Exploring the theory of open quantum systems: The Lindblad master equation and Decoherence

Kalle‐Antti Suominen

Arnab Sarker, Harshita Bhuyan, Moon Moon Devi

We discuss the effect of environmental decoherence on matter-effective neutrino oscillation probabilities. Decoherence is a phenomenon observed in systems interacting with the environment. We treat the neutrinos as an open quantum system and by using the Lindblad Master equation we study the evolution of neutrino states. The matter effect is incorporated for neutrinos passing through matter with the help of the Cayley-Hamilton formalism. In this work, we have developed a general algorithm that attempts to solve the Lindblad Master Equation to compute the neutrino oscillation probabilities in presence of environmental decoherence. We extensively validate the algorithm and explore how environmentally induced decoherence can potentially affect the oscillation probabilities, particularly in the long-baseline sector.

裕樹 真島

Eugenia Pyurbeeva, Ronnie Kosloff

Abstract The Bloch equation which first inspired the field of open quantum systems, was conceived by pure physical reasoning. Since then, the Lindblad (GKLS) form of a quantum master equation, its most general mathematical representation, became an established staple in the open quantum systems toolbox. It allows the description of a multitude of quantum phenomena, however its universality comes at a cost—without additional constraints, the resultant dynamics are not necessarily thermodynamically consistent, and the equation itself lacks an intuitive interpretation. We present a mathematically equivalent form of the Lindblad master equation under a single constraint of strict energy conservation, which reinstates physical intuition, separating the system dynamics into its elemental parts: thermal mixing, dephasing, and energy relaxation. The analytical capabilities of the formalism are illustrated by calculating the fixed point of the dynamics and exploring the conditions for canonical invariance in quantum systems.

Xiang‐Guo Meng, Ji‐Suo Wang, Bao‐Long Liang

Rémi Azouit, Alain Sarlette, Pierre Rouchon

We consider an open quantum system described by a Lindblad-type master equation with two time 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.