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Author: Mertens, Lotte × Publisher: Basel : MDPI ×

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    Environment-Assisted Invariance Does Not Necessitate Born’s Rule for Quantum Measurement
    (Basel : MDPI, 2023) Mertens, Lotte; van Wezel, Jasper
    The argument of environment-assisted invariance (known as envariance) implying Born’s rule is widely used in models for quantum measurement to reason that they must yield the correct statistics, specifically for linear models. However, it has recently been shown that linear collapse models can never give rise to Born’s rule. Here, we address this apparent contradiction and point out an inconsistency in the assumptions underlying the arguments based on envariance. We use a construction in which the role of the measurement machine is made explicit and shows that the presence of envariance does not imply that every measurement will behave according to Born’s rule. Rather, it implies that every quantum state allows a measurement machine to be constructed, which yields Born’s rule when measuring that particular state. This resolves the paradox and is in agreement with the recent result of objective collapse models necessarily being nonlinear.
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    Two-Dimensional Discommensurations: An Extension to McMillan’s Ginzburg–Landau Theory
    (Basel : MDPI, 2023) Mertens, Lotte; van den Brink, Jeroen; Wezel, Jasper van
    Charge density waves (CDWs) profoundly affect the electronic properties of materials and have an intricate interplay with other collective states, like superconductivity and magnetism. The well-known macroscopic Ginzburg–Landau theory stands out as a theoretical method for describing CDW phenomenology without requiring a microscopic description. In particular, it has been instrumental in understanding the emergence of domain structures in several CDW compounds, as well as the influence of critical fluctuations and the evolution towards or across lock-in transitions. In this context, McMillan’s foundational work introduced discommensurations as the objects mediating the transition from commensurate to incommensurate CDWs, through an intermediate nearly commensurate phase characterised by an ordered array of phase slips. Here, we extended the simplified, effectively one-dimensional, setting of the original model to a fully two-dimensional analysis. We found exact and numerical solutions for several types of discommensuration patterns and provide a framework for consistently describing multi-component CDWs embedded in quasi-two-dimensional atomic lattices.