In this paper, we study holomorphic discs in K3 surfaces and defined the open Gromov-Witten invariants. Using this new invariant, we can establish a version of correspondence between tropical discs and holomorphic discs with non-trivial invariants. W
e give an example of wall-crossing phenomenon of the invariant and expect it satisfies Kontsevich-Soibelman wall-crossing formula.
We use the hyperKaler geometry define an disc-counting invariants with deformable boundary condition on hyperKahler manifolds. Unlike the reduced Gromov-Witten invariants, these invariants can have non-trivial wall-crossing phenomenon and are expecte
d to be the generalized Donaldson-Thomas invariants in the construction of hyperKahler metric proposed by Gaiotto-Moore-Neitzke.
We present a protocol for the amplification and distribution of a one-time-pad cryptographic key over a point-to-multipoint optical network based on computational ghost imaging (GI) and compressed sensing (CS). It is shown experimentally that CS imag
ing can perform faster authentication and increase the key generation rate by an order of magnitude compared with the scheme using computational GI alone. The protocol is applicable for any number of legitimate user, thus, the scheme could be used in real intercity networks where high speed and high security are crucial.
The internal dynamics of a double quantum dot system is renormalized due to coupling respectively with transport electrodes and a dissipative heat bath. Their essential differences are identified unambiguously in the context of full counting statisti
cs. The electrode coupling caused level detuning renormalization gives rise to a fast-to-slow transport mechanism, which is not resolved at all in the average current, but revealed uniquely by pronounced super-Poissonian shot noise and skewness. The heat bath coupling introduces an interdot coupling renormalization, which results in asymmetric Fano factor and an intriguing change of line shape in the skewness.
We examine the full counting statistics of electron transport through double quantum dots coupled in series, with particular attention being paid to the unique features originating from level renormalization. It is clearly illustrated that the energy
renormalization gives rise to a dynamic charge blockade mechanism, which eventually results in super-Poissonian noise. Coupling of the double dots to an external heat bath leads to dephasing and relaxation mechanisms, which are demonstrated to suppress the noise in a unique way.
