Related papers: Twisted Spectral Triples without the First-Order C…
Grating spectra exhibit sharp variations of the scattered light, known as grating anomalies. The latter are due to resonances that have fascinated specialists of optics and physics for decades and are nowadays used in many applications. We…
Trust-region subproblem (TRS) is an important problem arising in many applications such as numerical optimization, Tikhonov regularization of ill-posed problems, and constrained eigenvalue problems. In recent decades, extensive works focus…
Fluctuation effects at first order phase transitions driven by changes of other-than-temperature factors like pressure, concentration, or external fields are investigated by perturbation theory. The results for the fluctuation contributions…
We explain how a simple twisting of the notion of spectral triple allows to incorporate type III examples, such as those arising from the transverse geometry of codimension one foliations. Since the twisting of the commutators turns the…
General first- and higher-order intertwining relations between non-stationary one-dimensional Schr\"odinger operators are introduced. For the first-order case it is shown that the intertwining relations imply some hidden symmetry which in…
Through the example of the quantum symplectic 4-sphere, we discuss how the notion of twisted spectral triple fits into the framework of quantum homogeneous spaces.
Any oriented Riemannian manifold with a Spin-structure defines a spectral triple, so the spectral triple can be regarded as a noncommutative Spin-manifold. Otherwise for any unoriented Riemannian manifold there is the two-fold covering by…
As an extension of our previous study, we derive slow-roll conditions for multiple scalar fields which are non-minimally coupled with gravity and for generalized gravity theories of the form $f(\phi,R)$. We provide simple formulae of the…
The elastic scattering of twisted electrons by neutral atoms is studied within the fully relativistic framework. The electron-atom interaction is taken into account in all orders, thus allowing us to explore high-order effects beyond the…
We give various examples of asymmetric orbifold models to possess intertwining currents which convert untwisted string states to twisted ones, and vice versa, and see that such asymmetric orbifold models are severely restricted. The…
We continue and extend our earlier investigation ``Strings in a Time-Dependent Orbifold'' (hep-th/0204168). We formulate conditions for an orbifold to be amenable to perturbative string analysis and classify the low dimensional orbifolds…
Initially straight slender elastic rods with geometrically constrained ends buckle and form stable two-dimensional shapes when compressed by bringing the ends together. It is also known that beyond a critical value of the pre-stress,…
We calculate fluctuation corrections to the longitudinal conductivity of disordered superconductors subject to an external magnetic field. We derive analytic expressions that are valid in the entire metallic part of the temperature-magnetic…
We perform conformal perturbation theory by marginal operators to first order. A suitable renormalization method is needed that makes the conformal invariance of the deformed correlation functions manifest. Combining the embedding space…
The common eigenfunctions of the twisted Cherednik operators can be first analyzed in the limit of $q\longrightarrow 1$. Then, the polynomial eigenfunctions form a simple set originating from the symmetric ground state of non-vanishing…
The perturbation of the symmetric orbifold of $\mathbb{T}^4$ under the triplet of exactly marginal operators from the $2$-cycle twisted sector is studied in perturbation theory. We show that the structure of the triplet perturbation is very…
Twisted spectral triples are a twisting of the notion of spectral triple aiming at dealing with some type III geometric situations. In the first part of the paper, we give a geometric construction of the index map of a twisted spectral…
Based on Document (1), by considering the retarded interaction of radiation fields, the third order transition probabilities of stimulated radiations and absorptions of light are calculated. The revised formulas of nonlinear polarizations…
We give a proof of an analogue of Connes' Hochschild character theorem for twisted spectral triples obtained from twisting a spectral triple by scaling automorphisms, under some suitable conditions. We also survey some of the properties of…
The nature of the insulating and superconducting states in twisted bilayer graphene systems is intensely debated. While many works seek for explanations in the few flat bands near the Fermi level, theory and a number of experiments suggest…