Related papers: Analytical operator solution of master equations d…
The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by…
Practical optimization problems may contain different kinds of difficulties that are often not tractable if one relies on a particular optimization method. Different optimization approaches offer different strengths that are good at…
In the Super-Transition-Array statistical method for the computation of radiative opacity of hot dense matter, the moments of the absorption or emission features involve partition functions with reduced degeneracies, occurring through the…
Dissipation and irreversibility are central to most physical processes, yet they lead to non-unitary dynamics that are challenging to realise on quantum processors. High-order operator splitting is an attractive approach for simulating…
Implicit time integration schemes are widely used in computational fluid dynamics numerical codes to speed-up computations. Indeed, implicit schemes usually allow for less stringent time-step stability constraints than their explicit…
Convolution-type integral equations arise from various fields, \textit{e.g.}, finite impulse response filters in signal processing and deblurring problems in image processing. When solving these equations, conventional numerical methods,…
We study linear problems of mathematical physics in which the adiabatic approximation is used in the wide sense. Using the idea that all these problems can be treated as problems with operator-valued symbol, we propose a general regular…
Applied to the master equation, the usual numerical integration methods, such as Runge-Kutta, become inefficient when the rates associated with various transitions differ by several orders of magnitude. We introduce an integration scheme…
We first strictly expressed the basic notions and research methods of abstract operators, which systematically expounded the main results of abstract operator theory. By combining abstract operators with the Laplace transform, we can easily…
Quantum master equations are an invaluable tool to model the dynamics of a plethora of microscopic systems, ranging from quantum optics and quantum information processing, to energy and charge transport, electronic and nuclear spin…
Motivated by potential applications to partial differential equations, we develop a theory of fine scales of decay rates for operator semigroups. The theory contains, unifies, and extends several notable results in the literature on decay…
We derive Heisenberg equations for arbitrary high order moments of creation and annihilation operators in the case of the quantum master equation with a multimode generator which is quadratic in creation and annihilation operators and…
The problem of estimating a generic phase-shift experienced by a quantum state is addressed for a generally degenerate phase shift operator. The optimal positive operator-valued measure is derived along with the optimal input state. Two…
Advances in numerical optimization have supported breakthroughs in several areas of signal processing. This paper focuses on the recent enhanced variants of the proximal gradient numerical optimization algorithm, which combine quasi-Newton…
The monodomain model is widely used in in-silico cardiology to describe excitation propagation in the myocardium. Frequently, operator splitting is used to decouple the stiff reaction term and the diffusion term in the monodomain model so…
The alternating current optimal power flow (AC-OPF) problem is critical to power system operations and planning, but it is generally hard to solve due to its nonconvex and large-scale nature. This paper proposes a scalable decomposition…
This paper introduces a unified framework for accelerated gradient methods through the variable and operator splitting (VOS). The operator splitting decouples the optimization process into simpler subproblems, and more importantly, the…
We show set of transformations which allow to obtain analytic solutions in several quantum-optical problems. We start with the ion-laser (time dependent) interaction, continue with the problem of a slow atom interacting with a quantized…
We present efficient implementations of a number of operations for quantum computers. These include controlled phase adjustments of the amplitudes in a superposition, permutations, approximations of transformations and generalizations of…
The computation of higher order processes very often involves a large number of diagrams. In addition, it is in general not possible to solve the occurring integrals explicitly and expansions in small quantities have to be performed. This…