Symmetry Origin of Nonlinear Monopole

We revisit the non-linear BPS equation: the Dirac monopole of the Born-Infeld theory in the B-field background. The rotation used in our previous papers to discuss the scalar field by transforming the BPS equation into a linear one is extended to the case of gauge field. We also find that this transformation is a symmetry of the action. Moreover using the Legendre-dual formalism we present a simple expression of the BPS equation.Comment: 29 pages, 1 fugur

Ueda's lemma via uniform H\"ormander estimates for flat line bundles

We establish H\"ormander-type $L^2$-estimates for the $\overline{\partial}$-operators that hold uniformly for all nontrivial flat holomorphic line bundles on compact K\"ahler manifolds. Our result can be regarded as a $\overline{\partial}$-version of Ueda's lemma on the operator norm of \v{C}ech coboundaries for flat line bundles and indeed recovers the original version of Ueda's lemma for compact K\"ahler manifolds. A partial generalisation for $(p,0)$-forms on Ricci-flat manifolds is also given.Comment: Minor modifications, details adde

Flow-Induced Transport via Optical Heating of a Single Gold Nanoparticle

Optothermal trapping has gained increasing popularity in manipulation such as selecting, guiding, and positioning submicron objects because of a few mW laser power much lower than that required for optical trapping. The optotothermal trapping uses thermal gradient-induced phoretic motions, but the underlying physics of driving force has not been fully understood. In this study, we performed optotothermal trapping of 500-nm-diameter colloidal silica via a continuous laser illumination of a single gold nanoparticle from the bottom in a closed chamber. Under illumination, the tracer particles were attracted to the gold nanoparticle and trapped. Notably, the direction of migrating particles was always to hot gold nanoparticle regardless of the configuration of gold nanoparticle placed at two opposite sides of the chamber, on the bottom surface of an upper substrate (ceiling) or on the top surface of a lower substrate (floor). The previous interpretation based on thermal convective flow from the bottom to the top and circulating inside the chamber was only applicable to floor configuration and failed to explain our observation for ceiling. Instead, temperature-induced Marangoni effect at the water/superheated water interface is likely to play a role. This study promoted a better understanding of the driving mechanism in optothermal trapping. Moreover, as an application of the single-particle platform, we showed the photothermal phase separation-induced microdroplet formation of thermoresponsive polymers and the coating of non-thermoresponsive polymers on nanoparticles