ABSTRACT
We study a system of spins (qubits) coupled to a common noisy environment, each precessing at its own frequency. The correlated noise experienced by the spins implies long-lived correlations that relax only due to the differing frequencies. We use a mapping to a non-Hermitian integrable Richardson-Gaudin model to find the exact spectrum of the quantum master equation in the high-temperature limit and, hence, determine the decay rate. Our solution can be used to evaluate the effect of inhomogeneous splittings on a system of qubits coupled to a common bath.
ABSTRACT
We describe a method to predict and control the lattice parameters of hexagonal and gyroid mesoporous materials formed by liquid crystal templating. In the first part, we describe a geometric model with which the lattice parameters of different liquid crystal mesophases can be predicted as a function of their water/surfactant/oil volume fractions, based on certain geometric parameters relating to the constituent surfactant molecules. We demonstrate the application of this model to the lamellar (Lα), hexagonal (H1), and gyroid bicontinuous cubic (V1) mesophases formed by the binary Brij-56 (C16EO10)/water system and the ternary Brij-56/hexadecane/water system. In this way, we demonstrate predictable and independent control over the size of the cylinders (with hexadecane) and their spacing (with water). In the second part, we produce mesoporous platinum using as templates hexagonal and gyroid phases with different compositions and show that in each case the symmetry and lattice parameter of the metal nanostructure faithfully replicate those of the liquid crystal template, which is itself in agreement with the model. This demonstrates a rational control over the geometry, size, and spacing of pores in a mesoporous metal.
