Relaxation dynamics in a Hubbard dimer coupled to fermionic baths: Phenomenological description and its microscopic foundation

Kleinherbers, Eric; Szpak, Nikodem; König, Jürgen; Schützhold, Ralf

doi:10.1103/physrevb.101.125131

Cited by 32 publications

(28 citation statements)

References 78 publications

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“…Unlike the common secular approximation [75,76], this approximation retains nontrivial effects due to the coupling of coherence and population dynamics, i.e., off-diagonal elements of ρ in the local energy eigenbasis couple to diagonal elements, see also Ref. [80]. Moreover, unlike, e.g., the Wangsness-Bloch-Redfield approximation [71,72,81], this scheme is guaranteed to yield completely positive trace-preserving (CPTP) dynamics [73,74]-an essential requirement for a physical, probabilistic interpretation of the reduced density matrix ρ(t ).…”

Section: Introductionmentioning

confidence: 99%

Parity-to-charge conversion in Majorana qubit readout

Munk

Schulenborg

Egger

et al. 2020

Phys. Rev. Research

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Section: Introductionmentioning

confidence: 99%

Parity-to-charge conversion in Majorana qubit readout

Munk

Schulenborg

Egger

et al. 2020

Phys. Rev. Research

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“…But such negative eigenvalues will be quite close to zero, and can be shown to be below accuracy level of the Redfield equation [39,45,47,54]. Several more-refined Lindblad equations have been proposed to circumvent these drawbacks [55][56][57][58][59][60]. Nevertheless, it has been shown that all of these approaches have inherent limitations even to the leading order in the system-bath coupling strength when describing a system coupled to multiple thermal baths [45].…”

Section: Introductionmentioning

confidence: 99%

Lyapunov equation in open quantum systems and non-Hermitian physics

Purkayastha

2022

Preprint

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The continuous-time differential Lyapunov equation is widely used in linear optimal control theory, a branch of mathematics and engineering. In quantum physics, it is known to appear in Markovian descriptions of linear (quadratic Hamiltonian, linear equations of motion) open quantum systems, typically from quantum master equations. Despite this, the Lyapunov equation is seldom considered a fundamental formalism for linear open quantum systems. In this work we aim to change that. We establish the Lyapunov equation as a fundamental and efficient formalism for linear open quantum systems that can go beyond the limitations of various standard quantum master equation descriptions, while remaining of much less complexity than general exact formalisms. This also provides valuable insights for non-Hermitian quantum physics. In particular, we derive the Lyapunov equation for the most general number conserving linear system in a lattice of arbitrary dimension and geometry, connected to an arbitrary number of baths at different temperatures and chemical potentials. Three slightly different forms of the Lyapunov equation are derived via an equation of motion approach, by making increasing levels of controlled approximations, without reference to any quantum master equation. Then we discuss their relation with quantum master equations, positivity, accuracy and additivity issues, the possibility of describing dark states, general perturbative solutions in terms of single-particle eigenvectors and eigenvalues of the system, and quantum regression formulas. Our derivation gives a clear understanding of the origin of the non-Hermitian Hamiltonian describing the dynamics and separates it from the effects of quantum and thermal fluctuations. Many of these results would have been hard to obtain via standard quantum master equation approaches.

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“…Recently, a novel approach termed PERLind (position and energy resolved Lindblad equation) was introduced [29] in an attempt to interpolate between the local and global approach. Since then, multiple microscopic derivations were given [30][31][32][33], showing that the PERLind approach does not require any additional assumptions going beyond the ones already present when performing Born-Markov approximations. Compared to the global and local approaches, the PERLind approach thus has an increased regime of validity, making it a very promising approach.…”

Section: Introductionmentioning

confidence: 99%

A thermodynamically consistent Markovian master equation beyond the secular approximation

2021

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Markovian master equations provide a versatile tool for describing open quantum systems when memory effects of the environment may be neglected. As these equations are of an approximate nature, they often do not respect the laws of thermodynamics when no secular approximation is performed in their derivation. Here we introduce a Markovian master equation that is thermodynamically consistent and provides an accurate description whenever memory effects can be neglected. The thermodynamic consistency is obtained through a rescaled Hamiltonian for the thermodynamic bookkeeping, exploiting the fact that a Markovian description implies a limited resolution for heat. Our results enable a thermodynamically consistent description of a variety of systems where the secular approximation breaks down.

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Relaxation dynamics in a Hubbard dimer coupled to fermionic baths: Phenomenological description and its microscopic foundation

Cited by 32 publications

References 78 publications

Parity-to-charge conversion in Majorana qubit readout

Parity-to-charge conversion in Majorana qubit readout

Lyapunov equation in open quantum systems and non-Hermitian physics

A thermodynamically consistent Markovian master equation beyond the secular approximation

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