Related papers: A generic framework of adiabatic approximation for…
In this paper we study up to which extent we can apply adiabatic control strategies to a quantum control model obtained by rotating wave approximation. In particular, we show that, under suitable assumptions on the asymptotic regime between…
We restate the adiabatic elimination approximation as the first term in a singular perturbation expansion. We use the invariant manifold formalism for singular perturbations in dynamical systems to identify systematic improvements on…
A proof of the adiabatic theorem for quantum systems whose time evolution proceeds along discrete time, e.g., quantum maps and quantum circuits, is shown.
Adiabatic state engineering is a powerful technique in quantum information and quantum control. However, its performance is limited by the adiabatic theorem of quantum mechanics. In this scenario, shortcuts to adiabaticity, such as provided…
We present a system composed of two flux qubits and a transmission-line resonator. Instead of using the rotating wave approximation (RWA), we analyse the system by the adiabatical approximation methods under two opposite extreme conditions.…
The article addresses the convergence of implicit and semi-implicit, fully discrete approximations of a class of nonlinear parabolic evolution problems. Such schemes are popular in the numerical solution of evolutions defined with the…
The Heimburg-Jackson model, or thermodynamic soliton theory of nervous impulses, has a well-established record as an alternative model for studying the dynamics of nerve impulses and lipid bilayers. Within this framework, nerve impulses can…
Adiabatic quantum computation employs a slow change of a time-dependent control function (or functions) to interpolate between an initial and final Hamiltonian, which helps to keep the system in the instantaneous ground state. When the…
We present a framework for constructing a first-order hyperbolic system whose solution approximates that of a desired higher-order evolution equation. Constructions of this kind have received increasing interest in recent years, and are…
We show that the adiabatic approximation for nonselfadjoint hamiltonians seems to induce two non-equal expressions for the geometric phase. The first one is related to the spectral projector involved in the adiabatic theorem, the other one…
Shortcuts to adiabaticity (STA) are fast methods to realize the same final state evolution of quantum adiabatic process. We develop a general theory to construct a new kind of STA by solely sampling the points of the adiabatic path of the…
This paper provides the first ab-initio on-the-fly example of using the Quasi-Diabatic (QD) scheme for non-adiabatic simulations with diabatic dynamics approaches. The QD scheme provides a seamless interface between diabatic quantum…
In the conventional quantum mechanics (i.e., hermitian QM) the adia- batic theorem for systems subjected to time periodic fields holds only for bound systems and not for open ones (where ionization and dissociation take place) [D. W. Hone,…
This research is concerned with evolution equations and their forward-backward discretizations. Our first contribution is an estimation for the distance between iterates of sequences generated by forward-backward schemes, useful in the…
Adiabatic quantum computation is a paradigmatic model aiming to solve a computational problem by finding the many-body ground state encapsulating the solution. However, its use of an adiabatic evolution depending on the spectral gap of an…
We investigate adiabatic solutions to general relativity for a spacetime with spatial slices with boundary, by Manton approximation. This approximation tells us for a theory with a Lagrangian in the natural form, a motion that is described…
Generalized models provide a framework for the study of evolution equations without specifying all functional forms. The generalized formulation of problems has been shown to facilitate the analytical investigation of local dynamics and has…
In the empirical study of evolutionary algorithms, the solution quality is evaluated by either the fitness value or approximation error. The latter measures the fitness difference between an approximation solution and the optimal solution.…
Big Data is characterized by Volume, Velocity, Veracity and Complexity. The interaction between this huge data is complex with an associated free will having dynamic and non linear nature. We reduced big data based on its characteristics,…
Several misprints and small mistakes were in the initial version. They have been corrected. Following the recent experimental realization of synthetic gauge magnetic forces, Jean Dalibard adressed the question whether the adiabatic ansatz…