Nucleation of membrane adhesions

Recent experimental and theoretical studies of biomimetic membrane adhesions [Bruinsma et al., Phys. Rev. E 61, 4253 (2000); Boulbitch et al., Biophys. J. 81, 2743 (2001)] suggested that adhesion mediated by receptor interactions is due to the interplay between membrane undulations and a double-well adhesion potential, and should be a first-order transition. We study the nucleation of membrane adhesion by finding the minimum-energy path on the free energy surface constructed from the bending free energy of the membrane and the double-well adhesion potential. We find a nucleation free energy barrier around 20kBT for adhesion of flexible membranes, which corresponds to fast nucleation kinetics with a time scale of the order of seconds. For cell membranes with a larger bending rigidity due to the actin network, the nucleation barrier is higher and may require active processes such as the reorganization of the cortex network to overcome this barrier. Our scaling analysis suggests that the geometry of the membrane shapes of the adhesion contact is controlled by the adhesion length that is determined by the membrane rigidity, the barrier height, and the length scale of the double-well potential, while the energetics of adhesion is determined by the depths of the adhesion potential. These results are verified by numerical calculations

Classification of Symmetry-Protected Phases for Interacting Fermions in Two Dimensions

Recently, it has been shown that two-dimensional bosonic symmetry-protected topological(SPT) phases with on-site unitary symmetry $G$ can be completely classified by the group cohomology class $H^3(G, \mathrm{U}(1))$. Later, group super-cohomology class was proposed as a partial classification for SPT phases of interacting fermions. In this work, we revisit this problem based on the mathematical framework of $G$-extension of unitary braided tensor category(UBTC) theory. We first reproduce the partial classifications given by group super-cohomology, then we show that with an additional $H^1(G, \mathbb{Z}_2)$ structure, a complete classification of SPT phases for two-dimensional interacting fermion systems for a total symmetry group $G\times\mathbb{Z}_2^f$ can be achieved. We also discuss the classification of interacting fermionic SPT phases protected by time-reversal symmetry.Comment: references added; published versio

Scars in Dirac fermion systems: the influence of an Aharonov--Bohm flux

Time-reversal ($\mathcal{T}$-) symmetry is fundamental to many physical processes. Typically, $\mathcal{T}$-breaking for microscopic processes requires the presence of magnetic field. However, for 2D massless Dirac billiards, $\mathcal{T}$-symmetry is broken automatically by the mass confinement, leading to chiral quantum scars. In this paper, we investigate the mechanism of $\mathcal{T}$-breaking by analyzing the local current of the scarring eigenstates and their magnetic response to an Aharonov--Bohm flux. Our results unveil the complete understanding of the subtle $\mathcal{T}$-breaking phenomena from both the semiclassical formula of chiral scars and the microscopic current and spin reflection at the boundaries, leading to a controlling scheme to change the chirality of the relativistic quantum scars. Our findings not only have significant implications on the transport behavior and spin textures of the relativistic pseudoparticles, but also add basic knowledge to relativistic quantum chaos.Comment: 37 pages, 11 figure

The NLO contributions to the scalar pion form factors and the O(αs2){\cal O}(\alpha_s^2) annihilation corrections to the B→ππB\to \pi\pi decays

In this paper, by employing the $k_{T}$ factorization theorem, we made the first calculation for the space-like scalar pion form factor $Q^2 F(Q^2)$ at the leading order (LO) and the next-to-leading order (NLO) level, and then found the time-like scalar pion form factor $F'^{(1)}_{\rm a,I}$ by analytic continuation from the space-like one. From the analytical evaluations and the numerical results, we found the following points: (a) the NLO correction to the space-like scalar pion form factor has an opposite sign with the LO one but is very small in magnitude, can produce at most $10\%$ decrease to LO result in the considered $Q^2$ region; (b) the NLO time-like scalar pion form factor $F'^{(1)}_{\rm a,I}$ describes the ${\cal O}(\alpha_s^2)$ contribution to the factorizable annihilation diagrams of the considered $B \to \pi\pi$ decays, i.e. the NLO annihilation correction; (c) the NLO part of the form factor $F'^{(1)}_{\rm a,I}$ is very small in size, and is almost independent with the variation of cutoff scale $\mu_0$, but this form factor has a large strong phase around $-55^\circ$ and may play an important role in producing large CP violation for $B\to \pi\pi$ decays; and (d) for $B^0 \to \pi^+\pi^-$ and $\pi^0\pi^0$ decays, the newly known NLO annihilation correction can produce only a very small enhancement to their branching ratios, less than $3\%$ in magnitude, and therefore we could not interpret the well-known $\pi\pi$-puzzle by the inclusion of this NLO correction to the factorizable annihilation diagrams.Comment: 26 pages, 12 figures, 1 Table; Minor correction