Related papers: Strong Analytic Controllability for Hydrogen Contr…
In this paper, we present a controllability analysis of the quantum Ising periodic chain of n spin 1/2 particles where the interpolating parameter between the two Hamiltonians plays the role of the control. A fundamental result in the…
In this paper we study up to which extent we can apply adiabatic control strategies to a quantum control model obtained by rotating wave approximation. In particular, we show that, under suitable assumptions on the asymptotic regime between…
For quantum mechanics of a charged particle in a classical external electromagnetic field, there is an apparent puzzle that the matrix element of the canonical momentum and Hamiltonian operators is gauge dependent. A resolution to this…
We study feedback control of classical Hamiltonian systems with the controlling parameter varying slowly in time. The control aims to change system's energy. We show that the control problems can be solved with help of an adiabatic…
Controllability properties are studied for control-affine systems depending on a parameter and with constrained control values. The uncontrolled systems in dimension two and three are subject to a homoclinic bifurcation. This generates two…
The time evolution of a closed quantum system is connected to its Hamiltonian through Schroedinger's equation. The ability to estimate the Hamiltonian is critical to our understanding of quantum systems, and allows optimization of control.…
Control of multi-level quantum systems is sensitive to implementation errors in the control field and uncertainties associated with system Hamiltonian parameters. A small variation in the control field spectrum or the system Hamiltonian can…
A quantum theory in a finite-dimensional Hilbert space can be geometrically formulated as a proper Hamiltonian theory as explained in [2, 3, 7, 8]. From this point of view a quantum system can be described in a classical-like framework…
Controllability -- the possibility of performing any target dynamics by applying a set of available operations -- is a fundamental requirement for the practical use of any physical system. For finite-dimensional systems, as for instance…
A close inspection on the 3D hydrogen atom Hamiltonian revealed formal eigenvectors often discarded in the literature. Although not in its domain, such eigenvectors belong to the Hilbert space, and so their time evolution is well defined.…
This document explores structural controllability of polynomial dynamical systems or polysystems. We extend Lin's concept of structural controllability for linear systems, offering hypergraph-theoretic methods to rapidly assess strong…
Conventional approaches for controlling open quantum systems use coherent control which affects the system's evolution through the Hamiltonian part of the dynamics. Such control, although being extremely efficient for a large variety of…
An effective Hamiltonian is considered for hydrogen bonding between two molecules due to the quantum mechanical interaction between the orbitals of the H-atom and the donor and acceptor atoms in the molecules. The Hamiltonian acts on two…
Quantum coherence inherently affects the dynamics and the performances of a quantum machine. Coherent control can, at least in principle, enhance the work extraction and boost the velocity of evolution in an open quantum system. Using…
Simulating Hamiltonian dynamics is one of the most fundamental and significant tasks for characterising quantum materials. Recently, a series of quantum algorithms employing block-encoding of Hamiltonians have succeeded in providing…
The long-standing problem of finding coherent states for the (bound state portion of the) hydrogen atom is positively resolved. The states in question: (i) are normalized and are parameterized continuously, (ii) admit a resolution of unity…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…
Given a fixed initial state, a desired Hamiltonian, and an amount of time, we provide a complete characterization of the set of Hamiltonians which perform the same action as the desired Hamiltonian on the state of interest. An example is…
It is well-known that time-dependent Schr\"{o}dinger equation can only be exactly solvable in very rare cases, even for two-level quantum systems. Therefore, finding exact quantum dynamics under time-dependent Hamiltonian is not only of…
We study the stability of the Schr\"odinger equation generated by time-dependent Hamiltonians with constant form domain. That is, we bound the difference between solutions of the Schr\"odinger equation by the difference of their…