❯♥✐✈❡rs✐❞❛❞❡ ❊st❛❞✉❛❧ ❞❡ ▼❛r✐♥❣á
Pr♦❣r❛♠❛ ❞❡ Pós✲❣r❛❞✉❛çã♦ ❡♠ ❋ís✐❝❛
❱✐t♦r ❙❛♥t❛❡❧❧❛ ❩❛♥✉t♦
Pr❡ssã♦ ❞❡ ❘❛❞✐❛çã♦✿
s♦❜r❡ ♦s ❡❢❡✐t♦s ❞❛s ❢♦rç❛s ❞❡ r❛❞✐❛çã♦
❡♠ á❣✉❛
❯♥✐✈❡rs✐❞❛❞❡ ❊st❛❞✉❛❧ ❞❡ ▼❛r✐♥❣á
Pr♦❣r❛♠❛ ❞❡ Pós✲❣r❛❞✉❛çã♦ ❡♠ ❋ís✐❝❛
❱✐t♦r ❙❛♥t❛❡❧❧❛ ❩❛♥✉t♦
Pr❡ssã♦ ❞❡ ❘❛❞✐❛çã♦✿
s♦❜r❡ ♦s ❡❢❡✐t♦s ❞❛s ❢♦rç❛s ❞❡ r❛❞✐❛çã♦ ❡♠ á❣✉❛
❚❡s❡ ❞❡ ❉♦✉t♦r❛❞♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ ❉❡♣❛r✲ t❛♠❡♥t♦ ❞❡ ❋ís✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❊st❛✲ ❞✉❛❧ ❞❡ ▼❛r✐♥❣á ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ❉♦✉t♦r ❡♠ ❋ís✐❝❛
❖r✐❡♥t❛çã♦✿
Pr♦❢✳ ❉r✳ ◆❡❧s♦♥ ●✉✐❧❤❡r♠❡ ❈❛st❡❧❧✐ ❆str❛t❤ ✲ ❯❊▼ ✭❖r✐❡♥t❛❞♦r✮ Pr♦❢✳ ❉r✳ ▲✉✐s ❈❛r❧♦s ▼❛❧❛❝❛r♥❡ ✲ ❯❊▼ ✭❈♦♦r✐❡♥t❛❞♦r✮
❇❛♥❝❛ ❊①❛♠✐♥❛❞♦r❛✿
Pr♦❢✳ ❉r✳ ◆❡❧s♦♥ ●✉✐❧❤❡r♠❡ ❈❛st❡❧❧✐ ❆str❛t❤ ✲ ❯❊▼ ✭❖r✐❡♥t❛❞♦r✮ Pr♦❢✳ ❉r✳ ❈❛r❧♦s ❏❛❝✐♥t♦ ❞❛ ❙✐❧✈❛ ✲ ❯❋❆▲
Pr♦❢❛✳ ❉r❛✳ ❆♥❞r❡ss❛ ◆♦✈❛ts❦✐ ✲ ❯❊P● Pr♦❢✳ ❉r✳ ❏✉r❛♥❞✐r ❍✐❧❧♠❛♥♥ ❘♦❤❧✐♥❣ ✲ ❯❊▼ Pr♦❢✳ ❉r✳ ❍❛r♦❧❞♦ ❱❛❧❡♥t✐♥ ❘✐❜❡✐r♦ ✲ ❯❊▼
Pr♦❢✳ ❉r✳ ▲❡❛♥❞r♦ ❍❡r❝✉❧❛♥♦ ❞❛ ❙✐❧✈❛ ✲ ❯❚❋P❘✴❙❛♥t❛ ❍❡❧❡♥❛ ✭❙✉♣❧❡♥t❡✮ Pr♦❢❛✳ ❉r❛✳ ❋r❛♥❝✐❡❧❧❡ ❙❛t♦ ✲ ❯❊▼ ✭❙✉♣❧❡♥t❡✮
Dados Internacionais de Catalogação na Publicação (CIP) (Biblioteca Central - UEM, Maringá, PR, Brasil)
Zanuto, Vitor Santaella
Z34p Pressão de radiação : sobre os efeitos das forças de radiação em água / Vitor Santaella Zanuto. -- Maringá, 2015.
vii, 103 f. : il. (algumas color.), figs., tabs.
Orientador: Prof. Dr. Nelson Guilherme Castelli Astrath.
Coorientador: Prof. Dr. Luis Carlos Malacarne. Tese (doutorado) - Universidade Estadual de
Maringá, Programa de Pós-Graduação em Física, 2015.
1. Pressão de radiação. 2. Interação luz e
matéria. 3. Efeitos de superfície - Eletro/mecânico. 4. Espelho térmico. 5. Controvérsia de Abraham-Minkowski. I. Astrath, Nelson Guilherme Castelli, orient. II. Malacarne, Luis Carlos, coorient. III. Universidade Estadual de Maringá. Programa de Pós-Graduação em Física. IV. Título.
❉❡❞✐❝♦ ❛♦s ♠❡✉s ♣❛✐s✱ ❋át✐♠❛ ❡ ❱❛❧❝✐♥❡✐ q✉❡✱ ♠❡s♠♦ ❡♥❢r❡♥t❛♥❞♦ ♠✉✐t❛s ❞✐✜❝✉❧❞❛❞❡s✱ ♣r✐♦r✐③❛r❛♠ ❛ ❡❞✉❝❛çã♦ ❞❡ s❡✉s ✜❧❤♦s✳
❚❛♠❜é♠ ❞❡❞✐❝♦ à ♠✐♥❤❛ ❛✈ó✱ ❉♦♥❛ ❍✐❧❞❛✱ q✉❡ s❡♠♣r❡ q✉✐s ✉♠ ❞♦✉t♦r ♥❛ ❢❛♠í❧✐❛✳
❆❣r❛❞❡❝✐♠❡♥t♦s
➱ ❞✐❢í❝✐❧ ❛❣r❛❞❡❝❡r à t♦❞❛s ♣❡ss♦❛s q✉❡ ❞❡ ❛❧❣✉♠ ♠♦❞♦✱ s❡❥❛ ♥♦s ❜♦♥s ♠♦♠❡♥t♦s ♦✉ ♥♦s ♠❛✐s ❛❞✈❡rs♦s✱ ✜③❡r❛♠ ♦✉ ❢❛③❡♠ ♣❛rt❡ ❞❛ ♠✐♥❤❛ ✈✐❞❛✱ ♣♦r ✐ss♦ ♣r✐♠❡✐r❛♠❡♥t❡ ❛❣r❛❞❡ç♦ à t♦❞♦s✳
▼❛s ❡♠ ❡s♣❡❝✐❛❧✱ ❛❣r❛❞❡ç♦ ❛♦ ♠❡✉ ♦r✐❡♥t❛❞♦r✱ Pr♦❢❡ss♦r ◆❡❧s♦♥ ●✳ ❈✳ ❆str❛t❤✱ q✉❡ t❡♠ ♠❡ ❣✉✐❛❞♦ ❡♠ t♦❞❛ ♠✐♥❤❛ ❝❛♠✐♥❤❛❞❛ ❝✐❡♥tí✜❝❛ ❛té ❛q✉✐✳ ❖❜r✐❣❛❞♦ ♣❡❧❛ ♣❛❝✐ê♥❝✐❛✱ ♦r✐❡♥t❛çã♦✱ ❛♠✐③❛❞❡ ❡ ❝♦♥✜❛♥ç❛ ❞❡♣♦s✐t❛❞❛ ❡♠ ♠✐♠❀
❆♦s ♠❡✉s ♣❛✐s ❡ ✐r♠ã♦s ♣❡❧♦ ✐♥❝❡♥t✐✈♦ ❡ ❛♠♦r❀
➚ ♠✐♥❤❛ ♥❛♠♦r❛❞❛✱ ❘❛❢❛❡❧❛✱ ♣❡❧❛ ❞❡❞✐❝❛çã♦✱ ❝♦♠♣r❡❡♥sã♦ ❡ ♣❛❝✐ê♥❝✐❛ q✉❡ t❡✈❡✱ ❡s♣❡r♦ q✉❡ ♣♦ss❛ r❡❝♦♠♣❡♥s❛✲❧á ♣♦r t✉❞♦❀
❆♦s ❛♠✐❣♦s ❞❡ ❧♦♥❣❛ ❞❛t❛✿ ❇❛r❞❛❤✱ P❧í♥✐♦✱ ❖s❝❛r✱ ❩✐rt♦✱ ❩é✱ ❘❛❢❛❡❧✱ ❚♦♥❤ã♦ ❡ ●❛rç❛❀
❆♦s ❝♦❧❡❣❛s ❞❡ ❧❛❜♦r❛tór✐♦✱ ▲❡❛♥❞r♦✱ ●✉st❛✈♦✱ ❖tá✈✐♦✱ ❊❧t♦♥✱ ❱✐♥✐❝✐✉s✱ ●✉✲ t✐❡rr❡③✱ ●✐✱ ❘♦❣ér✐♦✱ ❆♥❣❡❧❛✱ P❛❜❧♦✱ ❲❡s❧❡②✱ ❚❤✐❛❣♦ ▼✳ ❡ ❚❤✐❛❣♦ P✳✱ ♣❡❧❛ ❛❥✉❞❛ ❡ ❞❡s❝♦♥tr❛çã♦ ♥♦s ✈ár✐♦s ❤♦rár✐♦s ❞♦ ❝❛❢é❀
❆♦ ❘♦❜s♦♥✱ ❘❛q✉❡❧ ❡ ▼❛r❝❡❧♦✱ ♣❡❧❛ ❛♠✐③❛❞❡✱ ❡①♣❡r✐ê♥❝✐❛s ❞❡ ✈✐❞❛ tr❛♥s♠✐t✐❞❛s ❡ ♣♦r ♠❡ ❛❝♦♠♣❛♥❤❛r ♥❛s ❛✈❡♥t✉r❛s q✉❡ ❛ ♣ós✲❣r❛❞✉❛çã♦ ♥♦s ♣r♦♣♦r❝✐♦♥❛♠❀
❆♦s ♣r♦❢❡ss♦r❡s ❞♦ ❣r✉♣♦✱ ❆♥tô♥✐♦ ▼❡❞✐♥❛ ◆❡t♦✱ ❏✉r❛♥❞✐r ❍✳ ❘♦❤❧✐♥❣✱ ❆♥tô♥✐♦ ❈✳ ❇❡♥t♦✱ ❋r❛♥❝✐❡❧❧❡ ❙❛t♦✱ ▲✉✐s ❈✳ ▼❛❧❛❝❛r♥❡✱ ❡ ▼❛✉r♦ ▲✳ ❇❛❡ss♦✱ ♣♦r ♥♦s ❢♦r♥❡❝❡r❡♠ t♦❞♦s s❡✉s ❝♦♥❤❡❝✐♠❡♥t♦s ♣❛r❛ q✉❡ ♣♦ss❛♠♦s ❛♠♣❧✐❛r ♦s ♥♦ss♦s❀
❆♦ ♣r♦❢❡ss♦r ❙t❡♣❤❡♥ ❊✳ ❇✐❛❧❦♦✇s❦✐✱ ♣♦r t❡r ♠❡ ❛❝❡✐t❛❞♦ ❡♠ s❡✉ ❧❛❜♦r❛tór✐♦ ♥❛ ❯t❛❤ ❙t❛t❡ ❯♥✐✈❡rs✐t② ❡ ♠❡ ♣♦ss✐❜✐❧✐t❛r ✉♠❛ ❞❛s ❡①♣❡r✐ê♥❝✐❛s ♠❛✐s ♣r♦❞✉t✐✈❛s ❞❡ ♠✐♥❤❛ ✈✐❞❛❀
❆♦s ❢✉♥❝✐♦♥ár✐♦s ❞♦ ❉❋■✲❯❊▼ ❡✱ ❡♠ ❡s♣❡❝✐❛❧✱ à ▼ô♥✐❝❛❀
➚s ❛❣ê♥❝✐❛s ❞❡ ❢♦♠❡♥t♦✿ ❈❛♣❡s✱ ❈◆Pq ❡ ❋✉♥❞❛çã♦ ❆r❛✉❝ár✐❛✱ ♣❡❧♦ ❛♣♦✐♦ ✜✲ ♥❛♥❝❡✐r♦✳
❘❡s✉♠♦
❉♦s ❡❢❡✐t♦s ✐♥❞✉③✐❞♦s ♣❡❧❛ ✐♥t❡r❛çã♦ r❛❞✐❛çã♦✲♠❛tér✐❛✱ ✉♠❛ ❞❛s q✉❡stõ❡s ♠❛✐s ❞✉r❛❞♦✉r❛s ❛✐♥❞❛ ❡①✐st❡♥t❡ é ❛ ❞❡✜♥✐çã♦ ❞♦ ♠♦♠❡♥t♦ ❞♦ ❢ót♦♥ ✈✐❛❥❛♥❞♦ ♣♦r ✉♠ ♠❛t❡✲ r✐❛❧ ❞✐❡❧étr✐❝♦✳ ❉✐✈❡rs♦s ❢♦r♠❛❧✐s♠♦s ❢♦r❛♠ ❞❡s❡♥✈♦❧✈✐❞♦s❀ ❡♥tr❡t❛♥t♦✱ ♦s ❢♦r♠❛❧✐s♠♦s ❞❡ ❆❜r❛❤❛♠ ❡ ▼✐♥❦♦✇s❦✐ ♦❜t✐✈❡r❛♠ ♠❛✐♦r ❞❡st❛q✉❡ ♣♦r s❡r❡♠ ❝♦♥✢✐t✉♦s♦s✱ ❝r✐❛♥❞♦ ❛ ❝♦♥tr♦✈érs✐❛ ❞❡ ❆❜r❛❤❛♠✲▼✐♥❦♦✇s❦✐✳ ▼✐♥❦♦✇s❦✐ ♣r♦♣ôs q✉❡ ♦ ♠♦♠❡♥t♦ ❞♦ ❢ót♦♥ ❡♠ ✉♠ ❞✐❡❧étr✐❝♦ s❡r✐❛ ♣r♦♣♦r❝✐♦♥❛❧ ❛♦ s❡✉ í♥❞✐❝❡ ❞❡ r❡❢r❛çã♦✱ n✱ ❡ ❛♦ ♠♦♠❡♥t♦ ❞♦
❢ót♦♥ ♥♦ ✈á❝✉♦✱ p~0✱ t❛❧ ❝♦♠♦ p~M = n ~p0✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ❆❜r❛❤❛♠ ♣r♦♣ôs q✉❡ ♦ ♠♦♠❡♥t♦ ❞♦ ❢ót♦♥ ♥♦ ♠❡✐♦ s❡r✐❛ ♣r♦♣♦r❝✐♦♥❛❧ ❛♦ ♠♦♠❡♥t♦ ♥♦ ✈á❝✉♦ ❡ ✐♥✈❡rs❛♠❡♥t❡ ♣r♦♣♦r❝✐♦♥❛❧ ❛♦ í♥❞✐❝❡ ❞❡ r❡❢r❛çã♦ ❞♦ ♠❡✐♦✱ ❞❡ t❛❧ ❢♦r♠❛ q✉❡ p~A =p~0/n✳ ❆té ❛❣♦r❛✱ ♥ã♦ ❢♦✐ ♣♦ssí✈❡❧ ♦❜t❡r ❛ r❡s♣♦st❛ ♣❛r❛ ❡ss❛ q✉❡stã♦ ♣♦r ♥❡♥❤✉♠ ♠ét♦❞♦ ❞✐r❡t♦✳ ▼❛s ❛ ♣❛ss❛❣❡♠ ❞❡ ✉♠ ❢ót♦♥ ♣♦r ✉♠ ♠❡✐♦ ❡①❡r❝❡ ✉♠❛ ❢♦rç❛✱ ❝❛✉s❛♥❞♦ ✉♠❛ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦ s♦❜r❡ ❡ss❡ ♠❡✐♦✱ q✉❡ t❛♠❜é♠ ❥á ✈❡♠ s❡♥❞♦ ❡st✉❞❛❞❛ ❛ ♠✉✐t♦ t❡♠♣♦✳ ❊st❡ tr❛❜❛❧❤♦ ❛♣r❡s❡♥t❛ ✉♠ ❡st✉❞♦ s♦❜r❡ ♦s ❡❢❡✐t♦s ❞❛s ❢♦rç❛s ✐♥❞✉③✐❞❛s ♣♦r r❛❞✐❛çã♦ ❡♠ ✐♥t❡r❢❛❝❡s ❡♥tr❡ ♠❛t❡r✐❛✐s ❞✐❡❧étr✐❝♦s✱ ❡s♣❡❝✐✜❝❛♠❡♥t❡✿ ♥❛ ✐♥t❡r❢❛❝❡ ❛r✴á❣✉❛✳ Pr♦✲ ♣♦r❝✐♦♥❛ ♠❛✐s ❛✈❛♥ç♦s ♥❛ t❡♥t❛t✐✈❛ ❞❡ ❞❡✜♥✐r ♦ ✈❡r❞❛❞❡✐r♦ ♠♦♠❡♥t♦ ❞♦ ❢ót♦♥ ❡♠ ♠❡✐♦s ❞✐❡❧étr✐❝♦s ❡ ❝♦♠♦ s❡ ❞á ❛ ❢♦rç❛ ❣❡r❛❞❛ ♥❡ss❡ ♠❡✐♦✳ ➱ ✉t✐❧✐③❛❞♦ ✉♠ ❛rr❛♥❥♦ ❡①♣❡r✐♠❡♥t❛❧ ❞❛ té❝♥✐❝❛ ❞❡ ❊s♣❡❧❤♦ ❋♦t♦tér♠✐❝♦ ❛❞❛♣t❛❞♦ ❡ ❛✈❛❧✐❛✲s❡ ❛ ❞❡❢♦r♠❛çã♦ s✉♣❡r✜❝✐❛❧ ❞❛ á❣✉❛ ❡♠ ❞✐❢❡r❡♥t❡s ❝♦♥✜❣✉r❛çõ❡s ❞♦ ❛rr❛♥❥♦ ❡①♣❡r✐♠❡♥t❛❧✳ ❙ã♦ ❛♣r❡✲ s❡♥t❛❞♦s ❡①♣❡r✐♠❡♥t♦s ❡♠ q✉❡ ✉♠ ❢❡✐①❡ ❧❛s❡r ❛tr❛✈❡ss❛ ❛ ✐♥t❡r❢❛❝❡ ♥♦s s❡♥t✐❞♦s ❛r
→ á❣✉❛✱ á❣✉❛ → ❛r ❡ ❛r → á❣✉❛ → ❛r ✭❞✉♣❧❛ ❡①❝✐t❛çã♦✮✳ ❈♦♥s✐❞❡r❛✲s❡ ❛ ♠✉❞❛♥ç❛
♥❛s ❞✐♠❡♥sõ❡s r❛❞✐❛✐s ❞♦ ❢❡✐①❡ ✐♥❝✐❞❡♥t❡ ❡ ❛✐♥❞❛ ❛♥❛❧✐s❛♠♦s ♦ q✉❡ ❢♦✐ ❞✐t♦ s❡r ❛ ❡✈✐✲ ❞ê♥❝✐❛ ❡①♣❡r✐♠❡♥t❛❧ q✉❡ ❝♦♥❝♦r❞❛ ❝♦♠ ❛ ♣r❡✈✐sã♦ ❞❡ ❆❜r❛❤❛♠✳ ❚♦❞♦s ♦s r❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s sã♦ ❝♦♠♣❛r❛❞♦s ❝♦♠ ♠♦❞❡❧♦s ♥✉♠ér✐❝♦s ✉t✐❧✐③❛♥❞♦ ♦ ▼ét♦❞♦ ❞♦s ❊❧❡✲ ♠❡♥t♦s ❋✐♥✐t♦s ♣❛r❛ ❝♦♠♣r❡❡♥❞❡r ❛s ❝♦♥tr✐❜✉✐çõ❡s ❞❛s ❢♦rç❛s ❞❡ r❛❞✐❛çã♦ ❛t✉❛♥t❡s ♥❛ s✉♣❡r❢í❝✐❡ ❡ ♥♦ ✈♦❧✉♠❡ ❞❡ á❣✉❛✳
❆❜str❛❝t
❆♠♦♥❣ t❤❡ ❡✛❡❝ts ✐♥❞✉❝❡❞ ❜② t❤❡ ✐♥t❡r❛❝t✐♦♥ ♦❢ r❛❞✐❛t✐♦♥ ✇✐t❤ ♠❛tt❡r✱ ♦♥❡ ♦❢ t❤❡ ❧♦♥❣st❛♥❞✐♥❣ ✐ss✉❡s ✐s t❤❡ ❞❡✜♥✐t✐♦♥ ♦❢ t❤❡ ♠♦♠❡♥t✉♠ ♦❢ ❛ tr❛✈❡❧✐♥❣ ♣❤♦t♦♥ ✐♥ ❛ ❞✐❡❧❡❝tr✐❝ ♠❛t❡r✐❛❧✳ ❙❡✈❡r❛❧ ❢♦r♠❛❧✐s♠s ❤❛✈❡ ❜❡❡♥ ❞❡✈❡❧♦♣❡❞✱ ❛♥❞ t❤❡ ❢♦r♠✉❧❛t✐♦♥s ♦❢ ❆❜r❛❤❛♠ ❛♥❞ ▼✐♥❦♦✇s❦✐ ❤❛✈❡ ❛ttr❛❝t❡❞ ❝♦♥s✐❞❡r❛❜❧❡ ❛tt❡♥t✐♦♥ ❡s♣❡❝✐❛❧❧② ❞✉❡ t♦ t❤❡✐r ❝♦♥tr♦✈❡rs✐❛❧ ♥❛t✉r❡✱ t❤❡ s♦✲❝❛❧❧❡❞ ❆❜r❛❤❛♠✲▼✐♥❦♦✇s❦✐ ❝♦♥tr♦✈❡rs②✳ ▼✐♥❦♦✇s❦✐ ♣r♦♣♦s❡❞ t❤❛t t❤❡ ♠♦♠❡♥t✉♠ ♦❢ t❤❡ ♣❤♦t♦♥ ✐♥ ❛ ❞✐❡❧❡❝tr✐❝ ✐s ♣r♦♣♦rt✐♦♥❛❧ t♦ ✐ts r❡❢r❛❝t✐✈❡ ✐♥❞❡①✱ n✱ ❛♥❞ t♦ t❤❡ ♣❤♦t♦♥ ♠♦♠❡♥t✉♠ ✐♥ t❤❡ ✈❛❝✉✉♠✱ p~0✱ t❤❛t ✐s p~M =
n ~p0✳ ■♥ ❝♦♥tr❛st✱ ❆❜r❛❤❛♠ ♣r♦♣♦s❡❞ t❤❛t t❤❡ ♠♦♠❡♥t✉♠ ♦❢ t❤❡ ♣❤♦t♦♥ ✐♥ t❤❡ ♠❡❞✐✉♠ ✐s ♣r♦♣♦rt✐♦♥❛❧ t♦ t❤❡ ♠♦♠❡♥t✉♠ ✐♥ t❤❡ ✈❛❝✉✉♠ ❛♥❞ ✐♥✈❡rs❡❧② ♣r♦♣♦rt✐♦♥❛❧ t♦ t❤❡ r❡❢r❛❝t✐✈❡ ✐♥❞❡① ♦❢ t❤❡ ♠❡❞✐✉♠✱ s✉❝❤ t❤❛tp~A=p~0/n✳ ❚❤❡r❡ ✐s ♥♦ ❞✐r❡❝t ♠❡t❤♦❞ ❢♦r ❛♥s✇❡r✐♥❣ t❤✐s q✉❡st✐♦♥ ②❡t✳ ❍♦✇❡✈❡r✱ t❤❡ ♣❛ss❛❣❡ ♦❢ ❛ ♣❤♦t♦♥ t❤r♦✉❣❤ ❛ ♠❡❞✐✉♠ ❡①❡rts ❛ ❢♦r❝❡✱ ❝❛✉s✐♥❣ ❛ r❛❞✐❛t✐♦♥ ♣r❡ss✉r❡ ♦♥ t❤✐s ♠❡❞✐✉♠✱ t❤❛t ❤❛s ❛❧r❡❛❞② ❜❡❡♥ st✉❞✐❡❞ ❢♦r ❛ ❧♦♥❣ t✐♠❡✳ ❚❤✐s ✇♦r❦ ♣r❡s❡♥ts ❛ st✉❞② ♦♥ t❤❡ ❡✛❡❝ts ♦❢ ❢♦r❝❡s ✐♥❞✉❝❡❞ ❜② r❛❞✐❛t✐♦♥ ❛t ❞✐❡❧❡❝tr✐❝ ♠❛t❡r✐❛❧s ✐♥t❡r❢❛❝❡s✱ s♣❡❝✐✜❝❛❧❧② ❛t t❤❡ ❛✐r✴✇❛t❡r ✐♥t❡r❢❛❝❡✳ ■t ♣r♦✈✐❞❡s ❢✉rt❤❡r ❛❞✈❛♥❝❡♠❡♥ts ✐♥ tr②✐♥❣ t♦ ❞❡✜♥❡ t❤❡ r❡❛❧ ♣❤♦t♦♥ ♠♦♠❡♥t✉♠ ✐♥ ❞✐❡❧❡❝tr✐❝ ♠❡❞✐✉♠ ❛♥❞ ❤♦✇ t❤❡ ❢♦r❝❡ ✐s ❣❡♥❡r❛t❡❞ ✐♥ t❤❡ ♠❡❞✐✉♠✳ ■t ✇❛s ✉s❡❞ ❛♥ ❛❞❛♣t❡❞ P❤♦t♦t❤❡r♠❛❧ ▼✐rr♦r s❡t✉♣ ❛♥❞ ❡✈❛❧✉❛t❡❞ t❤❡ s✉r❢❛❝❡ ❞❡❢♦r♠❛t✐♦♥ ♦❢ ✇❛t❡r ✐♥ ❞✐✛❡r❡♥t ❝♦♥✜❣✉r❛t✐♦♥s ♦❢ t❤❡ ❡①♣❡r✐♠❡♥t❛❧ ❛rr❛♥❣❡♠❡♥t✳ ■♥ t❤❡s❡ ❛rr❛♥❣❡♠❡♥ts✱ t❤❡ ❧❛s❡r ❜❡❛♠ ♣❛ss❡s t❤r♦✉❣❤ t❤❡ ✐♥t❡r❢❛❝❡ ❛✐r → ✇❛t❡r✱ ✇❛t❡r → ❛✐r ❛♥❞ ❛✐r →
✇❛t❡r →❛✐r ✭❞♦✉❜❧❡ ❡①❝✐t❛t✐♦♥✮✳ ■t ✐s ❝♦♥s✐❞❡r❡❞ ❝❤❛♥❣❡s ✐♥ t❤❡ r❛❞✐❛❧ ❞✐♠❡♥s✐♦♥s ♦❢
t❤❡ ✐♥❝✐❞❡♥t ❜❡❛♠ ❛♥❞ ✇❡ ❧♦♦❦ ❛t ✇❤❛t ✇❛s s❛✐❞ t♦ ❜❡ ❛♥ ❡①♣❡r✐♠❡♥t❛❧ ❡✈✐❞❡♥❝❡ t❤❛t ❛❣r❡❡s ✇✐t❤ t❤❡ ♣r❡❞✐❝t✐♦♥ ♦❢ ❆❜r❛❤❛♠✳ ❆❧❧ ❡①♣❡r✐♠❡♥t❛❧ r❡s✉❧ts ❛r❡ ❝♦♠♣❛r❡❞ ✇✐t❤ ♥✉♠❡r✐❝❛❧ ♠♦❞❡❧s ✉s✐♥❣ t❤❡ ❋✐♥✐t❡ ❊❧❡♠❡♥t ▼❡t❤♦❞ t♦ ✉♥❞❡rst❛♥❞ t❤❡ ❝♦♥tr✐❜✉t✐♦♥s ♦❢ r❛❞✐❛t✐♦♥ ❢♦r❝❡s ❛❝t✐♥❣ ♦♥ t❤❡ s✉r❢❛❝❡ ❛♥❞ ✐♥ t❤❡ ✇❛t❡r ✈♦❧✉♠❡✳
❙✉♠ár✐♦
❘❡s✉♠♦ ✐✈
❆❜str❛❝t ✈
✶ ■♥tr♦❞✉çã♦ ✶
✷ ❆ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦ ❛♦ ❧♦♥❣♦ ❞♦s sé❝✉❧♦s ✹
✷✳✶ ❙é❝✉❧♦s ❳❱■■✱ ❳❱■■■ ❡ ❳■❳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✷✳✷ ❙é❝✉❧♦ ❳❳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼ ✷✳✸ ❙é❝✉❧♦ ❳❳■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺
✸ ❉❡s❡♥✈♦❧✈✐♠❡♥t♦ t❡ór✐❝♦ ✶✽
✸✳✶ ❊❧❡tr♦♠❛❣♥❡t✐s♠♦ ❡♠ ❞✐❡❧étr✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✸✳✷ ❋♦rç❛s ❡❧❡tr♦♠❛❣♥ét✐❝❛s ♥❛ ♠❛tér✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✸✳✷✳✶ ❚❡♥s♦r❡s ❞❡ str❡ss ❡❧étr✐❝♦ ❡ ♠❛❣♥ét✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✸✳✷✳✷ ❋♦rç❛s ❡❧❡tr♦♠❛❣♥ét✐❝❛s ❡♠ ❞✐❡❧étr✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✸✳✷✳✸ Pr❡ssã♦ ❞❡✈✐❞♦ à r❛❞✐❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✸✳✸ ❉❡❢♦r♠❛çã♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞❡✈✐❞♦ à ♣r❡ssã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✸✳✹ ❙✐♠✉❧❛çõ❡s ❞❛s ❞❡❢♦r♠❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼
✹ ❋♦t♦✲❞❡❢♦r♠❛çã♦ ✸✶
✹✳✶ ❊s♣❡❝tr♦♠❡tr✐❛ ❞❡ ❊s♣❡❧❤♦ ❋♦t♦tér♠✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✹✳✶✳✶ ▼♦❞❡❧♦ t❡ór✐❝♦ ❞❡ ❊s♣❡❧❤♦ ❋♦t♦tér♠✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✹✳✶✳✷ ❆rr❛♥❥♦ ❡①♣❡r✐♠❡♥t❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✹✳✷ ❊s♣❡❧❤♦ ❋♦t♦♠❡❝â♥✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹
✺ ❘❡s✉❧t❛❞♦s ❡ ❞✐s❝✉ssã♦ ✹✼
✺✳✶ ▼❡❞✐❞❛s ❝♦♠ ❡①❝✐t❛çã♦ ♣♦r ❝✐♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✺✳✷ ▼❡❞✐❞❛s ❝♦♠ ❡①❝✐t❛çã♦ ♣♦r ❜❛✐①♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✺✳✸ ▼❡❞✐❞❛s ❝♦♠ ❞✉♣❧❛ ❡①❝✐t❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✺✳✹ ❉❡s❢♦❝❛♥❞♦ ❡ ❢♦❝❛♥❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾
✺✳✺ ❆♥á❧✐s❡ ❞❛ ❡✈✐❞ê♥❝✐❛ ❡①♣❡r✐♠❡♥t❛❧ ❞❛ ♣r❡ssã♦ ❞❛ ❧✉③ ❞❡ ❆❜r❛❤❛♠ ✳ ✳ ✻✸
✻ ❈♦♥❝❧✉sã♦ ✻✼
❆♣ê♥❞✐❝❡s ✻✾
❆ ❚❡♥s♦r ❞❡ str❡ss ✼✵
❇ ❯t✐❧✐③❛çã♦ ❞♦ ▼ét♦❞♦ ❞♦s ❊❧❡♠❡♥t♦s ❋✐♥✐t♦s ✼✺
❈ P✉❜❧✐❝❛çõ❡s ✼✾
❇✐❜❧✐♦❣r❛✜❛ ✾✵
Cap´ıtulo
1
■♥tr♦❞✉çã♦
❆ ❞❡s❝r✐çã♦ ❝♦rr❡t❛ ❞♦ ♠♦♠❡♥t♦ ❞❛ ❧✉③ ❡♠ ♠❛t❡r✐❛✐s ❞✐❡❧étr✐❝♦s ❡ ♦s ❡❢❡✐t♦s ❝❛✉s❛❞♦s ♣❡❧❛s ❢♦rç❛s ❞❡ r❛❞✐❛çã♦✱ q✉❛♥❞♦ ❛ ❧✉③ ❛tr❛✈❡ss❛ ❛ ✐♥t❡r❢❛❝❡ ❞❡ss❡s ♠❛t❡r✐❛✐s✱ t❡♠ s✐❞♦ ❡①t❡♥s✐✈❛♠❡♥t❡ ❞❡❜❛t✐❞♦s ♣♦r ♠❛✐s ❞❡ ✉♠ sé❝✉❧♦✳ ❊ss❡ t❡♠❛ ♣♦ss✉✐ ✉♠ ❞♦s ❞✐❧❡♠❛s ♠❛✐s ❞✉r❛❞♦✉r♦s ❞❛ ár❡❛ ❞❡ ✐♥t❡r❛çã♦ r❛❞✐❛çã♦✲♠❛tér✐❛✿ ❛ ❈♦♥tr♦✈érs✐❛ ❞❡ ❆❜r❛❤❛♠✲▼✐♥❦♦✇s❦✐✳
❆s ❢♦rç❛s ✐♥❞✉③✐❞❛s ♣❡❧❛ r❛❞✐❛çã♦ ❡stã♦ ❞✐r❡t❛♠❡♥t❡ r❡❧❛❝✐♦♥❛❞❛s à ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦✱ ❡❢❡✐t♦ ♣r♦♣♦st♦ ♣♦r ❑❡♣❧❡r ❬✶✱✷❪✱ ♥♦ ✐♥í❝✐♦ ❞♦ sé❝✉❧♦ ❳❱■■✱ ❛♦ t❡♥t❛r ❡①♣❧✐❝❛r ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❛s ❝❛✉❞❛s ❞❡ ❝♦♠❡t❛s q✉❡ s♦❢r❡♠ r❡♣✉❧sã♦ ❛♦ s❡ ❛♣r♦①✐♠❛r❡♠ ❞♦ ❙♦❧✳ ❊♠ s✉❛ ❡①♣❧✐❝❛çã♦✱ ❡❧❡ ♣r♦♣ôs ❛ ❡①✐stê♥❝✐❛ ❞❡ ❢♦rç❛s ❡①❡r❝✐❞❛s ♣❡❧❛ r❛❞✐❛çã♦ s♦❧❛r✱ ♦✉ s❡❥❛✱ ✉♠❛ ♣r❡ssã♦ ❞❡✈✐❞♦ à r❛❞✐❛çã♦✳ ❉❡s❞❡ ❡♥tã♦✱ ❡ss❡ ❡❢❡✐t♦ ♣❛ss♦✉ ♣❡❧❛s ♠❡♥t❡s ❞❡ ❣r❛♥❞❡s ❝✐❡♥t✐st❛s✱ ❝♦♠♦ ◆❡✇t♦♥ ❬✷✱✸❪✱ ▼❛①✇❡❧❧ ❬✹❪✱ P♦②♥t✐♥❣ ❬✺✕✶✵❪✱ ❚❤♦♠s♦♥ ❬✶✶✱ ✶✷❪✱ ❍❡❛✈✐s✐❞❡ ❬✶✸✱✶✹❪✱ ▲♦r❡♥t③ ❬✶✺❪✱ ❊✐♥st❡✐♥ ❬✶✻✱✶✼❪ ❡ ♠✉✐t♦s ♦✉tr♦s✳
❆ ❝♦♥tr♦✈érs✐❛ é ❞❡♥♦♠✐♥❛❞❛ ❆❜r❛❤❛♠✲▼✐♥❦♦✇s❦✐✱ ♣♦✐s ♦s ❞♦✐s ❡st✉❞✐♦s♦s ♣r♦✲ ♣✉s❡r❛♠ t❡♦r✐❛s ♣❛r❛ ❡①♣❧✐❝❛r ♦ t❡♥s♦r ❞❡ ❡♥❡r❣✐❛✲♠♦♠❡♥t♦ ❞❛ ❧✉③ ❜❛s❡❛❞♦s ♥♦s ♠❡s♠♦s ❢✉♥❞❛♠❡♥t♦s✱ ❝♦♥t✉❞♦✱ ❝♦♠ ♣r❡❞✐çõ❡s ❝♦♠♣❧❡t❛♠❡♥t❡ ❞✐✈❡r❣❡♥t❡s✳ ❆♠❜♦s t❡♥t❛r❛♠ ❞❡s❝r❡✈❡r ♦ ♠♦♠❡♥t♦ ❞♦ ❢ót♦♥ ❡♠ ♠❡✐♦s ❞✐❡❧étr✐❝♦s ❡ ♦s ❡❢❡✐t♦s ❝❛✉s❛❞♦s ♣❡❧❛s ❢♦rç❛s ❞❛ r❛❞✐❛çã♦ q✉❛♥❞♦ ❡❧❡ ✐♥❝✐❞❡ ❞♦ ✈á❝✉♦ ❡♠ ✉♠ ♠❡✐♦ ❞✐❡❧étr✐❝♦✳
▼✐♥❦♦✇s❦✐ ❬✶✽❪✱ ❡♠ ✶✾✵✽✱ ♣r♦♣ôs q✉❡ ♦ ♠♦♠❡♥t♦ ❞♦ ❢ót♦♥ ❡♠ ✉♠ ♠❡✐♦ ❞✐❡❧étr✐❝♦ s❡r✐❛ ♣r♦♣♦r❝✐♦♥❛❧ ❛♦ í♥❞✐❝❡ ❞❡ r❡❢r❛çã♦ ❞♦ ♠❡✐♦✱ n✱ ❡ ❛♦ s❡✉ ♠♦♠❡♥t♦ ♥♦ ✈á❝✉♦✱ p~0✱ t❛❧ ❝♦♠♦ p~M = n ~p0✳ ❊ss❡ ♠♦♠❡♥t♦ ✐♥❞✉③✐r✐❛ ♥♦ ♠❡✐♦ ✉♠❛ ❢♦rç❛ s✉♣❡r✜❝✐❛❧ ♣❛r❛ s❡✉ ❡①t❡r✐♦r ❝♦♠♦ ✉♠❛ ❡①♣❛♥sã♦✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ❆❜r❛❤❛♠ ❬✶✾❪✱ ❡♠ ✶✾✵✾✱ ❞❡❢❡♥❞❡✉ q✉❡ ♦ ♠♦♠❡♥t♦ ❞♦ ❢ót♦♥ ♥♦ ♠❡✐♦ s❡r✐❛ ♣r♦♣♦r❝✐♦♥❛❧ ❛♦ s❡✉ ♠♦♠❡♥t♦ ♥♦ ✈á❝✉♦ ❡ ✐♥✈❡rs❛♠❡♥t❡ ♣r♦♣♦r❝✐♦♥❛❧ ❛♦ í♥❞✐❝❡ ❞❡ r❡❢r❛çã♦ ❞♦ ♠❡✐♦✱ ❞❡ t❛❧ ❢♦r♠❛ q✉❡p~A=p~0/n✳
✶✳ ■♥tr♦❞✉çã♦ ✷
❊ ❛✐♥❞❛✱ ❛ ❢♦rç❛ ❣❡r❛❞❛ ♥♦ ♠❡✐♦ s❡r✐❛ ♣❛r❛ s❡✉ ✐♥t❡r✐♦r✱ ❝♦♠♦ ✉♠❛ ❝♦♠♣r❡ssã♦✳ P❛r❛ ♦❜s❡r✈❛r ♦ ❡❢❡✐t♦ ❞❛ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦✱ ❞✐❢❡r❡♥t❡s tr❛❜❛❧❤♦s ❡①♣❡r✐♠❡♥✲ t❛✐s ❢♦r❛♠ r❡❛❧✐③❛❞♦s ❬✷✵✕✷✾❪✳ ◆♦ ❡♥t❛♥t♦✱ ♦s r❡s✉❧t❛❞♦s ♥ã♦ ❝♦♥✈❡r❣✐❛♠ ❞✐r❡t❛♠❡♥t❡ ♣❛r❛ ♥❡♥❤✉♠ ❞♦s ❢♦r♠❛❧✐s♠♦s✳ ❉❡s❞❡ ♦ ✐♥í❝✐♦ ❞❡st❡ sé❝✉❧♦✱ ❞✐❢❡r❡♥t❡s ♠ét♦❞♦s ❢♦✲ r❛♠ ❡❧❛❜♦r❛❞♦s ♣❛r❛ t❡♥t❛r ❞❡t❡r♠✐♥❛r q✉❛❧ s❡r✐❛ ❛ ❞❡✜♥✐çã♦ ❝♦rr❡t❛ ❞♦ ♠♦♠❡♥t♦ ❞♦ ❢ót♦♥ ❬✸✵✕✸✻❪✳ ❖ tr❛❜❛❧❤♦ ❞❡ ❆str❛t❤ ❡t ❛❧✳ ❬✸✺❪ ❣❛♥❤♦✉ ❞❡st❛q✉❡✱ ✉♠❛ ✈❡③ q✉❡ ❝♦♥✲ s❡❣✉✐✉ ❝♦♥❞✉③✐r ❡①♣❡r✐♠❡♥t♦s ❞❡ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦ ❞❡ ❛❧t❛ s❡♥s✐❜✐❧✐❞❛❞❡✱ ♦s q✉❛✐s ❛♣r❡s❡♥t❛♠ ❣r❛♥❞❡ ❝♦♥❝♦r❞â♥❝✐❛ q✉❛♥t✐t❛t✐✈❛ ❝♦♠ s✐♠✉❧❛çõ❡s ♣♦r ♠❡✐♦ ❞♦ ♠ét♦❞♦ ❞❡ ❡❧❡♠❡♥t♦s ✜♥✐t♦s✳ ❖s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❡stã♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ ♠♦♠❡♥t♦ ♣r♦♣♦st♦ ♣♦r ▼✐♥❦♦✇s❦✐✳ ❊ss❡ ❢♦✐ ✉♠ ✐♠♣♦rt❛♥t❡ ♣❛ss♦ ♥❛ ❝❛♠✐♥❤❛❞❛ ❞❡ ❝♦♥❤❡❝❡r ♠❡❧❤♦r ❛s ❢♦rç❛s ❡①❡r❝✐❞❛s ♣❡❧❛ ❧✉③✳ ❖✉tr♦ tr❛❜❛❧❤♦ ❞❡ ❞❡st❛q✉❡ ❢♦✐ ♦ ❞❡ ❩❤❛♥❣ ❡t ❛❧✳ ❬✸✻❪ q✉❡✱ ❛♦ r❡❛❧✐③❛r ❡①♣❡r✐♠❡♥t♦s ♠❛✐s s✐♠♣❧❡s q✉❡ ♦s ❞❡ ❆str❛t❤ ❡t ❛❧✳✱ ♦❜t✐✈❡r❛♠ r❡s✉❧t❛❞♦s ❝♦rr❡s♣♦♥❞❡♥t❡s ❝♦♠ ♦ ♠♦♠❡♥t♦ ❞❡ ❆❜r❛❤❛♠✳
❊st❡ tr❛❜❛❧❤♦ ❛♣r❡s❡♥t❛ ✉♠ ❡st✉❞♦ s♦❜r❡ ♦s ❡❢❡✐t♦s ❞❛s ❢♦rç❛s ✐♥❞✉③✐❞❛s ♣♦r r❛❞✐❛çã♦ ❡♠ ✐♥t❡r❢❛❝❡s ❡♥tr❡ ♠❛t❡r✐❛✐s ❞✐❡❧étr✐❝♦s✳ ❖ ❢♦❝♦ é ❞❛❞♦ à ✐♥t❡r❢❛❝❡ ❛r✴á❣✉❛✱ ❛ss✐♠ ❝♦♠♦ ♥♦ tr❛❜❛❧❤♦ ❞❡ ❆str❛t❤ ❡t ❛❧✳✱ ♦ q✉❛❧ é ✉t✐❧✐③❛❞♦ ❝♦♠♦ ❜❛s❡ ♣❛r❛ ❡st❛ ♣❡sq✉✐s❛✳ ❖ ✐♥t✉✐t♦ ❞❡st❛ t❡s❡ é ♣r♦♣♦r❝✐♦♥❛r ♠❛✐s ✉♠ ❛✈❛♥ç♦ ♥❛ ❜✉s❝❛ ❡♠ ❞❡✜♥✐r ♦ ✈❡r❞❛❞❡✐r♦ ♠♦♠❡♥t♦ ❞♦ ❢ót♦♥ ❡♠ ♠❡✐♦s ❞✐❡❧étr✐❝♦s ❡ ❝♦♠♦ s❡ ❞á ❛ ❢♦rç❛ ❣❡r❛❞❛ ♥❡ss❡ ♠❡✐♦✳
P❛r❛ t❛♥t♦✱ ❛ t❡s❡ ❡stá ❞✐✈✐❞✐❞❛ ♥❛ s❡❣✉✐♥t❡ ♠❛♥❡✐r❛✿
➱ ❢❡✐t❛ ✉♠❛ r❡✈✐sã♦ ❤✐stór✐❝❛ ❛ r❡s♣❡✐t♦ ❞❛ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦ ♥♦ ❝❛♣ít✉❧♦ ✷✳ ➱ ❡①♣♦st♦ q✉❡ ♦ ❡❢❡✐t♦ ❝♦♥st❛ ♥❛ ❤✐stór✐❛ ❞❛ ❝✐ê♥❝✐❛ ❞❡s❞❡ ♦s ú❧t✐♠♦s ❝✐♥❝♦ sé❝✉❧♦s✱ ❜❡♠ ❝♦♠♦ q✉❡ ❛ ❝♦♥tr♦✈érs✐❛ ❞❡ ❆❜r❛❤❛♠✲▼✐♥❦♦✇s❦✐ ♣❡r❞✉r❛ ♣♦r ♠❛✐s ❞❡ ❝❡♠ ❛♥♦s✳ P♦r s❡r ✉♠ t❡♠❛ ❡st✉❞❛❞♦ ❤á ♠✉✐t♦ t❡♠♣♦ ❡ ♣♦r ❞✐✈❡rs♦s ♣❡sq✉✐s❛❞♦r❡s✱ ❡①✐st❡ ✉♠ ❡♥♦r♠❡ ❛❝❡r✈♦ ❝✐❡♥tí✜❝♦ s♦❜r❡ ♦ t❡♠❛ t❛♥t♦ t❡ór✐❝♦ q✉❛♥t♦ ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡✳ P♦r ✐ss♦✱ é ❛♣r❡s❡♥t❛❞❛ ✉♠❛ ❜r❡✈❡ r❡✈✐sã♦ ❛ r❡s♣❡✐t♦ ❞♦s ♣r✐♥❝✐♣❛✐s tr❛❜❛❧❤♦s ❡ ❛✈❛♥ç♦s q✉❡ ❤♦✉✈❡ ❛té ♦s ❞✐❛s ❛t✉❛✐s✳
✶✳ ■♥tr♦❞✉çã♦ ✸
♣❛r❛ ✢✉✐❞♦s ✐♥❝♦♠♣r❡ssí✈❡✐s✳
◆♦ ❝❛♣ít✉❧♦ ✹✱ ❤á ✉♠❛ ❛♣r❡s❡♥t❛çã♦ s♦❜r❡ ❛ té❝♥✐❝❛ ❞❡ ❊s♣❡❧❤♦ ❋♦t♦tér♠✐❝♦✱ q✉❡ ♣♦ss✉✐ ❣r❛♥❞❡ s❡♥s✐❜✐❧✐❞❛❞❡ ❡ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❞❡t❡❝t❛r ❞❡❢♦r♠❛çõ❡s s✉♣❡r✜❝✐❛✐s ❞❛ ♦r❞❡♠ ❞❡ ♠❛❣♥✐t✉❞❡ ❞❡ ♥❛♥ô♠❡tr♦s✳ ❖ ♠♦❞❡❧♦ t❡ór✐❝♦ é s✉t✐❧♠❡♥t❡ ❡①✐❜✐❞♦ ❡ ♦ ❛rr❛♥❥♦ ❡①♣❡r✐♠❡♥t❛❧ é ❡①♣♦st♦ ❡ ❛❞❛♣t❛❞♦ ♣❛r❛ ❛ ❞❡t❡❝çã♦ ❞❛ ❞❡❢♦r♠❛çã♦ ❣❡r❛❞❛ ♣♦r ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦✳
❖ ♦❜❥❡t✐✈♦ ❞♦ ❝❛♣ít✉❧♦ ✺ é ❛✈❛❧✐❛r ❞✐❢❡r❡♥t❡s ❝♦♥✜❣✉r❛çõ❡s ❞♦ ❛rr❛♥❥♦ ❡①♣❡r✐✲ ♠❡♥t❛❧✱ s❡♠♣r❡ ❝♦♠ ♦ ✉s♦ ❞❛ ✐♥t❡r❢❛❝❡ ❛r✴á❣✉❛✳ ❊①♣❡r✐♠❡♥t♦s ❝♦♠♦ ♦s ❞❡ ❆str❛t❤ ❡t ❛❧✳ sã♦ r❡❛❧✐③❛❞♦s✱ ✐st♦ é✱ ❡①♣❡r✐♠❡♥t♦s ❡♠ q✉❡ ❛ r❛❞✐❛çã♦ ✐♥❝✐❞❡ ♥♦ s❡♥t✐❞♦ ❛r
→ á❣✉❛✱ ❝♦♥s✐❞❡r❛♥❞♦ ❢❡✐①❡s ❞❡ ❧❛s❡r ❝♦♥tí♥✉♦ ❡ ♣✉❧s❛❞♦✳ ❈♦♠♦ ♣r✐♠❡✐r❛ ❛✈❛❧✐❛çã♦
❡①♣❡r✐♠❡♥t❛❧ ❞❛ ✐♥✢✉ê♥❝✐❛ ❞❛s ❢♦rç❛s ❛t✉❛♥t❡s ♥❛ s✉♣❡r❢í❝✐❡ ❡ ♥♦ ✈♦❧✉♠❡✱ sã♦ ❛♣r❡✲ s❡♥t❛❞♦s ❛rr❛♥❥♦s ❡①♣❡r✐♠❡♥t❛✐s ❡♠ q✉❡ ❛s ✐♥❝✐❞ê♥❝✐❛s ❞❛ r❛❞✐❛çã♦ sã♦ ♥♦s s❡♥t✐❞♦s á❣✉❛ → ❛r ✭✏❡①❝✐t❛çã♦ ♣♦r ❜❛✐①♦✑✮ ❡ ❛r → á❣✉❛ → ❛r ✭✏❞✉♣❧❛ ❡①❝✐t❛çã♦✑✮✱ ❝♦♠ ✉♠
❡s♣❡❧❤♦ ❞❡♥tr♦ ❞❛ á❣✉❛✳ ❚❛♠❜é♠ sã♦ ❛♣r❡s❡♥t❛❞♦s ❡①♣❡r✐♠❡♥t♦s ❝✉❥❛s ❞✐♠❡♥sõ❡s r❛❞✐❛✐s ❞♦ ❢❡✐①❡ ✈❛r✐❛♠ ❛♦ ❧♦♥❣♦ ❞♦ ✈♦❧✉♠❡ ❞❡ á❣✉❛✱ ❝♦♥s✐❞❡r❛♥❞♦ ❛s s✐t✉❛çõ❡s ❡♠ q✉❡ ♦ ❢❡✐①❡ ❢♦❝❛ ❡ ❞❡s❢♦❝❛ ❛♦ ❧♦♥❣♦ ❞♦ ✈♦❧✉♠❡ ❞❡ á❣✉❛✳ P♦r ✜♠✱ é ❛♥❛❧✐s❛❞❛ ❛ ♣♦ssí✈❡❧ ❡✈✐❞ê♥❝✐❛ ❡①♣❡r✐♠❡♥t❛❧ q✉❡ ❝♦♥❝♦r❞❛ ❝♦♠ ❛ ♣r❡✈✐sã♦ ❞❡ ❆❜r❛❤❛♠✱ ♣r♦♣♦st❛ ♥♦ tr❛✲ ❜❛❧❤♦ ❞❡ ❩❤❛♥❣ ❡t ❛❧✳ ❬✸✻❪✳ ◆♦ ú❧t✐♠♦ ❝❛♣ít✉❧♦ sã♦ ❛♣r❡s❡♥t❛❞❛s ❛s ❝♦♥❝❧✉sõ❡s ❞❡st❡ tr❛❜❛❧❤♦✳
Cap´ıtulo
2
❆ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦ ❛♦ ❧♦♥❣♦ ❞♦s sé❝✉❧♦s
❖ s✉r❣✐♠❡♥t♦ ❞❛ ✐❞❡✐❛ ❞♦ ❡❢❡✐t♦ ❞❡ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦ ❡stá ♣❛r❛ ❝♦♠♣❧❡t❛r q✉❛tr♦❝❡♥t♦s ❛♥♦s ♥❛ ❤✐stór✐❛ ❞❛ ❝✐ê♥❝✐❛✳ ❆♦ ❝♦♥s✐❞❡r❛r s✉❛ ❡①t❡♥s❛ tr❛❥❡tór✐❛✱ ❛ q✉❛❧ ♠✉✐t♦s ♣❡sq✉✐s❛❞♦r❡s ❡ ♣❡♥s❛❞♦r❡s ♣❛rt✐❝✐♣❛r❛♠✱ ❡①✐st❡ ✉♠ ❣r❛♥❞❡ ❛❝❡r✈♦ ❞❡ ❡st✉❞♦s ❡ tr❛❜❛❧❤♦s s♦❜r❡ ♦ ❡❢❡✐t♦✳ ◆❡st❡ ❝❛♣ít✉❧♦✱ s❡rá ❡①♣♦st❛ ✉♠❛ ✐♥tr♦❞✉çã♦ ❤✐stór✐❝❛ ❛♦ ❡❢❡✐t♦ ❞❡ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦✳ ❆❧❣✉♥s tr❛❜❛❧❤♦s q✉❡ ❢♦r❛♠ ❞❡s❡♥✈♦❧✈✐❞♦s ♥♦s ú❧t✐♠♦s ❝✐♥❝♦ sé❝✉❧♦s✱ ❛❧❣✉♥s ❞♦s ❡①♣❡r✐♠❡♥t♦s q✉❡ ❜✉s❝❛r❛♠ ♠❡❞✐r ♦ ❡❢❡✐t♦ ❡ ❛❧❣✉♠❛s ❞❛s t❡♦r✐❛s q✉❡ t❡♥t❛r❛♠ ❞❡s❝r❡✈ê✲❧♦ s❡rã♦ ❛♣r❡s❡♥t❛❞♦s ❡ ❞✐s❝✉t✐❞♦s✳
✷✳ ❆ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦ ❛♦ ❧♦♥❣♦ ❞♦s sé❝✉❧♦s ✺
✷✳✶ ❙é❝✉❧♦s ❳❱■■✱ ❳❱■■■ ❡ ❳■❳
❖ ♣r✐♠❡✐r♦ r❡❧❛t♦ ❞♦❝✉♠❡♥t❛❞♦ s♦❜r❡ ❛ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦ ❢♦✐ ❞❛❞♦ ♣♦r ❑❡♣❧❡r ♥♦ ❛♥♦ ❞❡ ✶✻✶✾✳ ❊♠ s❡✉ tr❛❜❛❧❤♦ ❉❡ ❈♦♠❡t✐s ▲✐❜❡❧❧✐ ❚r❡s ❬✶✱✷❪✱ ♦ ❛strô♥♦♠♦ ❡①♣❧✐❝❛ ♦ ❢❛t♦ ❞❛s ❝❛✉❞❛s ❞❡ ❝♦♠❡t❛s s❡r❡♠ r❡♣❡❧✐❞❛s ♣❡❧♦ s♦❧✱ ❝♦♠♦ ✐❧✉str❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✶✳ ❙❡❣✉♥❞♦ ♦ ♣❡sq✉✐s❛❞♦r✱ ✉♠ ❝♦♠❡t❛ é ❝♦♠♣♦st♦ ❝♦♠♣❧❡t❛♠❡♥t❡ ❞❡ s✉❜stâ♥❝✐❛ ♥❡❜✉✲ ❧♦s❛ ❡ s✉❛s ♣❛rt❡s sã♦ ❣r❛❞✉❛❧♠❡♥t❡ q✉❡❜r❛❞❛s ❡ ❞✐s♣❡rs❛s ♣❡❧❛ ✐♥❝❡ss❛♥t❡ ❛çã♦ ❞♦s r❛✐♦s s♦❧❛r❡s✳ ◆❛s ♣❛❧❛✈r❛s ❞♦ ❛✉t♦r ✏❛ ❝❛✉❞❛ r❡♣r❡s❡♥t❛ ❛ ♠♦rt❡ ❞❛ ❝❛❜❡ç❛✑ ❬✸✼❪✳
❋✐❣✉r❛ ✷✳✶✿ ■♠❛❣❡♠ ✐❧✉str❛t✐✈❛ ❞❛ ❝❛✉❞❛ ❞❡ ✉♠ ❝♦♠❡t❛ ❛♦ t♦♠❛r ❛ ❞✐r❡çã♦ ❝♦♥trár✐❛ ❛♦ s♦❧✳ P✉❜❧✐❝❛❞❛ ♥♦ tr❛t❛❞♦ s♦❜r❡ ❝♦♠❡t❛s ❞❡ P❡t❡r ❆♣✐❛♥ ❡♠ ✶✺✸✷ ❡ r❡♣r♦❞✉③✐❞❛ ❡♠ ✏❚❤❡ ❖♣t✐❝❛❧ ❚❤❡♦r② ♦❢ ❈♦♠❡ts✑ ❞❡ ❇❛r❦❡r ❬✷❪✳
❆ ♣r❡ssã♦ ❞❡✈✐❞♦ à r❛❞✐❛çã♦ ♥♦ â♠❜✐t♦ ❛str♦♥ô♠✐❝♦ ❢♦✐ ✉♠❛ q✉❡stã♦ ❛♠♣❧❛✲ ♠❡♥t❡ ❞✐s❝✉t✐❞❛ ❛♦ ❧♦♥❣♦ ❞♦ sé❝✉❧♦ ❳❱■■✳ ❖ t❡♠❛ ✈♦❧t♦✉ ❛ s❡r ❞✐❢✉♥❞✐❞♦ ❡♠ ✶✽✼✸ ❬✹❪✱ q✉❛♥❞♦ ▼❛①✇❡❧❧ ❛♣r❡s❡♥t♦✉ s❡✉ tr❛❜❛❧❤♦ ❆ ❚r❡❛t✐s❡ ♦♥ ❊❧❡❝tr✐❝✐t② ❛♥❞ ▼❛❣♥❡t✐s♠✱ ❡♠ q✉❡ ❞❡s❝r❡✈❡ ❛ ❧✉③ ❝♦♠♦ ✉♠❛ ♦♥❞❛ ❡❧❡tr♦♠❛❣♥ét✐❝❛✳ ❊♠ s❡✉ tr❛❜❛❧❤♦✱ ▼❛①✇❡❧❧ ♣r❡✈ê ❛ ❡①✐stê♥❝✐❛ ❞❡ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦ ❞❡✈✐❞♦ à ❞❡♥s✐❞❛❞❡ ✈♦❧✉♠étr✐❝❛ ❞❡ ❡♥❡r❣✐❛ ❞❛ ♦♥❞❛ ♣r♦♣❛❣❛♥t❡✿
✷✳ ❆ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦ ❛♦ ❧♦♥❣♦ ❞♦s sé❝✉❧♦s ✻
❊♥q✉❛♥t♦ ▼❛①✇❡❧❧ ❝♦♥tr✐❜✉í❛ ❝♦♠ ♦ ❡❧❡tr♦♠❛❣♥❡t✐s♠♦✱ ♦ ✐t❛❧✐❛♥♦ ❆❞♦❧❢♦ ❇❛r✲ t♦❧✐ ♣r❡✈✐❛ ♦ ❡❢❡✐t♦ ❞❛ ♣r❡ssã♦ ❞❡✈✐❞♦ à r❛❞✐❛çã♦ ♣♦r ♠❡✐♦ ❞❛ s❡❣✉♥❞❛ ❧❡✐ ❞❛ t❡r♠♦❞✐✲ ♥â♠✐❝❛ ❬✸✽❪✳ ❊♠❜♦r❛ ❛♠❜❛s ♣r❡✈✐sõ❡s ❝♦♥❝♦r❞❡♠ ❡♥tr❡ s✐ ❬✸✾❪✱ ♦s ❡st✉❞♦s ❞❡ ❇❛rt♦❧✐ ❢♦r❛♠ ❞❡✐①❛❞♦s ❡♠ s❡❣✉♥❞♦ ♣❧❛♥♦✱ ♠❡s♠♦ ❛♣ós t❡r s✐❞♦ s❡❣✉✐❞♦ ♣♦r ❇♦❧t③♠❛♥♥✳ ❖ ❡❧❡tr♦♠❛❣♥❡t✐s♠♦✱ ♣♦r s✉❛ ✈❡③✱ ❢♦✐ ✐♥str✉♠❡♥t♦ ♣❛r❛ q✉❡ ❛ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦ ✈❡♥❤❛ s❡♥❞♦ ❡st✉❞❛❞❛ ❛té ♦s ❞✐❛s ❛t✉❛✐s✳
❋✐❣✉r❛ ✷✳✷✿ ❘❛❞✐ô♠❡tr♦ ❞❡
❈r♦♦❦❡s ❬✹✶❪✳ ❖ ❡❢❡✐t♦ ❢♦✐ ❝♦♥s✐❞❡r❛❞♦ ❞❡♥tr♦ ❞❡
✉♠ ❧❛❜♦r❛tór✐♦ ♣❡❧❛ ♣r✐♠❡✐r❛ ✈❡③ ❡♠ ✶✽✼✸✱ q✉❛♥❞♦ ❢❡✐①❡s ❞❡ ❧✉③ s♦❧❛r✱ ❛♦ ♣❛ss❛r ♣❡❧❛ ❥❛✲ ♥❡❧❛✱ ✐♥❝✐❞✐r❛♠ s♦❜r❡ ✉♠❛ ❜❛❧❛♥ç❛ ❛ ✈á❝✉♦ ❡ ❛rr✉✐♥❛r❛♠ ❛s ♠❡❞✐❞❛s ❞❡ ❲✐❧❧✐❛♠ ❈r♦♦✲ ❦❡s ❬✹✵❪✳ ❈r♦♦❦❡s ♣❡r❝❡❜❡✉ q✉❡ ❡ss❡ ❢❡♥ô✲ ♠❡♥♦ ❛❧t❡r❛✈❛ ♦s ✈❛❧♦r❡s ❞❛s ♠❛ss❛s ♠❡❞✐❞❛s ❡ ✐♥❞✐❝♦✉ q✉❡ ❡ss❛ ♠✉❞❛♥ç❛ ❞❛ ♠❛ss❛ ❡r❛ ❡♠ r❛③ã♦ ❞❛ ♣r❡ssã♦ ❡①❡r❝✐❞❛ ♣❡❧❛ ❧✉③✳ ❖ ❝✐❡♥✲ t✐st❛ ❞❡s❡♥✈♦❧✈❡✉ ✉♠ r❛❞✐ô♠❡tr♦✱ ❝♦♠♦ ♦ ❞❛ ❋✐❣✉r❛ ✷✳✷✱ ♣❛r❛ ♣♦ss✐❜✐❧✐t❛r ♦ ❡st✉❞♦ s♦❜r❡ ♦ ❡❢❡✐t♦ ❞❛ ♣r❡ssã♦ ♣♦r r❛❞✐❛çã♦✳
❖ r❛❞✐ô♠❡tr♦ ❝♦♥s✐st✐❛ ❞❡ ✉♠ ❜✉❧❜♦ ❞❡ ✈✐❞r♦ ❝♦♠ ❜❛✐①❛ ♣r❡ssã♦ ✐♥t❡r♥❛✱ q✉❛tr♦ ♣❛✲ ❧❤❡t❛s ♣♦❧✐❞❛s ❞❡ ✉♠ ❧❛❞♦ ❡ ♣✐♥t❛❞❛s ❞❡ ♣r❡t♦ ❞♦ ♦✉tr♦✳ ❆s ♣❛❧❤❡t❛s ❡r❛♠ ♣r❡s❛s ❡ s✉st❡♥✲ t❛❞❛s ♣♦r ❤❛st❡s ❞❡ ❧❛tã♦✳
❆ ✐♥❝✐❞ê♥❝✐❛ ❞❡ ❧✉③ ❢❡③ q✉❡ ❛s ♣❛❧❤❡t❛s r♦t❛❝✐♦♥❡♠✱ ❞❡ss❛ ❢♦r♠❛✱ ♦ ❛❝♦♥t❡❝✐✲ ♠❡♥t♦ ❢♦✐ ❝♦♥s✐❞❡r❛❞♦ ❛ ❛t✉❛çã♦ ❞❛ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦✳ P♦ré♠✱ ❥á ❡♠ ✶✽✼✻✱ ❖s❜♦r♥❡ ❘❡②♥♦❧❞s ❬✹✷❪ ❡ ❆rt❤✉r ❙❝❤✉st❡r ❬✹✸❪ ❝♦♠♣r❡❡♥❞❡r❛♠ q✉❡ ♦ ❡❢❡✐t♦ ✈✐st♦ ♣♦r ❈r♦♦❦❡s ❡r❛ ✉♠❛ ❝♦♥s❡q✉ê♥❝✐❛ ♠❛✐s ❝♦♠♣❧✐❝❛❞❛ ❞❡ ❛q✉❡❝✐♠❡♥t♦ ❡ ♥ã♦ ♦ ♣ró♣r✐♦ ❡❢❡✐t♦ ❞❡ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦✳
✷✳ ❆ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦ ❛♦ ❧♦♥❣♦ ❞♦s sé❝✉❧♦s ✼
✷✳✷ ❙é❝✉❧♦ ❳❳
❊♠ ✶✾✵✶✱ ♦ r✉ss♦ ▲❡❜❡❞❡✇ ❡ ♦s ❡st❛❞✉♥✐❞❡♥s❡s ◆✐❝❤♦❧s ❡ ❍✉❧❧ ♣✉❜❧✐❝❛r❛♠ ❛rt✐❣♦s ❝♦♠ ❞❡s❝r✐çõ❡s s♦❜r❡ ❛s ♣r✐♠❡✐r❛s ♦❜s❡r✈❛çõ❡s r❡❛✐s ❞❛ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦ ❞❡♥tr♦ ❞❡ ❧❛❜♦r❛tór✐♦✳
▲❡❜❡❞❡✇ ❬✷✵❪ ❝♦♥s✐❞❡r♦✉ q✉❡✱ ♣❛r❛ ♦❜s❡r✈❛r ♦ ❡❢❡✐t♦ ❞❡ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦✱ ❤❛✈✐❛♠ ❞✉❛s ❞✐✜❝✉❧❞❛❞❡s ❡ss❡♥❝✐❛✐s✿ ❝♦rr❡♥t❡s ❞❡ ❝♦♥✈❡❝çã♦ ❡ ❢♦rç❛s r❛❞✐♦♠étr✐❝❛s✳ ❆ ♠❛♥❡✐r❛ q✉❡ ♦ ♣❡sq✉✐s❛❞♦r ❡♥❝♦♥tr♦✉ ♣❛r❛ ❞✐♠✐♥✉✐r ❡ss❛s ♣❡rt✉r❜❛çõ❡s ❢♦✐ ♠❛♥t❡r ♦ s✐st❡♠❛ ❝♦♠ ♦ ❛♠❜✐❡♥t❡ ♦ ♠❛✐s r❛r❡❢❡✐t♦ ♣♦ssí✈❡❧✳ ❆✐♥❞❛ ❛ss✐♠✱ ♦s ❡❢❡✐t♦s ❞❡✈❡r✐❛♠ s❡r ❝♦♥s✐❞❡r❛❞♦s✳ ❊❧❡ ✉t✐❧✐③♦✉ ✉♠ ❜✉❧❜♦ ❞❡ ✈✐❞r♦ ♠❛✐♦r q✉❡ ♦ ❞❡ ❈r♦♦❦❡s✱ ❝♦♠♦ ♠♦str❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✸✳❛✳ ❆s r❛❞✐❛çõ❡s q✉❡ ♣♦❞❡r✐❛♠ s❡r ❛❜s♦r✈✐❞❛s ♣❡❧♦ ♣ró♣r✐♦ ❜✉❧❜♦ ❢♦r❛♠ ❡❧✐♠✐♥❛❞❛s✳
❋✐❣✉r❛ ✷✳✸✿ ■❧✉str❛çã♦ ❞♦ ❡①♣❡r✐♠❡♥t♦ ✉t✐❧✐③❛❞♦ ♣♦r ▲❡❜❡❞❡✇ ❬✷✵❪✳ ❛✮ ❞❡s❡♥❤♦ ❡sq✉❡♠át✐❝♦ ❞♦ ❛rr❛♥❥♦ ❡①♣❡r✐♠❡♥t❛❧ ❡ ❜✮ ♦♣çõ❡s ❞❡ ❤é❧✐❝❡s ✉t✐❧✐③❛❞❛s ❞❡♥tr♦ ❞♦ ❜✉❧❜♦ ❞❡ ✈✐❞r♦✳
❖ ❡①♣❡r✐♠❡♥t♦ ❞❡ ▲❡❜❡❞❡✇ ❝♦♥s✐st✐✉ ❞❡ ✉♠❛ ❧â♠♣❛❞❛✱ ❇✱ ❝♦♠ ♣❛rt❡ ❞❡ s✉❛ ❡♠✐ssã♦ ♣❛ss❛♥❞♦ ♣♦r ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❧❡♥t❡s✱ ❈✱ ✉♠ ❞✐❛❢r❛❣♠❛✱ ❉✱ ❡ ♦✉tr♦ ❝♦♥❥✉♥t♦ ❞❡ ❧❡♥t❡s✱ ❑✱ ❝♦♠ ✉♠ ❢❡✐①❡ ❝♦❧✐♠❛❞♦ ❞❡ ❞✐â♠❡tr♦ ♣ró①✐♠♦ ❛ 5 cm✳ P❛r❛ ❡❧✐♠✐♥❛r ❛
✷✳ ❆ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦ ❛♦ ❧♦♥❣♦ ❞♦s sé❝✉❧♦s ✽
❢♦r❛♠ ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛❧✐♥❤❛r ♦ ❢❡✐①❡ ❞❛ ❡sq✉❡r❞❛ ♣❛r❛ ❛ ❞✐r❡✐t❛✳ ❖s ❡s♣❡❧❤♦s ❙1 ❡ ❙4 ❛♦ ❢♦r♠❛r❡♠ ✉♠❛ ♣❡ç❛ ú♥✐❝❛ q✉❡ tr❛♥s❧❛❞❛✱ ♣❡r♠✐t✐❛ ❡s❝♦❧❤❡r q✉❛❧ ❝❛♠✐♥❤♦ ♦ ❢❡✐①❡ ♣♦❞❡r✐❛ ♣❡r❝♦rr❡r✳ ❆♥t❡s ❞♦ ❢❡✐①❡ ✐♥❝✐❞✐r ♥♦ ❜✉❧❜♦✱ ❢♦r❛♠ ❛❞✐❝✐♦♥❛❞❛s ❛s ❧❡♥t❡s✱ ▲1 ❡ ▲2✱ ♣❛r❛ ❢♦❝❛r ♦ ❢❡✐①❡ ❞❡♥tr♦ ❞♦ ❜✉❧❜♦ ❡ ✉♠❛ ❧â♠✐♥❛ ❞❡ ✈✐❞r♦✱ P1✱ ♣❛r❛ ❞❡s✈✐❛r ♣❛rt❡ ❞❛ ♣♦tê♥❝✐❛ ❞♦ ❢❡✐①❡ ♣❛r❛ ✉♠❛ t❡r♠♦♣✐❧❤❛✳ ❆ ❧â♠✐♥❛ P2 ❢♦✐ ♣♦st❛ ❛♦ ❧❛❞♦ ❡sq✉❡r❞♦ ♣❛r❛ ❝♦♠♣❡♥s❛r ❛ ♣♦tê♥❝✐❛ ❞❡s✈✐❛❞❛ ❞♦ ❧❛❞♦ ❞✐r❡✐t♦✳
❋✐❣✉r❛ ✷✳✹✿ ■❧✉str❛çã♦
❞♦ s✉♣♦rt❡ ✉t✐❧✐③❛❞♦ ♣❛r❛ ♣r❡♥❞❡r ❛s ❤é❧✐❝❡s ❬✷✵❪✳ ❋✐❣✉r❛ ✷✳✸✳❜ ❡❧✉❝✐❞❛ ❛s ♦♣çõ❡s ❞❡ ❤é❧✐❝❡s
✉s❛❞❛s ♥♦ ❡①♣❡r✐♠❡♥t♦✳ ❊♠❜♦r❛ ❢❡✐t❛s ❞❡ ✜♥❛s ♣❛❧❤❡t❛s ❞❡ ♠❡t❛❧✱ ❝❛❞❛ ✉♠❛ ♣♦ss✉✐ s✉❛ ❡s♣❡❝✐✜✲ ❝❛çã♦ ❞❡ ❡s♣❡ss✉r❛✱ ♠❛t❡r✐❛❧ ❡ ♠❛ss❛✳ ❆s ❤é❧✐❝❡s sã♦ ❝♦❧♦❝❛❞❛s ❞❡♥tr♦ ❞♦ ❜✉❧❜♦ ❛♥t❡s ❞❡ ❞✐♠✐♥✉✐r ❛ ♣r❡ssã♦ ✐♥t❡r♥❛ ❡ sã♦ ♣r❡s❛s ❛ ✉♠ ❝❛♣✐❧❛r ❞❡ ✈✐❞r♦✱ ❝♦♠♦ ♥❛ ❋✐❣✉r❛ ✷✳✹✳ P❛r❛ ♦❜s❡r✈❛r ❛ r♦✲ t❛çã♦ ❞❛s ❤é❧✐❝❡s✱ ❛♥❡①❛✲s❡ ✉♠ ❡s♣❡❧❤♦ ♣❧❛♥♦ ❛♦ ❝❛♣✐❧❛r ❞❡ ✈✐❞r♦✱ ✉t✐❧✐③❛✲s❡ ✉♠ ❛♥t❡♣❛r♦ ❣r❛❞✉✲ ❛❞♦ ❡ ❧❡♥t❡s t❡❧❡s❝ó♣✐❝❛s✱ ❛s q✉❛✐s sã♦ ❛❧✐♥❤❛❞❛s ❞❡ t❛❧ ❢♦r♠❛ q✉❡ ♣❡r♠✐t❛ ❡♥①❡r❣❛r ❛ ❣r❛❞✉❛çã♦ ❞♦ ❛♥t❡♣❛r♦ ❝♦♠ ♦ ❡s♣❡❧❤♦ ❛♥❡①♦ ❛♦ ❝❛♣✐❧❛r✳
❆♦ ❞✐s♣♦r ❞❡ s✉❛ ❝♦♥s✐❞❡r❛çõ❡s✱ ▲❡❜❡❞❡✇ ❣❛r❛♥t❡ q✉❡ ♦s ♣♦ssí✈❡✐s ❡rr♦s ❞❡ s❡✉s ❡①♣❡r✐♠❡♥✲ t♦s ❡st❛r✐❛♠ ❡♠ t♦r♥♦ ❞❡ 20%✳ ❚❡♥t♦✉ ❞❡t❡r♠✐✲
♥❛r ❛ ✐♥✢✉ê♥❝✐❛ ❞❛s ❢♦rç❛s r❛❞✐♦♠étr✐❝❛s ❛♦ ❝♦♠✲ ♣❛r❛r ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❝♦♠ ♣❛❧❤❡t❛s ✜♥❛s ❡ ❝♦♠ ❣r♦ss❛s✱ ❡♥tr❡t❛♥t♦✱ ♥ã♦ ❛ ❞❡t❡❝t♦✉ ❝❧❛r❛✲ ♠❡♥t❡✱ ♦ q✉❡ ❧❡✈♦✉ ❛ ❝r❡r q✉❡✱ ❡♠ s❡✉ s✐st❡♠❛✱
❡ss❛s ❢♦rç❛s s❡r✐❛♠ ❝♦♠♣❛rá✈❡✐s ❛♦s ❡rr♦s✳ P♦rt❛♥t♦✱ ❝♦♥❝❧✉✐✉ q✉❡ ❛s ❢♦rç❛s ❛s q✉❛✐s s❡r✐❛♠ ❞❡✈✐❞♦ à r❛❞✐❛çã♦ ♥ã♦ ❡st❛r✐❛♠ ❝♦♥❡❝t❛❞❛s à ❝♦♥✈❡❝çã♦ ♦✉ às ❢♦rç❛s r❛❞✐♦✲ ♠étr✐❝❛s✳ ❆ ♣r❡ssã♦ ❞❛ ❧✉③ é ❞✐r❡t❛♠❡♥t❡ ♣r♦♣♦r❝✐♦♥❛❧ à ❡♥❡r❣✐❛ ❞♦ ❢❡✐①❡ ✐♥❝✐❞❡♥t❡ ❡ ♥ã♦ ❞❡♣❡♥❞❡ ❞❡ s❡✉ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♦♥❞❛✳
✷✳ ❆ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦ ❛♦ ❧♦♥❣♦ ❞♦s sé❝✉❧♦s ✾
❋✐❣✉r❛ ✷✳✺✿ ❋♦t♦❣r❛✜❛ ❞♦ ❛rr❛♥❥♦ ❡①♣❡r✐♠❡♥t❛❧ ✉t✐❧✐③❛❞♦ ♣♦r ◆✐❝❤♦❧s ❡ ❍✉❧❧ ❬✹✹❪✳
◆✐❝❤♦❧s ❡ ❍✉❧❧ ♣r♦♣✉s❡r❛♠ q✉❛tr♦ ❛❧t❡r♥❛t✐✈❛s ♣❛r❛ ❞✐♠✐♥✉✐r ❛ ✐♥✢✉ê♥❝✐❛ ❞❛ ❝♦♥✈❡❝çã♦ ❞❡ ❛r ❞❡♥tr♦ ❞♦ ❜✉❧❜♦✿ ✐✮ ❛ s✉♣❡r❢í❝✐❡ ❞❛ ♣❛❧❤❡t❛ q✉❡ r❡❝❡❜❡r✐❛ ❛ r❛❞✐❛çã♦ ❞❡✈❡r✐❛ ❡st❛r ♦ ♠❛✐s r❡✢❡t♦r❛ ♣♦ssí✈❡❧✱ ♣❛r❛ ❡✈✐t❛r ❛ ❛❜s♦rçã♦ ❡✱ ❛ss✐♠✱ ♦ ❛q✉❡❝✐♠❡♥t♦❀ ✐✐✮ ❢❛③❡r ♠❡❞✐❞❛s ✈❛r✐❛♥❞♦ ❛ ♣r❡ssã♦ ✐♥t❡r♥❛✱ ♣♦✐s✱ ❡♠ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ♣r❡ssã♦✱ ♦ ❡❢❡✐t♦ ❞❡✈❡r✐❛ s❡r ♠✐♥✐♠✐③❛❞♦❀ ✐✐✐✮ ❛s ❞✉❛s ♣❛❧❤❡t❛s ❛♥❡①❛s à ❤é❧✐❝❡ ❞❡✈❡r✐❛♠ s❡r ❛s ♠❛✐s s❡♠❡❧❤❛♥t❡s ♣♦ssí✈❡✐s ❡ ❡st❛r❡♠ ♣♦s✐❝✐♦♥❛❞❛s s✐♠❡tr✐❝❛♠❡♥t❡ ❡♠ r❡❧❛çã♦ ❛♦ ❝❛♣✐❧❛r❀ ✐✈✮ ❛ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦ s❡r✐❛ ✉♠ ❡❢❡✐t♦ ✐♥st❛♥tâ♥❡♦✱ ❥á ❛ ❝♦♥✈❡❝çã♦ ❞♦ ❣ás ♦✉ ♦ ❛q✉❡❝✐♠❡♥t♦ sã♦ ❞❡♣❡♥❞❡♥t❡s ❞♦ t❡♠♣♦ ❞❡ ❡①♣♦s✐çã♦✱ ❝❤❡❣❛♥❞♦ à ✉♠❛ ❝♦♥❞✐çã♦ ❡st❛❝✐♦♥ár✐❛✳
✷✳ ❆ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦ ❛♦ ❧♦♥❣♦ ❞♦s sé❝✉❧♦s ✶✵
❋✐❣✉r❛ ✷✳✻✿ ■❧✉str❛çã♦ ❞♦ ❡①♣❡r✐♠❡♥t♦ ✉t✐❧✐③❛❞♦ ♣♦r ◆✐❝❤♦❧s ❡ ❍✉❧❧ ❬✷✶❪✳ ❛✮ ❞❡s❡♥❤♦ ❡sq✉❡♠át✐❝♦ ❞♦ ❛rr❛♥❥♦ ❡①♣❡r✐♠❡♥t❛❧ ❡ ❜✮ ❜✉❧❜♦ ❞❡ ✈✐❞r♦ ❝♦♠ ❛ ❤é❧✐❝❡✳
❡♥tr❡11,2❡0,05mmHg✱ ❛ ❝♦♥✈❡❝çã♦ ♣✉①❛ ❛ ♣❛❧❤❡t❛✳ ❙❡♥❞♦ ❛ss✐♠✱ ❡❧❡s ❝♦♥❝❧✉ír❛♠
q✉❡✱ ❛♦ ❡♠♣r❡❣❛r ✉♠❛ ♣r❡ssã♦ ❡♥tr❡ 19,8❡ 11,2mmHg✱ ♦ ❡❢❡✐t♦ ❞❡ ❝♦♥✈❡❝çã♦ s❡r✐❛
♦ ♠❡♥♦s ✐♥✢✉❡♥t❡ ♣♦ssí✈❡❧✳ ❖ s✐st❡♠❛ ❡♠ ♣r❡ssã♦ ❞❡ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ 16 mmHg
❢♦✐ ❛❞♦t❛❞♦ ♣♦r ❡❧❡s ♥❛s ♠❡❞✐❞❛s✳ ❈♦♥s✐❞❡r❛r❛♠ ♦ t❡♠♣♦ ❞❡ ❡①♣♦s✐çã♦ ❞❛ r❛❞✐❛çã♦ s♦❜r❡ ❛ ♣❛❧❤❡t❛s ❡ ♦ ❞❡♥♦♠✐♥❛r❛♠ ❝❛s♦ ❡stát✐❝♦✱♣♦r ❞❡♠♦♥str❛r ✉♠ ❧♦♥❣♦ ✐♥t❡r✈❛❧♦ ❞❡ t❡♠♣♦ ❞❡ ❡①♣♦s✐çã♦✱ ❡♠ q✉❡ ❛ ❤é❧✐❝❡ ❝❤❡❣❛✈❛ ❛♦ s❡✉ ❡st❛❞♦ ❡st❛❝✐♦♥ár✐♦❀ ❥á ♥♦ ❝❛s♦ ❜❛❧íst✐❝♦✱ ♦ t❡♠♣♦ ❞❡ ❡①♣♦s✐çã♦ ❡r❛ ❝♦♥s✐❞❡r❛❞♦ ❝✉rt♦ s✉✜❝✐❡♥t❡ ♣❛r❛ ♥ã♦ ❣❡r❛r ❛q✉❡❝✐♠❡♥t♦ ❞♦ ❣ás✳ ■ss♦ ♣♦st♦✱ ❞❡✜♥✐r❛♠ q✉❡✱ ♣❛r❛ ♦ ❡①♣❡r✐♠❡♥t♦ ❞❡❧❡s✱ ♦ ✐♥t❡r✲ ✈❛❧♦ ❞❡ t❡♠♣♦ ❜❛❧íst✐❝♦ s❡r✐❛ ❞❡ ✻ s❡❣✉♥❞♦s✱ ♦ q✉❡ s✐❣♥✐✜❝❛r✐❛ ✉♠ q✉❛rt♦ ❞♦ ♣❡rí♦❞♦ ♥❡❝❡ssár✐♦ ♣❛r❛ ❛ ❤é❧✐❝❡ ❝❤❡❣❛r ❛♦ ❡st❛❞♦ ❡st❛❝✐♦♥ár✐♦✳
❚❛♥t♦ ▲❡❜❡❞❡✇ q✉❛♥t♦ ◆✐❝❤♦❧s ❡ ❍✉❧❧ ❝♦♥❝❧✉ír❛♠ t❡r❡♠ ✈✐st♦ ♦s ❡❢❡✐t♦s ❞❡ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦ ❡ q✉❡ ❡ss❡s ❡❢❡✐t♦s ♥ã♦ sã♦ ❞❡♣❡♥❞❡♥t❡s ❞♦ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♦♥❞❛✱ ❡ s✐♠ ❞❛ ♣♦tê♥❝✐❛ ❞❡ ❧✉③ ✐♥❝✐❞❡♥t❡✳ ❊♥q✉❛♥t♦ ▲❡❜❡❞❡✇ ❣❛r❛♥t❡ ❡rr♦s ♠❡♥♦r❡s q✉❡20%♥❛s ♠❡❞✐❞❛s ❞❛ r♦t❛çã♦ ❞❡ s✉❛s ❤é❧✐❝❡s✱ ◆✐❝❤♦❧s ❡ ❍✉❧❧ ♦❢❡r❡❝❡♠ ✈❛❧♦r❡s ♣❛r❛
❛ ♣r❡ssã♦ ❣❡r❛❞❛✳ ❈♦♠♣❛r❛❞♦s ❝♦♠ ✈❛❧♦r❡s ♣r❡✈✐st♦s ♣♦r ▼❛①✇❡❧❧✱ ❡❧❡s ♦❜t✐✈❡r❛♠ ✉♠ ❞❡s✈✐♦ ❞❡ 0,6%✱ ♦ q✉❡ r❡❛✜r♠❛ q✉❛♥t✐t❛t✐✈❛♠❡♥t❡ ❛ t❡♦r✐❛ ❞❡ ▼❛①✇❡❧❧✳
✷✳ ❆ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦ ❛♦ ❧♦♥❣♦ ❞♦s sé❝✉❧♦s ✶✶
✈á❝✉♦ ❡ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ♠♦♠❡♥t♦✳ ◆♦ ❡♥t❛♥t♦✱ ❛♦ ❝♦♥s✐❞❡r❛r ❡ss❡s ❝❛♠♣♦s s❡ ♣r♦♣❛✲ ❣❛♥❞♦ ❞❡♥tr♦ ❞❡ ✉♠ ♠❛t❡r✐❛❧✱ ❞❡✈❡✲s❡ ❞❡❝✐❞✐r ♦ q✉❡ s❡r✐❛ ❛❞❡q✉❛❞♦✿ ✉s❛r ♦ ❝❛♠♣♦ ❡❧étr✐❝♦ ✭E~✮ ♦✉ ♦ ❞❡s❧♦❝❛♠❡♥t♦ ❡❧étr✐❝♦ ✭D~✮❀ ♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ✭H~✮ ♦✉ ❛ ✐♥❞✉çã♦
♠❛❣♥ét✐❝❛ ✭B~✮✳ ❊♠ ✶✾✵✽ ❡ ✶✾✵✾✱ s✉r❣✐r❛♠ ❛s ♣r♦♣♦st❛s ❞❡ ▼✐♥❦♦✇s❦✐ ❡ ❞❡ ❆❜r❛❤❛♠
♣❛r❛ ❞❡✜♥✐r ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ♠♦♠❡♥t♦ ❡❧❡tr♦♠❛❣♥ét✐❝♦ ❡♠ ❞✐❡❧étr✐❝♦s✳ ❊✐♥st❡✐♥ ❡ ▲❛✉❜ t❛♠❜é♠ s✉❣❡r✐r❛♠ ❢♦r♠❛❧✐s♠♦s ♣❛r❛ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ♠♦♠❡♥t♦ ❡♠ ❞✐❡❧étr✐❝♦s ♣♦ré♠✱ ♥ã♦ t✐✈❡r❛♠ ❛❝❡✐t❛çã♦ ♥❛ é♣♦❝❛✱ ♦ ♣ró♣r✐♦ ❊✐♥st❡✐♥ r❡❝♦♥❤❡❝❡✉✱ ❡♠ ✉♠❛ ❝❛rt❛ ♣❛r❛ ❲❛❧t❡r ❉ä❧❧❡♥❜❛❝❤ ❡♠ ✶✾✶✽✱ q✉❡ s❡✉ ❢♦r♠❛❧✐s♠♦ ♥ã♦ ❡st❛r✐❛ ❝♦rr❡t♦ ❬✹✺❪✿
✏■t ❤❛s ❧♦♥❣ ❜❡❡♥ ❦♥♦✇♥ t❤❛t t❤❡ ✈❛❧✉❡s ■ ❤❛❞ ❞❡r✐✈❡❞ ✇✐t❤ ▲❛✉❜ ❛t t❤❡ t✐♠❡ ❛r❡ ✇r♦♥❣❀ ❆❜r❛❤❛♠✱ ✐♥ ♣❛rt✐❝✉❧❛r✱ ✇❛s t❤❡ ♦♥❡ ✇❤♦ ♣r❡s❡♥t❡❞ t❤✐s ✐♥ ❛ t❤♦r♦✉❣❤ ♣❛♣❡r✳ ❚❤❡ ❝♦rr❡❝t str❛✐♥ t❡♥s♦r ❤❛s ✐♥❝✐❞❡♥t❛❧❧② ❛❧r❡❛❞② ❜❡❡♥ ♣♦✐♥t❡❞ ♦✉t ❜② ▼✐♥❦♦✇s❦✐✳✑
▼✐♥❦♦✇s❦✐ ❬✶✽❪ ♣r♦♣ôs ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ♠♦♠❡♥t♦ ❝♦♠♦
~gM =D~ ×B ,~ ✭✷✳✶✮
❥á ❛ ❞❡ ❆❜r❛❤❛♠ ❬✶✾❪ é ❞❛❞❛ ♣♦r
~gA=
~
E×H~
c2 . ✭✷✳✷✮
❆♦ ❝♦♥s✐❞❡r❛r ♠❛t❡r✐❛✐s ❤♦♠♦❣ê♥❡♦s ❡ ✐s♦tró♣✐❝♦s✱ ♦ ♠♦♠❡♥t♦ ❞❡ ✉♠ ❢ót♦♥ ♣❛r❛ ❝❛❞❛ ❝❛s♦ ❛❝✐♠❛ é
pM =
Z
~gMdV =n
~ω
c ✭✷✳✸✮
❡
pA =
Z
~gAdV =
1 n
~ω
c . ✭✷✳✹✮
✷✳ ❆ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦ ❛♦ ❧♦♥❣♦ ❞♦s sé❝✉❧♦s ✶✷
♠❛t❡r✐❛❧ s❡❥❛♠ ❝♦♥trár✐❛s t❛♠❜é♠✳
❆♦ ❧❡✈❛r ❡♠ ❝♦♥t❛ ♦ t❡♥s♦r ❞❡ ❡♥❡r❣✐❛✲♠♦♠❡♥t♦ ♣r♦♣♦st♦ ♣♦r ▼✐♥❦♦✇s❦✐✱ s✉❝❡❞❡ q✉❡ ❛ ❢♦rç❛ ✐♥❞✉③✐❞❛ ♥♦ ♠❛t❡r✐❛❧ t❡r✐❛ ✉♠ ❝❛rát❡r ❞❡ ❡①♣❛♥sã♦✿ t♦❞❛s ❛s ❢♦rç❛s ✐♥t❡r♥❛s ❣❡r❛♠ ✉♠❛ ❢♦rç❛ r❡s✉❧t❛♥t❡ ♥❛ s✉♣❡r❢í❝✐❡ ♣♦r ♦♥❞❡ ♦s ❝❛♠♣♦s ✐♥❝✐❞❡♠✱ ❛ss✐♠✱ ❡❧❛ é ❞✐r❡❝✐♦♥❛❞❛ ♣❛r❛ s❡✉ ❡①t❡r✐♦r ❡ ❛❝❛rr❡t❛ ♥❛ ❡①♣❛♥sã♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞♦ ♠❛t❡r✐❛❧✳ ❆♦ ❝♦♥s✐❞❡r❛r ♦ t❡♥s♦r ❞❡ ❡♥❡r❣✐❛✲♠♦♠❡♥t♦ ❞❡ ❆❜r❛❤❛♠✱ q✉❡ ❛ ❢♦rç❛ ✐♥❞✉③✐❞❛ ♥♦ ♠❛t❡r✐❛❧ ❛t✉❛ ♥♦ ✈♦❧✉♠❡ ❝♦♠ ❝❛rát❡r ❞❡ ❝♦♠♣r❡ssã♦✱ s✉❛ ❢♦rç❛ r❡s✉❧t❛♥t❡ é ❛♣❧✐❝❛❞❛ ♥❛ s✉♣❡r❢í❝✐❡ ❞✐r❡❝✐♦♥❛❞❛ ♣❛r❛ s❡✉ ✐♥t❡r✐♦r✱ ❝♦♥tr❛✐♥❞♦ ❛ s✉♣❡r❢í❝✐❡✳
▼✉✐t♦s ❞❡❜❛t❡s s✉r❣✐r❛♠ ♣❛r❛ ❞❡✜♥✐r q✉❛❧ ♣r♦♣♦st❛ ❡st❛r✐❛ ❝♦rr❡t❛✱ ❝♦♠ ❛ ❝♦♥s✲ t✐t✉✐çã♦ t❡ór✐❝❛ ❞♦ ❡❢❡✐t♦ s❡♠♣r❡ ❡♠ ❢♦❝♦✳ ▼✉✐t♦s tr❛❜❛❧❤♦s t❡ór✐❝♦s ❡✈✐❞❡♥❝✐❛r❛♠ ❛
❋✐❣✉r❛ ✷✳✼✿ ■❧✉str❛çã♦ ❞♦ ❛rr❛♥❥♦ ❡①♣❡✲ r✐♠❡♥t❛❧ ✉t✐❧✐③❛❞♦ ♣♦r ❏♦♥❡s ❬✷✸❪✳ ♥❡❝❡ss✐❞❛❞❡ ❞❛ ♦❜s❡r✈❛çã♦ ❡①♣❡r✐✲
♠❡♥t❛❧ ♣❛r❛ ♠❡❧❤♦r ❣✉✐❛r ♦ ❛✈❛♥ç♦ ♥❛ ❝❛r❛❝t❡r✐③❛çã♦ ❞♦ ❡❢❡✐t♦✳ ❉❡ss❛ ♠❛♥❡✐r❛✱ ✈ár✐♦s ❡①♣❡r✐♠❡♥t♦s ❢♦r❛♠ r❡❛❧✐③❛❞♦s ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ❞❡✜♥✐r q✉❛❧ ❞♦s ❢♦r♠❛❧✐s♠♦s s❡r✐❛ ♦ ❝♦rr❡t♦✳ ❏♦♥❡s ❬✷✸❪✱ ❡♠ ✶✾✺✶✱ ❢♦✐ ♦ ♣r✐✲ ♠❡✐r♦ ❛ ❝♦♥s❡❣✉✐r ♦❜s❡r✈❛r ❛ ♣r❡s✲ sã♦ ❞❡ r❛❞✐❛çã♦ ❡♠ ♠❡✐♦s r❡❢r❛t✐✈♦s✳ ❈♦♠ ♦ ❛rr❛♥❥♦ ❡①♣❡r✐♠❡♥t❛❧ ❝♦♥✲ ❢♦r♠❡ ❛ ❋✐❣✉r❛ ✷✳✼✱ ♦ ♣❡sq✉✐s❛❞♦r ✐♥✲ ❝✐❞✐✉ ✉♠ ❢❡✐①❡ ❞❡ ❧✉③ ❛ss✐♠étr✐❝♦ s♦✲ ❜r❡ ✉♠ ❡s♣❡❧❤♦✱ V✱ ✐♠❡rs♦ ❡♠ ❞✐❢❡✲
r❡♥t❡s ❧íq✉✐❞♦s ❞✐❡❧étr✐❝♦s✱ ❡♥q✉❛♥t♦ ♠♦♥✐t♦r❛✈❛ ♣♦r ♦✉tr♦ ❡s♣❡❧❤♦✱ M✳
❆♠❜♦s ❡s♣❡❧❤♦s ❡r❛♠ ❛♥❡①❛❞♦s ❛ ✉♠ ✜♦ ❞❡ ❝♦❜r❡✱ H✱ ♦ q✉❛❧ s❡r✐❛ ♦
❡✐①♦ ❞❡ r♦t❛çã♦ ❞❡✈✐❞♦ ❛♦ t♦rq✉❡ q✉❡ ❛ r❛❞✐❛çã♦ ❝❛✉s❛r✐❛✳ ❆♦ ♠❡❞✐r ♦ â♥✲ ❣✉❧♦ q✉❡ ♦ ❡s♣❡❧❤♦ M ❣✐r❛✈❛✱ ❡r❛ ❞❡✲
t❡r♠✐♥❛❞♦ ♦ t♦rq✉❡ ❡✱ ❛ss✐♠✱ ❛ t❛①❛ ❞❡ ♠♦♠❡♥t♦ tr❛♥s❢❡r✐❞♦ ❛♦ ❡s♣❡❧❤♦ V✳ ❆♦ ❢❛③❡r
✷✳ ❆ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦ ❛♦ ❧♦♥❣♦ ❞♦s sé❝✉❧♦s ✶✸
✲ ❆❜r❛❤❛♠ ♦✉ ▼✐♥❦♦✇s❦✐ ✲ ❡r❛ ♠❛✐s ♣❡rt✐♥❡♥t❡✳ P♦st❡r✐♦r♠❡♥t❡ ❬✷✹❪✱ ❏♦♥❡s r❡♣❡✲ t✐✉ s❡✉s ❡①♣❡r✐♠❡♥t♦s✱ ♥♦ ❡♥t❛♥t♦✱ s✉❜st✐t✉✐✉ ❛ ❧â♠♣❛❞❛ ❞❡ t✉♥❣stê♥✐♦✱ ❡♠♣r❡❣❛❞❛ ❡♠ s❡✉ tr❛❜❛❧❤♦ ♣r❡❝❡❞❡♥t❡✱ ♣♦r ✉♠ ❧❛s❡r✳ ❉❡ss❡ ♠♦❞♦✱ ❝♦♥s❡❣✉✐✉ ♠❛✐♦r ❞❡✜♥✐çã♦ q✉❛♥t♦ ❛♦ í♥❞✐❝❡ ❞❡ r❡❢r❛çã♦ ❞❡ ❝❛❞❛ ❧íq✉✐❞♦ ❡✱ ❞❡st❛ ✈❡③✱ ❝♦♥❝❧✉✐✉ q✉❡ ♦ ♠♦♠❡♥t♦ t♦t❛❧ ♣♦❞❡r✐❛ ❡st❛r r❡❧❛❝✐♦♥❛❞♦ à ✈❡❧♦❝✐❞❛❞❡ ❞❡ ❢❛s❡✱ nφp✱ ❡♠ ❛❝♦r❞♦ ❝♦♠ ▼✐♥❦♦✇s❦✐✱
♦✉ r❡❧❛❝✐♦♥❛♥❞♦ à ✈❡❧♦❝✐❞❛❞❡ ❞❡ ❣r✉♣♦✱ p/ng✱ ❡♠ ❛❝♦r❞♦ ❝♦♠ ❆❜r❛❤❛♠✳
❋✐❣✉r❛ ✷✳✽✿ ■❧✉str❛çã♦ ❞♦ ❛rr❛♥❥♦ ❡①✲ ♣❡r✐♠❡♥t❛❧ ✉t✐❧✐③❛❞♦ ♣♦r ❲❛❧❦❡r ❡t ❛❧✳ ❬✷✾❪✳
❊♠ ✶✾✻✽✱ ❏❛♠❡s ❞❡t❡❝t♦✉ ❛ ❢♦rç❛ ❞❡ ❆❜r❛❤❛♠ ❬✹✻❪✱ ❛ ❞❡s❝♦❜❡rt❛ ❢♦✐ ❢❡✐t❛ ❞❛ s❡❣✉✐♥t❡ ♠❛♥❡✐r❛✿ ❝♦♠ ❞♦✐s t♦r♦✐✲ ❞❡s ❞❡ ❢❡rr✐t❡ ❛❧✐♥❤❛❞♦s ❡♥tr❡ s✐ ❡ ❝♦✲ ♥❡❝t❛❞♦s ❛ ✉♠ tr❛♥s❞✉t♦r ♣✐❡③♦❡❧étr✐❝♦✱ q✉❛♥❞♦ s✉❥❡✐t♦s ❛ ❝❛♠♣♦s ❡❧étr✐❝♦s ❡ ♠❛❣♥ét✐❝♦s ✈❛r✐❛♥❞♦ ♥♦ t❡♠♣♦✱ ❤á ✐♥✲ ❞✉çã♦ ❞❡ t♦rq✉❡ s❡❣✉♥❞♦ ♦s t❡♥s♦r❡s ❞❡ ❡♥❡r❣✐❛✲♠♦♠❡♥t♦ ❞❡ ▼✐♥❦♦✇s❦✐ ❡ ❆❜r❛❤❛♠✱ ❝♦♥t✉❞♦✱ ❞✐❢❡r❡♠ ❡♠ ♠❛❣✲ ♥✐t✉❞❡✳ ❆♦ ♠❡❞✐r ♦ t♦rq✉❡ ❞♦s t♦r♦✐✲ ❞❡s✱ ♦ ♣❡sq✉✐s❛❞♦r ♥♦t♦✉ q✉❡ ❛ ♠❛❣✲ ♥✐t✉❞❡ ❝♦♥❝♦r❞❛✈❛ ❝♦♠ ♦ ♣r❡✈✐st♦ ♣♦r ❆❜r❛❤❛♠✳
❆❧é♠ ❞❡ ❏❛♠❡s✱ ❲❛❧❦❡r ❡t ❛❧✳ ❬✷✽✱ ✷✾❪✱ ❡♠ ✶✾✼✺✱ ❛♣❧✐❝❛r❛♠ ✉♠ ❝❛♠♣♦ ❡❧é✲ tr✐❝♦ ✈❛r✐á✈❡❧ ♥♦ t❡♠♣♦ ❡♠ ✉♠ ❞✐s❝♦ ❞❡ t✐t❛♥❛t♦ ❞❡ ❜ár✐♦ s✉s♣❡♥s♦ ♣♦r ✉♠❛ ✜✲ ❜r❛ ❞❡ t♦rçã♦ ❡ s♦❜ ✉♠ ❝❛♠♣♦ ♠❛❣♥é✲ t✐❝♦ ❝♦♥st❛♥t❡✱ ❝♦♠♦ ✐❧✉str❛❞♦ ♥❛ ❋✐✲ ❣✉r❛ ✷✳✽✳ ❈♦♠ ✉♠ ❡s♣❡❧❤♦ ❛♥❡①❛❞♦ à
❧❛t❡r❛❧ ❞♦ ❞✐s❝♦✱ ♦❜s❡r✈❛r❛♠ q✉❡ ♦ ❞✐s❝♦ ♣♦ss✉í❛ ✉♠❛ r♦t❛çã♦ ♦s❝✐❧❛♥t❡ ❡ q✉❡ ♦ ♣❡✲ rí♦❞♦ ❞❡ ♦s❝✐❧❛çã♦ ❡r❛ ❝♦♥st❛♥t❡✱ ❡♠ ❛❝♦r❞♦ ❝♦♠ ♦ ❢♦r♠❛❧✐s♠♦ ❞❡ ❆❜r❛❤❛♠✳ ❖ ♠❡s♠♦ ❢♦✐ ❝♦♥✜r♠❛❞♦ ♣♦r ♠❡✐♦ ❞♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ✈❛r✐á✈❡❧ ♥♦ t❡♠♣♦✳
✷✳ ❆ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦ ❛♦ ❧♦♥❣♦ ❞♦s sé❝✉❧♦s ✶✹
❖s ❡①♣❡r✐♠❡♥t♦s ♠❛✐s r❡❧❡✈❛♥t❡s ❛♣❧✐❝❛❞♦s ❡♠ ❧íq✉✐❞♦s ❞✐❡❧étr✐❝♦s ❢♦r❛♠ ❛♣r❡✲ s❡♥t❛❞♦s ♣♦r ❆s❤❦✐♥ ❬✷✺❪✱ ♦ q✉❛❧ r❡♣♦rt♦✉ ❛ ♣r✐♠❡✐r❛ ♦❜s❡r✈❛çã♦ ❞❡ s✉s♣❡♥sã♦ ❞❡ ♣❛rtí❝✉❧❛s ❡♠ ❧íq✉✐❞♦s ❝♦♠ ❧❛s❡r ❝♦♥tí♥✉♦✱ ♦ ❛❝♦♥t❡❝✐♠❡♥t♦ ❢♦✐ ❝♦♥s✐❞❡r❛❞♦ ✉♠ ❞♦s ♠❛✐♦r❡s ❛✈❛♥ç♦s ❞❛ ♥❛t✉r❡③❛ ❞❛ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦✳
❆♦ ✉t✐❧✐③❛r ✉♠ ❧❛s❡r ❞❡ ❆r❣ô♥✐♦✱ ❝♦♠ ❝♦♠♣r✐♠❡♥t♦ ❞❡ ♦♥❞❛ λ = 514,5 nm ❡
❢♦❝❛❞♦ ❝♦♠ r❛✐♦r = 6,2µm✱ ❆s❤❦✐♥ s✉s♣❡♥❞❡✉ ❡s❢❡r❛s ❞❡ ❧át❡① ✐♠❡rs❛s ❡♠ á❣✉❛ ❝♦♠ 0,59µm✱ 1,31µm✱ ❡2,68µm ❞❡ ❞✐â♠❡tr♦✳ ■ss♦ ♣♦st♦✱ ❡❧❡ ♣❡r❝❡❜❡✉ q✉❡✿ ❛♦ ✐♥❝✐❞✐r
♦ ❧❛s❡r✱ ❛s ♣❛rtí❝✉❧❛s ❡r❛♠ ♣✉①❛❞❛s ♣❛r❛ ♦ ❝❡♥tr♦ ❞♦ ❢❡✐①❡ ❡ ❛❝❡❧❡r❛❞❛s ♥❛ ❞✐r❡çã♦ ❞♦ ❢❡✐①❡✱ ♠♦✈❡♥❞♦✲s❡ ❝♦♠ ✈❡❧♦❝✐❞❛❞❡ ❞❡ ❛❧❣✉♥s ♠✐❝r♦♠❡tr♦s ♣♦r s❡❣✉♥❞♦✱ ❛té ❝♦❧✐❞✐r❡♠ ❝♦♠ ❛ s✉♣❡r❢í❝✐❡ ❞♦ s✉♣♦rt❡ ✉t✐❧✐③❛❞♦❀ ❛♦ ❜❧♦q✉❡❛r ❛ ✐♥❝✐❞ê♥❝✐❛ ❞♦ ❧❛s❡r✱ ❛ ♣❛rtí❝✉❧❛ ✈♦❧t❛✈❛ ❛ t❡r ♠♦✈✐♠❡♥t♦ ❇r♦✇♥✐❛♥♦✳ ❈♦♠ ♦ ✉s♦ ❞❡ ❞♦✐s ❧❛s❡rs ✐❣✉❛✐s✱ ✐♥❝✐❞✐♥❞♦ ❡♠ s❡♥t✐❞♦s ♦♣♦st♦s✱ ❛ ♣❛rtí❝✉❧❛ s❡ ♠❛♥t❡✈❡ ❡♠ ✉♠ ♣♦♥t♦ ❞❡ ❡q✉✐❧í❜r✐♦✱ ❛♣r✐s✐♦♥❛❞❛✳ ❊ ❛ss✐♠✱ ♣❡❧❛ ♣r✐♠❡✐r❛ ✈❡③✱ ❢♦✐ r❡❛❧✐③❛❞♦ ♦ ❡①♣❡r✐♠❡♥t♦ q✉❡ ❤♦❥❡ é ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ P✐♥ç❛ Ót✐❝❛✳
❆s❤❦✐♥ ❡ ❉③✐❡❞③✐❝ ❬✷✻❪ r❡❛❧✐③❛r❛♠ ♦✉tr♦ ❡①♣❡r✐♠❡♥t♦ ♣❛r❛ ♦❜s❡r✈❛r ♦s ❡❢❡✐t♦s ❞❡ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦✱ ♠❛s ❞❡st❛ ✈❡③ ❝♦♠ ✉♠ ❧❛s❡r ♣✉❧s❛❞♦ ❛♣❡♥❛s ❡♠ á❣✉❛✳ ❈♦♠♦ ✐❧✉str❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✾✳❛✱ r❡❛❧✐③❛r❛♠ ❡①♣❡r✐♠❡♥t♦s ♣❛ss❛♥❞♦ ✈❡rt✐❝❛❧♠❡♥t❡ ✉♠ ❢❡✐①❡ ❞❡ ❧❛s❡r ❛tr❛✈és ❞❡ ✉♠ r❡s❡r✈❛tór✐♦ ❝♦♥t❡♥❞♦ á❣✉❛ ❡ ❛r✳ P♦r ♦ ❧❛s❡r ❡st❛r ❢♦❝❛❞♦ ♥❛ ✐♥t❡r❢❛❝❡ ❞♦s ✢✉✐❞♦s✱ ❛ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦ ❞❡✈❡ ❣❡r❛r ✉♠❛ ❞❡❢♦r♠❛çã♦✱ ❛ q✉❛❧ s❡r✐❛ ✈✐st❛ ❝♦♠♦ ✉♠ ❡❢❡✐t♦ ❞❡ ❧❡♥t❡ ♥❛ s✉♣❡r❢í❝✐❡ ❞❛ á❣✉❛✳
✷✳ ❆ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦ ❛♦ ❧♦♥❣♦ ❞♦s sé❝✉❧♦s ✶✺
❖ ❡①♣❡r✐♠❡♥t♦ ❝♦♥s✐st✐✉ ❡♠ ♠❡❞✐r ❛s ❞✐♠❡♥sõ❡s ❞♦ ❢❡✐①❡ ❛♦ ♣❛ss❛r ♣❡❧❛ á❣✉❛✳ ■♥✐❝✐❛❧♠❡♥t❡✱ ❛s ♠❡❞✐❞❛s ❢♦r❛♠ r❡❛❧✐③❛❞❛s ♣♦r ♠❡✐♦ ❞♦ ❧❛s❡r ♦♣❡r❛♥❞♦ ❝♦♠ ❜❛✐①❛ ♣♦tê♥❝✐❛ ✭▲P✮✱ ❝♦♠ ♦ ✜♠ ❞❡ ♥ã♦ ❝❛✉s❛r ❛ ❞❡❢♦r♠❛çã♦✱ ♥❛ s❡q✉ê♥❝✐❛✱ ❛s ♠❡❞✐❞❛s ❢♦r❛♠ r❡❛❧✐③❛❞❛s ❝♦♠ ❛❧t❛ ♣♦tê♥❝✐❛ ✭❍P✮ ♣❛r❛ ❣❡r❛r ♦ ❡❢❡✐t♦✳ ❆s ♣r❡❞✐çõ❡s ❞♦s ❛✉t♦r❡s ❡stã♦ ♥❛ ❋✐❣✉r❛ ✷✳✾✳❛✳
❈♦♥s✐❞❡r❛♥❞♦ ❛ ✐♥❝✐❞ê♥❝✐❛ ❞♦ ❢❡✐①❡ ❞❡ ❝✐♠❛ ♣❛r❛ ❜❛✐①♦✱ ♥♦ ❝❛s♦ ❆✿ s❡ ❛ ❢♦rç❛ ❢♦r ♣❛r❛ ❢♦r❛✱ ❛ s✉♣❡r❢í❝✐❡ ❞❡✈❡ ❞✐❧❛t❛r✱ ❛t✉❛♥❞♦✱ ❛ss✐♠✱ ❝♦♠♦ ✉♠❛ ❧❡♥t❡ ❝♦♥✈❡r❣❡♥t❡ ♥♦ ♣ró♣r✐♦ ❢❡✐①❡❀ ♥♦ ❝❛s♦ ❇✱ s❡ ❛ ❢♦rç❛ ❛t✉❛r ♣❛r❛ ❞❡♥tr♦ ❞❛ á❣✉❛✱ ❛ s✉♣❡r❢í❝✐❡ ❞❡✈❡ ❝♦♥tr❛✐r✱ ❛❣✐♥❞♦ ❝♦♠♦ ✉♠❛ ❧❡♥t❡ ❞✐✈❡r❣❡♥t❡✳ ❖s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❢♦r❛♠ ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ ❝❛s♦ ❆✱ é ♣♦ssí✈❡❧ ♦❜s❡r✈❛r ✉♠❛ ❝♦♥✈❡r❣ê♥❝✐❛ ❞♦ ❢❡✐①❡✱ ❝♦♠♦ ♠♦str❛❞♦ ♥❛ ❋✐❣✉r❛ ✷✳✾✳❜✳ ❆s❤❦✐♥ ❡ ❉③✐❡❞③✐❝ ❛✐♥❞❛ ❜✉s❝❛r❛♠ ❝♦♥st❛t❛r s❡ ❛ ❞✐r❡çã♦ ❞❡ ✐♥❝✐❞ê♥❝✐❛ ❞♦ ❢❡✐①❡ ❢❛r✐❛ ❞✐❢❡r❡♥ç❛ ❝♦♠ ♦ ❢❡✐①❡ ✐♥❝✐❞✐♥❞♦ ❞❡ ❜❛✐①♦ ♣❛r❛ ❝✐♠❛✱ ❝❛s♦ ❈✳ ❖ ♠❡s♠♦ r❡s✉❧t❛❞♦ ❢♦✐ ♦❜s❡r✈❛❞♦✱ ✐st♦ é✱ ❛ s✉♣❡r❢í❝✐❡ ❞❛ á❣✉❛ s❡ ❞✐❧❛t❛✳
✷✳✸ ❙é❝✉❧♦ ❳❳■
◆♦ ✜♠ ❞❛ ❞é❝❛❞❛ ❞❡ ✶✾✻✵✱ ❛❧❣✉♥s tr❛❜❛❧❤♦s ❛♣r❡s❡♥t❛r❛♠ ❛ ✐♠♣♦rtâ♥❝✐❛ ❞♦s t❡♥s♦r❡s ❞❡ ❡♥❡r❣✐❛✲♠♦♠❡♥t♦ ❞❡ ♠❛t❡r✐❛✐s ❬✹✼✕✺✸❪✳ ❞❡ ●r♦♦t ❡ ❙✉tt♦r♣ ❬✺✵✕✺✷❪✱ P❡♥✜✲ ❡❧❞ ❡ ❍❛✉s ❬✺✹❪ ❡ t❛♠❜é♠ ●♦r❞♦♥ ❬✺✺❪✱ ♣❡♥s❛♥❞♦ ♥❡ss❡s t❡♥s♦r❡s✱ r❡✈✐r❛♠ ♦ ♣r♦❜❧❡♠❛ ❝♦♠ ♦s t❡♥s♦r❡s ❞❡ ▼✐♥❦♦✇s❦✐ ❡ ❆❜r❛❤❛♠✳ ❊❧❡s ❞❡t❡r♠✐♥❛r❛♠ q✉❡ ❛♦ ❝♦♥s✐❞❡r❛r ♦s ❝❛♠♣♦s ❡❧❡tr♦♠❛❣♥ét✐❝♦s ❞❡♥tr♦ ❞❡ ✉♠ ♠❡✐♦✱ ❞❡✈❡✲s❡ ❞❡✜♥✐r ✉♠ t❡♥s♦r t♦t❛❧✱ ♦ q✉❛❧ s❡r✐❛ ❛ s♦♠❛ ❞♦ t❡♥s♦r ❞❡ ❡♥❡r❣✐❛✲♠♦♠❡♥t♦ ❡❧❡tr♦♠❛❣♥ét✐❝♦✱ T~EM✱ ❝♦♠ ♦ t❡♥s♦r ❞♦
♠❛t❡r✐❛❧✱ T~M E✱
~
T =T~EM +T~M E, ✭✷✳✺✮
❛ss✐♠ ❝♦♠♦ ❛ ❞❡♥s✐❞❛❞❡ ❞❡ ♠♦♠❡♥t♦✱
~g =~gEM +~gM E. ✭✷✳✻✮
✷✳ ❆ ♣r❡ssã♦ ❞❡ r❛❞✐❛çã♦ ❛♦ ❧♦♥❣♦ ❞♦s sé❝✉❧♦s ✶✻
♠♦♠❡♥t♦ ❝❛♥ô♥✐❝♦✱ ❡ ❆❜r❛❤❛♠ r❡❧❛❝✐♦♥❛❞♦ ❛♦ ♠♦♠❡♥t♦ ❝✐♥ét✐❝♦✱ ❞❡ t❛❧ ❢♦r♠❛ q✉❡
~p❝❛♥ô♥✐❝♦meio + Z
~gMdV =~p❝✐♥ét✐❝♦meio +
Z
~gAdV , ✭✷✳✼✮
♦ q✉❡ t♦r♥❛ ❛ ❝♦♥tr♦✈érs✐❛ ❡♠ ❛♣❡♥❛s ✉♠❛ q✉❡stã♦ ❞❡ ❡s❝♦❧❤❛ ❞♦ t❡♥s♦r ❞❡ ❡♥❡r❣✐❛✲ ♠♦♠❡♥t♦ ❞♦ ♠❡✐♦✳ ◆♦ ❡♥t❛♥t♦✱ ✈ár✐♦s ♣❡sq✉✐s❛❞♦r❡s ❛✐♥❞❛ ❜✉s❝❛♠ ❞❡✜♥✐r ♦ ❢♦r♠❛✲ ❧✐s♠♦ ❝♦rr❡t♦ ♦✉ ♦ ♠♦♠❡♥t♦ ❝♦rr❡t♦✳
▼✉✐t♦s tr❛❜❛❧❤♦s t❡ór✐❝♦s ❡ ❡①♣❡r✐♠❡♥t❛✐s ❝♦♥t✐♥✉❛♠ s❡♥❞♦ r❡❛❧✐③❛❞♦s✱ ✉♠❛ ✈❡③ q✉❡ ♠❡s♠♦ q✉❡ ❛ ❝♦♥tr♦✈érs✐❛ t❡♥❤❛ s✐❞♦ r❡s♦❧✈✐❞❛✱ ♥ã♦ ❤á ❝♦♥s❡♥s♦ ❛ r❡s♣❡✐t♦ ❞❡ ❝♦♠♦ s❡r✐❛ ♦ ♠♦♠❡♥t♦ ❞♦ ❢ót♦♥ ✈✐❛❥❛♥❞♦ ❞❡♥tr♦ ❞❡ ✉♠ ♠❡✐♦✱ ❡ ❛✐♥❞❛✱ s♦❜r❡ ❛s ❢♦rç❛s q✉❡ ❛❣❡♠ ❞❡♥tr♦ ❞♦ ♠❛t❡r✐❛❧ ❞❡✈✐❞♦ à ♣r❡s❡♥ç❛ ❞❡ ❝❛♠♣♦s ❡❧❡tr♦♠❛❣♥ét✐❝♦s ♦s❝✐❧❛♥t❡s ❡ ❛s ✐♥✢✉ê♥❝✐❛s ❞❡ss❛s ❢♦rç❛s✳
❉♦s tr❛❜❛❧❤♦s ♠❛✐s r❡❝❡♥t❡s✱ ♦ ❞❡ ❆str❛t❤ ❡t ❛❧✳ ❬✸✺❪ ❡ ♦ ❞❡ ❩❤❛♥❣ ❡t ❛❧✳ ❬✸✻❪ ❡stã♦ r❡❧❛❝✐♦♥❛❞♦s ❞✐r❡t❛♠❡♥t❡ ❛♦ t❡♠❛ ❞❡st❛ t❡s❡ ❡ s❡rã♦ ❞✐s❝✉t✐❞♦s ♥♦s ♣ró①✐♠♦s ❝❛♣ít✉❧♦s✳
❆str❛t❤ ❡t ❛❧✳✱ ❝♦♠ ❜❛s❡ ♥♦ ❡①♣❡r✐♠❡♥t♦ ❞❡ ❆s❤❦✐♥ ❡ ❉③✐❡❞③✐❝ ❬✷✻❪ ❡ ❝♦♠ ♦ ✉s♦ ❞❛ té❝♥✐❝❛ ❞❡ ❊s♣❡❧❤♦ ❋♦t♦tér♠✐❝♦ ❛❞❛♣t❛❞❛✱ ♦❜t✐✈❡r❛♠ ❛ ❞❡❢♦r♠❛çã♦ s✉♣❡r✜❝✐❛❧ ❞❛ á❣✉❛ ❣❡r❛❞❛ ♣♦r r❛❞✐❛çã♦ ❞❡ ❢❡✐①❡ ❧❛s❡r ❝♦♠ ♣r❡❝✐sã♦✱ t❛♥t♦ ♣✉❧s❛❞♦ q✉❛♥t♦ ❝♦♥tí♥✉♦✳ ❉♦✐s ❢❡✐①❡s ❧❛s❡r ❢♦r❛♠ ✉t✐❧✐③❛❞♦s✱ ✉♠ ♣❛r❛ ✐♥❞✉③✐r ❛ ♣r❡ssã♦ ❡ ♦✉tr♦ ♣❛r❛ ♣r♦✈á✲❧❛✳ ◆♦s ❡①♣❡r✐♠❡♥t♦s ❞❡ ❆s❤❦✐♥ ❡ ❉③✐❡❞③✐❝✱ ❛ ♣r❡ssã♦ ✐♥❞✉③✐❛ ✉♠❛ ❞❡❢♦r♠❛çã♦ ❞❛ s✉♣❡r✲ ❢í❝✐❡✱ ❛t✉❛♥❞♦✱ ❛ss✐♠✱ ❝♦♠♦ ✉♠❛ ❧❡♥t❡ ♣❛r❛ ♦ ❢❡✐①❡ tr❛♥s♠✐t✐❞♦✳ ❉❡ss❛ ❢♦r♠❛✱ ❆str❛t❤ ❡t ❛❧✳ ♠♦♥✐t♦r❛r❛♠ ❡ss❛ ❞❡❢♦r♠❛çã♦ ♣♦r ♠❡✐♦ ❞❡ ✉♠ ❢❡✐①❡ ❞❡ ♣r♦✈❛ ❡ ❛❝♦♠♣❛♥❤❛r❛♠ s✉❛ r❡✢❡①ã♦ ♥❛ s✉♣❡r❢í❝✐❡ ❞♦ ✢✉✐❞♦✳ ❈❛s♦ ❛ s✉♣❡r❢í❝✐❡ ❝♦♥tr❛íss❡✱ ❡❧❛ ❛❣✐r✐❛ ❝♦♠♦ ✉♠ ❡s♣❡❧❤♦ ❝ô♥❝❛✈♦✱ ❢❛③❡♥❞♦ q✉❡ ♦ r❛✐♦ ❞♦ ❢❡✐①❡ r❡✢❡t✐❞♦ ❞✐♠✐♥✉íss❡✱ ♥♦ ❡♥t❛♥t♦✱ s❡ ❛ s✉✲ ♣❡r❢í❝✐❡ ❡①♣❛♥❞✐ss❡✱ ❡❧❛ ❛❣✐r✐❛ ❝♦♠♦ ✉♠ ❡s♣❡❧❤♦ ❝♦♥✈❡①♦✱ ❢❛③❡♥❞♦ q✉❡ ♦ r❛✐♦ ❞♦ ❢❡✐①❡ r❡✢❡t✐❞♦ ❛✉♠❡♥t❛ss❡✳ ◆❛ s❡q✉ê♥❝✐❛ ❆str❛t❤ ❡t ❛❧✳ ❝♦♠♣❛r❛r❛♠ q✉❛♥t✐t❛t✐✈❛♠❡♥t❡ s❡✉s r❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ❝♦♠ ❛s s♦❧✉çõ❡s ♥✉♠ér✐❝❛s ❞❛ ❞❡♥s✐❞❛❞❡ ❞❡ ❢♦rç❛ ❡❧❡✲ tr♦♠❛❣♥ét✐❝❛ ❞❡ ❍❡❧♠❤♦❧t③✱ ♣♦r ♠❡✐♦ ❞♦ ▼ét♦❞♦ ❞❡ ❊❧❡♠❡♥t♦s ❋✐♥✐t♦s ❡ ✈❡r✐✜❝❛r❛♠ ♥♦tá✈❡❧ ❝♦♥❝♦r❞â♥❝✐❛✳ ❖✉tr♦ r❡s✉❧t❛❞♦ ✈❡r✐✜❝❛❞♦ ❢♦✐ q✉❡ ❛ ❞❡❢♦r♠❛çã♦ é ❞❡ ❝❛rát❡r ❡①♣❛♥s✐✈♦✱ t❛❧ ❡✈✐❞ê♥❝✐❛ ❝♦♥❝♦r❞❛ ❝♦♠ ♦s ❡①♣❡r✐♠❡♥t♦s ❞❡ ❆s❤❦✐♥ ❡ ❉③✐❡❞③✐❝ ❡ ❝♦♠ ♦ ♠♦♠❡♥t♦ ❞❡ ▼✐♥❦♦✇s❦✐✳
