Related papers: On Symmetries in Analytic Input-Output Systems
There is a relation between the irreversibility of thermodynamic processes as expressed by the breaking of time-reversal symmetry, and the entropy production in such processes. We explain on an elementary mathematical level the relations…
Symmetries play a central role in both equilibrium and nonequilibrium phase transitions, yet their quantitative characterization in dynamical quantum phase transitions (DQPTs) remains an open challenge. In this work, we establish a direct…
Symmetry is a powerful tool for understanding phases of matter in equilibrium. Quantum circuits with measurements have recently emerged as a platform for novel states of matter intrinsically out of equilibrium. Can symmetry be used as an…
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…
The safety region of operation of a system is the subset of allowed outputs for which no undesirable outcome would occur. Knowing if a system would ever leave its safety regions of operation is important information for the planning and…
Any coarse-grained description of a nonequilibrium system should faithfully represent its latent irreversible degrees of freedom. However, standard dimensionality reduction methods typically prioritize accurate reconstruction over physical…
The goal of the paper is two-fold. The first of which is to derive an explicit formula to compute the generating series of a closed-loop system when a plant, given in a Chen-Fliess series description is in multiplicative output feedback…
The goal of this paper is to compute the generating series of a closed-loop system when the plant is described in terms of a Chen-Fliess series and an additive static output feedback is applied. The first step is to consider the so called…
Mechanical systems naturally evolve on principal bundles describing their inherent symmetries. The ensuing factorization of the configuration manifold into a symmetry group and an internal shape space has provided deep insights into the…
A new type of symmetry, ren-symmetry describing anyon physics and the corresponding topological physics, is proposed. Ren-symmetry is a generalization of super-symmetry which is widely applied in super-symmetric physics such as the…
A general way to construct chain models with certain Lie algebraic or quantum Lie algebraic symmetries is presented. These symmetric models give rise to series of integrable systems. As an example the chain models with $A_n$ symmetry and…
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…
We recently showed that the two-dimensional Ising spin glass allows for a line of renormalization group fixed points which explains properties observed in numerical studies. We observe that this exact result corresponds to enhancement to a…
The steady states of three families of one-dimensional non-equilibrium models with open boundaries, first proposed in [22], are studied using a matrix product formalism. It is shown that their associated quadratic algebras have…
Symmetry is fundamental to understanding our physical world. An antisymmetry operation switches between two different states of a trait, such as two time-states, position-states, charge-states, spin-states, chemical-species etc. This review…
In this work I show by a first principles calculation that quantum states describing massive relativistic free spinning particles obey kinematical conditions whose origin can be traced to parity as a good quantum number. These conditions…
We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better…
Space-filling designs are commonly used in computer experiments to fill the space of inputs so that the input-output relationship can be accurately estimated. However, in certain applications such as inverse design or feature-based…
This research investigates a novel class of one-dimensional theories characterised by a distinctly defined infinite interaction range. We propose that such theories emerge naturally through a mesoscopic feedback mechanism. In this…
Symmetry is a fundamentally important concept in many branches of physics. In this work, we discuss two types of symmetries, external symmetry and internal symmetry, which appear frequently in controlled quantum spin chains and apply them…