Symmetry and Natural Quantum Structures for Three-Particles in One-Dimension

Harshman, N. L.

doi:10.1142/9781786341419_0011

Cited by 4 publications

(6 citation statements)

References 32 publications

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“…As discussed in [26], this kind of spectral separability distinguishes Hamiltonians with 'silver' and 'gold' separability from 'bronze' separability (this is a different notion of separability than topological separability; see more discussion in Sect. IV D below).…”

Section: B Observable-induced Direct Sum Decompositionmentioning

confidence: 99%

“…For many models, the joint spectrum cannot be decomposed into the product of spectra. When it can (see [26] for examples of separable three-body Hamiltonians), then the decomposition can be further reduced into independent sums…”

Section: B Observable-induced Direct Sum Decompositionmentioning

confidence: 99%

“…The 'gold standard' is when each differential equation only depends on a single separation constant λ i [26]. Then each differential operator Λ i defines a Zanardi-like subsystem and the whole Hilbert space can be decomposed as…”

Section: Top-down Approach To Emergent Tensor Product Structuresmentioning

confidence: 99%

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Symmetry, Structure, and Emergent Subsystems

Harshman¹

2019

Quantum Worlds

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Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of interpretation. For models with symmetry, the properties of irreducible representations constrain the possibilities of Hilbert space arithmetic, i.e. how a Hilbert space can be decomposed into sums of subspaces and factored into products of subspaces. Partitioning the Hilbert space is equivalent to parsing the system into subsystems, and these emergent subsystems provide insight into the kinematics, dynamics, and informatics of a quantum model. This article provides examples of how complex models can be built up from irreducible representations that correspond to 'natural' ontological units like spins and particles. It also gives examples of the reverse process in which complex models are partitioned into subsystems that are selected by the representations of the symmetries and require no underlying ontological commitments. These techniques are applied to a few-body model in one-dimension with a Hamiltonian depending on an interaction strength parameter. As this parameter is tuned, the Hamiltonian runs dynamical spectrum from integrable to chaotic, and the subsystems relevant for analyzing and interpreting the dynamics shift accordingly.

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Section: B Observable-induced Direct Sum Decompositionmentioning

confidence: 99%

Section: B Observable-induced Direct Sum Decompositionmentioning

confidence: 99%

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Symmetry, Structure, and Emergent Subsystems

Harshman¹

2019

Quantum Worlds

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“…Sometimes, the preferred structure is postulated [12] or expected to exist due to the additional symmetry-based requirements, see e.g. [13].…”

Section: Outlines Of a Top-down Approach To Quantum Structuresmentioning

confidence: 99%

A Top-down versus a Bottom-up Hidden-variables Description of the Stern–Gerlach Experiment

Arsenijevic

Jeknić-Dugić

Dugić

2016

Quantum Structural Studies

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We employ the Stern-Gerlach experiment to highlight the basics of a minimalist, non-interpretational top-down approach to quantum foundations. Certain benefits of the here highlighted "quantum structural studies" are detected and discussed. While the top-down approach can be described without making any reference to the fundamental structure of a closed system, the hidden variables theoryá la Bohm proves to be more subtle than it is typically regarded.

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“…56 56 Harshman ha brindado un estudio profundo y claro de las estructuras cuánticas inducidas por las simetrías de los sistemas (ver Ref. [146] y las referencias allí).…”

Section: Correlaciones Cuánticas Bajo Operaciones Unitarias Globalesunclassified

Repercusiones cuánticas de los estados clásicamente correlacionados

Bellomo¹

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La Información Cuántica, como disciplina que hereda virtudes y defectos de la Teoría de la Información y de la Mecánica Cuántica, ha brindado, durante los últimos años, un avance considerable en el entendimiento y resolución de ciertos problemas de Fundamentos de la Cuántica. El formalismo, sin embargo, no está exento de interrogantes propios que son intensamente estudiados. Algunas de las contribuciones más importantes se vinculan con las potencialidades de los sistemas mecánico-cuánticos como recursos computacionales más poderosos que los implementables mediante sistemas que no evidencian efectos cuánticos. La clave, en esos casos, está en el tipo de correlaciones que pueden establecerse entre dos o más partes de los sistemas. En este trabajo, presento varios resultados en los que estudio aspectos informacionales de los sistemas cuánticos, presentes incluso en los estados denominados clásicamente correlacionados.

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Symmetry and Natural Quantum Structures for Three-Particles in One-Dimension

Cited by 4 publications

References 32 publications

Symmetry, Structure, and Emergent Subsystems

Symmetry, Structure, and Emergent Subsystems

A Top-down versus a Bottom-up Hidden-variables Description of the Stern–Gerlach Experiment

Repercusiones cuánticas de los estados clásicamente correlacionados

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