We show with first-principles molecular dynamics the persistence of intrinsic $langle111rangle$ Ti off-centerings for BaTiO$_3$ in its cubic paraelectric phase. Intriguingly, these are inconsistent with the known space group for this phase. Inspired
by this observation, we deploy a systematic symmetry analysis to construct representative structural models in the form of supercells that satisfy a desired point symmetry but are built from the combination of lower-symmetry primitive cells. We define as structural prototypes the smallest of these that are both energetically and dynamically stable. Remarkably, two 40-atom prototypes can be identified for paraelectric BaTiO$_3$; these are also common to many other ABO$_3$ perovskites. These prototypes can offer structural models of paraelectric phases that can be used for the computational engineering of functional materials displaying such hidden order. Last, we show that the emergence of B-cation off-centerings and the consequent disappearance of the phonon instabilities is controlled by the equilibrium volume, in turn dictated by the filler A cation.
A central characteristic of living beings is the ability to learn from and respond to their environment leading to habit formation and decision making1-3. This behavior, known as habituation, is universal among forms of life with a central nervous sy
stem, and interestingly observed even in single cellular organisms that do not possess a brain4-5. Here, we report the discovery of habituation based plasticity utilizing a perovskite quantum system by dynamical modulation of electron localization via reversible dopant incorporation. Microscopic mechanisms and pathways that enable this organismic collective charge-lattice interaction are elucidated by a combination of first-principles theory, synchrotron investigations, ab-initio dynamical simulations and in-situ environmental breathing studies. We implement a new learning algorithm inspired from the conductance relaxation behavior of perovskites that naturally incorporates habituation and demonstrate learning to forget: a key feature of animal and human brains6. Most surprisingly, our results show that incorporating this elementary skill in learning dramatically boosts the capability of artificial cognitive systems.
