Geometric Phases in Open Quantum Systems: Analysis and Applications
- URL: http://arxiv.org/abs/2307.03825v1
- Date: Fri, 7 Jul 2023 20:39:24 GMT
- Title: Geometric Phases in Open Quantum Systems: Analysis and Applications
- Authors: Ludmila Viotti
- Abstract summary: This thesis explores the relation between decoherence and environmentally-induced dissipative effects.
The first mention of such an object in the context of quantum mechanics goes back to the seminal work by Berry.
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: This thesis consists of several studies performed over different few-dof
quantum systems exposed to the effect of an uncontrolled environment. The
primary focus of the work is to explore the relation between decoherence and
environmentally-induced dissipative effects, and the concept known as geometric
phases. The first mention of such an object in the context of quantum mechanics
goes back to the seminal work by Berry. He demonstrated that the phase acquired
by an eigenstate of a time-dependent Hamiltonian in an adiabatic cycle consists
of two distinct contributions: one termed 'geometric' and the other known as
the dynamical phase. Since Berry's work, the notion of geometric phase has been
extended far beyond the original context, encompassing definitions applicable
to arbitrary unitary evolutions. These geometric phases naturally arise in the
geometric description of Hilbert space, where they manifest as holonomies and
possess significance in the fundamental understanding of quantum mechanics and
its mathematical framework, and in explaining various physical phenomena,
including the Fractional Hall Effect. Moreover, from a modern perspective,
geometric phases hold promise for practical applications, such as constructing
geometric gates for quantum information processing and storage. However, in
practice, a pure state of a quantum system is an idealized concept, and every
experimental or real-world implementation must account for the presence of an
environment that interacts with the observed system. This interaction
necessitates a description in terms of mixed states and non-unitary evolutions.
The definition of a geometric phase applicable in such scenarios remains an
open problem, giving rise to multiple proposed solutions. Consequently,
characterizing these geometric phases encompase motivations from fundamental
aspects of quantum mechanics to technological applications.
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