Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials
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By using the properties of orthogonal polynomials, we present an exact unitary transformation that maps the Hamiltonian of a quantum system coupled linearly to a continuum of bosonic or fermionic modes to a Hamiltonian that describes a one-dimensional chain with only nearest-neighbor interactions. This analytical transformation predicts a simple set of relations between the parameters of the chain and the recurrence coefficients of the orthogonal polynomials used in the transformation and allows the chain parameters to be computed using numerically stable algorithms that have been developed to compute recurrence coefficients. We then prove some general properties of this chain system for a wide range of spectral functions and give examples drawn from physical systems where exact analytic expressions for the chain properties can be obtained. Crucially, the short-range interactions of the effective chain system permit these open-quantum systems to be efficiently simulated by the density matrix renormalization group methods.
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Multisite networks may exhibit more complex behaviour due to interplay between constructive and destructive interference effects and environmental noise.
“While linear networks can already exhibit interesting noise assisted transport phenomena [16, 107-111], multisite networks may exhibit more complex behaviour which arises due to the interplay between a wealth of constructive and destructive interference effects in a quantum dynamical system on the one hand and environmental noise on the other hand [16, 62, 67-70, 77, 112].”
From Vibrations, quanta and biology (2013) · cites this paper as [69]
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References 20 · Cited by 320
Research works printed but not linked: 4
- [1][1] Weiss, U.: Quantum Dissipative Systems . World Scientific, Singapore (2001). -
- [13][13] Gautschi, W.: Orthogonal Polynomials . Oxford University Press, New York (2004). -
- [17][17] Altland, A. and Simons, B.D.: Condensed Matter Field Theory . Cambridge University Press, Cambridge (2010). -
- [19][19] Baik, J., Kriecherbauer, T., McLaughlin, K.T.-R. and Miller, P.D.: Discrete orthogonal polynomials: asymptotics and applications . Princeton University Press, New Jersey (2007). -
- Authors
- Chin, A. W., Rivas, Á., Huelga, S. F., & Plenio, M. B.
- Affiliations
- Universität Ulm (DE)
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 2010-09-01
- Volume
- 51
- Issue
- 9
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W2074203794
- Cited by
- 320
- References
- 20
- Citations by year
- 2026: 17 · 2025: 28 · 2024: 39 · 2023: 25 · 2022: 26 · 2021: 28 · 2020: 29 · 2019: 24 · 2018: 20 · 2017: 13 · 2016: 16 · 2015: 14 · 2014: 11 · 2013: 14 · 2012: 10
- FWCI
- 5.14
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Journal of Mathematical Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- 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 › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
- Keywords
- open quantum systems, system-reservoir coupling, orthogonal polynomials, recurrence coefficients, semi-infinite chain, nearest-neighbor interactions, spectral function, density matrix renormalization group, quantum simulation
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