Related papers: Symmetry restoration methods
Lie symmetry group method is applied to study the Telegraph equation. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra…
Symmetry is a fundamental tool in the exploration of a broad range of complex systems. In machine learning symmetry has been explored in both models and data. In this paper we seek to connect the symmetries arising from the architecture of…
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…
Nuclear fission plays an important role in fundamental and applied science, from astrophysics to nuclear engineering, yet it remains a major challenge to nuclear theory. Theoretical methods used so far to compute fission observables rely on…
We present a clear and mathematically simple procedure explaining spontaneous symmetry breaking in quantum mechanical systems. The procedure is applicable to a wide range of models and can be easily used to explain the existence of a…
We analyze the role played by Long Distance Symmetries within the context of the Similarity Renormalization Group (SRG) approach, which is based on phase-shift preserving continuous unitary transformations that evolve hamiltonians with a…
Several topics concerning nuclear structure and electromagnetic interactions of heavy nuclei are reviewed. These comprehend the deformed single-particle shell model, nuclear collective motion, symmetry breaking and approximate symmetry…
Efforts to extract information on magnitude and density dependence of the nuclear symmetry energy are discussed. The utilized data include those on mass dependence of the excitation energies to the isobaric analog states of ground states,…
Spectral properties of nuclei near the critical point of the quantum phase transition between spherical and axially symmetric shapes are studied in a hybrid collective model which combines the $\gamma$-stable and $\gamma$-rigid collective…
A major goal of nuclear theory is to explain the spectra and stability of nuclei in terms of effective many-body interactions amongst the nucleus' constituents-the nucleons, i.e., protons and neutrons. Such an approach, referred to below as…
We investigate the concept of symmetry and its role in problem solving. This paper first defines precisely the elements that constitute a "problem" and its "solution," and gives several examples to illustrate these definitions. Given…
Symmetry is an important problem in many combinatorial problems. One way of dealing with symmetry is to add constraints that eliminate symmetric solutions. We survey recent results in this area, focusing especially on two common and useful…
Lie symmetry analysis is applied to study the nonlinear rotating shallow water equations. The 9-dimensional Lie algebra of point symmetries admitted by the model is found. It is shown that the rotating shallow water equations are related…
Symmetry can be used to help solve many problems. For instance, Einstein's famous 1905 paper ("On the Electrodynamics of Moving Bodies") uses symmetry to help derive the laws of special relativity. In artificial intelligence, symmetry has…
This paper presents a series of general results about the optimal estimation of physical transformations in a given symmetry group. In particular, it is shown how the different symmetries of the problem determine different properties of the…
Using the relativistic mean-field theory, we adopt two different methods, namely, the coexisting phase method and the self-consistent Thomas-Fermi approximation, to study the impacts of the nuclear symmetry energy on properties of neutron…
According to standard textbooks, the nuclear symmetry energy originates from the {\it kinetic} energy and the {\it interaction} itself. We argue that this view requires certain modifications. We ascribe the physical origin of the {\it…
A full Lie point symmetry analysis of rational difference equations is performed. Non-trivial symmetries are derived and exact solutions using these symmetries are obtained.
Spontaneous symmetry breaking in non-relativistic quantum systems has previously been addressed in the framework of effective field theory. Low-lying excitations are constructed from Nambu-Goldstone modes using symmetry arguments only. We…
Statistical learning methods show great promise in providing an accurate prediction of materials and molecular properties, while minimizing the need for computationally demanding electronic structure calculations. The accuracy and…