Geometry defects in Bosonic symmetry protected topological phases

In this paper we focus on the interplay between geometry defects and topological properties in bosonic symmetry protected topological(SPT) phases. We start from eight copies of 3D time-reversal($\mathcal{T}$) invariant topological superconductors(TSC) on a crystal lattice. We melt the lattice by condensation of disclinations and therefore restore the rotation symmetry. Such disclination condensation procedure confines the fermion and afterwards turns the system into a 3D boson topological liquid crystal(TCL). The low energy effective theory of this crystalline-liquid transition contains a topological term inherited from the geometry axion response in TSC. In addition, we investigate the interplay between dislocation and superfluid vortex on the surface of TCL. We demonstrate that the $\mathcal{T}$ and translation invariant surface state is a double $[e\mathcal{T}m\mathcal{T}]$ state with intrinsic surface topological order. We also look into the exotic behavior of dislocation in 2D boson SPT state described by an $O(4)$ non-linear $\sigma$-model(NL$\sigma$M) with topological $\Theta$-term. By dressing the $O(4)$ vector with spiral order and gauge the symmetry, the dislocation has mutual semion statistics with the gauge flux. Further reduce the $O(4)$ NL$\sigma M$ to the Ising limit, we arrive at the Levin-Gu model with stripy modulation whose dislocation has nontrivial braiding statistics

Stripe melting, a transition between weak and strong symmetry protected topological phases

For a gapped disordered many-body system with both internal and translation symmetry, one can define the corresponding weak and strong Symmetry Protected Topological (SPT) phases. A strong SPT phase is protected by the internal symmetry $G$ only while a weak SPT phase, fabricated by alignment of strong SPT state in a lower dimension, requires additional discrete translation symmetry protection. In this paper, we construct a phase transition between weak and strong SPT phase in strongly interacting boson system. The starting point of our construction is the superconducting Dirac fermions with pair density wave(PDW) order in $2d$. We first demonstrate that the nodal line of the PDW contains a $1d$ boson SPT phase. We further show that melting the PDW stripe and condensing the nodal line provoke the transition from weak to strong SPT phase in $2d$. The phase transition theory contains an O(4) non-linear-$\sigma$-model(NL$\sigma$M) with topological $\Theta$-term emerging from the proliferation of domain walls bound to an SPT chain. Similar scheme also applies to weak-strong SPT transition in other dimensions and predicts possible phase transition from $2d$ to $3d$ topological order

New example of CP violation from search for the permanent electric dipole moment of Cs atoms

Using special capacitors three experiments to search for a permanent electric dipole moment (EDM) of Cesium atom were completed. The electric susceptibility xe of Cs vapor varies in direct proportion to the density N, where xe =70 when N=7.37*1022 m-3! The relationship between xe of Cs vapor and the absolute temperatures T is xe =B/T, where the slope B=320(k) as polar molecules H2O(B=1.50(k)). Its capacitance C at different voltage V was measured. The C-V curve shows that the saturation polarization of Cs vapor has be observed when the field E=7.4*104V/m. Our measurements give the EDM of an Cs atom : dCs=2.97*10-29 C.m=1.86*10-8 e.cm. New example of CP (charge conjugation and parity) violation occurred in Cs atoms. Our results are easy to be repeated because the details of the experiment are described in the article.Comment: 7 pages, 7 figures,1 tabl

PI-REC: Progressive Image Reconstruction Network With Edge and Color Domain

We propose a universal image reconstruction method to represent detailed images purely from binary sparse edge and flat color domain. Inspired by the procedures of painting, our framework, based on generative adversarial network, consists of three phases: Imitation Phase aims at initializing networks, followed by Generating Phase to reconstruct preliminary images. Moreover, Refinement Phase is utilized to fine-tune preliminary images into final outputs with details. This framework allows our model generating abundant high frequency details from sparse input information. We also explore the defects of disentangling style latent space implicitly from images, and demonstrate that explicit color domain in our model performs better on controllability and interpretability. In our experiments, we achieve outstanding results on reconstructing realistic images and translating hand drawn drafts into satisfactory paintings. Besides, within the domain of edge-to-image translation, our model PI-REC outperforms existing state-of-the-art methods on evaluations of realism and accuracy, both quantitatively and qualitatively.Comment: 15 pages, 13 figure

Two puzzling problems in explanation of the linear Stark effect of hydrogen atom and space quantization of the dipole moment

The linear Stark effect for the first excited state of the hydrogen atom shows that, in the unperturbed states, the atom has a permanent electric dipole moment (EDM) of magnitude 3eao (ao is Bohr radius). The EDM is not induce by the external field but is inherent behavior of the atom. But the calculation of quantum mechanics tells us that unperturbed states of hydrogen atom have no EDM! In the effect, two of four states have no energy shift. What are the EDM of the hydrogen atoms in the two states? Quantum mechanics can not answer the problem. The statement that the EDM of the two states is perpendicular to the field only comes from guesses in quantum mechanics. The two problems had puzzled physicists for more than 80 years. By introducing a new parameter this article gives a satisfactory explanation for the effect. Our calculation discovered that, in the unperturbed states, the atoms not only have EDM with 3eao but also can have only three directions of quantization! It is an entirely unexpected discovery. This research is a vital clue that not all is well with quantum mechanics. We prophesy that hydrogen-like atoms, such as K, Rb and Cs atom etc, may have large EDM of the order of magnitude eao in their ground state (see arXiv:0809.4767, arXiv:0810.0770 and arXiv:0810.2026).Comment: 6 pages, 2 table

Clear evidence of charge conjugation and parity violation in K atoms from atomic permanent electric dipole moment experiments

Quantum mechanics thinks that atoms do not have permanent electric dipole moment (EDM) because of their spherical symmetry. Therefore, there is no polar atom in nature except for polar molecules. The electric susceptibility Xe caused by the orientation of polar substances is inversely proportional to the absolute temperature T while the induced susceptibility of atoms is temperature independent. This difference in temperature dependence offers a means of separating the polar and non-polar substances experimentally. Using special capacitor our experiments discovered that the relationship between Xe of Potassium atom and T is just Xe=B/T, where the slope B is approximately 283(K) as polar molecules, but appears to be disordered using the traditional capacitor. Its capacitance C at different voltage V was measured. The C-V curve shows that the saturation polarization of K vapor has be observed when E more than 105V/m and nearly all K atoms (over 98.9 per cent) are lined up with the field! The ground state neutral K atom is polar atom with a large EDM: dK more than 2.3*10-9e.cm.The results gave clear evidence for CP (charge conjugation and parity) violation in K atoms. If K atom has a large EDM, why the linear Stark effect has not been observed? The article discussed the question thoroughly. Our results are easy to be repeated because the details of the experiment are described in the article.Comment: 7 pages, 6 figures, 2 table

Injectable Spontaneous Generation of Tremendous Self-Fueled Liquid Metal Droplet Motors in a Moment

Micro motors that could run in liquid environment is very important for a variety of practices such as serving as pipeline robot, soft machine, drug delivery, or microfluidics system etc. However, fabrication of such tiny motors is generally rather time and cost consumptive and has been a tough issue due to involve too many complicated procedures and tools. Here, we show a straightforward injectable way for spontaneously generating autonomously running soft motors in large quantity. A basic fabrication strategy thus enabled is established and illustrated. It was found that, injecting the GaIn alloy pre-fueled with aluminum into electrolyte would automatically split in seconds into tremendous droplet motors swiftly running here and there. The driving force originated from the galvanic cell reaction among alloy, aluminum and surrounding electrolyte which offers interior electricity and hydrogen gas as motion power. This finding opens the possibility to develop injectable tiny-robots, droplet machines or microfluidic elements. It also raised important scientific issues regarding characterizing the complicated fluid mechanics stimulated by the quick running of the soft metal droplet and the gases it generated during the traveling.Comment: 12 pages, 5 figure

Branching random walk in random environment with random absorption wall

We consider the branching random walk in random environment with a random absorption wall. When we add this barrier, we discuss some topics related to the survival probability. We assume that the random environment is i.i.d., $S_i$ is a particular i.i.d. random walk depend on the random environment $\mathcal{L}$. Let the random barrier function (the random absorption wall) is $g_i(\mathcal{L}):=ai^\alpha-S_i,$ where $i$ present the generation. We show that there exists a critical value $a_c>0$ such that if $a>a_c,\alpha=\frac{1}{3}$, the survival probability is positive almost surly and if $a<a_c,\alpha=\frac{1}{3}$ ,the survival probability is zero almost surely. Moreover, if we denote $Z_n$ is the total populations in $n$-th generation in the new system (with barrier),under some conditions, we show $\ln\mathbb{P}_{\mathcal{L}}(Z_n>0)/n^{1/3}$ will converges to a negative constant almost surely if $\alpha\in[0,\frac{1}{3})$.Comment: 18 page

Can We Reach the Scale of New Physics Behind the BB Anomalies?

Indirect signs of new physics beyond the Standard Model may be appearing in $B \to K^{(*)}\mu^+\mu^-$ decays. If confirmed, the title question will be of paramount importance in determining the strategy for future colliders. We answer it by estimating the sensitivity to minimal, anomaly-compatible $Z^\prime$ and leptoquark models at the high luminosity LHC, 27 TeV HE-LHC, and 100 TeV FCC-hh; this conservative analysis outlines an upper bound on the available parameter space and the conditions for a reasonable guarantee of direct discovery.Comment: 4 pages, 4 figures. Contribution to the proceedings of the 53rd Rencontres de Morion

Non-Abelian defects in Fracton phase of matter

Fracton phase of matter host fractionalized topological quasiparticles with restricted mobility. A wide variety of fracton models with abelian excitations had been proposed and extensively studied while the candidates for non-Abelian fracton phases are less explored. In this work, we investigate the effect of twisted defect in abelian fracton models. The twisted defect is launched by introducing a branch cut line hosting anyon condensate. In particular, these twisted defects, which alter different types of quasiparticles, carry projective non-Abelian zero modes. En route, such defects can be engineered via strong onsite hybridization along a branch cut which provides wide tunability and flexibility in experiment platforms. The braiding of twisted defects with projective non-Abelian Berry phase renders a new avenue toward fault-tolerant quantum computation