相关论文: Symmetries on Spin Chains: Limited Controllability…
We consider left-invariant optimal control problems on connected Lie groups such that generic stabilizer of the coadjoint action is connected and has dimension not more than 1. We introduce a construction for symmetries of the exponential…
In this article, we investigate the problem of simultaneously steering an uncountable family of finite dimensional time-varying linear systems. We call this class of control problems Ensemble Control, a notion coming from the study of spin…
Quantum spin chains are prototype quantum many-body systems. They are employed in the description of various complex physical phenomena. The goal of this paper is to provide an introduction to the subject by focusing on the time evolution…
The environment of an open quantum system is usually modelled as a large many-body quantum system. However, when an isolated quantum system itself is a many-body quantum system, the question of how large and complex it must be in order to…
Symmetries are a key concept to connect mathematical elegance with physical insight. We consider measurement assemblages in quantum mechanics and show how their symmetry can be described by means of the so-called discrete bundles. It turns…
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…
This dissertation studies spin squeezing, entanglement and decoherence in large ensembles of cold, trapped alkali atoms with hyperfine spin f interacting with optical fields. Restricting the state of each atom to a qutrit embedded in the…
Spin squeezing serves as both a fundamental witness of quantum entanglement and a critical resource for quantum-enhanced metrology. While generating substantial spin squeezing in finite-range interacting systems remains challenging, such…
Level statistics is discussed for XXZ spin chains with discrete symmetries for some values of the next-nearest-neighbor (NNN) coupling parameter. We show how the level statistics of the finite-size systems depends on the NNN coupling and…
The Heisenberg-Ising spin ladder is one of the few short-range models showing confinement of elementary excitations without the need of an external field, neither transverse nor longitudinal. This feature makes the model suitable for an…
Control systems of interest are often invariant under Lie groups of transformations. For such control systems, a geometric framework based on Lie symmetry is formulated, and from this a sufficient condition for dynamic feedback…
A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…
We treat control of several two-level atoms interacting with one mode of the electromagnetic field in a cavity. This provides a useful model to study pertinent aspects of quantum control in infinite dimensions via the emergence of…
With the purpose to reveal consistency between multiple quantum (MQ) coherences and entanglement, we investigate numerically the dynamics of these phenomena in one-dimensional linear chains and ring of nuclear spins 1/2 coupled by dipole…
Massive higher spin fields are notoriously difficult to introduce interactions when they are described by symmetric (spin)-tensors. An alternative approach is to use chiral description that does not have unphysical longitudinal modes. For…
We investigate the possibility of the electrical control of spin transfer in monoatomic chains incorporating spin-impurities. Our theoretical framework is the mixed quantum-classical (Ehrenfest) description of the spin dynamics, in the…
In this paper, we study the network pinning control problem in the presence of two different types of coupling: (i) node-to-node coupling among the network nodes and (ii) input-to-node coupling from the source node to the `pinned nodes'.…
Structural symmetries of linear dynamical systems can be exploited for decoupling the dynamics and reducing the computational complexity of the controller implementation. However, in practical applications, inexact structural symmetries…
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…
This paper considers a spin chain model by numerically solving the exact model to explore the non-perturbative dynamical decoupling regime, where an important issue arises recently (J. Jing, L.-A. Wu, J. Q. You and T. Yu, arXiv:1202.5056.).…