Related papers: Towards a perturbation theory for eventually posit…
Assume that $\Phi:\mathbb{M}_{n}(\mathbb{C})\rightarrow\mathbb{M}_{n}(\mathbb{C})$ is a superoperator which preserves hermiticity. We give an algorithm determining whether $\Phi$ preserves semipositivity (we call $\Phi$ positive in this…
For transitive shifts of finite type, and more generally for shifts with specification, it is well-known that every equilibrium state for a Holder continuous potential has positive entropy as long as the shift has positive topological…
This paper considers the problem of robust stability for a class of uncertain quantum systems subject to unknown perturbations in the system Hamiltonian. Some general stability results are given for different classes of perturbations to the…
A mathematical model describing the initial stage of the capture into the parametric autoresonance in nonlinear oscillating systems with a dissipation is considered. Solutions with unboundedly growing energy in time at infinity are…
We discuss linear autonomous evolution equations on function spaces which have the property that a positive initial value leads to a solution which initially changes sign, but then becomes - and stays - positive again for sufficiently large…
We prove new results on inheritance of Green's relations by subsemigroups in the presence of stability of elements. We provide counterexamples in other cases to show in particular that not all right-stable semigroups are embeddable in…
A solution to a given equation is structurally stable if it suffers only an infinitesimal change when the equation (not the solution) is perturbed infinitesimally. We have found that structural stability can be used as a velocity selection…
An effective field theory is derived that describes the quantum critical behavior of itinerant ferromagnets in the presence of quenched disorder. In contrast to previous approaches, all soft modes are kept explicitly. The resulting…
In this work we analyze and bound the effect of modeling errors on the stabilization of pure states or subspaces for quantum stochastic evolutions. Different approaches are used for open-loop and feedback control protocols. For both, we…
This thesis consists of two separate parts: in each we study the stability under small perturbations of certain probability models in different contexts. In the first, we study small random perturbations of a deterministic dynamical system…
For a given set of input-output pairs of quantum states or observables, we ask the question whether there exists a physically implementable transformation that maps each of the inputs to the corresponding output. The physical maps on…
In this paper the Jessen's type inequality for normalized positive $C_0$-semigroups is obtained. An adjoint of Jessen's type inequality has also been derived for the corresponding adjoint-semigroup, which does not give the analogous results…
We construct a family of map which is shown to be positive when imposing certain condition on the parameters. Then we show that the constructed map can never be completely positive. After tuning the parameters, we found that the map still…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
It is known that the stability of a feedback interconnection of two linear time-invariant systems implies that the graphs of the open-loop systems are quadratically separated. This separation is defined by an object known as the multiplier.…
We investigate the class of quasitrivial semigroups and provide various characterizations of the subclass of quasitrivial and commutative semigroups as well as the subclass of quasitrivial and order-preserving semigroups. We also determine…
Relaxation rates are key characteristics of quantum processes, as they determine how quickly a quantum system thermalizes, equilibrates, decoheres, and dissipates. While they play a crucial role in theoretical analyses, relaxation rates are…
The energy transition is causing many stability-related challenges for power systems. Transient stability refers to the ability of a power grid's bus angles to retain synchronism after the occurrence of a major fault. In this paper a…
We study invariant theory of the general linear supergroup in positive characteristic. In particular, we determine when the symmetric group algebra acts faithfully on tensor superspace and demonstrate that the symmetric group does not…
In this paper, we develop the theory of equivariant motivic homotopy theory, both unstable and stable. While our original interest was in the case of profinite group actions on smooth schemes, we discuss our results in as broad a setting as…