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Propagation and Reduction of Coherent States in Bargmann Spaces.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Propagation and Reduction of Coherent States in Bargmann Spaces./
作者:	Rousseva, Jenia.
面頁冊數:	1 online resource (140 pages)
附註:	Source: Dissertations Abstracts International, Volume: 84-04, Section: B.
Contained By:	Dissertations Abstracts International84-04B.
標題:	Applied mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29712072click for full text (PQDT)
ISBN:	9798845450203

Propagation and Reduction of Coherent States in Bargmann Spaces.
Rousseva, Jenia.

Propagation and Reduction of Coherent States in Bargmann Spaces. - 1 online resource (140 pages)

Source: Dissertations Abstracts International, Volume: 84-04, Section: B.

Thesis (Ph.D.)--University of Michigan, 2022.

Includes bibliographical references

Coherent states are special types of wavefunctions that minimize a generalized uncertainty principle for a suitable pair of operators. Equivalently, they are eigenstates of an appropriate annihilation operator. Their applications are extensive throughout physics including in quantum optics, nuclear physics, quantum field theory, path integral formulations, and quantum information through the study of entanglement and quantum measurement. This thesis explores two main topics. First, we consider the Schrodinger evolution of a Gaussian coherent state under a non-Hermitian Hamiltonian. We develop a symbol calculus and use it to construct an approximate solution to the time-dependent Schrodinger equation. We find the evolution equations of the center and the Gaussian matrix of the coherent state, which form a system. This result generalizes the previously-known case where the classical Hamiltonian is quadratic. In the second part of the thesis, we apply a quantum version of dimensional reduction to construct Gaussian coherent states in the Bargmann space of complex projective space. The semiclassical properties of these reduced states are controlled by a suitable notion of symbol. Making use of these properties, we provide norm estimates and a propagation result for Hermitian Hamiltonians. As a special case of these reduced states, we define and examine spin-squeezed states that live naturally in the Bargmann space of the Riemann sphere.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798845450203Subjects--Topical Terms:

2122814
Applied mathematics.
Subjects--Index Terms:

Gaussian coherent statesIndex Terms--Genre/Form:

542853
Electronic books.

Propagation and Reduction of Coherent States in Bargmann Spaces.
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520 $a Coherent states are special types of wavefunctions that minimize a generalized uncertainty principle for a suitable pair of operators. Equivalently, they are eigenstates of an appropriate annihilation operator. Their applications are extensive throughout physics including in quantum optics, nuclear physics, quantum field theory, path integral formulations, and quantum information through the study of entanglement and quantum measurement. This thesis explores two main topics. First, we consider the Schrodinger evolution of a Gaussian coherent state under a non-Hermitian Hamiltonian. We develop a symbol calculus and use it to construct an approximate solution to the time-dependent Schrodinger equation. We find the evolution equations of the center and the Gaussian matrix of the coherent state, which form a system. This result generalizes the previously-known case where the classical Hamiltonian is quadratic. In the second part of the thesis, we apply a quantum version of dimensional reduction to construct Gaussian coherent states in the Bargmann space of complex projective space. The semiclassical properties of these reduced states are controlled by a suitable notion of symbol. Making use of these properties, we provide norm estimates and a propagation result for Hermitian Hamiltonians. As a special case of these reduced states, we define and examine spin-squeezed states that live naturally in the Bargmann space of the Riemann sphere.
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