Related papers: CFT data and spontaneously broken conformal invari…
This paper presents conditions for ensuring forward invariance of safe sets under sampled-data system dynamics with piecewise-constant controllers and fixed time-steps. First, we introduce two different metrics to compare the…
We discuss the problem to develop a mathematical theory of a certain class of nonrational conformal field theories (CFT) which contain the unitary CFT. A variant of the concept of a modular functor is proposed that appears to be suitable…
In quantum/wave systems with chaotic classical analogs, wavefunctions evolve in highly complex, yet deterministic ways. A slight perturbation of the system, though, will cause the evolution to diverge from its original behavior increasingly…
We present examples of continuous variable (CV) states having high fidelity to a given target, say $F > 0.9$ or $F > 0.99$, and still showing striking differences in their physical properties, including classical and quantum states within…
Apparent violations of CPT and Lorentz symmetry might arise in nature as a result of spontaneous symmetry breaking in a theory beyond the standard model. This talk summarizes a few relevant theoretical and experimental issues, with some…
This paper is concerned with the stabilization problem of singular fractional order systems with order $\alpha\in(0,2)$. In addition to the sufficient and necessary condition for observer based control, a sufficient and necessary condition…
Compositional data (i.e., data comprising random variables that sum up to a constant) arises in many applications including microbiome studies, chemical ecology, political science, and experimental designs. Yet when compositional data serve…
A new phase space criterion, encoding the physically motivated behavior of coincidence arrangements of local observables, is proposed in this work. This condition entails, in particular, uniqueness and purity of the energetically accessible…
We review the role of self-consistency in density functional theory. We apply a recent analysis to both Kohn-Sham and orbital-free DFT, as well as to Partition-DFT, which generalizes all aspects of standard DFT. In each case, the analysis…
We present a new method for generating confidence sets within the split conformal prediction framework. Our method performs a trainable transformation of any given conformity score to improve conditional coverage while ensuring exact…
We theoretically and numerically demonstrate that completely integrable scattering processes may exhibit fractal transmission fluctuations, due to typical spectral properties of integrable systems. Similar properties also occur with…
The structure of type A and B trace anomalies is reanalyzed in terms of the universal behaviour of dimension -2 invariant amplitudes. Based on it a general argument for trace anomaly matching between the unbroken and broken phases of a CFT…
Conformal prediction provides a distribution-free framework for uncertainty quantification. This study explores the application of conformal prediction in scenarios where covariates are missing, which introduces significant challenges for…
A method of Parity-Time (PT)-symmetry analysis is introduced to study the high dimensional, complicated parameter space of drift wave instabilities. We show that spontaneous PT-symmetry breaking leads to the Ion Temperature Gradient (ITG)…
The two-dimensional case occupies a special position in the theory of critical phenomena due to the exact results provided by lattice solutions and, directly in the continuum, by the infinite-dimensional character of the conformal algebra.…
The explicit analytical expression of the Nonlinear Fourier Transform (NFT) of a finite set of data is provided. Then a simple recursion relation for the NFT is constructed as a function of the spectral parameter. These tools provide a…
We prove a strong form of spontaneous breaking of rotational symmetry for a simple model of two-dimensional crystals with random defects in thermal equilibrium at low temperature. The defects consist of isolated missing atoms.
The aim of this paper is to propose a criterion of spontaneous symmetry breaking that makes reference to the properties of pure phases defined by a translationally invariant state. By avoiding any reference to the ground state, at the basis…
We made a careful study of Polyakov's Diofantian equations for 2D turbulence and found several additional CFTs which meet his criterion. This fact implies that we need further conditions for CFT in order to determine the exponent of the…
We consider two $d \geq 2$ conformal field theories (CFTs) glued together along a codimension one conformal interface. The conformal anomaly of such a system contains both bulk and interface contributions. In a curved-space setup, we…