Condensed Matter Theory

Abstract:

We study the statistics of matrix elements of local operators in the basis of energy eigenstates in a paradigmatic, integrable, many-particle quantum theory, the Lieb-Liniger model of bosons with repulsive delta-function interactions. Using methods of quantum integrability, we determine the scaling of matrix elements with system size. As a consequence of the extensive number of conservation laws, the structure of matrix elements is fundamentally different from, and much more intricate than, the predictions of the eigenstate thermalization hypothesis for generic models. We uncover an interesting connection between this structure for local operators in interacting integrable models and the one for local operators that are not local with respect to the elementary excitations in free theories. We find that typical off-diagonal matrix elements ⟨𝝁⁢|𝒪|⁢𝝀⟩ in the same macrostate scale as exp⁡(−𝑐𝒪⁢𝐿⁢ln⁡(𝐿)−𝐿⁢𝑀𝒪 𝝁,𝝀), where the probability distribution function for 𝑀𝒪 𝝁,𝝀 is well described by Fréchet distributions and 𝑐𝒪 depends only on macrostate information. In contrast, typical off-diagonal matrix elements between two different macrostates scale as exp⁡(−𝑑𝒪⁢𝐿2), where 𝑑𝒪 depends only on macrostate information. Diagonal matrix elements depend only on macrostate information up to finite-size corrections.

Abstract:

Director field alignment in inkjet printed droplets of chiral nematic liquid crystalline materials is investigated using both experiments and numerical simulations. Experimental investigations are performed by depositing droplets of varying sizes and pitches on homeotropic alignment layers. The competition between the bulk behaviour of the chiral nematic liquid crystal and the boundary conditions imposed by the droplet surface leads to the formation of a range of possible internal director configurations. Numerical investigations are performed using a free energy minimisation approach, and the resultant simulated polarising optical microscope images are found to agree well with experimental observations.

Abstract:

SciPost Submission Detail Pivoting through the chiral-clock family