Numerical investigation of turbulence of surface gravity waves

In this paper, we numerically study the wave turbulence of surface gravity waves in the framework of Euler equations of the free surface. The purpose is to understand the variation of the scaling of the spectra with wavenumber $k$ and energy flux $P$ at different nonlinearity levels under different forcing/free-decay conditions. For all conditions (free decay and narrow-band and broad-band forcing) that we consider, we find that the spectral forms approach the wave turbulence theory (WTT) solution $S_\eta \sim k^{-5/2}$ and $S_\eta \sim P^{1/3}$ at high nonlinearity levels. With a decrease of nonlinearity level, the spectra for all cases become steeper, with the narrow-band forcing case exhibiting the most rapid deviation from WTT. We investigate bound waves and the finite-size effect as possible mechanisms causing the spectral variations. Through a tri-coherence analysis, we find that the finite-size effect is present in all cases, which is responsible for the overall steepening of the spectra and the reduced capacity of energy flux at lower nonlinearity levels. The fraction of bound waves in the domain generally decreases with the decrease of nonlinearity level, except for the narrow-band case, which exhibits a transition at a critical nonlinearity level below which a rapid increase is observed. This increase serves as the main reason for the fastest deviation from WTT with the decrease of nonlinearity in the narrow-band forcing case.

Performance of passive decoy-state quantum key distribution with mismatched local detectors

In quantum key distribution (QKD), passive decoy-state method can simplify the intensity modulation and reduce some of side-channel information leakage and modulation errors. It is usually implemented with a heralded single-photon source. In [Physical Review A 96, 032312 (2016)], a novel passive decoy-state method is proposed by Wang et al., which uses two local detectors to generate more detection events for tightly estimating channel parameters. However, in original scheme, the two local detectors are assumed to be identical, including same detection efficiency and dark count rate, which is often not satisfied in realistic experiment. Therefore, in this paper, we construct a model for this passive decoy-state QKD scheme with two mismatched detectors and explore the effect on QKD performance with certain parameter. We also take the finite-size effect into consideration, showing the performance with statistical fluctuations. The results show that the efficiencies of local detectors affect the key rate more obviously than dark count rates. Our work provides a reference value for realistic QKD system.

Security Analysis of a Passive Continuous-Variable Quantum Key Distribution by Considering Finite-Size Effect

We perform security analysis of a passive continuous-variable quantum key distribution (CV-QKD) protocol by considering the finite-size effect. In the passive CV-QKD scheme, Alice utilizes thermal sources to passively make preparation of quantum state without Gaussian modulations. With this technique, the quantum states can be prepared precisely to match the high transmission rate. Here, both asymptotic regime and finite-size regime are considered to make a comparison. In the finite-size scenario, we illustrate the passive CV-QKD protocol against collective attacks. Simulation results show that the performance of passive CV-QKD protocol in the finite-size case is more pessimistic than that achieved in the asymptotic case, which indicates that the finite-size effect has a great influence on the performance of the single-mode passive CV-QKD protocol. However, we can still obtain a reasonable performance in the finite-size regime by enhancing the average photon number of the thermal state.

Precise Phase Structure in Four-fermion Interaction Model on Torus

We investigate finite-size effects on chiral symmetry breaking in a four-fermion interaction model at a finite temperature and a chemical potential. Applying the imaginary time formalism, the thermal quantum field theory is constructed on an S1 in the imaginary time direction. In this paper, the finite-size effect is introduced by a compact S1 spatial direction with a U(1)-valued boundary condition. Thus, we study the model on a $\mathbb {R}^{D-2} \times S^{1} \times S^{1}$ torus. Phase diagrams are obtained by evaluating the local minima of the effective potential in the leading order of the 1/N expansion. From the grand potential, we calculate the particle number density and the pressure, then we illustrate the correspondence with the phase structure. We obtain a stable size for which the sign of the pressure flips from negative to positive as the size decreases. Furthermore, the finite chemical potential expands the parameter range that the stable size exists.

Finite size effect on Dissociation and Diffusion of chiral partners in Nambu-Jona-Lasinio model

The masses of pion and sigma meson modes, along with their dissociation in the quark medium, provide detailed spectral structures of the chiral partners. One has seen collectivity in pA and pp systems both at LHC and RHIC. In this article, we study the restoration of chiral symmetry by investigating the finite size effect on the detailed structure of the chiral partners in the framework of the Nambu-Jona-Lasinio model. Their diffusions and conductions have been studied through this dissociation mechanism. It is found that the masses, widths, diffusion coefficients, conductivities of chiral partners merge at different temperatures in the restoration phase of chiral symmetry. However, merging points are shifted to lower temperatures when one introduces the finite size effect into the picture. The strengths of diffusions and conductions are also reduced once the finite size is introduced in the calculations.

Noiseless Attenuation for Continuous-Variable Quantum Key Distribution over Ground-Satellite Uplink

Satellite-based quantum key distribution (QKD) has lately received considerable attention due to its potential to establish a secure global network. Associated with its application is a turbulent atmosphere that sets a notable restriction to the transmission efficiency, which is especially challenging for ground-to-satellite uplink scenarios. Here, we propose a novel noiseless attenuation (NA) scheme involving a zero-photon catalysis operation for source preparation to improve the performance of continuous-variable (CV) QKD over uplink. Numerical analysis shows that the NA-based CV-QKD, under attenuation optimization, outperforms the traditional CV-QKD, which is embodied in extending the allowable zenith angle while improving the effective communication time. Attributing to characteristics of the attenuation optimization, we find that the NA-involved source preparation improves the security bound by relatively reducing the amount of information available to eavesdroppers. Taking the finite-size effect into account, we achieve a tighter bond of security, which is more practical compared with the asymptotic limit.

Negative Autoregulation Controls size Scaling in Confined Gene Expression Reactions

Gene expression via transcription-translation is the most fundamental reaction to sustain biological systems, and complex reactions such as this one occur in a small compartment of living cells. Transcriptional feedback that controls gene expression during mRNA synthesis is a vital mechanism that regulates protein synthesis in cells. There is increasing evidence that the cellular compartment induces steric effects in gene expression reactions. However, the finite-size effect of spatial constraints on feedback regulation is not well understood. Here, we study the confinement effect on transcriptional negative feedback regulation of gene expression reactions using a theoretical model. We find that negative feedback regulation alters the scaling relation of gene expression level on compartment volume, approaching the regular scaling relation without the steric effect. Our findings suggest that negative autoregulatory feedback at the transcription step can dampen the size-dependence of protein expression levels in heterogeneous cell populations.

Resonance-forbidden second-harmonic generation in nonlinear photonic crystals

Second harmonic generation through nonlinear nano-photonic structures is important in both classical and quantum applications. It is commonly expected that the second harmonic frequency can always be generated as long as appropriate quadratic nonlinearity is provided by the material and the phase-matching condition is satisfied. Here, we present an anomaly to this common wisdom by showing that second-harmonic dipoles generated in a nonlinear photonic crystal slab can be completely nonradiative. As a result, no energy is transferred from the fundamental frequency to the second harmonic even when the phase-matching condition is satisfied – a phenomenon we call “resonance-forbidden second-harmonic generation”. Through numerical simulation, we identify two mechanisms that can achieve this phenomenon: symmetry protection and parameter tuning. The finite-size effect and the topological origin of this phenomenon are also discussed.