Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials

Chin, Alex W.; Rivas, Ana María Rivas; Huelga, Susana F.; Plenio, Martin B.

doi:10.1063/1.3490188

Cited by 286 publications

(399 citation statements)

References 27 publications

(57 reference statements)

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“…(6) or techniques such as path integral 41 or bath renormalization approaches to modeling decoherence dynamics. 42,43 In the former case, we need to characterize first the range of accuracy of the TC2 equation by comparison with the exact solutions from the approaches in Ref. [41][42][43].…”

Section: Discussionmentioning

confidence: 99%

Geometrical effects on energy transfer in disordered open quantum systems

Mohseni

Shabani²,

Lloyd³

et al. 2013

The Journal of Chemical Physics

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Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials Journal of Mathematical Physics 51, 092109 (2010) We explore various design principles for efficient excitation energy transport in complex quantum systems. We investigate energy transfer efficiency in randomly disordered geometries consisting of up to 20 chromophores to explore spatial and spectral properties of small natural/artificial LightHarvesting Complexes (LHC). We find significant statistical correlations among highly efficient random structures with respect to ground state properties, excitonic energy gaps, multichromophoric spatial connectivity, and path strengths. These correlations can even exist beyond the optimal regime of environment-assisted quantum transport. For random configurations embedded in spatial

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Section: Discussionmentioning

confidence: 99%

Geometrical effects on energy transfer in disordered open quantum systems

Mohseni

Shabani²,

Lloyd³

et al. 2013

The Journal of Chemical Physics

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“…This arises because N av (n) actually diverges along the chain in the magnetic phase. This can be shown directly using the chain mapping [19], which predicts that N av (n) ∝ n 1−2s as n → ∞ when M is finite. As in NRG, the DMRG approach uses a finite number of bosonic fock states N b to represent each oscillator of the chain, and the divergence of the chain populations in the AOD ansatz for s < 0.5 cannot be described in this truncated basis.…”

Section: Fidelity Of Aod Ansatz With Dmrg Ground Statementioning

confidence: 99%

“…Unlike the mapping onto a Wilson chain that is used in NRG approaches, our mapping does not require any discretisation of the spectral density of the bath, although our mapping can also be carried out analytically for linear and logarithmically-discretised baths, as shown in Ref. [19]. Once mapped to a chain, the ground state of the model is obtained using imaginary-time t-DMRG evolution.…”

Section: Fidelity Of Aod Ansatz With Dmrg Ground Statementioning

confidence: 99%

Generalized Polaron Ansatz for the Ground State of the Sub-Ohmic Spin-Boson Model: An Analytic Theory of the Localization Transition

et al. 2011

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The sub-ohmic spin-boson model is known to possess a novel quantum phase transition at zero temperature between a localised and delocalised phase. We present here an analytical theory based on a variational ansatz for the ground state, which describes a continuous localization transition with mean-field exponents for 0 < s < 0.5. Our results for the critical properties show good quantitiative agreement with previous numerical results, and we present a detailed description of all the spin observables as the system passes through the transition. Analysing the ansatz itself, we give an intuitive microscopic description of the transition in terms of the changing correlations between the system and bath, and show that it is always accompanied by a divergence of the lowfrequency boson occupations. The possible relevance of this divergence for some numerical approaches to this problem is discussed and illustrated by looking at the ground state obtained using density matrix renormalisation group methods.The physics of quantum systems in contact with environmental degrees of freedom plays a fundamental role in many areas of physics, chemsitry and biology, including systems as diverse as solid state quantum computers[1, 2], quantum impurities [3], and photosynthetic biomolecules [4][5][6][7][8]. A key theoretical model for the study of system-environment interactions is the spin-boson model (SBM), which consists of a two-level system (TLS) that is linearly coupled to an 'environment' of harmonic oscillators [9,10]. Although this model has been studied extensively, there are still many open problems in SBM physics, most notably those concerning the quantum phase transition (QPT) between delocalised and localised phases that exists in the SBM when the oscillators are characterised by sub-Ohmic spectral densities.The standard quantum-classical mapping predicts that the sub-ohmic SBM should be equivalent to a classical Ising spin chain with long-range interactions, and predicts a continuous magnetic transition with mean-field critical exponents for 0 < s < 0.5. In Ref.[11], a continuous transition in the sub-Ohmic SBM was observed using the numerical renormalisation group (NRG) technique for all values of 0 < s < 1, but the critical properties of the transition were found to be non-mean-field for 0 < s < 0.5. It was suggested that this implied a breakdown of the classical to quantum mapping, and some subsequent work in this and other systems has supported this claim [12,13]. However, it is now believed that the nonmean-field results found by NRG in 0 < s < 0.5 are incorrect, and arise from the truncation of the number of states N b used to describe each oscillator in the Wilson chain [14,15]. Recent studies of the sub-Ohmic QPT using quantum monte carlo (QMC) [16], sparse polynomial space approach (SPSA) [17], and an extended coherent state technique have indeed found mean-field critical exponents for 0 < s < 0.5 [18].In this article we propose a variational ansatz for the ground state of the sub-Ohmic SBM for 0 < s < 0.5 whi...

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“…The candidate expression (12) does not resolve the selective evolution of S under monitoring. This selection is only given by the SSE (21) together with its interpretation (22). As we said before, the signal b out would be the standard complex white-noise (6) of zero mean had we switched off the interaction.…”

mentioning

confidence: 99%

“…First, a certain asymptotic Markovianity of the system-plusmemory reduced dynamics is readily seen for the Szegö class of couplings [22,23]. Investigations of asymptotic Markovianity should be extended for our class of couplings together with considering double-sided chain representations for both input and output regimes, respectively.…”

mentioning

confidence: 99%

Non-Markovian open quantum systems: Input-output fields, memory, and monitoring

Diósi

2012

Phys. Rev. A

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Principles of monitoring non-Markovian open quantum systems are analyzed. We use the field representation of the environment (Gardiner and Collet, 1985) for the separation of its memory and detector part, respectively. We claim the system-plus-memory compound becomes Markovian, the detector part is tractable by standard Markovian monitoring. Because of non-Markovianity, only the mixed state of the system can be predicted, the pure state of the system can be retrodicted. We present the corresponding non-Markovian stochastic Schrödinger equation.PACS numbers: 03.65. Yz, 42.50.Lc In a seminal paper [1] Gardiner and Collett used quantum white-noise and the related Markovian quantum field to represent the dynamics of a quantum oscillator bath in the Markovian (memory-less) limit. This allowed the construction of exact stochastic differential equations to describe the influence of the bath B on the embedded (i.e.: open) quantum system S, the reaction of S on B, and the time-continuous monitoring of S. The theory became standard in quantum optics [2] and in many fields where a quantum system is open to natural or designed environmental influence [3]. If the memory of B cannot be ignored for S then Markovian tools become jeopardized. In non-Markovian (NM) case, S is coherently interacting with a finite part of B over a finite time. From different theoretical efforts [4-10] we distill a central question: how can we divide the environment B into the memory M and detector D? Part M is continuously entangled with S but the compound S+M becomes a Markovian open system, as we shall argue. Part D contains information on S and can be continuously disentangled, i.e.: monitored, without changing the dynamics of S.As a matter of fact, the Markovian field representation [1] of B is capable to account for memory effects and leads to a natural separation between M and D. The local Markov field interacts with S in a finite range: this part makes the memory M. The output field carries away information on S, it makes the detector D. Markovian field, non-Markovian coupling. The composite S+B dynamics is based on the total HamiltonianwhereĤ S is the Hamiltonian of S, the bath Hamiltonian isĤ B = ωb † ωbω dω andĤ SB = iŝ κ ωb † ω dω+h.c. is their interaction, whereŝ is a S-operator that couples to the Bmodes. Hereb ω are boson annihilation operators for the ω-frequency modes of B, satisfying. B can be called Markovian because of the flat spectrum. Memory effects are fully encoded in the coupling κ ω . If the coupling is frequency-independent, κ ω = const, then S is Markovian open system, otherwise it has a memory. We are interested in the latter case, i.e., in NM open systems. We assume that S and B are initially uncorrelated. Let, for simplicity's, the initial B-state be the vacuum |0 defined byb ω |0 = 0 for all ω.We switch for an abstract field representation [1-3]. The bath fieldb(z) is defined bŷwhere z is a real 1-dimensional spatial coordinate. For convenience, we set the velocity of propagation to 1. The canonical commutation r...

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Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials

Cited by 286 publications

References 27 publications

Geometrical effects on energy transfer in disordered open quantum systems

Geometrical effects on energy transfer in disordered open quantum systems

Generalized Polaron Ansatz for the Ground State of the Sub-Ohmic Spin-Boson Model: An Analytic Theory of the Localization Transition

Non-Markovian open quantum systems: Input-output fields, memory, and monitoring

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