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An evolution equation is introduced which governs a two-sided optical cavity under spontaneous photon emission. This equation implies a system of rate equations for expectation values of combinations of operators relevant to the cavity. This system of equations closes with respect to these variables and it can be solved completely in closed form. Some of the properties of the solutions such as the large time behavior of the expectation values and other properties will be discussed.

We solve exactly the master equation of the degenerate and nondegenerate parametric oscillator in the presence of a squeezed reservoir. We show that the formal solutions of both systems can be obtained in terms of the density operator by applying squeeze transformations and using the superoperators formalism.

Data from a recent field campaign in the Himalayan Kali Gandaki Valley are used to construct master equations for the along-valley flow component as observed at a station and the pressure difference between this location and another one in the valley. The inspection of these equations reveals a pronounced difference between the flow dynamics during the day when strong up-valley winds prevail and those during the night when weak down-valley winds are observed. This difference is not captured by a corresponding regression model. Predictions by the master equation cease to be useful after one hour. The relation of master equations to data based Fokker–Planck equations is briefly discussed.

We show how random unitary dynamics arise from the coupling of an open quantum system to a static environment. Subsequently, we derive a master equation for the reduced system random unitary dynamics and study three specific cases: commuting system and interaction Hamiltonians, the short-time limit, and the Markov approximation.

A longstanding tool to characterize the evolution of open Markovian quantum systems is the GKSL (Gorini-Kossakowski-Sudarshan-Lindblad) master equation. However, in some cases, open quantum systems can be effectively described with non-Hermitian Hamiltonians, which have attracted great interest in the last twenty years due to a number of unconventional properties, such as the appearance of exceptional points. Here, we present a short review of these two different approaches aiming in particular to highlight their relation and illustrate different ways of connecting non-Hermitian Hamiltonian to a GKSL master equation for the full density matrix.

In this contribution to the memorial issue of Göran Lindblad, we investigate the periodically driven Lindblad equation for a two-level system. We analyze the system using both adiabatic diagonalization and numerical simulations of the time-evolution, as well as Floquet theory. Adiabatic diagonalization reveals the presence of exceptional points in the system, which depend on the system parameters. We show how the presence of these exceptional points affects the system evolution, leading to a rapid dephasing at these points and a staircase-like loss of coherence. This phenomenon can be experimentally observed by measuring, for example, the population inversion. We also observe that the presence of exceptional points seems to be related to which underlying Lie algebra the system supports. In the Floquet analysis, we map the time-dependent Liouvillian to a non-Hermitian Floquet Hamiltonian and analyze its spectrum. For weak decay rates, we find a Wannier-Stark ladder spectrum accompanied by corresponding Stark-localized eigenstates. For larger decay rates, the ladders begin to dissolve, and new, less localized states emerge. Additionally, their eigenvalues are exponentially sensitive to perturbations, similar to the skin effect found in certain non-Hermitian Hamiltonians.

Complete positivity (CP) of a quantum dynamical map (QDM) is, in general, difficult to show when its master equation (ME) does not conform to the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) form. The GKSL ME describes Markovian dynamics, comprising a unitary component with time-independent Hermitian operators and a nonunitary component with time-independent Lindblad operators and positive time-independent damping rates. Recently, non-Markovian dynamics have received growing attention, and the various types of GKSL-like MEs with time-dependent operators are widely discussed; however, rigorous discussions on their CP conditions remain limited. This paper presents conditions for QDMs to be CP, whose MEs take the GKSL-like form with arbitrary time dependence. One case considered is where its ME takes the time-local integro-differential GKSL-like form, which includes CP-divisible cases. Another case considered is where the ME is time-non-local but can be approximated to be time-local in the weak-coupling regime. As a special case of the time-non-local case, the same discussion holds for the time-convoluted GKSL-like form, which should be compared to previous studies.

The concept of a nuclear molecule or a dinuclear system assumes two touching nuclei which carry out motion in the internuclear distance and exchange nucleons by transfer. The dinuclear model can be applied to nuclear structure, to fusion reactions leading to superheavy nuclei and to multi-nucleon transfer reactions.

An extended model for coupled networks considering three possible links, i.e. rewiring links, direct links, and cross links, is proposed in this paper. Following the establishment of the master equations of degree distributions, the exact asymptotic solutions in power law form and their corresponding exponents are obtained. It is indicated that the minimal model used can describe the acquaintance webs well. The results also show that more other known consequences can be inferred just by tuning the parameters properly.