Symmetries and monotones in Markovian quantum dynamics

Styliaris, Georgios; Zanardi, Paolo

doi:10.22331/q-2020-04-30-261

Cited by 6 publications

(6 citation statements)

References 35 publications

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“…For example, exploiting properties (P1)-(P2) and the framework of Ref. [71] (see in particular Eq. ( 22) therein), one can obtain the following one parameter family of monotones:…”

Section: Discussionmentioning

confidence: 99%

Continuous thermomajorization and a complete set of laws for Markovian thermal processes

Lostaglio,

Korzekwa

2021

Preprint

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The standard dynamical approach to quantum thermodynamics is based on Markovian master equations describing the thermalization of a system weakly coupled to a large environment, and on tools such as entropy production relations. Here we introduce a new framework overcoming the limitations that the current dynamical and information theory approaches encounter when applied to this setting. More precisely, based on a newly introduced notion of continuous thermomajorization, we obtain necessary and sufficient conditions for the existence of a Markovian thermal process transforming between given initial and final energy distributions of the system. These lead to a complete set of generalized entropy production inequalities including the standard one as a special case. Importantly, these conditions can be reduced to a finitely verifiable set of constraints governing non-equilibrium transformations under master equations. What is more, the framework is also constructive, i.e., it returns explicit protocols realizing any allowed transformation. These protocols use as building blocks elementary thermalizations, which we prove to be universal controls. Finally, we also present an algorithm constructing the full set of energy distributions achievable from a given initial state via Markovian thermal processes and provide a Mathematica implementation solving d = 6 on a laptop computer in minutes.

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“…For example, exploiting properties (P1)-(P2) and the framework of Ref. [71] (see in particular Eq. ( 22) therein), one can obtain the following one parameter family of monotones:…”

Section: Discussionmentioning

confidence: 99%

Continuous thermomajorization and a complete set of laws for Markovian thermal processes

Lostaglio,

Korzekwa

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…For example, exploiting properties (P1)-(P2) and the framework of Ref. [73] [see in particular Eq. ( 22) therein], one can obtain the following one-parameter family of monotones:…”

Section: Appendix C: Remarks On Fundamental Constraints On Coherencementioning

confidence: 99%

Continuous thermomajorization and a complete set of laws for Markovian thermal processes

Lostaglio

Korzekwa

2022

Phys. Rev. A

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The standard dynamical approach to quantum thermodynamics is based on Markovian master equations describing the thermalization of a system weakly coupled to a large environment, and on tools such as entropy production relations. Here we develop a framework overcoming the limitations that the current dynamical and information theory approaches encounter when applied to this setting. More precisely, we introduce the notion of continuous thermomajorization and employ it to obtain necessary and sufficient conditions for the existence of a Markovian thermal process transforming between given initial and final energy distributions of the system. These lead to a complete set of generalized entropy production inequalities including the standard one as a special case. Importantly, these conditions can be reduced to a finitely verifiable set of constraints governing nonequilibrium transformations under master equations. What is more, the framework is also constructive, i.e., it returns explicit protocols realizing any allowed transformation. These protocols use as building blocks elementary thermalizations, which we prove to be universal controls. Finally, we also present an algorithm constructing the full set of energy distributions achievable from a given initial state via Markovian thermal processes and provide a Mathematica implementation solving d = 6 on a laptop computer in minutes.

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“…In finite dimensions, it is always the case that there is a steady state ρ ∞ of the dynamics that satisfies L(ρ ∞ ) = 0 (see for example [30,Proposition 5]). It was discussed in [31,32,33] how the symmetries of L k are inherited by L and the steady state. However, Lindbladians with translation-invariance in the infinite system have not been studied extensively although some results exist [34,4].…”

Section: Lindblad Systems On the Infinite Latticementioning

confidence: 99%

Spectra of Lindbladians on the infinite line: From non-Hermitian to full evolution via tridiagonal Laurent matrices

Klausen¹,

Werner²

2022

Preprint

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We determine the spectra of single-particle translation-invariant Lindblad operators on the infinite line. In the case where the Hamiltonian is given by the discrete Laplacian and the Lindblad operators are rank r, finite range and translates of each other, we obtain a representation of the Lindbladian as a direct integral of finite range bi-infinite Laurent matrices with rank-r-perturbations. By analyzing the direct integral we rigorously determine the complete spectrum in the general case and calculate it explicitly for several types of dissipation e.g. dephasing, coherent hopping. We further use the detailed information about the spectrum to prove gaplessness, absence of residual spectrum and a condition for convergence of finite volume spectra to their infinite volume counterparts. We finally extend the discussion to the case of the Anderson Hamiltonian, which enables us to study a Lindbladian recently associated to localization in open quantum systems.

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Symmetries and monotones in Markovian quantum dynamics

Cited by 6 publications

References 35 publications

Continuous thermomajorization and a complete set of laws for Markovian thermal processes

Continuous thermomajorization and a complete set of laws for Markovian thermal processes

Continuous thermomajorization and a complete set of laws for Markovian thermal processes

Spectra of Lindbladians on the infinite line: From non-Hermitian to full evolution via tridiagonal Laurent matrices

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