相关论文: Symmetries on Spin Chains: Limited Controllability…

Spontaneous symmetry breaking is a cornerstone of modern physics, defining a wealth of phenomena in condensed-matter and high-energy physics, and beyond. It requires an infinite number of degrees of freedom, and even then, for continuous…

The search for symmetry as an unusual yet profoundly appealing phenomenon, and the origin of regular, repeating configuration patterns have long been a central focus of complexity science and physics. To better grasp and understand symmetry…

Symmetries of nonlinear control systems in state representation are considered. To this end, a geometric approach to ordinary differential equations is advocated. Invariant feedback laws for systems with Lie symmetries, i.e. feedback laws…

We show how a Heisenberg spin chain emerges from the two-dimensional ${\mathcal N}$=(2,2) gauge theory at an intermediate scale, which relies on the renormalization group flow guided by the global symmetries and the dynamics of domain…

Supersymmetry operators that change a spin chain's length have appeared in numerous contexts, ranging from the AdS/CFT correspondence to statistical mechanics models. In this article, we present, via an analysis of the Bethe equations, all…

The two ways of constrained systems quantization are considered from the point of view of their self-consistency at the quantum level. With a transparent example of a particle in the external electromagnetic field we demonstrate that the…

This paper studies controllability of a discrete-time linear dynamical system using nonnegative and sparse inputs. These constraints on the control input arise naturally in many real-life systems where the external influence on the system…

Symmetry is one of the most general and useful concepts in physics. A theory or a system that has a symmetry is fundamentally constrained by it. The same constraints do not apply when the symmetry is broken. The quantitative determination…

Interactions between the different degrees of freedom form the basis of many manifestations of intriguing physics in condensed matter. In this respect, quantifying the dynamics of normal modes that themselves arise from these interactions…

We discuss smooth nonlinear control systems with symmetry. For a free and proper action of the symmetry group, the reduction of symmetry gives rise to a reduced smooth nonlinear control system. If the action of the symmetry group is only…

We discuss three questions related to the critical behavior of hierarchical spin models: 1) the hyperscaling relations in the broken symmetry phase; 2) the combined use of dual expansions to calculate the non-universal quantities; 3) the…

We consider spin chain models with exotic symmetries that change the length of the spin chain. It is known that the XXZ Heisenberg spin chain at the supersymmetric point $\Delta=-1/2$ possesses such a symmetry: it is given by the…

Given a finite-dimensional time continuous control system and $\varepsilon>0$, we address the question of the existence of controls that maintain the corresponding state trajectories in the $\varepsilon$-neighborhood of any prescribed path…

This paper provides a framework for the control of quantum mechanical systems with scattering states, i.e., systems with continuous spectra. We present the concept and prove a criterion of the approximate strong smooth controllability. Our…

Lieb-Schultz-Mattis (LSM) anomalies are powerful symmetry-based constraints on the correlation, entanglement and dynamics of quantum many-body systems. In this review, we discuss various LSM anomalies and anomaly matching. We start with a…

In quantum control theory, the fundamental issue of controllability covers the questions whether and under which conditions a system can be steered from one pure state into another by suitably tuned time evolution operators. Even though Lie…

Quantum phenomena of interest in connection with applications to computation and communication almost always involve generating specific transfers between eigenstates, and their linear superpositions. For some quantum systems, such as spin…

These are intended to be review notes on emergent symmetries, i.e., symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some…

A general scheme is proposed and tested to control the symmetry breaking instability of a homogeneous solution of a spatially extended multispecies model, defined on a network. The inherent discreteness of the space makes it possible to act…

This paper studies a kind of minimal time control problems related to the exact synchronization for a controlled linear system of parabolic equations. Each problem depends on two parameters: the bound of controls and the initial state. The…