Liouville space description of thermofields and their generalisations
Open accessAbstract
The thermofield representation of a thermal state by a pure-state wavefunction in a doubled Hilbert space is generalised to arbitrary and pure states. The authors employ a Liouville space formalism to investigate the connection between these generalised thermofield wavefunctions and a generalised thermofield state vector in Liouville space which is valid for all cases of the quantum density operator. The system dynamics in the Schrodinger and Heisenberg pictures are discussed.
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There are introductions where neither '⊗' nor '×' are explicitly used but either the symbolic approach or the literal one is implicitly implied in the operations.
“There are also those introductions where neither ' ⊗ ' nor ' × ' are explicitly used but either the symbolic approach or the literal one are implicitly implied in the operations (see for example [1, 16]).”
From Fundamentals of quantum mechanics in Liouville space (2020) · cites this paper as [16]
In the passage labelled Abstract (page unavailable), the paper explicitly introduces the superoperator as “F = F, x F;”. Its copy therefore uses x as an operator-product symbol, contrary to the claim that neither product symbol is explicitly used. (LLM, conf=0.83)
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Cites
Thermo Field Dynamics and Condensed States
Umezawa, H., Matsumoto, H., & Tachiki, M. (1982) · CERN Document Server (European Organization for Nuclear Research) · Cited by 595 · see citing works
Theory and applications of the density matrix
ter Haar, D. (1961) · Reports on Progress in Physics · doi:10.1088/0034-4885/24/1/307 · Cited by 259 · see citing works
Thermofield analysis of squeezing and statistical mixtures in quantum optics
Barnett, S. M., & Knight, P. L. (1985) · Journal of the Optical Society of America B · doi:10.1364/josab.2.000467 · Cited by 231 · see citing works
Self-citationReal-time green's functions in many body problems
Schmutz, M. (1978) · The European Physical Journal B · doi:10.1007/bf01323673 · Cited by 139 · see citing works
A General Formulation of Nonequilibrium Thermo Field Dynamics
Arimitsu, T., & Umezawa, H. (1985) · Progress of Theoretical Physics · doi:10.1143/ptp.74.429 · Cited by 138 · see citing works
IMPACT THEORY OF RAMAN LINE BROADENING
Fiutak, J., & Kranendonk, J. V. (1962) · Canadian Journal of Physics · doi:10.1139/p62-117 · Cited by 113 · see citing works
An alternative method of quantization: the existence of classical fields
Crawford, J. A. (1958) · Il Nuovo Cimento · doi:10.1007/bf02859806 · Cited by 58 · see citing works
Liouville space theory of sequential quantum processes. I. General theory
Dalton, B. J. (1982) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/15/7/026 · Cited by 23 · see citing works
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Fundamentals of quantum mechanics in Liouville space
Gyamfi, J. A. (2020) · European Journal of Physics · doi:10.1088/1361-6404/ab9fdd · Cited by 77 · see citing works
- Authors
- Barnett, S. M., & Dalton, B. J.
- Affiliations
- Imperial College London (GB)
- Venue
- Journal of Physics A: Mathematical and General
- Publisher
- IOP Publishing
- Published
- 1987-02-01
- Volume
- 20
- Issue
- 2
- Pages
- 411-418
- ISSN
- 0305-4470 (ISSN-L)
- 1361-6447
- OpenAlex
- W1971417054
- Cited by
- 27
- References
- 9
- Citations by year
- 2025: 1 · 2023: 3 · 2022: 2 · 2021: 2 · 2020: 2 · 2019: 1 · 2018: 2 · 2017: 4 · 2016: 2 · 2015: 1 · 2014: 2
- FWCI
- 0.96
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Physics A Mathematical and General (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Keywords
- Liouville space, thermal states, pure states, Schrödinger picture, Heisenberg picture, quantum statistical mechanics
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