Related papers: Adaptive Perturbation Method in Quantum Mechanics
An alternative perturbative expansion in quantum mechanics which allows a full expression of the scaling arbitrariness is introduced. This expansion is examined in the case of the anharmonic oscillator and is conveniently resummed using a…
Adaptive techniques make practical many quantum measurements that would otherwise be beyond current laboratory capabilities. For example: they allow discrimination of nonorthogonal states with a probability of error equal to the Helstrom…
We advocate the replacement of standard alphas(mu)-based QCD perturbation theory, in which the coupling and truncated perturbative predictions are dependent on the chosen renormalisation scheme, by a Lambda-based approach in which QCD…
For a wide class of Hamiltonians, a novel method to obtain lower and upper bounds for the lowest energy is presented. Unlike perturbative or variational techniques, this method does not involve the computation of any integral (a…
This paper considers the problem of controlling a piecewise continuously differentiable system subject to time-varying uncertainties. The uncertainties are decomposed into a time-invariant, linearly-parameterized portion and a time-varying…
In the standard approach, predictions of perturbative Quantum Chromodynamics for ratios of cross sections are computed as the ratio of fixed-order predictions for the numerator and the denominator. Beyond the lowest order in the…
We study effects of perturbation Hamiltonian to quantum spin systems which can include quenched disorder. Model-independent inequalities are derived, using an additional artificial disordered perturbation. These inequalities enable us to…
In this work we present an adaptive Newton-type method to solve nonlinear constrained optimization problems in which the constraint is a system of partial differential equations discretized by the finite element method. The adaptive…
We propose a new approach to the Rayleigh-Schr\"{o}dinger perturbation expansions of bound states in quantum mechanics. We are inspired by the enormous flexibility of solvable interactions with several (N) discontinuities. Their standard…
A test on the numerical accuracy of the semiclassical approximation as a function of the principal quantum number has been performed for the Pullen--Edmonds model, a two--dimensional, non--integrable, scaling invariant perturbation of the…
The harmonic oscillator Hamiltonian, when augmented by a non-Hermitian $\cal{PT}$-symmetric part, can be transformed into a Hermitian Hamiltonian. This is achieved by introducing a metric which, in general, renders other observables such as…
This paper proposes a novel direct adaptive control method for rejecting unknown deterministic disturbances and tracking unknown trajectories in systems with uncertain dynamics when the disturbances or trajectories are the summation of…
In a previous paper (J. Phys. A 36, 11807 (2003)), we introduced the `asymptotic iteration method' for solving second-order homogeneous linear differential equations. In this paper, we study perturbed problems in quantum mechanics and we…
We analyze the problem of quantum-limited estimation of a stochastically varying phase of a continuous beam (rather than a pulse) of the electromagnetic field. We consider both non-adaptive and adaptive measurements, and both dyne detection…
The averaging method is a classical powerful tool in perturbation theory of dynamical systems. There are two major obstacles to applying the averaging method, resonances and separatrices. In this paper we obtain realistic asymptotic…
In this paper, we analyze the convergence and optimality of a standard adaptive nonconforming linear element method for the Stokes problem. After establishing a special quasi--orthogonality property for both the velocity and the pressure in…
A very general calculational strategy is applied to the evaluation of the divergent physical amplitudes which are typical of perturbative calculations. With this approach in the final results all the intrinsic arbitrariness of the…
In this work we study the topic of high-resolution adaptive sampling of a given deterministic signal and establish a connection with classic approaches to high-rate quantization. Specifically, we formulate solutions for the task of optimal…
In this paper, we introduce a notion of quantum discrepancy, a non-commutative version of combinatorial discrepancy which is defined for projection systems, i.e. finite sets of orthogonal projections, as non-commutative counterparts of set…
We devise powerful algorithms based on differential evolution for adaptive many-particle quantum metrology. Our new approach delivers adaptive quantum metrology policies for feedback control that are orders-of-magnitude more efficient and…