Related papers: Embedded Representations and Quasi-Dynamical Symme…
Simple examples are used to introduce and examine symmetries of open quantum dynamics that can be described by unitary operators. For the Hamiltonian dynamics of an entire closed system, the symmetry takes the expected form which, when the…
We discuss the the notion of a partial dynamical symmetry (PDS), for which a prescribed symmetry is obeyed by only a subset of solvable eigenstates, while other eigenstates are strongly mixed. We present an explicit construction of…
Physical theories grounded in mathematical symmetries are an essential component of our understanding of a wide range of properties of the universe. Similarly, in the domain of machine learning, an awareness of symmetries such as rotation…
Several finite dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted…
This theoretical review is intended to give non-theorists a flavor of the ideas driving the current efforts to experimentally find supersymmetry. We discuss the main reasons behind the expectation that supersymmetry may be "just around the…
The relevance of the pseudospin symmetry in nuclei is considered. New insight is obtained from looking at the continuous transition from a model satisfying the spin symmetry to another one satisfying the pseudospin symmetry. This study…
The engineering design process often relies on mathematical modeling that can describe the underlying dynamic behavior. In this work, we present a data-driven methodology for modeling the dynamics of nonlinear systems. To simplify this…
Realistic nucleon-nucleon (NN) interactions, derived within the framework of meson theory or more recently in terms of chiral effective field theory, yield new possibilities for achieving a unified microscopic description of atomic nuclei.…
Beginning from a discussion of the known most fundamental dynamical structures of the Standard Model of physics, extended into the realms of mathematics and theory by the concept of "supersymmetry" or "SUSY," an introduction to efforts to…
Here I briefly discuss why supersymmetry is considered a leading candidate of physics beyond the standard model. I also highlight the salient features of different supersymmetry breaking models. A few other symmetries, broken or intact,…
Understanding and simulating how a quantum system interacts and exchanges information or energy with its surroundings is a ubiquitous problem, one which must be carefully addressed in order to establish a coherent framework to describe the…
Many biological phenomena such as locomotion, circadian cycles, and breathing are rhythmic in nature and can be modeled as rhythmic dynamical systems. Dynamical systems modeling often involves neglecting certain characteristics of a…
Entanglement asymmetry has emerged as a powerful tool for characterizing symmetry breaking in quantum many-body systems. In this Letter, we explore how symmetry is dynamically broken through the lens of entanglement asymmetry in two…
We consider the problem of quantum behavior in the finite background. Introduction of continuum or other infinities into physics leads only to technical complications without any need for them in description of empirical observations. The…
The concept of partial symmetry is introduced for an interacting fermion system. The associated Hamiltonians are shown to be closely related to a realistic nuclear quadrupole-quadrupole interaction. An application to $^{12}$C is presented.
We introduce the notion of a partial dynamical symmetry for which a prescribed symmetry is neither exact nor completely broken. We survey the different types of partial dynamical symmetries and present empirical examples in each category.
Learning dynamical models from data plays a vital role in engineering design, optimization, and predictions. Building models describing dynamics of complex processes (e.g., weather dynamics, or reactive flows) using empirical knowledge or…
Deep neural networks come in many sizes and architectures. The choice of architecture, in conjunction with the dataset and learning algorithm, is commonly understood to affect the learned neural representations. Yet, recent results have…
We show, in a simple quantum mechanical model, how a theory can become supersymmetric in the presence of interactions even when the free theory is not. This dynamical generation of supersymmetry relaxes the condition on the equality of…
Modeling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are sample efficient, and interpretable but often rely on rigid assumptions. Furthermore, direct numerical approximation…