Employing magma ocean crystallization models to constrain structure and composition of the lunar interior

The process of lunar magma ocean solidification provides constraints on the properties of distinct chemical reservoirs in the lunar mantle that formed during the early evolution of the Moon. We use a combination of phase equilibria models consistent with experimental results on lunar magma ocean crystallization to study the effect of bulk silicate Moon composition on the properties of lunar mantle reservoirs. We find that the densities and relative proportions of these mantle reservoirs, in particular of the late forming ilmenite bearing cumulates (IBC), strongly depend on the FeO content of the bulk silicate Moon. This relation has implications for post-magma ocean mantle dynamics and the mass distribution in the lunar interior, because the dense IBC form at shallow depths but tend to sink towards the core mantle boundary. We quantify the relations between bulk silicate Moon FeO content, IBC thickness and bulk Moon density as well as mantle stratigraphy and bulk silicate Moon moment of inertia to constrain the bulk silicate Moon FeO content and the efficiency of IBC sinking. In combination with seismic and selenodetic constraints on mantle stratigraphy, core radius, extent of the low velocity zone at the core mantle boundary, considerations about the present day selenotherm and the effects of reservoir mixing by convection our model indicates that the bulk silicate Moon is only moderately enriched in FeO compared to the Earths mantle and contains about 9.4 - 10.9 weight percent FeO (with a lowermost limit of 8.3 weight percent and an uppermost limit of 11.9 weight percent). We also conclude that the observed bulk silicate Moon moment of inertia requires incomplete sinking of the IBC layer by mantle convection: only 20 - 60 percent of the IBC material might have reached the core mantle boundary, while the rest either remained at the depth of origin or was mixed into the middle mantle

Overturn of ilmenite‐bearing cumulates in a rheologically weak lunar mantle

©2019. American Geophysical UnionThe crystallization of the lunar magma ocean (LMO) determines the initial structure of the solid Moon. Near the end of the LMO crystallization, ilmenite‐bearing cumulates (IBC) form beneath the plagioclase crust. Being denser than the underlying mantle, IBC are prone to overturn, a hypothesis that explains several aspects of the Moon's evolution. Yet the formation of stagnant lid due to the temperature dependence of viscosity can easily prevent IBC from sinking. To infer the rheological conditions allowing IBC to sink, we calculated the LMO crystallization sequence and performed high‐resolution numerical simulations of the overturn dynamics. We assumed a diffusion creep rheology and tested the effects of reference viscosity, activation energy, and compositional viscosity contrast between IBC and mantle. The overturn strongly depends on reference viscosity and activation energy and is facilitated by a low IBC viscosity. For a reference viscosity of 1021 Pa s, characteristic of a dry rheology, IBC overturn cannot take place. For a reference viscosity of 1020 Pa s, the overturn is possible if the activation energy is a factor of 2–3 lower than the values typically assumed for dry olivine. These low activation energies suggest a role for dislocation creep. For lower‐reference viscosities associated with the presence of water or trapped melt, more than 95% IBC can sink regardless of the activation energy. Scaling laws for Rayleigh‐Taylor instability confirmed these results but also showed the need of numerical simulations to accurately quantify the overturn dynamics. Whenever IBC sink, the overturn occurs via small‐scale diapirs

Quantifying non-Markovianity of continuous-variable Gaussian dynamical maps

We introduce a non-Markovianity measure for continuous-variable open quantum systems based on the idea put forward in H.-P. Breuer, that is, by quantifying the flow of information from the environment back to the open system. Instead of the trace distance we use here the fidelity to assess distinguishability of quantum states. We employ our measure to evaluate non-Markovianity of two paradigmatic Gaussian channels: the purely damping channel and the quantum Brownian motion channel with Ohmic environment. We consider different classes of Gaussian states and look for pairs of states maximizing the backflow of information. For coherent states we find simple analytical solutions, whereas for squeezed states we provide both exact numerical and approximate analytical solutions in the weak coupling limit

Two-qubit entanglement dynamics for two different non-Markovian environments

We study the time behavior of entanglement between two noninteracting qubits each immersed in its own environment for two different non-Markovian conditions: a high-$Q$ cavity slightly off-resonant with the qubit transition frequency and a nonperfect photonic band-gap, respectively. We find that revivals and retardation of entanglement loss may occur by adjusting the cavity-qubit detuning, in the first case, while partial entanglement trapping occurs in non-ideal photonic-band gap.Comment: 8 pages, 2 figure

Zeno and anti-Zeno effects for quantum Brownian motion

In this paper we investigate the occurrence of the Zeno and anti-Zeno effects for quantum Brownian motion. We single out the parameters of both the system and the reservoir governing the crossover between Zeno and anti-Zeno dynamics. We demonstrate that, for high reservoir temperatures, the short time behaviour of environment induced decoherence is the ultimate responsible for the occurrence of either the Zeno or the anti-Zeno effect. Finally we suggest a way to manipulate the decay rate of the system and to observe a controlled continuous passage from decay suppression to decay acceleration using engineered reservoirs in the trapped ion context .Comment: 4 pages, 1 figure. v2: Replaced with the published version. Minor modifications in the text and titl

Non-Markovian waiting time distribution

Simulation methods based on stochastic realizations of state vector evolutions are commonly used tools to solve open quantum system dynamics, both in the Markovian and non-Markovian regime. Here, we address the question of waiting time distribution (WTD) of quantum jumps for non-Markovian systems. We generalize Markovian quantum trajectory methods in the sense of deriving an exact analytical WTD for non-Markovian quantum dynamics and show explicitly how to construct this distribution for certain commonly used quantum optical systems.Comment: journal versio

Studying Io's Volcanic History Using Thermal Infrared Measurements

A new thermal infrared instrumentation to observe Io combined with the unique capabilities of PEL will provide new insights into the evolution of Io

Entanglement Trapping in Structured Environments

The entanglement dynamics of two independent qubits each embedded in a structured environment under conditions of inhibition of spontaneous emission is analyzed, showing entanglement trapping. We demonstrate that entanglement trapping can be used efficiently to prevent entanglement sudden death. For the case of realistic photonic band-gap materials, we show that high values of entanglement trapping can be achieved. This result is of both fundamental and applicative interest since it provides a physical situation where the entanglement can be preserved and manipulated, e.g. by Stark-shifting the qubit transition frequency outside and inside the gap.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Lett. on Friday 16 May 200

Non-Markovian dynamics of a qubit

In this paper we investigate the non-Markovian dynamics of a qubit by comparing two generalized master equations with memory. In the case of a thermal bath, we derive the solution of the post-Markovian master equation recently proposed in Ref. [A. Shabani and D.A. Lidar, Phys. Rev. A {\bf 71}, 020101(R) (2005)] and we study the dynamics for an exponentially decaying memory kernel. We compare the solution of the post-Markovian master equation with the solution of the typical memory kernel master equation. Our results lead to a new physical interpretation of the reservoir correlation function and bring to light the limits of usability of master equations with memory for the system under consideration.Comment: Replaced with published version (minor changes

Limits in the characteristic function description of non-Lindblad-type open quantum systems

In this paper I investigate the usability of the characteristic functions for the description of the dynamics of open quantum systems focussing on non-Lindblad-type master equations. I consider, as an example, a non-Markovian generalized master equation containing a memory kernel which may lead to nonphysical time evolutions characterized by negative values of the density matrix diagonal elements [S.M. Barnett and S. Stenholm, Phys. Rev. A {\bf 64}, 033808 (2001)]. The main result of the paper is to demonstrate that there exist situations in which the symmetrically ordered characteristic function is perfectly well defined while the corresponding density matrix loses positivity. Therefore nonphysical situations may not show up in the characteristic function. As a consequence, the characteristic function cannot be considered an {\it alternative complete} description of the non-Lindblad dynamics.Comment: Revised version. 4 pages, 1 figur