Search results for "Functional analysis"
showing 10 items of 1059 documents
Laser control for the optimal evolution of pure quantum states
2005
Starting from an initial pure quantum state, we present a strategy for reaching a target state corresponding to the extremum (maximum or minimum) of a given observable. We show that a sequence of pulses of moderate intensity, applied at times when the average of the observable reaches its local or global extremum, constitutes a strategy transferable to different control issues. Among them, post-pulse molecular alignment and orientation are presented as examples. The robustness of such strategies with respect to experimentally relevant parameters is also examined.
Extraction of a squeezed state in a field mode via repeated measurements on an auxiliary quantum particle
2009
The dynamics of a system, consisting of a particle initially in a Gaussian state interacting with a field mode, under the action of repeated measurements performed on the particle, is examined. It is shown that regardless of its initial state the field is distilled into a squeezed state. The dependence on the physical parameters of the dynamics is investigated.
Non-Hermitian skin effect as an impurity problem
2021
A striking feature of non-Hermitian tight-binding Hamiltonians is the high sensitivity of both spectrum and eigenstates to boundary conditions. Indeed, if the spectrum under periodic boundary conditions is point gapped, by opening the lattice the non-Hermitian skin effect will necessarily occur. Finding the exact skin eigenstates may be demanding in general, and many methods in the literature are based on ansatzes and on recurrence equations for the eigenstates' components. Here we devise a general procedure based on the Green's function method to calculate the eigenstates of non-Hermitian tight-binding Hamiltonians under open boundary conditions. We apply it to the Hatano-Nelson and non-He…
Quantum Error Correction with magnetic molecules
2014
Quantum algorithms often assume independent spin qubits to produce trivial $|\uparrow\rangle=|0\rangle$, $|\downarrow\rangle=|1\rangle$ mappings. This can be unrealistic in many solid-state implementations with sizeable magnetic interactions. Here we show that the lower part of the spectrum of a molecule containing three exchange-coupled metal ions with $S=1/2$ and $I=1/2$ is equivalent to nine electron-nuclear qubits. We derive the relation between spin states and qubit states in reasonable parameter ranges for the rare earth $^{159}$Tb$^{3+}$ and for the transition metal Cu$^{2+}$, and study the possibility to implement Shor's Quantum Error Correction code on such a molecule. We also disc…
Killing (absorption) versus survival in random motion
2017
We address diffusion processes in a bounded domain, while focusing on somewhat unexplored affinities between the presence of absorbing and/or inaccessible boundaries. For the Brownian motion (L\'{e}vy-stable cases are briefly mentioned) model-independent features are established, of the dynamical law that underlies the short time behavior of these random paths, whose overall life-time is predefined to be long. As a by-product, the limiting regime of a permanent trapping in a domain is obtained. We demonstrate that the adopted conditioning method, involving the so-called Bernstein transition function, works properly also in an unbounded domain, for stochastic processes with killing (Feynman-…
Interaction free and decoherence free states
2015
An interaction free evolving state of a closed bipartite system composed of two interacting subsystems is a generally mixed state evolving as if the interaction were a c-number. In this paper we find the characteristic equation of states possessing similar properties for a bipartite systems governed by a linear dynamical equation whose generator is sum of a free term and an interaction term. In particular in the case of a small system coupled to its environment, we deduce the characteristic equation of decoherence free states namely mixed states evolving as if the interaction term were effectively inactive. Several examples illustrate the applicability of our theory in different physical co…
Two Dimensional Quantum Chromodynamics as the Limit of Higher Dimensional Theories
1994
We define pure gauge $QCD$ on an infinite strip of width $L$. Techniques similar to those used in finite $TQCD$ allow us to relate $3D$-observables to pure $QCD_2$ behaviors. The non triviality of the $L \arrow 0$ limit is proven and the generalization to four dimensions described. The glueball spectrum of the theory in the small width limit is calculated and compared to that of the two dimensional theory.
Coupled-channel meson-meson scattering in the diabatic framework
2021
We apply the diabatic framework, a QCD-based formalism for the unified study of quarkoniumlike systems in terms of heavy quark-antiquark and open-flavor meson-meson components, to the description of coupled-channel meson-meson scattering. For this purpose, we first introduce a numerical scheme to find the solutions of the diabatic Schr\"odinger equation for energies in the continuum, then we derive a general formula for calculating the meson-meson scattering amplitudes from these solutions. We thus obtain a completely nonperturbative procedure for the calculation of open-flavor meson-meson scattering cross sections from the diabatic potential, which is directly connected to lattice QCD calc…
Current correlators and form factors in the resonance region
2009
Within Resonance Chiral Theory and in the context of QCD current correlators at next-to-leading order in 1/N(C), we have analyzed the two-body form factors which include resonances as a final state . The short-distance constraints have been studied. One of the main motivations is the estimation of the chiral low-energy constants at subleading order, that is, keeping full control of the renormalization scale dependence. As an application we show the resonance estimation of some coupling, L(10)(mu_0)=(-4.4 \pm 0.9)10^{-3} and C(87)(mu_0)=(3.1 \pm 1.1)10^{-5}.
Including Tetraquark Operators in the Low-Lying Scalar Meson Sectors in Lattice QCD
2019
Lattice QCD allows us to probe the low-lying hadron spectrum in finite-volume using a basis of single- and multi-hadron interpolating operators. Here we examine the effect of including tetraquark operators on the spectrum in the scalar meson sectors containing the $K_0^*(700)$ ($\kappa$) and the $a_0(980)$ in $N_f = 2 + 1$ QCD, with $m_\pi \approx 230$ MeV. Preliminary results of additional finite-volume states found using tetraquark operators are shown, and possible implications of these states are discussed.