Диссертация (1149995), страница 10
Текст из файла (страница 10)
Ýòî ñâÿçàíî ñ òåì, ÷òî áîçîíèçàöèÿ íà÷èíàåòñÿ ñ ÑÒ óðàâíåíèé Ðà èàíàëèçèðóåò ñêåéëèíãîâûå ðàçìåðíîñòè âîçìóùåíèé âîêðóã íåå. Íàìè ïîêàçàíî, ÷òî ñêåéëèíãîâûå ðàçìåðíîñòè (ïîêàçàòåëè) ìàñøòàáèðîâàíèÿ íå çàâèñÿòîò âûáîðà ïîòîêà ÐÃ: ïðåôàêòîðû ïåðåä ïîêàçàòåëÿìè ìàñøòàáèðîâàíèÿ îïðåäåëÿþòñÿ êîíêðåòíîé òðàåêòîðèåé ÐÃ, âåäóùåé èç óäàëåííûõ òî÷åê â ïðîñòðàíñòâå ïàðàìåòðîâ ê îáëàñòè, ëåæàùåé â íåïîñðåäñòâåííîé áëèçîñòè îò ÑÒ. Ìûïîëàãàåì, ÷òî îáñóæäàåìàÿ íåîïðåäåëåííîñòü ìîæåò áûòü âàæíà äëÿ äàëüíåéøèõ òåîðåòè÷åñêèõ è ýêñïåðèìåíòàëüíûõ èññëåäîâàíèé â îáëàñòè X-îáðàçíûõêîíòàêòîâ ìåæäó êâàíòîâûìè ïðîâîëîêàìè.64ÇÀÊËÞ×ÅÍÈÅÏîäâîäÿ èòîãè äàííîé ðàáîòû, ìîæíî ñêàçàòü, ÷òî èñïîëüçîâàíèå íåïåðòóðáàòèâíîãî ôåðìèîííîãî ðåíîðìãðóïïîâîãî ïîäõîäà äëÿ àíàëèçà êîíäàòêàíñîâ êîíòàêòà êâàíòîâûõ íèòåé ïîçâîëÿåò óñïåøíî ïðîâîäèòü èõ èññëåäîâàíèå èèçó÷àòü îñîáåííîñòè âëèÿíèÿ âçàèìîäåéñòâèÿ â ñèëüíîêîððåëèðîâàííûõ ýëåêòðîííûõ ñèñòåìàõ.Ïåðå÷èñëèì îñíîâíûå ðåçóëüòàòû, èçëîæåííûå â äèññåðòàöèè.1.
Èññëåäîâàí êîíòàêò äâóõ ãåëèêîèäàëüíûõ ñîñòîÿíèé â ïîäõîäå ôåðìèîííîé ðåíîðìãðóïïû ñ ó÷åòîì âçàèìîäåéñòâèÿ ñ ïîìîùüþ ëåñòíè÷íîãîñóììèðîâàíèÿ. Ïðîâåäåí ïîëíûé Ðà àíàëèç êîíäàêòàíñîâ òàêîãî ñòûêà:ïîëó÷åíû Ðà óðàâíåíèÿ, èçó÷åíû èõ ñòàöèîíàðíûå òî÷êè è ñêåéëèíãîâûåïîêàçàòåëè êîíäàêòàíñîâ âáëèçè ýòèõ òî÷åê.
Ýòî ñäåëàíî â îáùåì ñëó÷àå, êîãäà âåëè÷èíû âçàèìîäåéñòâèÿ â ðàçíûõ êðàåâûõ ñîñòîÿíèé ìîãóòíå ñîâïàäàòü.2. Ïðîàíàëèçèðîâàíî òóííåëèðîâàíèå â ãåëèêîèäàëüíîå ñîñòîÿíèå èç êâàíòîâîé íèòè. Ðàññìîòðåíû äâà ñëó÷àÿ ïîëÿðèçàöèè ýëåêòðîíîâ ïî ñïèíóâ òàêîé íèòè. Äëÿ ñëó÷àÿ ýëåêòðîíîâ íåïîëÿðèçîâàííûõ ïî ñïèíó ïîëó÷åíî îïðåäåëåííîå ñîîòíîøåíèå ìåæäó êîíäàêòàíñàìè, êîòîðîå îñòàåòñÿ íåèçìåííûì ïðè èõ ïåðåíîðìèðîâêå. Äëÿ ñëó÷àÿ ïîëÿðèçàöèè ñïèíîâýëåêòðîíîâ ïîêàçàíî, ÷òî âîçíèêàåò ïåðåíîðìèðîâêà àñèììåòðèè êîíòàêòà ñîâìåñòíî ñ òóííåëüíûì êîíäàêòàíñîì òàêîé ñèñòåìû.3.
Îáíàðóæåíî ÿâëåíèå íåîäíîçíà÷íîãî îïðåäåëåíèÿ Ðà ïîòîêîâ êîíäàêòàíñîâ äëÿ êðåñòîîáðàçíîãî ñòûêà íèòåé ñ áåññïèíîâûìè ôåðìèîíàìè. Ýòèóðàâíåíèÿ âêëþ÷àþò äîïîëíèòåëüíóþ äèñêðåòíóþ ôàçó S -ìàòðèöû. Òàêèì îáðàçîì, ñóùåñòâóþò äâà íàáîðà Ðà óðàâíåíèé äëÿ ïðîèçâîëüíîãî íà÷àëüíîãî çíà÷åíèÿ êîíäàêòàíñîâ. Ýòà íåîäíîçíà÷íîñòü íå âëèÿåò íà ñêåéëèíãîâûå ïîêàçàòåëè êîíäàêòàíñîâ âáëèçè ñòàöèîíàðíûõ òî÷åê, ïîýòîìóâ àëüòåðíàòèâíîì ïîäõîäå áîçîíèçàöèè ýòî ÿâëåíèå íå îáíàðóæèòü. áóäóùåì ìåòîäû íåïåðòóðáàòèâíîé ôåðìèîííîé ðåíîðìãðóïïû ìîãóò îêàçàòüñÿ ïîëåçíûìè, íàïðèìåð, ïðè èçó÷åíèè êîíäàêòàíñîâ êîíòàêòîâ íèòåé äëÿ65íåðàâíîâåñíîãî ñëó÷àÿ [81] ñ èñïîëüçîâàíèåì òåõíèêè Êåëäûøà [82].
Ðåçóëüòàòû èçó÷åíèÿ êîíòàêòîâ íèòåé ìîæíî ïðèìåíèòü â óñòðîéñòâàõ ñ èñïîëüçîâàíèåì ïàð êîíòàêòîâ è êîëüöà â èíòåðôåðîìåòðàõ Ààðîíîâà-Áîìà [83]. Íàïðèìåð, ó÷åñòü âëèÿíèå âçàèìîäåéñòâèÿ íà ýëåêòðîííûé òðàíñïîðò òàêîãî óñòðîéñòâà [84] è ïðîâåñòè ðàñ÷åò êîíäàêòàíñà èíòåðôåðîìåòðà â ñëó÷àå âûñîêèõ òåìïåðàòóð [85] äëÿ ãåëèêîèäàëüíûõ ñîñòîÿíèé â êîëüöå.ÁëàãîäàðíîñòèÄèññåðòàíò õî÷åò ïîáëàãîäàðèòü ñâîåãî ñîàâòîðà è íàó÷íîãî ðóêîâîäèòåëÿä.ô.-ì.í. Ä.Í. Àðèñòîâà çà öåííûå ñîâåòû è ïîääåðæêó â ïîäãîòîâêå ìàòåðèàëîâ äèññåðòàöèè.Õîòåëîñü áû âûðàçèòü áëàãîäàðíîñòü ìîåé ñåìüå, âñåãäà ìåíÿ ïîääåðæèâàþùåé, â òîì ÷èñëå âî âðåìÿ ðàáîòû íàä äèññåðòàöèåé. Îñîáåííî áàáóøêå,ïåðåæèâàþùåé çà óñïåøíîñòü ìîåé çàùèòû èç-çà îáñòîÿòåëüñòâ, êîòîðûå ïîìåøàëè åé â ñâîå âðåìÿ çàùèòèòü êàíäèäàòñêóþ äèññåðòàöèþ.
È âäîõíîâëÿþùåìóìåíÿ ÷åëîâåêó Íåëëè Ïèëèïåíêî.Çà äîïîëíèòåëüíóþ ìîòèâàöèþ ê íàïèñàíèþ ðàáîòû õî÷ó ïîáëàãîäàðèòüäðóçåé, çàùèòèâøèõñÿ ðàíüøå ìåíÿ.66ÑÏÈÑÎÊ ËÈÒÅÐÀÒÓÐÛ1. Observation of majorana quantum critical behaviour in a resonant level cou-pled to a dissipative environment / H. T. Mebrahtu, I. V. Borzenets, H.
Zhenget al. // Nat Phys. — 2013. — Nov. — Vol. 9, no. 11. — P. 732–737.2. Atomically controlled quantum chains hosting a tomonaga-luttinger liquid /C. Blumenstein, J. Schafer, S. Mietke et al. // Nat Phys. — 2011. — Oct. —Vol. 7, no. 10. — P. 776–780.3. Tomonaga-luttinger physics in electronic quantum circuits / S.
Jezouin, M. Albert, F. D. Parmentier et al. // Nat Commun. — 2013. — Apr. — Vol. 4. —P. 1802–.4. Quantum spin hall insulator state in HgTe quantum wells / M. König,S. Wiedmann, C. Brune et al. // Science. — 2007. — nov. — Vol. 318, no.5851. — P. 766–770.5. Hasan M. Z., Kane C. L. Colloquium // Rev. Mod. Phys. — 2010. — Nov. —Vol. 82. — P. 3045–3067.6. Qi X.-L., Zhang S.-C. Topological insulators and superconductors // Rev.Mod.
Phys. — 2011. — Oct. — Vol. 83. — P. 1057–1110.7. Aristov D. N., Niyazov R. A. Ambiguity in renormalization of the conductanceof an x-junction between quantum wires with a luttinger-type interaction //Theoretical and Mathematical Physics. — 2015. — oct. — Vol. 185, no. 1. —P. 1408–1416.8. Aristov D.
N., Niyazov R. A. Tunneling into and between helical edge states:Fermionic approach // Phys. Rev. B. — 2016. — Jul. — Vol. 94. — P. 035429.9. Aristov D. N., Niyazov R. A. Spin-polarized tunneling into helical edge states:Asymmetry and conductances // EPL. — 2017. — Vol. 117, no. 2. — P. 27008.10. Sólyom J. The Fermi gas model of one-dimensional conductors // Advancesin Physics. — 1979. — Mar. — Vol.
28. — P. 201–303.6711. Shankar R. Renormalization-group approach to interacting fermions // Rev.Mod. Phys. — 1994. — Jan. — Vol. 66. — P. 129–192.12. Voit J. One-dimensional fermi liquids // Reports on Progress in Physics. —1995. — Vol. 58, no. 9. — P. 977.13. Fisher M. P. A., Glazman L. I.
Transport in a one-dimensional luttinger liquid. — arXiv : cond-mat.mes-hall/cond-mat/9610037v1.14. von Delft J., Schoeller H. Bosonization for beginners - refermionization forexperts // Annalen der Physik. — 1998. — Vol. 7, no. 4. — P. 225–305.15. Schulz H. J., Cuniberti G., Pieri P. Fermi liquids and luttinger liquids.
—arXiv : cond-mat.str-el/cond-mat/9807366v2.16. Gogolin A. O., Nersesyan A. A., Tsvelik A. M. Bosonization and stronglycorrelated systems. — Cambridge university press, 2004.17. Tsvelik A. M. Quantum field theory in condensed matter physics. — Cambridge university press, 2007.18. Maslov D. L. Fundamental aspects of electron correlations and quantumtransport in one-dimensional systems. — 2005. — Jun. — arXiv : condmat/0506035.19. Giamarchi T. Quantum Physics in One Dimension.
— Clarendon; Oxford University Press, 2004. — Vol. 121 of The international series of monographs onphysics.20. Schönhammer K. Physics in one dimension: theoretical concepts for quantummany-body systems // Journal of Physics: Condensed Matter. — 2013. —Vol. 25, no. 1. — P. 014001.21. Caux J.-S., Smith C. M. Celebrating haldane’s ‘luttinger liquid theory’. —arXiv : cond-mat.str-el/1702.03735v1.22. Guan X.-W., Batchelor M. T., Lee C. Fermi gases in one dimension: Frombethe ansatz to experiments // Rev.Vol.
85. — P. 1633–1691.68Mod.Phys. — 2013. — Nov. —23. Landau L. The theory of a fermi liquid // Soviet Physics Jetp-Ussr. — 1957. —Vol. 3, no. 6. — P. 920–925.24. Abrikosov A. A., Gorkov L. P., Dzyaloshinski I. E. Methods of quantum fieldtheory in statistical physics. — Courier Corporation, 2012.25. Bloch Z. Inkohärente röntgenstreuung und dichteschwankungen eines entarteten fermigases // Helv. Phys. Acta. — 1934. — Vol. 7.
— P. 385.26. Tomonaga S.-i.Remarks on bloch’s method of sound waves applied tomany-fermion problems // Progress of Theoretical Physics. — 1950. — Vol. 5,no. 4. — P. 544–569.27. Luttinger J. An exactly soluble model of a many-fermion system // Journalof Mathematical Physics. — 1963. — Vol. 4, no.
9. — P. 1154–1162.28. Theumann A. Single-particle green’s function for a one-dimensional manyfermion system // Journal of Mathematical Physics. — 1967. — Vol. 8,no. 12. — P. 2460–2467.29. Dzyaloshinskii I., Larkin A. Correlation functions for a one-dimensional fermisystem with long-range interaction (tomonaga model) // JETP.
— 1974. —jan. — Vol. 38, no. 1. — P. 202.30. Haldane F. ’luttinger liquid theory’ of one-dimensional quantum fluids. i.properties of the luttinger model and their extension to the general 1d interacting spinless fermi gas // Journal of Physics C: Solid State Physics. —1981. — Vol. 14, no. 19. — P. 2585.31. Giamarchi T., Schulz H.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
