Stochastic Rotation Dynamics for Nematic Liquid Crystals

We introduce a new mesoscopic model for nematic liquid crystals (LCs). We extend the particle-based stochastic rotation dynamics method, which reproduces the Navier-Stokes equation, to anisotropic fluids by including a simplified Ericksen-Leslie formulation of nematodynamics. We verify the applicability of this hybrid model by studying the equilibrium isotropic-nematic phase transition and nonequilibrium problems, such as the dynamics of topological defects, and the rheology of sheared LCs. Our simulation results show that this hybrid model captures many essential aspects of LC physics at the mesoscopic scale, while preserving microscopic thermal fluctuations

Simulating broken PT\cal PT-symmetric Hamiltonian systems by weak measurement

By embedding a $\cal PT$-symmetric (pseudo-Hermitian) system into a large Hermitian one, we disclose the relations between $\cal{PT}$-symmetric Hamiltonians and weak measurement theory. We show that the amplification effect in weak measurement on a conventional quantum system can be used to effectively simulate a local broken $\cal PT$-symmetric Hamiltonian system, with the pre-selected state in the $\cal PT$-symmetric Hamiltonian system and its post-selected state resident in the dilated Hamiltonian system.Comment: 4 pages; with Supplemental Materia

Solvable dilation model of PT\cal PT-symmetric systems

The dilation method is a practical way to experimentally simulate non-Hermitian, especially $\cal PT$-symmetric quantum systems. However, the time-dependent dilation problem cannot be explicitly solved in general. In this paper, we present a simple yet non-trivial exactly solvable dilation problem with two dimensional time-dependent $\cal PT$-symmetric Hamiltonian. Our system is initially set in the unbroken $\cal PT$-symmetric phase and later goes across the so-called exceptional point and enters the broken $\cal PT$-symmetric phase. For this system, the dilated Hamiltonian and the evolution of $\cal PT$-symmetric system are analytically worked out. Our result clearly showed that the exceptional points do not have much physical relevance in a \textit{time-dependent} system.Comment: 9 pages, 4 figures, close to the published versio

Multi-domain vertical alignment liquid crystal displays with improved angular dependent gamma curves.

Methods, systems and apparatus for a liquid crystal display panel having a first substrate with a color filter, an over-coating and a common electrode. The second substrate includes an insulating layer surface facing the first substrate, a pixel electrode, a plurality of common and pixel domain guides formed on the common and the pixel electrodes, a plurality of electric shields on one of the common or pixel electrodes and a liquid crystal layer vertically aligned between the first and second substrates. The panel also includes a drive circuit for applying a voltage to generate an electric field to control liquid crystal molecule orientation corresponding to the plurality of domain guides and electric shields to form a multi-domain liquid crystal display panel device. The plural domain guides are either protrusions or slits formed in the common electrode and the pixel electrode to form the multi-domain vertical alignment liquid crystal device