Related papers: On Adiabatic Renormalization with a Physically Mot…
In this chapter we review the field of radio-frequency dressed atom trapping. We emphasise the role of adiabatic potentials and give simple, but generic models of electromagnetic fields that currently produce traps for atoms at microkelvin…
Adiabatic quantum programming defines the time-dependent mapping of a quantum algorithm into an underlying hardware or logical fabric. An essential step is embedding problem-specific information into the quantum logical fabric. We present…
The evolution of a system induced by counter-diabatic driving mimics the adiabatic dynamics without the requirement of slow driving. Engineering it involves diagonalizing the instantaneous Hamiltonian of the system and results in the need…
Recently, it has been shown (Gavrilov et al., Nonlinear Dyn, 112, 2024) that in a linear solid discrete-continuous system with several slowly time-varying parameters, the amplitude of a strongly localized mode (a trapped wave) can be…
We provide model reduction formulas for open quantum systems consisting of a target component which weakly interacts with a strongly dissipative environment. The time-scale separation between the uncoupled dynamics and the interaction…
In this paper, we present an invariant perturbation theory of the adiabatic process based on the concepts of U(1)-invariant adiabatic orbit and U(1)-invariant adiabatic expansion. As its application, we propose and discuss new adiabatic…
We present here our study of the adiabatic quantum dynamics of a random Ising chain across its quantum critical point. The model investigated is an Ising chain in a transverse field with disorder present both in the exchange coupling and in…
Linear regression is a popular machine learning approach to learn and predict real valued outputs or dependent variables from independent variables or features. In many real world problems, its beneficial to perform sparse linear regression…
In this paper, we present a U(1)-invariant expansion theory of the adiabatic process. As its application, we propose and discuss new sufficient adiabatic approximation conditions. In the new conditions, we find a new invariant quantity…
A fictitious discussion is taken as a point of origin to present novel physical insight into the nature of gauge theory and the potential energy of QCD and QED at short distance. Emphasized is the considerable freedom in the cut-off…
The QED renormalization is restudied by using a mass-dependent subtraction which is performed at a time-like renormalization point. The subtraction exactly respects necessary physical and mathematical requirements such as the gauge…
We consider a periodically driven system where the high-frequency driving protocol consists of a sequence of potentials switched on and off at different instants within a period. We explore the possibility of introducing an adiabatic…
Within the effective mass approximation an adiabatic description of spheroidal and dumbbell quantum dot models in the regime of strong dimensional quantization is presented using the expansion of the wave function in appropriate sets of…
We extend the adiabatic regularization method by introducing an arbitrary mass scale $\mu$ in the construction of the subtraction terms. This allows us to obtain, in a very robust way, the running of the coupling constants by demanding…
When a composite Lindblad system consists of weakly coupled sub-systems with fast and slow timescales, the description of slow dynamics can be simplified by discarding fast degrees of freedom. This model reduction technique is called…
Artificial interface conditions parametrized by a complex number $\theta_{0}$ are introduced for 1D-Schr\"odinger operators. When this complex parameter equals the parameter $\theta\in i\R$ of the complex deformation which unveils the shape…
We consider quantum field theoretic systems subject to a time-dependent perturbation, and discuss the question of defining a time dependent particle number not just at asymptotic early and late times, but also during the perturbation.…
The universal analytical approach was developed to describe the process of particle slow extraction from a synchrotron using adiabatic crossing the betatron resonance of the third order. The obtained formulas make it possible to calculate…
Adiabatic dressed state potentials are created when magnetic sub-states of trapped atoms are coupled by a radio frequency field. We discuss their theoretical foundations and point out fundamental advantages over potentials purely based on…
The purpose of these notes is to provide a pedagogical introduction to the concept of renormalization in atomic physics. We study quantum dynamics of a model of a nonrelativistic single electron atom coupled to the quantum radiation field…