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Register a new userA quantum fluctuation theorem for any Lindblad master equation
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We present a general quantum fluctuation theorem for the entropy production of an open quantum system whose evolution is described by a Lindblad master equation. Such theorem holds for both local and global master equations, thus settling the dispute on the thermodynamic consistency of the local quantum master equations. The theorem is genuinely quantum, as it can be expressed in terms of conservation of an Hermitian operator, describing the dynamics of the system state operator and of the entropy change in the baths. The integral fluctuation theorem follows from the properties of such an operator. Furthermore, it is valid for arbitrary number of baths and for time-dependent Hamiltonians. As such, the quantum Jarzynski equality is a particular case of the general result presented here. Moreover, our result can be extended to non-thermal baths, as long as microreversibility is preserved. We finally present some numerical examples to showcase the exact results previously obtained.
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Realistic models of quantum systems must include dissipative interactions with an environment. For weakly-damped systems the Lindblad-form Markovian master equation is invaluable for this task due to its tractability and efficiency. This equation only applies, however, when the frequencies of any subset of the systems transitions are either equal (degenerate), or their differences are much greater than the transitions linewidths (far-detuned). Outside of these two regimes the only available efficient description has been the Bloch-Redfield (B-R) master equation, the efficacy of which has long been controversial due to its failure to guarantee the positivity of the density matrix. The ability to efficiently simulate weakly-damped systems across all regimes is becoming increasingly important, especially in the area of quantum technologies. Here we solve this long-standing problem. We discover that a condition on the slope of the spectral density is sufficient to derive a Lindblad form master equation that is accurate for all regimes. We further show that this condition is necessary for weakly-damped systems to be described by the B-R equation or indeed any Markovian master equation. We thus obtain a replacement for the B-R equation over its entire domain of applicability that is no less accurate, simpler in structure, completely positive, allows simulation by efficient quantum trajectory methods, and unifies the previous Lindblad master equations. We also show via exact simulations that the new master equation can describe systems in which slowly-varying transition frequencies cross each other during the evolution. System identification tools, developed in systems engineering, play an important role in our analysis. We expect these tools to prove useful in other areas of physics involving complex systems.
The correlated-projection technique has been successfully applied to derive a large class of highly non Markovian dynamics, the so called non Markovian generalized Lindblad type equations or Lindblad rate equations. In this article, general unravellings are presented for these equations, described in terms of jump-diffusion stochastic differential equations for wave functions. We show also that the proposed unravelling can be interpreted in terms of measurements continuous in time, but with some conceptual restrictions. The main point in the measurement interpretation is that the structure itself of the underlying mathematical theory poses restrictions on what can be considered as observable and what is not; such restrictions can be seen as the effect of some kind of superselection rule. Finally, we develop a concrete example and we discuss possible effects on the heterodyne spectrum of a two-level system due to a structured thermal-like bath with memory.
In this Comment, we show that the thermal Gibbs state given in terms of a time-independent system Hamiltonian is not a steady state solution of the quantum master equation introduced by Nathan and Rudner [Phys. Rev. B 102, 115109 (2020)], in contrast to their claim.
We consider an open quantum system described by a Lindblad-type master equation with two times-scales. The fast time-scale is strongly dissipative and drives the system towards a low-dimensional decoherence-free space. To perform the adiabatic elimination of this fast relaxation, we propose a geometric asymptotic expansion based on the small positive parameter describing the time-scale separation. This expansion exploits geometric singular perturbation theory and center-manifold techniques. We conjecture that, at any order, it provides an effective slow Lindblad master equation and a completely positive parameterization of the slow invariant sub-manifold associated to the low-dimensional decoherence-free space. By preserving complete positivity and trace, two important structural properties attached to open quantum dynamics, we obtain a reduced-order model that directly conveys a physical interpretation since it relies on effective Lindbladian descriptions of the slow evolution. At the first order, we derive simple formulae for the effective Lindblad master equation. For a specific type of fast dissipation, we show how any Hamiltonian perturbation yields Lindbladian second-order corrections to the first-order slow evolution governed by the Zeno-Hamiltonian. These results are illustrated on a composite system made of a strongly dissipative harmonic oscillator, the ancilla, weakly coupled to another quantum system.
We derive the quantum master equations for heavy quark systems in a high-temperature quark- gluon plasma in the Lindblad form. The master equations are derived in the influence functional formalism for open quantum systems in perturbation theory. These master equations have a wide range of applications, such as decoherence of a heavy quarkonium and Langevin dynamics of a heavy quark in the quark-gluon plasma. We also show the equivalence between the quarkonium master equations in the recoilless limit and the Schroedinger equations with stochastic potential.
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