Related papers: Hyperspheres and control of spin chains
In this paper we study the chain control sets of right-invariant control systems on the flag manifolds of a non-compact semisimple Lie group. We prove that each chain control set is partially (skew-) hyperbolic over the associated control…
A quantum system subject to external fields is said to be controllable if these fields can be adjusted to guide the state vector to a desired destination in the state space of the system. Fundamental results on controllability are reviewed…
The quantum spin $1/2$ XXZ chain with anisotropy parameter $\Delta=-1/2$ possesses a dynamic supersymmetry on the lattice. This supersymmetry and a generalisation to higher spin are investigated in the case of open spin chains. A family of…
Problems involving control of large ensmebles of structurally identical dynamical systems, called \emph{ensemble control}, arise in numerous scientific areas from quantum control and robotics to brain medicine. In many of such applications,…
This work recollects a non-universal set of quantum gates described by higher-dimensional Spin groups. They are also directly related with matchgates in theory of quantum computations and complexity. Various processes of quantum state…
Device concepts in semiconductor spintronics make long spin lifetimes desirable, and the requirements put on spin control by schemes of quantum information processing are even more demanding. Unfortunately, due to spin-orbit coupling…
We study the low energy states of finite spin chains with isotropic (Heisenberg) and anisotropic (XY and Ising-like) exchange interaction with uniform and non-uniform coupling constants. We show that for an odd number of sites a spin…
Mathematical theory of the quantum systems control is based on some ideas of the optimal control theory. These ideas are developed here as applied to these systems. The results obtained meet the deficiencies in the basis and algorithms of…
An effective spin concept is introduced to examine the mathematical and physical analogy between phase coherent charge transport in mesoscopic systems and quantum operations on spin based qubits. When coupled with the Bloch sphere concept,…
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…
This is a pedagogical review on recent progress in the exact evaluation of physical quantities in interacting quantum systems at finite temperatures. 1D quantum spin chains are discussed in detail as typical examples.
Exploiting analogies between the precessing quantum spin system and the charge-monopole system, we construct Bloch hyper-spheres with $\it{exact}$ spherical symmetries in arbitrary dimensions. Such Bloch hyper-spheres are realized as a…
We study the magnetic properties of two types of one dimensional XX spin 1/2 chains. The first type has only nearest neighbor interactions which can be either antiferromagnetic or ferromagnetic and the second type which has both nearest…
The concept of superintegrability in quantum mechanics is extended to the case of a particle with spin s=1/2 interacting with one of spin s=0. Non-trivial superintegrable systems with 8- and 9-dimensional Lie algebras of first-order…
Quantum ensemble systems arise in a variety of applications, including NMR spectroscopy and robust quantum control. While their theoretical properties have been extensively studied, relatively little attention has been given to the explicit…
Here we show a direct mapping between waveguide theory and spin chain transport, opening an alternative approach to quantum information transport in the solid-state. By applying temporally varying control profiles to a spin chain, we design…
Indirect controllability of an arbitrary finite dimensional quantum system (N-dimensional qudit) through a quantum accessor is investigated. Here, The qudit is coupled to a quantum accessor which is modeled as a fully controllable spin…
We consider the spin-1/2 XY chain in a transverse field with regularly varying exchange interactions and on-site fields. In two limiting cases of the isotropic XX and extremely anisotropic (Ising) exchange interaction the thermodynamic…
The possibility of control of phenomena at microscopic level compatible with quantum mechanics and quantum field theory is outlined. The theory could be used in nanotechnology.
The paper discusses various aspects of time-optimal control of quantum spin systems, modelled as right-invariant systems on a compact Lie group G. The main results are the reduction of such a system to an equivalent system on a homogeneous…