Analytic representations of bath correlation functions for ohmic and superohmic spectral densities using simple poles

Ritschel, Gerhard; Eisfeld, Alexander

doi:10.1063/1.4893931

Cited by 65 publications

(63 citation statements)

References 44 publications

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“…Such schemes have successfully been used in the context of non-Markovian quantum master equations [19,33] or within the hierarchical equations of motion theory [34,35]. Moreover, reference [36] proposes also other classes of functions to be used for this parametrization in the case when the self-energies exhibit super-ohmic behavior.…”

Section: Auxiliary-mode Expansionmentioning

confidence: 99%

Efficient auxiliary-mode approach for time-dependent nanoelectronics

Popescu

2016

New J. Phys.

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A new scheme for numerically solving the equations arising in the time-dependent non-equilibrium Greenʼs function formalism is developed. It is based on an auxiliary-mode expansion of the selfenergies which convert the complicated set of integro-differential equations into a set of ordinary differential equations. In the new scheme all auxiliary matrices are replaced by vectors or scalars. This drastically reduces the computational effort and memory requirements of the method, rendering it applicable to topical problems in electron quantum optics and molecular electronics. As an illustrative example we consider the dynamics of a Leviton wave-packet in a 1D wire.

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Section: Auxiliary-mode Expansionmentioning

confidence: 99%

Efficient auxiliary-mode approach for time-dependent nanoelectronics

Popescu

2016

New J. Phys.

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“…Here, we will only sketch the idea following the detailed exposition for a bosonic environment in Ref. [23]: Due to the symmetric behavior under reflection at the origin of the term in braces in (27), a symmetric continuatioñ…”

Section: Thermal Initial Statementioning

confidence: 99%

“…These only arise for an initial vacuum state of the bath (5) as indicated in the footnote on page 4. Remarkably, it is possible to map the equations of motion corresponding to an initial thermal state ρ tot (t = 0) = |ψ 0 ψ 0 | ⊗ ρ th (23) to the established zero-temperature NMQSD equation (9). Here, the thermal bath state is given by ρ th = e − Henv −µNenv T /Z, with the chemical potential µ and the partition function Z = Tr env e − Henv −µNenv T .…”

Section: Thermal Initial Statementioning

confidence: 99%

Hierarchical Equations for Open System Dynamics in Fermionic and Bosonic Environments

2015

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Abstract. We present novel approaches to the dynamics of an open quantum system coupled linearly to a non-Markovian fermionic or bosonic environment. In the first approach, we obtain a hierarchy of stochastic evolution equations of the diffusion type. For the bosonic case such a hierarchy has been derived and proven suitable for efficient numerical simulations recently [arXiv:1402.4647]. The stochastic fermionic hierarchy derived here contains Grassmannian noise, which makes it difficult to simulate numerically due to its anti-commutative multiplication. Therefore, in our second approach we eliminate the noise by deriving a related hierarchy of density matrices. A similar reformulation of the bosonic hierarchy of pure states to a master equation hierarchy is also presented.

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“…H I = αA ⊗ B, where A = σ x , and B is the same as in Eq. (27), but coupling coefficients are [38] g(ω) =    aγ |ω|γ ω 2 +γ 2 , ω ≥ 0, aγ |ω|γe βω ω 2 +γ 2 , ω < 0. FIG.…”

Section: Thermalisation Of a Qubit On Quantum Computermentioning

confidence: 99%

Quantum algorithm for the simulation of open-system dynamics and thermalization

2020

Phys. Rev. A

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The quantum open system simulation is an important category of quantum simulation. By simulating the thermalisation process of the zero temperature, we can solve the ground-state problem of quantum systems. To realise the open-system evolution on the quantum computer, we need to encode the environment using qubits. However, usually the environment is much larger than the system, i.e. plenty of qubits are required if the environment is directly encoded. In this paper, we propose a way to simulate open-system dynamics by reproducing reservoir correlation functions using a minimised Hilbert space. In this way, we only need a small number of qubits to represent the environment. To simulate the n-th-order expansion of the time-convolutionless master equation by reproducing up to n-th-order correlation functions, the number of qubits representing the environment is ∼ n 2 log 2 (NωN β ). Here, Nω is the number of frequencies in the discretised environment spectrum, and N β is the number of terms in the system-environment coupling. By reproducing second-order correlation functions, i.e. taking n = 2, we can simulate the Markovian quantum master equation. In our algorithm, the environment on the quantum computer could be even smaller than the system.

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Analytic representations of bath correlation functions for ohmic and superohmic spectral densities using simple poles

Cited by 65 publications

References 44 publications

Efficient auxiliary-mode approach for time-dependent nanoelectronics

Efficient auxiliary-mode approach for time-dependent nanoelectronics

Hierarchical Equations for Open System Dynamics in Fermionic and Bosonic Environments

Quantum algorithm for the simulation of open-system dynamics and thermalization

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