Related papers: Quotients of affine connection control systems

Quantum families of maps between quantum spaces are defined and studied. We prove that quantum semigroup (and sometimes quantum group) structures arise naturally on such objects out of more fundamental properties. As particular cases we…

The new necessary and sufficient affine invariant conditions for the existence and for determining the number of centers for general quadratic system are pointed out. These conditions correspond to the partition of 12-dimensional…

Given a wireless network where some pairs of communication links interfere with each other, we study sufficient conditions for determining whether a given set of minimum bandwidth Quality of Service (QoS) requirements can be satisfied. We…

Quantum control of atomic systems is largely enabled by the rich structure of selection rules in the spectra of most real atoms. Their macroscopic superconducting counterparts have been lacking this feature, being limited to a single…

In this work we present a model qubit whose basis states are eigenstates of a multi-layered quantum dot. We show that the proper design of the quantum dot results in qubit states that have excellent dynamical properties when a…

For a conformal manifold we introduce the notion of an ambient connection, an affine connection on an ambient manifold of the conformal manifold, possibly with torsion, and with conditions relating it to the conformal structure. The purpose…

In this paper, we study the distributions and the affine distributions of the quantum mechanical system. Also, we discuss the controllability of the quantum mechanical system with the related question concerning the minimum time needed to…

In affine formation control problems, the construction of the framework with universal rigidity and affine localizability is a critical prerequisite, but it has not yet been well addressed, especially when additional agents join the…

Degenerate dynamical systems are characterized by symplectic structures whose rank is not constant throughout phase space. Their phase spaces are divided into causally disconnected, nonoverlapping regions such that there are no classical…

We propose an active mechanism for coupling the quantized mode of a nanomechanical resonator to the persistent current in the loop of a superconducting Josephson junction (or phase slip) flux qubit. This coupling is independently controlled…

We show that globally defined quasiconformal mappings of rigid Carnot groups are affine, but that globally defined contact mappings of rigid Carnot groups need not be quasiconformal, and a fortiori not affine.

We give a categorical explanation for many properties of profinite coproducts of profinite groups, which were previously proven on a case-by-case basis. All of these properties take the form "certain functors preserve profinite coproducts".…

With recent improvements in coherence times, superconducting transmon qubits have become a promising platform for quantum computing. They can be flexibly engineered over a wide range of parameters, but also require us to identify an…

Superconducting quantum circuits, such as the superconducting phase qubit, have multiple quantum states that can interfere with ideal qubit operation. The use of multiple frequency control pulses, resonant with the energy differences of the…

We extend finding geometrically-significant preserved quantities by solving specific PDEs to the affine transformations and subgroups. This can be viewed not only as a purely geometrical problem but also as a subcase of finding physical…

We study higher order quantum maps in the context of a *-autonomous category of affine subspaces. We show that types of higher order maps can be identified with certain Boolean functions that we call type functions. By an extension of this…

We show that quantum optical systems preserving the total number of excitations admit a simple classification of possible resonant transitions (including effective), which can be classified by analizying the free Hamiltonian and the…

We propose a technique to design control algorithms for a class of finite dimensional quantum systems so that the control law does not present discontinuities. The class of models considered admits a group of symmetries which allows us to…

The conditions under which a given manifold $M$ may be given a tangent bundle or a cotangent bundle structure are analyzed. This is an important property arising in different contexts. For instance, in the study of integrability of a given…

In this paper, we present a geometric approach for computing the controlled invariant set of a continuous-time control system. While the problem is well studied for in the ellipsoidal case, this family is quite conservative for constrained…