♦s ❡❧étr♦♥s ❞♦ s✐st❡♠❛ ❡stã♦ ❡♠♣❛r❡❧❤❛❞♦s✱ s❡❣✉❡ q✉❡ só❧✐t♦♥s ♥❡✉tr♦s ♣♦ss✉❡♠ s♣✐♥ ±1/2 ❡

só❧✐t♦♥s ❝❛rr❡❣❛❞♦s tê♠ s♣✐♥ ♥✉❧♦✳ ❚❛✐s ❝♦♥✜❣✉r❛çõ❡s ❞❛s ❜❛♥❞❛s ❡♥❡r❣ét✐❝❛s sã♦ r❡♣r❡s❡♥t❛❞❛s ♥❛ ✜❣✉r❛ ✶✳✺✳

❋✐❣✉r❛ ✶✳✺✿ ❊str✉t✉r❛ ❞❡ ❜❛♥❞❛s ❞❡ ❡♥❡r❣✐❛ ❛ss♦❝✐❛❞❛s ❛ ♣r❡s❡♥ç❛ ❞❡ só❧✐t♦♥s

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✾

❛s ❢❛s❡s ❆ ❡ ❇ ❝♦♠♦ ♠♦str❛ ❛♣r❡s❡♥t❛ ♦ tr❛♥s✲♣♦❧✐❛❝❡t✐❧❡♥♦✳

❯♠❛ ♠♦❞✐✜❝❛çã♦ ❢♦✐ ❡♥tã♦ ✐♥tr♦❞✉③✐❞❛ ♥♦ ♠♦❞❡❧♦✿ ❛❞♠✐t✐✉✲s❡ ❛ ♣♦ss✐❜✐❧✐✲ ❞❛❞❡ ❞❛ ❡①✐stê♥❝✐❛ ❞❡ ❡str✉t✉r❛s ❡stá✈❡✐s q✉❡ s✉r❣✐ss❡♠ ❞❛ ✐♥t❡r❛çã♦ ❡♥tr❡ só❧✐t♦♥s✳ ❊st❛s ❡str✉t✉r❛s r❡❝❡❜❡r❛♠ ♦ ♥♦♠❡ ❞❡ ♣ó❧❛r♦♥✱ ♣♦✐s ♣♦❞❡r✐❛♠ s❡r ✐♥t❡r♣r❡t❛❞❛s ❝♦♠♦ ✉♠ r❡❛rr❛♥❥♦ ❞♦s ❡❧étr♦♥sπ✱ q✉❡ ♣♦❧❛r✐③❛✈❛♠ ❛ ❝❛❞❡✐❛ ♣♦❧✐♠ér✐❝❛ ❧♦❝❛❧♠❡♥t❡✱

r❡s✉❧t❛♥❞♦ ❡♠ ✉♠❛ ♠♦❞✐✜❝❛çã♦ ❞❡ ❝✉rt♦ ❛❧❝❛♥❝❡ ♥❛ ❝♦♥✜❣✉r❛çã♦ ❡s♣❛❝✐❛❧ ❞♦s át♦✲ ♠♦s ❞❡ ❝❛r❜♦♥♦ ❬✶✽❪✳ ◆♦s ❝♦♥❞✉t♦r❡s ♦r❣â♥✐❝♦s✱ ❡♥t❡♥❞❡✲s❡ ❝♦♠♦ ♣ó❧❛r♦♥ ✉♠ ❡st❛❞♦ ❧✐❣❛❞♦ ❞❡ ✉♠ ♣❛r ❞❡ só❧✐t♦♥s✳ ❉❡ ♠❛♥❡✐r❛ ❣❡r❛❧✱ q✉❛♥❞♦ ✉♠ ❡❧étr♦♥ s❡ ♠♦✈❡ ❡♠ ✉♠ ❝r✐st❛❧ ✐ô♥✐❝♦✱ s✉❛ ✈✐③✐♥❤❛♥ç❛ é ♣♦❧❛r✐③❛❞❛ ♣❡❧❛ ❛tr❛çã♦ ❞❡ í♦♥s ♣♦s✐t✐✈♦s ❡ r❡♣✉❧sã♦ ❞❡ í♦♥s ♥❡❣❛t✐✈♦s✳ ❈♦♠ ✐ss♦✱ s✉r❣❡ ✉♠ ♠♦✈✐♠❡♥t♦ r❡❧❛t✐✈♦ ❡♥tr❡ ♦s í♦♥s ❞❡ ❝❛r❣❛s ♦♣♦st❛s ❣❡r❛♥❞♦ ✉♠ ❝❛♠♣♦ ❞❡ ♣♦❧❛r✐③❛çã♦ q✉❡ ❛❢❡t❛ ♦ ♠♦✈✐♠❡♥t♦ ❞♦s ❡❧étr♦♥✱ ❡st❛ ❝♦♥❢♦r♠❛çã♦ é ❝❤❛♠❛❞❛ ❞❡ ♣ó❧❛r♦♥ ❬✶✾❪✳ ❖ t❡r♠♦ ♣ó❧❛r♦♥ é ✉s❛❞♦ t❛♠❜é♠ ♣❛r❛ ❞❡♥♦t❛r ✉♠ ❡st❛❞♦ ❡❧❡trô♥✐❝♦ ❧♦❝❛❧✐③❛❞♦ ❛❝♦♠♣❛♥❤❛❞♦ ❞❛ r❡s♣❡❝t✐✈❛ ❞✐st♦rçã♦ ❞❛ r❡❞❡✳ ❖✉ s❡❥❛✱ ♥♦s ♣♦❧í♠❡r♦s ❝♦♥❞✉t♦r❡s ♦ ♣ó❧❛r♦♥ é ✉♠❛ q✉❛s✐✲♣❛rtí❝✉❧❛ ❛❞✈✐♥❞❛ ❞❛ ✐♥t❡r❛çã♦ ❡❧étr♦♥✲❢ô♥♦♥ ♠❛♥✐❢❡st❛❞❛ ♥❛ ❢♦r♠❛ ❞❡ ✉♠❛ ❞✐st♦rçã♦ ❞❛ r❡❞❡ ❬✷✵❪✳

❆♦ ❝♦♥trár✐♦ ❞♦ só❧✐t♦♥✱ ♦ ❡s♣❡❝tr♦ ❡❧❡trô♥✐❝♦ ❞♦ ♣ó❧❛r♦♥ ❛♣r❡s❡♥t❛ ❞♦✐s ♥í✈❡✐s ❞❡ ❡♥❡r❣✐❛ ♥♦ ✐♥t❡r✐♦r ❞♦ ❣❛♣✱ ✉♠ ♣ró①✐♠♦ ❛ ❜❛♥❞❛ ❞❡ ❝♦♥❞✉çã♦ ❡ ♦ ♦✉tr♦ ♣ró①✐♠♦ ❛ ❜❛♥❞❛ ❞❡ ✈❛❧ê♥❝✐❛✱ ❝♦♠♦ é ♣♦ssí✈❡❧ ♦❜s❡r✈❛r ♥❛ ✜❣✉r❛ ✶✳✻✳ ❈♦♠♦ ♣♦❞❡♠♦s ❡♥t❡♥❞❡r q✉❡ ♣ó❧❛r♦♥s sã♦ ❡st❛❞♦s ❧✐❣❛❞♦s ❞❡ só❧✐t♦♥s✱ ✉♠ ❝❛rr❡❣❛❞♦ ❡ ♦ ♦✉tr♦ ♥❡✉tr♦✱ ❛ ❡str✉t✉r❛ r❡s✉❧t❛♥t❡ ♣♦ss✉✐ s♣✐♥ ±1/2 ❡ ❝❛r❣❛ _±e ❬✷✶✱ ✷✷❪✳ ❈♦♠ ✐ss♦✱ ♣ó❧❛r♦♥s

r❡s♣♦♥❞❡♠ s✐♠✉❧t❛♥❡❛♠❡♥t❡ ❛ ❝❛♠♣♦s ❡❧étr✐❝♦s ❡ ♠❛❣♥ét✐❝♦s✳

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✶✵

❯♠ ♦✉tr♦ t✐♣♦ ❞❡ ❞❡❢❡✐t♦ t♦♣♦❧ó❣✐❝♦ ♣♦❞❡ s❡r ❣❡r❛❞♦ ❛ ♣❛rt✐r ❞❛ ✐♥t❡r❛çã♦ ❡❧étr♦♥✲❢ô♥♦♥ ❡♠ ♣♦❧í♠❡r♦s ❝♦♥❥✉❣❛❞♦s✳ ❊ss❡ ❞❡❢❡✐t♦ r❡❝❡❜❡ ♦ ♥♦♠❡ ❞❡ ❜✐♣ó❧❛r♦♥✳ ❙ã♦ ❞❡❢❡✐t♦s ❡str✉t✉r❛✐s s❡♠❡❧❤❛♥t❡s ❛♦s ♣ó❧❛r♦♥s✱ ♣♦✐s ❛ ❢❛s❡ ❞❡ ❞✐♠❡r✐③❛çã♦ ❞❛ ❝❛❞❡✐❛ é ❛ ♠❡s♠❛ ❛❧é♠ ❞❡ ❡①✐st✐r ❞♦✐s ♥í✈❡✐s ❞❡ ❡♥❡r❣✐❛ ❛ss♦❝✐❛❞♦s ❛♦ ❞❡❢❡✐t♦ ♥♦ ✐♥t❡r✐♦r ❞♦ ❣❛♣ ❬✶✽✱ ✷✷❪✳ ◆♦ ❡♥t❛♥t♦✱ ♥♦ ❜✐♣ó❧❛r♦♥✱ ❛s ♦❝✉♣❛çõ❡s ❞♦s ♥í✈❡✐s ❞❡ ❡♥❡r❣✐❛ ♥♦ ✐♥t❡r✐♦r ❞♦ ❣❛♣ sã♦ ❞✐❢❡r❡♥t❡s ❡♠ r❡❧❛çã♦ ❛♦ ♣ó❧❛r♦♥✳ ❖ ❜✐♣ó❧❛r♦♥ ♣♦❞❡ s❡r ❝❛r❛❝t❡r✐③❛❞♦ ❝♦♠♦ ✉♠ ♣❛r ❞❡ só❧✐t♦♥s ❝❛rr❡❣❛❞♦s✱ ♣♦ss✉✐♥❞♦ ❝❛r❣❛ ±2e ❡ s♣✐♥

♥✉❧♦✳ ❈♦♠ r❡❧❛çã♦ ❛♦ ❡s♣❡❝tr♦ ❡♥❡r❣ét✐❝♦✱ ♥♦ ❜✐♣ó❧❛r♦♥✱ ♦s ♥í✈❡✐s ❞❡ ❡♥❡r❣✐❛ sã♦ ♠❛✐s ❡str❡✐t♦s ♦❝✉♣❛♥❞♦ ❛ r❡❣✐ã♦ ✐♥t❡r♠❡❞✐ár✐❛ ❞♦ ❣❛♣ ❬✷✶❪✱ ❝♦♠♦ r❡♣r❡s❡♥t❛❞♦ ♥❛ ✜❣✉r❛ ✶✳✼✳

❋✐❣✉r❛ ✶✳✼✿ ❊str✉t✉r❛ ❞❡ ❜❛♥❞❛s ❞❡ ❡♥❡r❣✐❛ ❛ss♦❝✐❛❞❛s ❛ ♣r❡s❡♥ç❛ ❞❡ ❜✐♣ó❧❛r♦♥s

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✶✶

✶✳✹ ❊st❛❜✐❧✐❞❛❞❡ ❡ ❊❢❡✐t♦s ❞❡ ❚❡♠♣❡r❛t✉r❛

❖ ❣r❛♥❞❡ ♣♦t❡♥❝✐❛❧ ❞♦s ❝♦♥❞✉t♦r❡s ♦r❣â♥✐❝♦s ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ❞✐s♣♦s✐t✐✈♦s ♦♣t♦❡❧❡trô♥✐❝♦s ✈ê♠ ❛tr❛✐♥❞♦ ❝r❡s❝❡♥t❡♠❡♥t❡ ♦ ✐♥t❡r❡ss❡ ❞❛ ❝♦♠✉♥✐❞❛❞❡ ❝✐❡♥tí✜❝❛ ♥♦s ú❧t✐♠♦s ❛♥♦s ❬✷✸✕✷✺✱ ✷✽❪✳ ❆s ❛♣❧✐❝❛çõ❡s ❞❡ss❡s ♠❛t❡r✐❛✐s ✐♥❝❧✉❡♠ ❞✐♦✲ ❞♦s ❡♠✐ss♦r❡s ❞❡ ❧✉③ ♦r❣â♥✐❝♦s ❬✸✵✱ ✸✶❪✱ tr❛♥s✐st♦r❡s ❞❡ ✜❧♠❡ ✜♥♦ ❬✸✷✕✸✹❪✱ ❞✐s♣❧❛②s ❬✸✺✱ ✸✻❪✱ ❢♦t♦❞✐♦❞♦s ❡ ❢♦t♦✈♦❧t❛✐❝♦s ♦r❣â♥✐❝♦s ❬✸✼✱ ✸✽❪✳ ❊♠ ❡s♣❡❝✐❛❧✱ ♦s ❢♦t♦✈♦❧t❛✐❝♦s ♦r❣â♥✐❝♦s sã♦ ♠✉✐t♦ ❛tr❛t✐✈♦s ♣♦r ❛♣r❡s❡♥t❛r❡♠ ✈❛♥t❛❣❡♥s ❝♦♠♦ ❝♦♥❞✉t✐✈✐❞❛❞❡ ❝♦♥✲ tr♦❧❛❞❛✱ ❛❧t❛ ♠❛❧❡❛❜✐❧✐❞❛❞❡ ❡ ❜❛✐①♦ ❝✉st♦ ❞❡ ♣r♦❞✉çã♦✳ ◆♦ ❡♥t❛♥t♦✱ ❡♠ ❝♦♠♣❛r❛çã♦ ❝♦♠ ❛s ❝é❧✉❧❛s s♦❧❛r❡s ❝♦♥✈❡♥❝✐♦♥❛✐s✱ ❛ ❝♦♠♣r❡❡♥sã♦ ❞❛ ❝✐ê♥❝✐❛ ❡♥✈♦❧✈✐❞❛ ♥❛s ❝é❧✉❧❛s s♦❧❛r❡s ♦r❣â♥✐❝❛s ❛✐♥❞❛ é ♠❡♥♦r✳ ❖ tr❛♥s♣♦rt❡ ❞❡ ❝❛r❣❛ t❡♠ s✐❞♦ ✐❞❡♥t✐✜❝❛❞♦ ❝♦♠♦ ✉♠ ✐♠♣♦rt❛♥t❡ ♣r♦❝❡ss♦ ❡♠ t♦❞❛s ❡ss❛s ❛♣❧✐❝❛çõ❡s✳ ❆❧é♠ ❞✐ss♦✱ ❛ ♠♦❜✐❧✐❞❛❞❡ ❞♦s ♣♦rt❛❞♦r❡s ❞❡ ❝❛r❣❛ t❡♠ ♣r♦✈❛❞♦ ❡st❛r ❞✐r❡t❛♠❡♥t❡ r❡❧❛❝✐♦♥❛❞❛ ❛ ♣❡r❢♦r♠❛♥❝❡ ❞♦ ❞✐s♣♦s✐t✐✈♦ ❬✸✾❪✳ ❚❛♠❜é♠✱ ♦ tr❛♥s♣♦rt❡ ❞❡ ❝❛r❣❛✱ ❡♠ ♠♦❧é❝✉❧❛s ♣❡q✉❡♥❛s ❡ ♣♦❧í♠❡r♦s✱ ✈❡♠ s❡♥❞♦ ❡①❛✉st✐✈❛♠❡♥t❡ ✐♥✈❡st✐❣❛❞♦✱ t❡♦r✐❝❛♠❡♥t❡ ❡ ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡ ❬✹✵✕✹✸❪✳ ❯♠ ❛s♣❡❝t♦ ❝❡♥tr❛❧ ♥❡ss❡s ❡st✉❞♦s t❡♠ s✐❞♦ ♦ ❡❢❡✐t♦ ❞❛ t❡♠♣❡r❛t✉r❛ s♦❜r❡ ♦ tr❛♥s✲ ♣♦rt❡ ❞❡ ❝❛r❣❛✳ ❈♦♠ ✐ss♦✱ ❡st✉❞♦s s♦❜r❡ ❛ ❡st❛❜✐❧✐❞❛❞❡ ❞❡ q✉❛s✐✲♣❛rtí❝✉❧❛s✱ ✐♥❝❧✉✐♥❞♦ ❡❢❡✐t♦s ❞❡ t❡♠♣❡r❛t✉r❛✱ sã♦ ❢✉♥❞❛♠❡♥t❛✐s ♣❛r❛ ❛ ❞❡s❝r✐çã♦ ❞♦ ♣r♦❝❡ss♦ ❞❡ ❝♦♥❞✉t✐✈✐✲ ❞❛❞❡ ♥❡ss❡s ♠❛t❡r✐❛✐s✳

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✶✷

♠♦✈❡✲s❡ ❝♦♠ ✈❡❧♦❝✐❞❛❞❡s s✉♣❡rsô♥✐❝❛s✳ ◆♦ ❡♥t❛♥t♦✱ ❡♠ ❡st✉❞♦s ❛♥❛❧✐s❛♥❞♦ ❛ ✈❡❧♦❝✐✲ ❞❛❞❡ ❞❡ ♣ó❧❛r♦♥s ❡♠ ❛❧t♦s r❡❣✐♠❡s ❞❡ ❝❛♠♣♦ ❡❧étr✐❝♦✱ ❙t❛❢strö♠ ❡ s❡✉s ❝♦❧❛❜♦r❛❞♦r❡s ♠♦str❛♠ q✉❡✱ ❡♠ ❞❡t❡r♠✐♥❛❞♦s r❡❣✐♠❡s✱ ♦ ♣ó❧❛r♦♥ ❛❞q✉✐r❡ ✈❡❧♦❝✐❞❛❞❡s s✉♣❡rsô♥✐❝❛s ❬✹✾❪✳

❊st✉❞♦s s♦❜r❡ ♦✉tr♦s ❡❢❡✐t♦s q✉❡ r❡s✉❧t❛r❛♠ ♥❛ r❡❞✉çã♦ ❞❛ ❡st❛❜✐❧✐❞❛❞❡ ❞❡ ♣ó❧❛r♦♥s✱ t❛✐s ❝♦♠♦ ❝♦❧✐sã♦ ❡♥tr❡ ♣♦rt❛❞♦r❡s ❞❡ ❝❛r❣❛ ❝♦♠ ❞✐❢❡r❡♥t❡s ❞❡❢❡✐t♦s ❡ ✐♠✲ ♣✉r❡③❛s✱ ❢♦r❛♠ ♣✉❜❧✐❝❛❞♦s r❡❝❡♥t❡♠❡♥t❡ ♣♦r ❙✐❧✈❛ ❡ s❡✉s ❝♦❧❛❜♦r❛❞♦r❡s ❬✺✵✱ ✺✶❪✳ ◆❡ss❡s tr❛❜❛❧❤♦s ❢♦✐ ✐♥✈❡st✐❣❛❞❛ ❛ ❡st❛❜✐❧✐❞❛❞❡ ❞❡ ♣ó❧❛r♦♥s s♦❜ ❝♦❧✐sõ❡s ❝♦♠ ❞❡✲ ❢❡✐t♦s ❡ ✐♠♣✉r❡③❛s ❡♠ ♣♦❧í♠❡r♦s ❝♦♥❥✉❣❛❞♦s ✉t✐❧✐③❛♥❞♦ ♦ ♠♦❞❡❧♦ ❙❙❍ ♠♦❞✐✜❝❛❞♦ ♣❛r❛ ✐♥❝❧✉✐r ✉♠ ❝❛♠♣♦ ❡❧étr✐❝♦ ❡①t❡r♥♦✱ ✐♥t❡r❛çõ❡s ❡❧étr♦♥✲❡❧étr♦♥ ❡ ✐♥t❡r❛çõ❡s ❝♦♠ ✐♠♣✉r❡③❛s ❬✺✵❪✳ ❈♦♠ ❛ ❛♣r♦①✐♠❛çã♦ ❞❡ ❍❛rtr❡❡✲❋♦❝❦ ♥ã♦✲r❡str✐t❛ ❞❡♣❡♥❞❡♥t❡ ❞♦ t❡♠♣♦✱ ❛♠❜♦s ❡st✉❞♦s ♠♦str❛r❛♠ q✉❡ ♥❛s ✐♥t❡r❛çõ❡s ♣ó❧❛r♦♥✲só❧✐t♦♥✱ ❡①✐st❡ ✉♠❛ ❣r❛♥❞❡ tr♦❝❛ ❞❡ ❡♥❡r❣✐❛ tr❛♥s❧❛❝✐♦♥❛❧ ❡♥tr❡ ❛s q✉❛s✐✲♣❛rtí❝✉❧❛s✱ s❡♥❞♦ ❛ ✈❛r✐❛çã♦ ❞❛ ❡♥❡r❣✐❛ ❞♦ ♣ó❧❛r♦♥ ♠❛✐♦r q✉❡ ❛ ❞♦ só❧✐t♦♥✳

❚❛♠❜é♠ ❢♦✐ ♦❜s❡r✈❛❞♦ ♥❡ss❡s ❡st✉❞♦s q✉❡ ♦s ♣ó❧❛r♦♥s ♥ã♦ sã♦ ❛♥✐q✉✐❧❛❞♦s ❡♠ r❛③ã♦ ❞❡ ❝♦❧✐sõ❡s ❝♦♠ ❞✐❢❡r❡♥t❡s ❞❡❢❡✐t♦s✳ P♦rt❛♥t♦✱ ❝♦❧✐sõ❡s ❡♥tr❡ ♣ó❧❛r♦♥s ❡ só❧✐✲ t♦♥s ♥ã♦ sã♦ r❡s♣♦♥sá✈❡✐s ♣❡❧❛ r❡❞✉çã♦ ❞❡ ❡st❛❜✐❧✐❞❛❞❡ ❞❡ ♣ó❧❛r♦♥s✳ ❊st❛ ♠❡t♦❞♦❧♦✲ ❣✐❛ t❛♠❜é♠ ❢♦✐ ✉t✐❧✐③❛❞❛ ♣❛r❛ ❛♥❛❧✐s❛r ❛ ❞✐♥â♠✐❝❛ ❞❡ ♣ó❧❛r♦♥s ❡♠ ♣♦❧í♠❡r♦s ❝♦♥❥✉❣❛✲ ❞♦s ❞♦♣❛❞♦s ❝♦♠ ✐♠♣✉r❡③❛s ❬✺✶❪✳ ❊st❛ ❛❜♦r❞❛❣❡♠ ❧❡✈♦✉ ❛ ❝♦♥❝❧✉sã♦ ❞❡ q✉❡ ♣ó❧❛r♦♥s ♣♦s✐t✐✈❛♠❡♥t❡ ❝❛rr❡❣❛❞♦s ❡stã♦ s✉❥❡✐t♦s ❛ s❡r❡♠ ❛tr❛í❞♦s ♣♦r ✐♠♣✉r❡③❛s ❞♦❛❞♦r❛s ❡ r❡♣❡❧✐❞♦s ♣♦r ✐♠♣✉r❡③❛s ❛❝❡✐t❛❞♦r❛s✳ ❊st❡s r❡s✉❧t❛❞♦s ❧❡✈❛r❛♠ à ❝♦♥❝❧✉sã♦ ❞❡ q✉❡ ♣ó❧❛r♦♥s ❡♠ ♠♦✈✐♠❡♥t♦ sã♦ ❡stá✈❡✐s t❛♠❜é♠ q✉❛♥❞♦ ♦s ❡❢❡✐t♦s ❞❡ ✐♠♣✉r❡③❛s sã♦ ❝♦♥s✐❞❡r❛❞♦s✳

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✶✸

♣❛r❛❧❡❧♦s✱ ♦ ♣ó❧❛r♦♥ ♣♦❞❡ ❢❛❝✐❧♠❡♥t❡ ♣❛ss❛r ❛tr❛✈és ❞♦ é①❝✐t♦♥✳ ◆♦ ❡♥t❛♥t♦✱ s❡ ♦ ♣ó❧❛r♦♥ ❡ ♦ é①❝✐t♦♥ ♣♦ss✉ír❡♠ s♣✐♥s ❛♥t✐✲♣❛r❛❧❡❧♦s✱ ❡①✐st✐rá ✉♠❛ ❢♦rt❡ r❡♣✉❧sã♦ ❡♥tr❡ ❡❧❡s✳ ❚❛♠❜é♠✱ ❛✉♠❡♥t❛❞♦ ♦ ❝❛♠♣♦ ❡❧étr✐❝♦ ❡①t❡r♥♦✱ ❛ ❞✐♥â♠✐❝❛ ❞❡ ❝♦❧✐sã♦ ♠✉❞❛ ❜r✉s❝❛♠❡♥t❡✱ r❡s✉❧t❛♥❞♦ ♥❛ ❞✐ss♦❝✐❛çã♦ ❞♦ ♣ó❧❛r♦♥ ❛♣ós ❝♦❧✐❞✐r ❝♦♠ ♦ é①❝✐t♦♥✱ ❝♦♠ ♦ ♠❡s♠♦ ♠❛♥t❡♥❞♦ s✉❛ ✐♥t❡❣r✐❞❛❞❡✳

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❈❛♣ít✉❧♦ ✷

▼♦❞❡❧❛♠❡♥t♦ ❚❡ór✐❝♦

◆♦ ♣r❡s❡♥t❡ ❝❛♣ít✉❧♦ ❛♣r❡s❡♥t❛✲s❡ ✉♠❛ r❡✈✐sã♦ ❜✐❜❧✐♦❣rá✜❝❛ ❞❛ ❢♦r♠✉❧❛çã♦ t❡ór✐❝❛ ♥❡❝❡ssár✐❛ ♣❛r❛ ❛ ❝♦♠♣r❡❡♥sã♦ ❞♦s ❢❡♥ô♠❡♥♦s ❡①♣❧♦r❛❞♦s ♥❡ss❡ tr❛❜❛❧❤♦✳ ❯♠ ❜r❡✈❡ r❡s✉♠♦ ❞♦ ♣r♦❜❧❡♠❛ ❞❡ ♠✉✐t♦s ❝♦r♣♦s✱ ♠♦❞❡❧♦ ❛❞♦t❛❞♦ ♣❛r❛ ♦ s✐st❡♠❛ ❡♠ ❛♥á❧✐s❡✱ é ❢♦r♥❡❝✐❞♦✳ ❖ ❡♥t❡♥❞✐♠❡♥t♦ ❞❛s ❢❡rr❛♠❡♥t❛s ♠❛t❡♠át✐❝❛s ❛♣r❡s❡♥t❛❞❛s ❛q✉✐ é ❢✉♥❞❛♠❡♥t❛❧ ♣❛r❛ ❛ ❝♦♠♣r❡❡♥sã♦ ❞♦ ♠♦❞❡❧♦ ❙❙❍ ♠♦❞✐✜❝❛❞♦✱ ❛♣r❡s❡♥t❛❞♦ ♥♦ ❝❛♣ít✉❧♦ s❡❣✉✐♥t❡✳

✷✳✶ ❖ Pr♦❜❧❡♠❛ ❞❡ ▼✉✐t♦s ❈♦r♣♦s

❖s ♣♦❧í♠❡r♦s ❝♦♥❞✉t♦r❡s sã♦ ♠♦❧é❝✉❧❛s ❢♦r♠❛❞❛s ❛ ♣❛rt✐r ❞❡ ✉♥✐❞❛❞❡s ❡s✲ tr✉t✉r❛✐s ♠❡♥♦r❡s ✭♠♦♥ô♠❡r♦s✮✱ ❝♦♠♦ ♦ ❣r✉♣♦ CH✳ ❚❛✐s ♠♦♥ô♠❡r♦s ♣♦r s✉❛ ✈❡③

sã♦ ❝♦♥st✐t✉í❞♦s ♣♦r ♥ú❝❧❡♦s ❡ ❡❧étr♦♥s✱ ❝❛r❛❝t❡r✐③❛♥❞♦ ❛ss✐♠ ✉♠ s✐st❡♠❛ ❞❡ ♠✉✐t♦s ❝♦r♣♦s✳ ❖ tr❛t❛♠❡♥t♦ q✉â♥t✐❝♦ ❞❡ss❡ s✐st❡♠❛ é ❢❡✐t♦ ✈✐❛ ❡q✉❛çã♦ ❞❡ ❙❝❤rö♥❞✐♥❣❡r ❞❡♣❡♥❞❡♥t❡ ❞♦ t❡♠♣♦✱

i~∂

∂t|Ψi=H|Ψi. ✭✷✳✶✮

P❛r❛ s✉❛ ❛♥á❧✐s❡✱ é ♣♦ssí✈❡❧ ❞❡s❝r❡✈❡r ♦ ♣r♦❜❧❡♠❛ ❝♦♠♦ ♠♦str❛ ❛ ❋✐❣✉r❛ ✷✳✶✱ ♦♥❞❡ ❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ ❞♦✐s ❡❧étr♦♥s✱ i❡ j é ❞❛❞❛ ♣♦r rij =|ri−rj| ❡ ❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ ❞♦✐s

♥ú❝❧❡♦s✱ A ❡ B✱ é ❞❡✜♥✐❞❛ ❝♦♠♦ RAB =|RA−RB|✳ ❏á ❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ ✉♠ ♥ú❝❧❡♦

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✶✺

❡ ✉♠ ❡❧étr♦♥ é ❞❡✜♥✐❞❛✱ ♣♦r ❡①❡♠♣❧♦✱ ❝♦♠♦ riA = |ri −RA|✳ ❈♦♠ ✐ss♦✱ ♦s ❣r❛✉s

❋✐❣✉r❛ ✷✳✶✿ ❙✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ♠♦❧❡❝✉❧❛r❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ ♠✉✐t♦s ❝♦r♣♦s✳

❞❡ ❧✐❜❡r❞❛❞❡ ❡❧❡trô♥✐❝♦ ❡ ♥✉❝❧❡❛r sã♦ ❞❡s❝r✐t♦s ♣♦r ✉♠ ❍❛♠✐❧t♦♥✐❛♥♦ HT ❞❡ ♠✉✐t♦s

❝♦r♣♦s✱

HT =Hn−n({❘}) +He−e({r}) +He−n({r,❘}). ✭✷✳✷✮

❖♥❞❡ Hn−n ❞❡s❝r❡✈❡ ❛ ❡♥❡r❣✐❛ ❞❡ ✐♥t❡r❛çã♦ ♥ú❝❧❡♦✲♥ú❝❧❡♦✱ ✐st♦ é✱ ❛ ❡♥❡r❣✐❛ ❝✐♥ét✐❝❛

❞♦ ♥ú❝❧❡♦ ❡ ♠✉t✉❛♠❡♥t❡ s✉❛ ❡♥❡r❣✐❛ ♣♦t❡♥❝✐❛❧ ❛❞✈✐♥❞❛ ❞❡ ✐♥t❡r❛çõ❡s ❝♦✉❧♦♠❜✐❛♥❛s✳ ❖ t❡r♠♦He−e ❝❛r❛❝t❡r✐③❛ ❛ ❡♥❡r❣✐❛ ❞❡ ✐♥t❡r❛çã♦ ❡❧étr♦♥✲❡❧étr♦♥✱ ❞❡s❝r❡✈❡♥❞♦ ❛ ❡♥❡r✲

❣✐❛ ❝✐♥ét✐❝❛ ❞♦s ❡❧étr♦♥s ❡ s✉❛s ❡♥❡r❣✐❛s ♣♦t❡♥❝✐❛s✳ P♦r ✜♠✱ ♦ t❡r♠♦ He−n ❞❡s✲

❝r❡✈❡ ❛ ❡♥❡r❣✐❛ ♣♦t❡♥❝✐❛❧ ❞❡✈✐❞♦ ❛s ✐♥t❡r❛çõ❡s ❝♦✉❧♦♠❜✐❛♥❛s ❡♥tr❡ ❡❧étr♦♥s ❡ ♥ú❝❧❡♦s✳ ❊s❝r❡✈❡♥❞♦ ❡①♣❧✐❝✐t❛♠❡♥t❡ ♦ ❍❛♠✐❧t♦♥✐❛♥♦ ❞❡ ♠✉✐t♦s ❝♦r♣♦s✱ ♦♥❞❡ ❝♦♥s✐❞❡r♦✉✲s❡ ✉♥✐❞❛❞❡s ❛tô♠✐❝❛s ❬✺✸❪✱ MA ❝♦♠♦ ❛ ♠❛ss❛ ❞♦ ♥ú❝❧❡♦ A ❡ ZA s❡✉ ♥ú♠❡r♦ ❛tô♠✐❝♦✱

♦❜tê♠✲s❡

HT = − N X i=1 1 2∇ 2 i − M X A=1 1 2MA∇

2 A− N X i=1 M X A=1 ZA riA + N X i=1 N X j>i 1 rij + M X A=1 M X B>A

ZAZB

RAB

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✶✻

✷✳✷ ❆♥t✐✲s✐♠❡tr✐❛ ❞❛ ❋✉♥çã♦ ❞❡ ❖♥❞❛ ❡ ♦s ❉❡t❡r♠✐♥❛♥t❡s ❞❡

❙❧❛t❡r

❖ ♣r✐♥❝í♣✐♦ ❞❛ ✐♥❞✐st✐♥❣✉✐❜✐❧✐❞❛❞❡ ♣❛r❛ s✐st❡♠❛s ❞❡ ❢ér♠✐♦♥s r❡q✉❡r q✉❡ ❛ ❢✉♥çã♦ ❞❡ ♦♥❞❛✱ q✉❡ ❝❛r❛❝t❡r✐③❛ ✉♠ s✐st❡♠❛ ❞❡ ♠✉✐t♦s ❡❧étr♦♥s✱ s❡❥❛ ❛♥t✐ss✐♠étr✐❝❛ ❝♦♠ r❡❧❛çã♦ ❛ ✉♠❛ ✐♥✈❡rsã♦ ❞❡ ❝♦♦r❞❡♥❛❞❛sx✭♣♦s✐çã♦ ❡ s♣✐♥✮ ❞❡ ❞♦✐s ❞❡ss❡s ❡❧étr♦♥s✱

❞❡ ♠❛♥❡✐r❛ q✉❡

Ψ(x1, ...xi, ...xj, ...xN) = −Ψ(x1, ...xj, ...xi, ...xN). ✭✷✳✹✮

❈♦♠♦ ❛ ❛♥t✐✲s✐♠❡tr✐❛ é ✉♠❛ ❝❛r❛❝t❡ríst✐❝❛ ✐♥trí♥s❡❝❛ ❛♦s ❞❡t❡r♠✐♥❛♥t❡s✱ ✉♠❛ ♠❛♥❡✐r❛ ❝♦♥✈❡♥✐❡♥t❡ ❞❡ s❡ ❡①♣r❡ss❛r ❛ ❢✉♥çã♦ ❞❡ ♦♥❞❛ ❡❧❡trô♥✐❝❛✱ ♣❛r❛ ✉♠ s✐st❡♠❛ ❞❡ ♠✉✐t♦s ❡❧étr♦♥s✱ é ❡①♣❛♥❞✐✲❧❛ ❡♠ t❡r♠♦s ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❝♦♠♣❧❡t♦ ❞❡ ❢✉♥çõ❡s✱ ❝❤❛♠❛❞❛s ❞❡ ❉❡t❡r♠✐♥❛♥t❡s ❞❡ ❙❧❛t❡r ❬✺✸❪✳ ❊st❡s ❞❡t❡r♠✐♥❛♥t❡s ♣♦❞❡♠ s❡r ❞❡✜♥✐❞♦s ❝♦♠♦ ✉♠❛ té❝♥✐❝❛ ♠❛t❡♠át✐❝❛✱ ✉t✐❧✐③❛❞❛ ❡♠ ♠❡❝â♥✐❝❛ q✉â♥t✐❝❛✱ ♣❛r❛ ❣❡r❛r ❢✉♥çõ❡s ❞❡ ♦♥❞❛ ❛♥t✐✲s✐♠étr✐❝❛s q✉❡ ❞❡s❝r❡✈❛♠ ♦s ❡st❛❞♦s ❝♦❧❡t✐✈♦s ❞❡ ✈ár✐♦s ❢ér♠✐♦♥s✳ P❛r❛ ✐ss♦✱ ♦s ❉❡t❡r♠✐♥❛♥t❡s ❞❡ ❙❧❛t❡r ❞❡✈❡♠ ♦❜❡❞❡❝❡r ❛♦ Pr✐♥❝í♣✐♦ ❞❛ ❊①❝❧✉sã♦ ❞❡ P❛✉❧✐✱ q✉❡ é ✉♠ ❞♦s ♣♦st✉❧❛❞♦s ❞❛ ♠❡❝â♥✐❝❛ q✉â♥t✐❝❛✳

P❛r❛ ❞❡s❝r❡✈❡r ❝♦♠♣❧❡t❛♠❡♥t❡ ♦ ❡❧étr♦♥ é ♣r❡❝✐s♦ ❡s♣❡❝✐✜❝❛r s❡✉s ❣r❛✉s ❞❡ ❧✐❜❡r❞❛❞❡ ❡s♣❛❝✐❛✐s ❡ ❞❡ s♣✐♥✳ P❛r❛ ✐ss♦✱ ❞❡✜♥✐✲s❡ ❞✉❛s ❢✉♥çõ❡s ♦rt♦♥♦r♠❛✐s α(ω)

❡ β(ω)✱ ✐st♦ é✱ s♣✐♥ ✉♣ ❡ s♣✐♥ ❞♦✇♥✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❆ ❢✉♥çã♦ ❞❡ ♦♥❞❛ ♣❛r❛ ✉♠

❡❧étr♦♥ q✉❡ ❞❡s❝r❡✈❡ ❛♠❜♦s s✐♠✉❧t❛♥❡❛♠❡♥t❡✱ ❞✐str✐❜✉✐çõ❡s ❡s♣❛❝✐❛✐s ✭ψ(x)✮ ❡ ❞❡

s♣✐♥ ✭α(ω) ♦✉ β(ω)✮✱ é ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ s♣✐♥ ♦r❜✐t❛❧ χ(①)✱ ♦♥❞❡ ① ✐♥❞✐❝❛ q✉❡ ♦ s♣✐♥

♦r❜✐t❛❧ ❞❡s❝r❡✈❡ ❛♠❜❛s ❛s ❝♦rr❞❡♥❛❞❛s✱ ❡s♣❛❝✐❛✐s ❡ ❞❡ s♣✐♥✳ ❆ss✐♠✱ ✉♠ s♣✐♥ ♦r❜✐❛❧ é ❝❛r❛❝t❡r✐③❛❞♦ ❝♦♠♦ ♠♦str❛❞♦ ❛ s❡❣✉✐r✳

χ(x) =

        

ψ(r)α(ω)

♦✉

ψ′₍_r₎_β₍_ω₎

✭✷✳✺✮

❖ ♦r❜✐t❛❧ ❡s♣❛❝✐❛❧ é ✉♠❛ ❢✉♥çã♦ ❞♦ ✈❡t♦r ♣♦s✐çã♦ r✳ ❉❡ss❛ ♠❛♥❡✐r❛✱ t❛❧