Related papers: A note on permutation twist defects in topological…
The topic of this letter is structure formation with topological defects. We first present a partially new, fully local and gauge invariant system of perturbation equations to treat microwave background and dark matter fluctuations induced…
We prove a new converse theorem for Borcherds' multiplicative theta lift which improves the previously known results. To this end we develop a newform theory for vector valued modular forms for the Weil representation, which might be of…
Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions,…
Modular forms appear in many facets of mathematics, and have played important roles in geometry, mathematical physics, number theory, representation theory, topology, and other areas. Around 1994, motivated by technical issues in homotopy…
A new method is proposed to predict the topological properties of one-dimensional periodic structures in wave physics, including quantum mechanics. From Bloch waves, a unique complex valued function is constructed, exhibiting poles and…
We show that signs of Fourier coefficients, on certain sub-families, determine the half-integral weight cuspidal eigenform uniquely, up to a positive constant. We also study sign change results for the product of the Fourier coefficients of…
We extend and generalize the seminal work of Brandenberger, Huang and Zhang on the formation of strings during chiral phase transitions(berger) and discuss the formation of abelian and non-abelian topological strings during such transitions…
We review our recent results on the physics of quantum Hall fluids at Jain and non conventional fillings within a general field theoretic framework. We focus on a peculiar conformal field theory (CFT), the one obtained by means of the…
We provide new type of decay estimate for scalar curvatures of steady gradient Ricci solitons. We also give certain upper bound for the diameter of a Riemannian manifold whose $\infty$-Bakry--Emery Ricci tensor is bounded by some positive…
We consider the problem of numerically computing the quantum dynamics of an electron in twisted bilayer graphene. The challenge is that atomic-scale models of the dynamics are aperiodic for generic twist angles because of the…
Equivariant quantum cohomology possesses the structure of a difference module by shift operators (Seidel representation) of equivariant parameters. Teleman's conjecture suggests that shift operators and equivariant parameters acting on…
We consider the number distribution of topological defects resulting from the finite-time crossing of a continuous phase transition and identify signatures of universality beyond the mean value, predicted by the Kibble-Zurek mechanism.…
We study the sum of additively twisted Fourier coefficients of a symmetric-square lift of a Maass form invariant under the full modular group. Our bounds are uniform in terms of the spectral parameter of the Maass form, as well as in terms…
Moir\'e materials have become one of the most active fields in material science in recent years due to their high tunability, and their unique properties emerge from the Moir\'e-scale structure modulation. Here, we propose twisted bilayer…
On base of differential biquaternions algebra and generalized functions theory the biquaternionic wave equation is considered under vector representation of its structural coefficient. Its generalized solutions are constructed, which…
Motivated by recent observation of the quantum spin Hall effect in monolayer germanene and twisted bilayer transition-metal-dichalcogenides (TMDs), we study the topological phases of moir\'e twisted bilayers with time-reversal symmetry and…
We prove an explicit formula conjectured recently by Wang and Levin for the anomaly of time-reversal symmetry in 2+1 dimensional fermionic topological quantum field theories. The crucial step is to determine the crosscap state in terms of…
The creation of moir\'e superlattices in twisted bilayers of two-dimensional crystals has been utilised to engineer quantum material properties in graphene and transition metal dichalcogenide (TMD) semiconductors. Here, we examine the…
We consider one-dimensional deterministic and random tight-binding Hamiltonians modeling electronic properties of twisted bilayer materials. When the twisted structure is incommensurate, we prove convergence of the density of states measure…
Simulations of a bilayer in a liquid solvent in the full range of areas from the floppy to the extended state also show the hole/tunnel spontaneous formation. Whether this change of topology is preceded by topological fluctuations of the…