Related papers: Riccati equation and the problem of decoherence
Seeking for a relativistic generalisation of the non-relativistic Schroedinger equation, one very soon arrives at equations with a square-root operator by having applied the quantum mechanical correspondence principle to the formula of…
We explore a strategy for protecting the evolution of a qubit against the effects of environmental noise based on the application of controlled time-dependent perturbations. In the case of a purely decohering coupling, an explicit sequence…
A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model by using perturbation theory, for the case when the…
We consider a particle coupled to a dissipative environment and derive a perturbative formula for the dephasing rate based on the purity of the reduced probability matrix. We apply this formula to the problem of a particle on a ring, that…
The spin of an electron in a semiconductor quantum dot represents a natural nanoscale solid state qubit. Coupling to nuclear spins leads to decoherence that limits the number of allowed quantum logic operations for this qubit. Traditional…
We find a quantum mechanical formulation of proper time for spin 1/2 particles within the framework of the Dirac theory. It is shown that the rate of proper time can be represented by an operator called the ` ` tempo operator'', and that…
Using deformations inspired by relativistic considerations and phase space symmetry, we deform the position and momentum operators in one dimension. The resulting algebra is shown to yield the q-oscillator algebra in one limiting case and…
We analyze decoherence of a quantum register in the absence of non-local operations i.e. of $n$ non-interacting qubits coupled to an environment. The problem is solved in terms of a sum rule which implies linear scaling in the number of…
We study the dynamics of a bipartite quantum system in a way such that its formal description keeps holding even if one of its parts becomes macroscopic: the problem is related with the analysis of the quantum-to-classical crossover, but…
This article is concerned with the optimal boundary control of the Maxwell system. We consider a Bolza problem, where the quadratic functional to be minimized penalizes the electromagnetic field at a given final time. Since the state is…
With a choice of boundary conditions for solutions of the Schr\"odinger equation, state vectors and density operators even for closed systems evolve asymmetrically in time. For open systems, standard quantum mechanics consequently predicts…
We introduce a formalism to describe fractional charging of a molecule due to interactions with its environment. The interactions which induce fractional charging are contained in the Hamiltonian of the full system (molecule and…
We study a particular form of interaction Hamiltonian between qubits and quantum harmonic oscillators, whose closed system dynamics results in qubit controlled displacement operations. We show how this interaction is realizable in many…
Instead of using local field equations - like the Dirac equation for spin-1/2 and the Klein-Gordon equation for spin-0 particles - one could try to use non-local field equations in order to describe scattering processes. The latter…
We study decoherence in a simple quantum mechanical model using two approaches. Firstly, we follow the conventional approach to decoherence where one is interested in solving the reduced density matrix from the perturbative master equation.…
We describe the relation between block Jacobi matrices and minimization problems for discrete time optimal control problems. Using techniques developed for the continuous case, we provide new algorithms to compute spectral invariants of…
We review recent advances on the theory of spin qubits in nanostructures. We focus on four selected topics. First, we show how to form spin qubits in the new and promising material graphene. Afterwards, we discuss spin relaxation and…
We study a system of a quantum particle interacting with a singular time-dependent uniformly rotating potential in 2 and 3 dimensions: in particular we consider an interaction with support on a point (rotating point interaction) and on a…
We study quantum decoherence numerically in a system consisting of a relativistic quantum field theory coupled to a measuring device that is itself coupled to an environment. The measuring device and environment are treated as quantum,…
We systematically analyze the nonlinear partial differential equation that determines the behaviour of a bounded radiating spherical mass in general relativity. Four categories of solution are possible. These are identified in terms of…