Related papers: Asymmetry in repeated isotropic rotations
The observed general time-asymmetric behavior of macroscopic systems -- embodied in the second law of thermodynamics -- arises naturally from time-symmetric microscopic laws due to the great disparity between macro and micro-scales. More…
Recognizing symmetries in data allows for significant boosts in neural network training. In many cases, however, the underlying symmetry is present only in an idealized dataset, and is broken in the training data, due to effects such as…
The replicated field theory of the random field Ising model involves the couplings of replicas of different indices. The resulting correlation functions involve a superposition of different types of long distance behaviours. However the…
Disordered magnets, martensitic mixed crystals, and glassy solids can be irreversibly deformed by subjecting them to external deformation. The deformation produces a smooth, reversible response punctuated by abrupt relaxation "glitches".…
Certain patterns of symmetry fractionalization in topologically ordered phases of matter are anomalous, in the sense that they can only occur at the surface of a higher dimensional symmetry-protected topological (SPT) state. An important…
We introduce a model which may generate particle number asymmetry in an expanding Universe. The model includes CP violating and particle number violating interactions. The model consists of a real scalar field and a complex scalar field.…
An aspect of the synchronization dynamics is investigated in this work. We argue analytically and confirm numerically that the chaotic dynamics on the synchronization manifold exhibits unstable dimension variability. Unstable dimension…
In this paper we show that in systems where the probability distribution of the the overlap is non trivial in the infinity volume limit, the property of ultrametricity can be proved in general starting from two very simple and natural…
The apparantly irregular (unpredictable) space-time fluctuations in atmospheric flows ranging from climate (thousands of kilometers - years) to turbulence (millimeters - seconds) exhibit the universal symmetry of self-similarity.…
Stokes phenomenon refers to the fact that the asymptotic expansion of complex functions can differ in different regions of the complex plane, and that beyond the so-called Stokes lines has an unphysical divergence. An important special case…
Geometric properties of $N$ random points distributed independently and uniformly on the unit sphere $\mathbb{S}^{d}\subset\mathbb{R}^{d+1}$ with respect to surface area measure are obtained and several related conjectures are posed. In…
We consider the relationship between symmetries of two-dimensional autonomous dynamical system in two common formulations; as a set of differential equations for the derivative of each state with respect to time, and a single differential…
It is shown that continuously changing the effective number of interacting particles in p-spin-glass-like model allows to describe the transition from the full replica symmetry breaking glass solution to stable first replica symmetry…
Errors quoted on results are often given in asymmetric form. An account is given of the two ways these can arise in an analysis, and the combination of asymmetric errors is discussed. It is shown that the usual method has no basis and is…
Appropriately normalized square random Vandermonde matrices based on independent random variables with uniform distribution on the unit circle are studied. It is shown that as the matrix sizes increases without bound, with respect to the…
Quantum multifractality is a fundamental property of systems such as non-interacting disordered systems at an Anderson transition and many-body systems in Hilbert space. Here we discuss the origin of the presence or absence of a fundamental…
The low-lying spectra of atomic nuclei display diverse behaviors, for example rotational bands, which can be described phenomenologically by simple symmetry groups such as spatial SU(3). This leads to the idea of dynamical symmetry, where…
We investigate the relation between spontaneous and explicit replica symmetry breaking in the theory of disordered systems. On general ground, we prove the equivalence between the replicon operator associated with the stability of the…
We treat a random number generation from an i.i.d. probability distribution of $P$ to that of $Q$. When $Q$ or $P$ is a uniform distribution, the problems have been well-known as the uniform random number generation and the resolvability…
The internal representations learned by language models consistently exhibit striking geometric structure: calendar months organize into a circle, historical years form a smooth one-dimensional manifold, and cities' latitudes and longitudes…