相关论文: Generic sets in spaces of measures and generic sin…
Let P -> M be a principal G-bundle. Using techniques from the loop representation of gauge theory, we construct well-defined substitutes for ``Lebesgue measure'' on the space A of connections on P and for ``Haar measure'' on the group Ga of…
We consider the problem of disorder chaos in the spherical mean-field model. It is concerned about the behavior of the overlap between two independently sampled spin configurations from two Gibbs measures with the same external parameters.…
We explore the influence of an arbitrary external potential perturbation V on the spectral properties of a weakly disordered conductor. In the framework of a statistical field theory of a nonlinear sigma-model type we find, depending on the…
The separately continuity topology is considered and some its properties are investigated. With help of these properties a generalization of Sierpinski theorem on determination of real separately continuous function by its values on an…
The generalized symmetry method is applied to a class of completely discrete equations including the Adler-Bobenko-Suris list. Assuming the existence of a generalized symmetry, we derive a few integrability conditions suitable for testing…
We study the orthospectrum and the simple orthospectrum of compact hyperbolic surfaces with geodesic boundary. We show that there are finitely many hyperbolic surfaces sharing the same simple orthospectrum and finitely many hyperbolic…
In this paper we contribute to the generic theory of Hamiltonians by proving that there is a C2-residual R in the set of C2 Hamiltonians on a closed symplectic manifold M, such that, for any H in R, there is a full measure subset of…
We describe the geometry of generic heterotic backgrounds preserving minimal supersymmetry in four dimensions using the language of generalised geometry. They are characterised by an $SU(3)\times Spin(6+n)$ structure within…
Pendulum-like dynamics is a universal motif across many areas of physics, underlying systems ranging from classical nonlinear oscillators to superconducting qubits and cold-atom tunneling platforms. Here we present an exact frequency-domain…
We prove that every closed set which is not sigma-finite with respect to the Hausdorff measure H^{N-1} carries singularities of continuous vector fields in the Euclidean space R^N for the divergence operator. We also show that finite…
This paper investigates the properties of trajectories in harmonic oscillator systems equipped with a point, absolutely continuous, or singular measure. As demonstrated in [30], infinite-dimensional linear flows of countable oscillator…
Unfolding singular points in linear differential equations is a classical technique for studying the properties of irregular singularities by relating them to regular singularities. In this paper, we propose a general framework for…
Symmetry postulates play a crucial role in various approaches to reconstruct quantum theory from a few basic principles. Discrete and continuous symmetries are under consideration. The continuous case better matches the physical needs for…
Generalized symmetry extends the usual notion of symmetry to ones that are of higher-form, acting on subsystems, non-invertible, etc. The concept was originally defined in the field theory context using the idea of topological defects. On…
Spherical Designs are finite sets of points on the sphere $\mathbb{S}^{d}$ with the property that the average of certain (low-degree) polynomials in these points coincides with the global average of the polynomial on $\mathbb{S}^{d}$. They…
We show how localization and smoothing techniques can be used to establish universality at the edge of the spectrum for a fixed positive measure on [-1,1]. Assume that the measure is a regular measure, and is absolutely continuous in some…
There exists a well established differential topological theory of singularities of ordinary differential equations. It has mainly studied scalar equations of low order. We propose an extension of the key concepts to arbitrary systems of…
When a quantum system is monitored in continuous time, the result of the measurement is a stochastic process. When the output process is stationary, at least in the long run, the spectrum of the process can be introduced and its properties…
Uniform measures are the functionals on the space of bounded uniformly continuous functions that are continuous on every bounded uniformly equicontinuous set. This paper describes the role of uniform measures in the study of convolution on…
The Hamiltonian of classical anti-de Sitter gravity is a pure boundary term on-shell. If this remains true in non-perturbative quantum gravity then i) boundary observables will evolve unitarily in time and ii) the algebra of boundary…