Related papers: Symmetry Classes
The dynamics of learning in modern large AI systems is hierarchical, often characterized by abrupt, qualitative shifts akin to phase transitions observed in physical systems. While these phenomena hold promise for uncovering the mechanisms…
The supersymmetric method is a powerful method for the evaluation of quenched averages in disordered systems. Among others, this method has been applied to the theory of S-matrix fluctuations, the theory of universal conductance…
A typical quantum state with no symmetry can be realized by letting a random unitary act on a fixed state, and the subsystem entanglement spectrum follows the Laguerre unitary ensemble (LUE). For integer-spin time reversal symmetry, we have…
A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…
Symmetry properties of the evolution equation and the state to be controlled are shown to determine the basic features of the linear control of unstable orbits. In particular, the selection of control parameters and their minimal number are…
Constrained Hamiltonian systems fall into the realm of presymplectic geometry. We show, however, that also Poisson geometry is of use in this context. For the case that the constraints form a closed algebra, there are two natural Poisson…
In this work the spontaneous symmetry breaking in certain nonlinear theories with second-class constraints is explored. Using the Dirac's method we perform an analysis of the constraints and the counting of the degrees of freedom. The…
The gauge symmetries of a general dynamical system can be systematically obtained following either a Hamiltonean or a Lagrangean approach. In the former case, these symmetries are generated, according to Dirac's conjecture, by the first…
We discuss the role and merits of symmetry methods for the analysis of biological systems. In particular, we consider systems of first order ordinary differential equations and provide a comprehensive review of the geometrical foundations…
We use the order complex corresponding to a symmetric matrix (defined by Giusti et al in 2015). In this note, we use it to define a class of models of random graphs, and show some surprising experimental results, showing sharp phase…
Symmetry is an important feature of many constraint programs. We show that any symmetry acting on a set of symmetry breaking constraints can be used to break symmetry. Different symmetries pick out different solutions in each symmetry…
We provide an overview of high dimensional dynamical systems driven by random matrices, focusing on applications to simple models of learning and generalization in machine learning theory. Using both cavity method arguments and path…
The role of symmetries in formation of quantum dynamics is discussed. A quantum version of the d'Alambert's principle is proposed to take into account symmetry constrains for quantum case. It is noted that in this approach one can find, in…
We investigate topological properties and classification of mean-field theories of stable bosonic systems. Of the three standard classifying symmetries, only time-reversal represents a real symmetry of the many-boson system, while the other…
Categorical symmetries have recently been shown to generalize the classification of phases of matter, significantly broadening the traditional Landau paradigm. To test these predictions, we propose a simple spin chain model that encompasses…
We introduce a machine-learning approach (denoted Symmetry Seeker Neural Network) capable of automatically discovering discrete symmetry groups in physical systems. This method identifies the finite set of parameter transformations that…
Symmetry is one of the most generic and useful concepts in physics and chemistry, often leading to conservation laws and selection rules. For example, symmetry considerations have been used to predict selection rules for transitions in…
New insight into the correspondence between Quantum Chaos and Random Matrix Theory is gained by developing a semiclassical theory for the autocorrelation function of spectral determinants. We study in particular the unitary operators which…
Spatial symmetries of quantum systems leads to important effects in spectroscopy, such as selection rules and dark states. Motivated by the increasing strength of light-matter interaction achieved in recent experiments, we investigate a set…
We start by introducing the basics of configurations of points and lines, and then move into discussing symmetry groups of these configurations. Specifically, we explore how we might classify the symmetries of $(9_3)$ and $(10_3)$ geometric…