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It is well-known that the conditional mutual information of a quantum state is zero if, and only if, the quantum state is a quantum Markov chain. Replacing the Umegaki relative entropy in the definition of the conditional mutual information by the Belavkin-Staszewski (BS) relative entropy, we obtain the BS-conditional mutual information, and we call the states with zero BS-conditional mutual information Belavkin-Staszewski quantum Markov chains. In this article, we establish a correspondence which relates quantum Markov chains and BS-quantum Markov chains. This correspondence allows us to find a recovery map for the BS-relative entropy in the spirit of the Petz recovery map. Moreover, we prove a structural decomposition of the Belavkin-Staszewski quantum Markov chains and also study states for which the BS-conditional mutual information is only approximately zero. As an application, we show that the conditional mutual information of the state associated to the Gibbs state of a quantum spin chain with local, finite-range, translation-invariant interactions at any positive temperature via this new correspondence decays superexponentially fast with the size of the middle system., Comment: 19 pages, 1 figure

Machine-learned interatomic potentials (MILPs) are rapidly gaining interest for molecular modeling, as they provide a balance between quantum-mechanical level descriptions of atomic interactions and reasonable computational efficiency. However, questions remain regarding the stability of simulations using these potentials, as well as the extent to which the learned potential energy function can be extrapolated safely. Past studies have reported challenges encountered when MILPs are applied to classical benchmark systems. In this work, we show that some of these challenges are related to the characteristics of the training datasets, particularly the inclusion of rigid constraints. We demonstrate that long stability in simulations with MILPs can be achieved by generating unconstrained datasets using unbiased classical simulations if the fast modes are correctly sampled. Additionally, we emphasize that in order to achieve precise energy predictions, it is important to resort to enhanced sampling techniques for dataset generation, and we demonstrate that safe extrapolation of MILPs depends on judicious choices related to the system's underlying free energy landscape and the symmetry features embedded within the machine learning models.

It is well known how to define the operator $Q$ for the total charge (i.e., positron number minus electron number) on the standard Hilbert space of the second-quantized Dirac equation. Here we ask about operators $Q_A$ representing the charge content of a region $A\subseteq \mathbb{R}^3$ in 3d physical space. There is a natural formula for $Q_A$ but, as we explain, there are difficulties about turning it into a mathematically precise definition. First, $Q_A$ can be written as a series but its convergence seems hopeless. Second, we show for some choices of $A$ that if $Q_A$ could be defined then its domain could not contain either the vacuum vector or any vector obtained from the vacuum by applying a polynomial in creation and annihilation operators. Both observations speak against the existence of $Q_A$ for generic $A$., Comment: 19 pages LaTeX

One of the oldest problems in quantum information theory is to study if there exists a state with negative partial transpose which is undistillable. This problem has been open for almost 30 years, and still no one has been able to give a complete answer to it. This work presents a new strategy to try to solve this problem by translating the distillability condition on the family of Werner states into a problem of partial trace inequalities, this is the aim of our first main result. As a consequence we obtain a new bound for the $2$-distillability of Werner states, which does not depend on the dimension of the system. On the other hand, our second main result provides new partial trace inequalities for bipartite systems, connecting some of them also with the separability of Werner states. Throughout this work we also present numerous partial trace inequalities, which are valid for many families of matrices.

Computational fluid dynamics is intensively used to deepen the understanding of aneurysm growth and rupture in the attempt to support physicians during therapy planning. Numerous studies have assumed fully-rigid vessel walls in their simulations, whose sole hemodynamics may fail to provide a satisfactory criterion for rupture risk assessment. Moreover, direct in-vivo observations of intracranial aneurysm pulsation have been recently reported, encouraging the development of fluid-structure interaction for their modelling and for new assessments. In this work, we describe a new fluid-structure interaction benchmark setting for the careful evaluation of different aneurysm shapes. The studied configurations consist of three real aneurysm domes positioned on a toroidal channel. All geometric features, meshing characteristics, flow quantities, comparisons with a rigid-wall model and corresponding plots are provided. Reported results emphasize the alteration of flow patterns and hemodynamic descriptors when moving from the rigid-wall model to the complete fluid-structure interaction framework, thereby underlining the importance of the coupling between hemodynamics and the surrounding vessel tissue., Comment: 23 pages, 14 figures

When viewed with a cross-polarized optical microscope (POM), liquid crystals display interference colors and complex patterns that depend on the material's microscopic orientation. That orientation can be manipulated by application of external fields, which provides the basis for applications in optical display and sensing technologies. The color patterns themselves have a high information content. Traditionally, however, calculations of the optical appearance of liquid crystals have been performed by assuming that a single-wavelength light source is employed, and reported in a monochromatic scale. In this work, the original Jones matrix method is extended to calculate the colored images that arise when a liquid crystal is exposed to a multi-wavelength source. By accounting for the material properties, the visible light spectrum and the CIE color matching functions, we demonstrate that the proposed approach produces colored POM images that are in quantitative agreement with experimental data. Results are presented for a variety of systems, including radial, bipolar, and cholesteric droplets, where results of simulations are compared to experimental microscopy images. The effects of droplet size, topological defect structure, and droplet orientation are examined systematically. The technique introduced here generates images that can be directly compared to experiments, thereby facilitating machine learning efforts aimed at interpreting LC microscopy images, and paving the way for the inverse design of materials capable of producing specific internal microstructures in response to external stimuli., Comment: 12 pages, 5 figures (main text). 6 pages, 6 figures (appendices)

A family of fast sampling methods is introduced here for molecular simulations of systems having rugged free energy landscapes. The methods represent a generalization of a strategy consisting of adjusting a model for the free energy as a function of one- or more collective variables as a simulation proceeds. Such a model is gradually built as a system evolves through phase space from both the frequency of visits to distinct states and generalized force estimates corresponding to such states. A common feature of the methods is that the underlying functional models and their gradients are easily expressed in terms of the same parameters, thereby providing faster and more effective fitting of the model from simulation data than other available sampling techniques. They also eliminate the need to train simultaneously separate neural networks, while retaining the advantage of generating smooth and continuous functional estimates that enable biasing outside the support grid. Implementation of the methods is relatively simple and, more importantly, they are found to provide gains of up to several orders of magnitude in computational efficiency over existing approaches.

We report the combined results of molecular dynamics simulations and theoretical calculations concerning various dynamical arrest transitions in a model system representing a dipolar fluid, namely, N (softcore) rigid spheres interacting through a truncated dipole-dipole potential. By exploring different regimes of concentration and temperature, we find three distinct scenarios for the slowing down of the dynamics of the translational and orientational degrees of freedom: At low ({$\eta$} = 0.2) and intermediate (${\eta}$ = 0.4) volume fractions, both dynamics are strongly coupled and become simultaneously arrested upon cooling. At high concentrations ({$\eta$} $\lt$ 0.6), the translational dynamics shows the features of an ordinary glass transition, either by compressing or cooling down the system, but with the orientations remaining ergodic, thus indicating the existence of partially arrested states. In this density regime, but at lower temperatures, the relaxation of the orientational dynamics also freezes. The physical scenario provided by the simulations is discussed and compared against results obtained with the self-consistent generalized Langevin equation theory, and both provide a consistent description of the dynamical arrest transitions in the system. Our results are summarized in an arrested states diagram which qualitatively organizes the simulation data and provides a generic picture of the glass transitions of a dipolar fluid.