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The Curious Case of the Inverted Oscillator: On the Dynamics and Symmetries of Quadratic Potentials in the Lowest Landau Level
The Curious Case of the Inverted Oscillator: On the Dynamics and Symmetries of Quadratic Potentials in the Lowest Landau Level
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202105209
- ISBN
- 9798291563632
- DDC
- 530
- 서명/저자
- The Curious Case of the Inverted Oscillator: On the Dynamics and Symmetries of Quadratic Potentials in the Lowest Landau Level
- 발행사항
- [Sl] : University of Illinois at Urbana-Champaign, 2023
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2023
- 형태사항
- 187 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 87-03, Section: B.
- 주기사항
- Advisor: Fradkin, Eduardo.
- 학위논문주기
- Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2023.
- 초록/해제
- 요약Scattering and interferometry in the lowest Landau level serve as important probes of quantum Hall matter. In this work, we focus on the non-commutative nature of the lowest Landau level and its invariance under area preserving transformations, and the physical implications of these properties on such probes. Borrowing from quantum optics literature, we model quantum point contacts and other and aspects of these probes as quadratic potentials, and study the dynamics they generate in the lowest Landau level, particularly in coherent states that obey the anyonic boundary condition. We study such dynamics in two ways - in terms of evolution of coherent state distributions over the lowest Landau level, as well as in terms of trajectories in an effective phase space obtained from these coherent states. These resulting trajectories offer interesting insights that serve to distinguish between Abelian anyons of differing statistical phase factors, as well as the emergence of an effective "statistical force" in the semi-classical limit. We then focus particularly on the properties of a specific quadratic potential - the inverted harmonic oscillator, as a model for quantum point contacts. In the lowest Landau level, the transmission amplitude of the point contact has a "thermal" form, and shares crucial parallels with the Hawking-Unruh effect in uniformly accelerated spacetimes, like those associated with black holes. We show these parallels to be a result of their shared isomorphic symmetries unique to the physics of (2+1) dimensional spaces. Consequently, these connections lead to the possibility of realizing other relativistic phenomena like Wigner rotation, and time-decaying modes with quantized decay rates among the scattered states in the lowest Landau level. We then demonstrate possible physical avenues where these modes can be detected. Lastly, we take a brief detour to discuss non-Abelian anyons and their exchange properties. Specifically, we study the nucleation of Majorana bound states in two dimensional topological Josephson junctions through the application of magnetic flux in the junction area. We locate the bound states in the geometry of our system and then construct trijunction and four-point crossroad junctions as an extension of these ideas. We then provide two proof-of-concept braiding schemes to exchange the Majorana bound states and design readout mechanisms that employ a series of projective measurements using quantum dots as charge or parity detectors. We finally end with a brief summary and outlook on the work presented here.
- 일반주제명
- Condensed matter physics
- 일반주제명
- Energy
- 일반주제명
- Quantum physics
- 일반주제명
- Atomic physics
- 키워드
- Anyons
- 키워드
- Rindler physics
- 키워드
- Squeezing
- 키워드
- Quantum optics
- 기타저자
- University of Illinois at Urbana-Champaign Physics
- 기본자료저록
- Dissertations Abstracts International. 87-03B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■020 ▼a9798291563632
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■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a530
■1001 ▼aSubramanyan, Varsha.
■24510▼aThe Curious Case of the Inverted Oscillator: On the Dynamics and Symmetries of Quadratic Potentials in the Lowest Landau Level
■260 ▼a[Sl]▼bUniversity of Illinois at Urbana-Champaign▼c2023
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2023
■300 ▼a187 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 87-03, Section: B.
■500 ▼aAdvisor: Fradkin, Eduardo.
■5021 ▼aThesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2023.
■520 ▼aScattering and interferometry in the lowest Landau level serve as important probes of quantum Hall matter. In this work, we focus on the non-commutative nature of the lowest Landau level and its invariance under area preserving transformations, and the physical implications of these properties on such probes. Borrowing from quantum optics literature, we model quantum point contacts and other and aspects of these probes as quadratic potentials, and study the dynamics they generate in the lowest Landau level, particularly in coherent states that obey the anyonic boundary condition. We study such dynamics in two ways - in terms of evolution of coherent state distributions over the lowest Landau level, as well as in terms of trajectories in an effective phase space obtained from these coherent states. These resulting trajectories offer interesting insights that serve to distinguish between Abelian anyons of differing statistical phase factors, as well as the emergence of an effective "statistical force" in the semi-classical limit. We then focus particularly on the properties of a specific quadratic potential - the inverted harmonic oscillator, as a model for quantum point contacts. In the lowest Landau level, the transmission amplitude of the point contact has a "thermal" form, and shares crucial parallels with the Hawking-Unruh effect in uniformly accelerated spacetimes, like those associated with black holes. We show these parallels to be a result of their shared isomorphic symmetries unique to the physics of (2+1) dimensional spaces. Consequently, these connections lead to the possibility of realizing other relativistic phenomena like Wigner rotation, and time-decaying modes with quantized decay rates among the scattered states in the lowest Landau level. We then demonstrate possible physical avenues where these modes can be detected. Lastly, we take a brief detour to discuss non-Abelian anyons and their exchange properties. Specifically, we study the nucleation of Majorana bound states in two dimensional topological Josephson junctions through the application of magnetic flux in the junction area. We locate the bound states in the geometry of our system and then construct trijunction and four-point crossroad junctions as an extension of these ideas. We then provide two proof-of-concept braiding schemes to exchange the Majorana bound states and design readout mechanisms that employ a series of projective measurements using quantum dots as charge or parity detectors. We finally end with a brief summary and outlook on the work presented here.
■590 ▼aSchool code: 0090.
■650 4▼aCondensed matter physics
■650 4▼aEnergy
■650 4▼aQuantum physics
■650 4▼aAtomic physics
■653 ▼aQuantum hall effect
■653 ▼aAnyons
■653 ▼aRindler physics
■653 ▼aQuantum point contacts
■653 ▼aSqueezing
■653 ▼aQuantum optics
■690 ▼a0611
■690 ▼a0599
■690 ▼a0748
■690 ▼a0791
■71020▼aUniversity of Illinois at Urbana-Champaign▼bPhysics.
■7730 ▼tDissertations Abstracts International▼g87-03B.
■790 ▼a0090
■791 ▼aPh.D.
■792 ▼a2023
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17359757▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
