Search results for "subspaces"
showing 10 items of 10 documents
Property (gab) through localized SVEP
2015
In this article we study the property (gab) for a bounded linear operator T 2 L(X) on a Banach space X which is a stronger variant of Browder's theorem. We shall give several characterizations of property (gab). These characterizations are obtained by using typical tools from local spectral theory. We also show that property (gab) holds for large classes of operators and prove the stability of property (gab) under some commuting perturbations. 2010 Mathematics Subject Classication. Primary 47A10, 47A11; Secondary 47A53, 47A55.
Degenerate Landau–Zener model in the presence of quantum noise
2019
The degenerate Landau–Zener–Majorana–Stückelberg model consists of two degenerate energy levels whose energies vary with time and in the presence of an interaction which couples the states of the two levels. In the adiabatic limit, it allows for the populations transfer from states of one level to the states of the other level. The presence of an interaction with the environment influences the efficiency of the process. Nevertheless, identification of possible decoherence-free subspaces permits to engineer coupling schemes for which the effects of quantum noise can be made negligible.
Quantum Zeno subspaces induced by temperature
2011
We discuss the partitioning of the Hilbert space of a quantum system induced by the interaction with another system at thermal equilibrium, showing that the higher the temperature the more effective is the formation of Zeno subspaces. We show that our analysis keeps its validity even in the case of interaction with a bosonic reservoir, provided appropriate limitations of the relevant bandwidth.
Entanglement generation and protection by detuning modulation
2006
We introduce a protocol for steady-state entanglement generation and protection based on detuning modulation in the dissipative interaction between a two-qubit system and a bosonic mode. The protocol is a global-addressing scheme which only requires control over the system as a whole. We describe a postselection procedure to project the register state onto a subspace of maximally entangled states. We also outline how our proposal can be implemented in a circuit-quantum electrodynamics setup.
Local spectral theory for Drazin invertible operators
2016
Abstract In this paper we investigate the transmission of some local spectral properties from a bounded linear operator R, as SVEP, Dunford property (C), and property (β), to its Drazin inverse S, when this does exist.
Local Spectral Theory for R and S Satisfying RnSRn = Rj
2020
In this paper, we analyze local spectral properties of operators R,S and RS which satisfy the operator equations RnSRn=Rj and SnRSn=Sj for same integers j&ge
Ulam Stability for the Composition of Operators
2020
Working in the setting of Banach spaces, we give a simpler proof of a result concerning the Ulam stability of the composition of operators. Several applications are provided. Then, we give an example of a discrete semigroup with Ulam unstable members and an example of Ulam stable operators on a Banach space, such that their sum is not Ulam stable. Another example is concerned with a C 0 -semigroup ( T t ) t &ge
The quantum trajectory approach to geometric phase for open systems
2005
The quantum jump method for the calculation of geometric phase is reviewed. This is an operational method to associate a geometric phase to the evolution of a quantum system subjected to decoherence in an open system. The method is general and can be applied to many different physical systems, within the Markovian approximation. As examples, two main source of decoherence are considered: dephasing and spontaneous decay. It is shown that the geometric phase is to very large extent insensitive to the former, i.e. it is independent of the number of jumps determined by the dephasing operator.
High-order regularization in lattice-Boltzmann equations
2017
A lattice-Boltzmann equation (LBE) is the discrete counterpart of a continuous kinetic model. It can be derived using a Hermite polynomial expansion for the velocity distribution function. Since LBEs are characterized by discrete, finite representations of the microscopic velocity space, the expansion must be truncated and the appropriate order of truncation depends on the hydrodynamic problem under investigation. Here we consider a particular truncation where the non-equilibrium distribution is expanded on a par with the equilibrium distribution, except that the diffusive parts of high-order nonequilibrium moments are filtered, i.e., only the corresponding advective parts are retained afte…
The Tan 2Θ Theorem in fluid dynamics
2017
We show that the generalized Reynolds number (in fluid dynamics) introduced by Ladyzhenskaya is closely related to the rotation of the positive spectral subspace of the Stokes block-operator in the underlying Hilbert space. We also explicitly evaluate the bottom of the negative spectrum of the Stokes operator and prove a sharp inequality relating the distance from the bottom of its spectrum to the origin and the length of the first positive gap.