114
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analogları ile ilişkilerini betimlemek açısından bir dizi çıkarım yapılmıştır. Buna göre, 𝑖) faz kazanan parçacıklar her iki etkide de özdeş olmalıdır, 𝑖𝑖) iki olay, singüler bölgelerindeki fiziksel niceliklerin duallerini içermelidir, 𝑖𝑖𝑖) parçacıkların etkileştiği skaler ve vektör potansiyeller (ya da benzeri fiziksel nicelikler) Lorentz ayarında (2.136) denklemini sağlamalıdır. Bu bakış açısından hareketle, VHMW vektör potansiyeli-benzeri teriminden türetilen skaler potansiyel-potansiyeli-benzeri teriminin etkisi ile ortaya çıkacağı düşünülen ve SAB tipi bir etki olan SHMW olayı için düşünsel bir deney düzeneği önerilmiştir.
Üçüncü bölüm, deneysel olarak gözlenen ve güncel çalışmalarla literatürde yer etmiş üç topolojik faz (VAB, VAC ve VHMW) ve ayrıca özel dinamik fazlar (SAB, SAC ve SHMW) için dualite ve özdeşlik ilişkilerinin incelenmesine ayrılmıştır. Yapılan tartışmalar ışığında fazların aralarında betimlenen dualite ve özdeşliklerinin, deneysel olarak henüz gözlenmemiş (manyetik potansiyellerle ilişkili) dördüncü bir topolojik fazın ve skaler analoğunun varlığına işaret ettikleri saptanmış, DVAB ve DSAB olarak isimlendirilen bu fazlar için matematiksel temellendirmeler yapılarak düşünsel deney düzenekleri önerilmiştir.
Dördüncü bölümde, bir ön hazırlık olarak kuantum mekaniğinde durum kavramının etraflıca incelenmesinin ardından, Einstein, Podolsky ve Rosen tarafından önerilen ve daha sonra yapılan çalışmalar ile şekillenen deterministik yerel saklı değişken modellerin uyması beklenen Bell eşitsizlikleri ve bu modellerin deneysel olarak sınanabilmesini olanaklı kılan (aynı zamanda Bell eşitsizliklerinin bir versiyonu olan) CHSH eşitsizlikleri türetilmiştir. Bell-CHSH eşitsizlikleri, iki ve üç boyutlu uzaylarda kuantum mekaniksel beklenen değerler tarafından maksimum derecede ihlal edilen açılarla birlikte sınanmıştır.
Tezin son evresinde, geometrik ve topolojik fazların dolanık kuantum durumlarına etkileri ele alınmıştır. Bu kapsamda, ilk olarak, geometrik fazın etkileşim Hamiltonyeninin anlık enerji özdeğerleri ve keyfi 𝒏̂ doğrultusundaki spin operatörünün ilişkili anlık özvektörlerinin bulunabildiği dolanık bir sisteme olan etkileri bulunmuş, CHSH eşitsizliğinin, geometrik fazın 𝑛𝜋 −1
2𝑐𝑜𝑠−1(√2 − 1) < 𝛾 < 𝑛𝜋 −12𝜋
aralığın-116
da alacağı tüm değerler için ihlal edildiği görülmüştür. Daha sonra, topolojik fazların dolanık kuantum sistemlerine olan etkilerinin ortaya konulabilmesi için, VAB ve VAC olaylarının (ya da dualite ve özdeşlik ilişkileri uyarınca DVAB ve VHMW olaylarının), üç boyutlu sistemlerin Hamiltonyenlerinin serbest ve etkileşim terimlerinin toplamı olarak ifade edilmesinde karşılaşılan güçlükler göz önünde bulundurularak, iki boyutlu uzaya sıkıştırılmış melez (hibrit) sistemlerde incelenmesine karar verilmiştir.
Bu bağlamda, ilk olarak, göreli olmayan kuantum mekaniği çerçevesinde ayar potansiyelleri vasıtası ile basitçe açıklanabilen VAB olayı, göreli kuantum mekaniği kapsamında ele alınarak fazın dolanık kuantum durumlarına olası etkileri araştırılmış, efektif VAB Hamiltonyeninin ve VAB fazının spin polarizasyonlarına bağlı olmamasından ötürü dolanık kuantum durumlarına ölçülebilir etkilerinin olamayacağı sonucuna ulaşılmıştır. Bu sonuç, spin polarizasyon durumlarına açıkça bağlı olmayan tüm topolojik fazlar için doğru olacağından, DVAB olayının da dolanık kuantum sistemlerine ölçülebilir etkilerinin olamayacağı şeklinde genelleştirilmiştir.
İkinci olarak, bütünüyle göreli kuantum mekaniği çerçevesinde incelenen VAC olayında, efektif VAC Hamiltonyeni ve topolojik fazın iki boyutlu uzayda Clifford cebrini sağlayan iki farklı temsili için (𝑠 = ± 1) yukarı ve aşağı spin polarizasyon durumlarına bağlı oldukları bulunmuş, çizgisel yük dağılımının dolanık bir kuantum sistemi için CHSH eşitsizliğine, 𝑆(𝛿𝑉𝐴𝐶) = √2 + √2|𝑐𝑜𝑠(2𝜇𝜆)|, yeni bir değişken olarak gireceği herhangi bir yaklaşıklık ya da kabul yapılmaksızın gösterilmiştir. VAC olayı için elde edilen sonuçlar (VHMW olayı için de doğrudur), kuantum mekaniğinin lokal olmayan özelliklerinin sınanması amacıyla gelecekte yapılacak olan çalışmalar açısından deneysel bir test niteliği taşımaktadır. Topolojik fazlar için iki boyutta yapılan incelemelerin ve ulaşılan sonuçların, geometrik fazlar için yapılan analizlerden daha sade ve uygulanabilir oldukları da açıktır. Bu perspektiften hareketle, VAC fazı VAB fazından daha genel bir topolojik faz olarak yorumlanmış; VAB fazı, VAC olayında hareketli dipollerin durgun çerçevelerinde ortaya çıkan polarize edilmiş, topolojik bir kuantum etkisi olarak tanımlanmıştır.
117
Son olarak, VAB olayı için tasarlanan melez deney düzeneğinin, literatürde sıklıkla yer alan ve VAB olayında elektronların spin oryantasyonlarının önemini araştıran çalışmalar açısından deneysel bir sınama aracı olarak kullanılabileceği gösterilerek çalışma tamamlanmıştır.
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131 ÖZGEÇMİŞ
Adı Soyadı : Hasan Özgür ÇILDIROĞLU Doğum Yeri : Ankara-Altındağ
Doğum Tarihi : 19 Nisan 1988 Medeni Hali : Bekar
Yabancı Dili : İngilizce - Almanca
Eğitim Durumu
Lise : Fethiye Kemal Mumcu Anadolu Lisesi (2006), Ankara Lisans : Hacettepe Üniversitesi Mühendislik Fakültesi
Fizik Mühendisliği Bölümü (2011), Ankara.
Anadolu Üniversitesi Açıköğretim Fakültesi Sosyoloji Bölümü (2020), Eskişehir.
Yüksek Lisans : Hacettepe Üniversitesi Fen Bilimleri Enstitüsü Fizik Mühendisliği Bölümü (2015), Ankara.
Doktora : Ankara Üniversitesi Fen Bilimleri Enstitüsü Fizik Mühendisliği Bölümü (2020), Ankara.
Çalıştığı Kurumlar
2014-2015 : Ankara Üniversitesi Mühendislik Fakültesi Fizik Mühendisliği Bölümü Genel Fizik Anabilim Dalı
2015-2016 : Hacettepe Üniversitesi Mühendislik Fakültesi Fizik Mühendisliği Bölümü Genel Fizik Anabilim Dalı
2016- : Ankara Üniversitesi Mühendislik Fakültesi Fizik Mühendisliği Bölümü Fizik Mühendisliği Anabilim Dalı
Yayınlar
Çıldıroğlu, H.O. and Yılmazer. A.U. 2018. Topological effects of Aharonov-Bohm type and the role of the quantum entanglement. AIP Conference Proceedings 2042, 020045.
Çıldıroğlu, H.O. and Yılmazer, A.U. 2019. Dual scalar Aharonov Bohm phase. AIP Conference Proceedings 2178, 030047.
Hashemi, B., Çıldıroğlu, H.O. and Yılmazer, A.U. 2019. Scalar He-Mckellar-Wilkens effect. AIP Conference Proceedings 2178, 030046.