Related papers: Unique continuation for the momentum ray transform
In this paper, we study the relativistic quantum problem of a particle constrained to a double cone surface. For this purpose, we build the Dirac equation in a curved space using the tetrads formalism. Two cases are analysed. First, we…
Unimodular gravity is characterized by an extra condition with respect to General Relativity: the determinant of the metric is constant. This extra condition leads to a more restricted class of invariance by coordinate transformation. Even…
We develop a method for calculating the persistence landscapes of affine fractals using the parameters of the corresponding transformations. Given an iterated function system of affine transformations that satisfies a certain compatibility…
Optically levitated particles have great potential to form the basis of novel quantum- enhanced sensors. These systems are very well suited for inertial sensing, as the particles are isolated from the environment when they are levitated at…
In this paper, we investigate the existence and uniqueness of fixed points for self-mappings defined on bipolar metric spaces using a new class of contractive conditions, namely polynomial-type contractions. Our main results establish…
The use of fractional momentum operators and fractionary kinetic energy used to model linear damping in dissipative systems such as resistive circuits and a spring-mass ensambles was extended to a quantum mechanical formalism. Three…
Our purpose is to prove the uniqueness of the representation for $G$-martingales with finite variation.
We associate to each iterated function system consisting of phi-max-contractions an operator (on the space of continuous functions from the shift space on the metric space corresponding to the system) having a unique fixed point whose image…
This expository note, written for the proceedings of ICCM 2023, presents recent work [arXiv:2004.13894]. We particularly prove an Carleman estimate on conic manifolds, using a multiple-weight Carleman argument.
Single particle states in the atomic trap employing the rotating magnetic field are found using the full time-dependent instantaneous trapping potential. These states are compared with those of the effective time-averaged potential. We show…
Structures which appear to move at or near the velocity of light contain singular points. Energy generated by the motion accumulates at these points into ever-narrowing peaks. In this paper we show that energy is generated by a curious…
In this article, the existence of mass-conserving solutions is investigated to the continuous coagulation and collisional breakage equation with singular coagulation kernels. Here, the probability distribution function attains singularity…
We investigate the quantitative unique continuation properties of solutions to second-order elliptic equations with lower-order terms. In particular, we establish quantitative forms of the strong unique continuation property for solutions…
The implications of conformal invariance, as relevant in quantum field theories at a renormalisation group fixed point, are analysed with particular reference to results for correlation functions involving conserved currents and the energy…
We observe clear precessional motion of highly birefringent liquid crystal (LC) particles trapped in a spherically aberrated optical trap which is built around a tilted refractive index stratified medium. For input circularly polarized…
We prove the strong unique continuation property for many-body Schr\"odinger operators with an external potential and an interaction potential both in $L^p_{\rm loc}(\mathbb{R}^d)$, where $p > \max(2d/3,2)$, independently of the number of…
Following Brown[1], we construct composite operators for the scalar $\phi^3$ theory in six dimensions using renormalisation group methods with dimensional regularisation. We express bare scalar operators in terms of renormalised composite…
Three results are presented: First, we solve the problem of persistence of dissipation for reduction of kinetic models. Kinetic equations with thermodynamic Lyapunov functions are studied. Uniqueness of the thermodynamic projector is…
We consider a family of manifolds with a class of degenerating warped product metrics $g_\epsilon=\rho(\epsilon,t)^{2a}dt^2 +\rho(\epsilon,t)^{2b}ds_M^2$, with $M$ compact, $\rho$ homogeneous degree one, $a \le -1$ and $b > 0$. We study the…
We show that the transfer of the plane wave spectrum of the pump beam to the fourth-order transverse spatial correlation function of the two-photon field generated by spontaneous parametric down-conversion leads to the conservation and…