Related papers: Random phase approximation and its extension for t…
We consider the relativistic generalization of the harmonic oscillator problem by addressing different questions regarding its classical aspects. We treat the problem using the formalism of Hamiltonian mechanics. A Lie algebraic technique…
We assess the performance of a recently proposed renormalized adiabatic local density approximation (rALDA) for \textit{ab initio} calculations of electronic correlation energies in solids and molecules. The method is an extension of the…
Rhythmic activity is ubiquitous in biological systems from the cellular to organism level. Reconstructing the instantaneous phase is the first step in analyzing the essential mechanism leading to a synchronization state from the observed…
An exact generalization of the Ramsey transition probability is derived to improve ultra-high precision measurement and quantum state engineering when a particle is subjected to independently-tailored separated oscillating fields. The…
We investigate the Shortcuts To Adiabaticity (STA) of a quantum harmonic oscillator under time-dependent frictional force, using invariant based inverse engineering method with a class of invariants characterized by a time-dependent…
We address the exploitation of an optical parametric oscillator (OPO) in the task of mitigating, at least partially, phase noise produced by phase diffusion. In particular, we analyze two scenarios where phase diffusion is typically…
In the present article we analyze Non-Perturbative Renormalization Group flow equations in the order phase of $\mathbb{Z}_2$ and $O(N)$ invariant scalar models in the derivative expansion approximation scheme. We first address the behavior…
A scheme for fine tuning of quantum operations to improve their performance is proposed. A quantum system in $\Lambda$ configuration with two-photon Raman transitions is considered without adiabatic elimination of the excited (intermediate)…
We study the stability of a stochastic oscillator whose frequency is a random process with finite time memory represented by an Ornstein-Uhlenbeck noise. This system undergoes a noise-induced bifurcation when the amplitude of the noise…
By coupling a doorway state to a see of random background states, we develop the theory of doorway states in the framework of the random-phase approximation (RPA). Because of the symmetry of the RPA equations, that theory is radically…
Rotation averaging (RA) is a fundamental problem in robotics and computer vision. In RA, the goal is to estimate a set of $N$ unknown orientations $R_{1}, ..., R_{N} \in SO(3)$, given noisy measurements $R_{ij} \sim R^{-1}_{i} R_{j}$ of a…
We construct a non-perturbative approach based on quantum averaging combined with resonant transformations to detect the resonances of a given Hamiltonian and to treat them. This approach, that generalizes the rotating-wave approximation,…
Second RPA (SRPA) calculations of nuclear response are performed and analyzed. Unlike in most other SRPA applications, the ground state, approximated by the Hartree-Fock (HF) ground state, and the residual couplings are described by the…
We consider the use of arbitrary phases in quantum amplitude amplification which is a generalization of quantum searching. We prove that the phase condition in amplitude amplification is given by $\tan(\varphi/2) = \tan(\phi/2)(1-2a)$,…
We discuss a general mean field plus random phase approximation (RPA) for describing composite systems at zero and finite temperature. We analyze in particular its implementation in finite systems invariant under translations, where for…
The Quasiparticle Random Phase Approximation equations are solved taking into account the Pauli Principle at the expectation value level, and allowing changes in the mean field occupation numbers to minimize the energy while having the…
Phase-rectified signal averaging (PRSA) is a widely used algorithm to analyze nonstationary biomedical time series. The method operates by identifying hinge points in the time series according to prescribed rules, extracting segments…
We present an approximation scheme of the nonperturbative renormalization group that preserves the momentum dependence of correlation functions. This approximation scheme can be seen as a simple improvement of the local potential…
We describe a quantum perturbative approach to evaluating the phase shift of an atom interferometer in a weakly anharmonic trap. This provides a simple way to evaluate quantum corrections to the standard semi-classical approximation. The…
The random-phase approximation has been used to compute the properties of parabolic two-dimensional quantum dots beyond the mean-field approximation. Special emphasis is put on the ground state correlation energy, the symmetry restoration…