Search results for "Quantum physic"
showing 10 items of 1596 documents
Contextuality in canonical systems of random variables
2017
Random variables representing measurements, broadly understood to include any responses to any inputs, form a system in which each of them is uniquely identified by its content (that which it measures) and its context (the conditions under which it is recorded). Two random variables are jointly distributed if and only if they share a context. In a canonical representation of a system, all random variables are binary, and every content-sharing pair of random variables has a unique maximal coupling (the joint distribution imposed on them so that they coincide with maximal possible probability). The system is contextual if these maximal couplings are incompatible with the joint distributions o…
On the presence of families of pseudo-bosons in nilpotent Lie algebras of arbitrary corank
2019
We have recently shown that pseudo-bosonic operators realize concrete examples of finite dimensional nilpotent Lie algebras over the complex field. It has been the first time that such operators were analyzed in terms of nilpotent Lie algebras (under prescribed conditions of physical character). On the other hand, the general classification of a finite dimensional nilpotent Lie algebra $\mathfrak{l}$ may be given via the size of its Schur multiplier involving the so-called corank $t(\mathfrak{l})$ of $\mathfrak{l}$. We represent $\mathfrak{l}$ by pseudo-bosonic ladder operators for $t(\mathfrak{l}) \le 6$ and this allows us to represent $\mathfrak{l}$ when its dimension is $\le 5$.
Intertwining operators for non-self-adjoint hamiltonians and bicoherent states
2016
This paper is devoted to the construction of what we will call {\em exactly solvable models}, i.e. of quantum mechanical systems described by an Hamiltonian $H$ whose eigenvalues and eigenvectors can be explicitly constructed out of some {\em minimal ingredients}. In particular, motivated by PT-quantum mechanics, we will not insist on any self-adjointness feature of the Hamiltonians considered in our construction. We also introduce the so-called bicoherent states, we analyze some of their properties and we show how they can be used for quantizing a system. Some examples, both in finite and in infinite-dimensional Hilbert spaces, are discussed.
Non-self-adjoint hamiltonians defined by Riesz bases
2014
We discuss some features of non-self-adjoint Hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a Riesz basis of Hilbert space. Among other things, {we give conditions under which these Hamiltonians} can be factorized in terms of generalized lowering and raising operators.
Fractional Laplacians in bounded domains: Killed, reflected, censored, and taboo Lévy flights.
2018
The fractional Laplacian $(- \Delta)^{\alpha /2}$, $\alpha \in (0,2)$ has many equivalent (albeit formally different) realizations as a nonlocal generator of a family of $\alpha $-stable stochastic processes in $R^n$. On the other hand, if the process is to be restricted to a bounded domain, there are many inequivalent proposals for what a boundary-data respecting fractional Laplacian should actually be. This ambiguity holds true not only for each specific choice of the process behavior at the boundary (like e.g. absorbtion, reflection, conditioning or boundary taboos), but extends as well to its particular technical implementation (Dirchlet, Neumann, etc. problems). The inferred jump-type …
A description of pseudo-bosons in terms of nilpotent Lie algebras
2017
We show how the one-mode pseudo-bosonic ladder operators provide concrete examples of nilpotent Lie algebras of dimension five. It is the first time that an algebraic-geometric structure of this kind is observed in the context of pseudo-bosonic operators. Indeed we don't find the well known Heisenberg algebras, which are involved in several quantum dynamical systems, but different Lie algebras which may be decomposed in the sum of two abelian Lie algebras in a prescribed way. We introduce the notion of semidirect sum (of Lie algebras) for this scope and find that it describes very well the behaviour of pseudo-bosonic operators in many quantum models.
Low-Noise Amplification and Frequency Conversion with a Multiport Microwave Optomechanical Device
2016
High-gain amplifiers of electromagnetic signals operating near the quantum limit are crucial for quantum information systems and ultrasensitive quantum measurements. However, the existing techniques have a limited gain-bandwidth product and only operate with weak input signals. Here we demonstrate a two-port optomechanical scheme for amplification and routing of microwave signals, a system that simultaneously performs high-gain amplification and frequency conversion in the quantum regime. Our amplifier, implemented in a two-cavity microwave optomechanical device, shows 41 dB of gain and has a high dynamic range, handling input signals up to $10^{13}$ photons per second, three orders of magn…
ROS/Gazebo-Based Simulation of Quadcopter Aircrafts
2018
The main purpose of this work is to present a tutorial description on how to design and develop an observer, which is capable of estimating the position and the orientation of a drone commanded by a controller, whose shape and structure are unknown. Starting from Newton's and Euler's laws, a mathematical model describing the dynamics of a quadcopter has first been obtained. By linearizing this model it is possible to implement a Luenberger observer and validate it with simulations in a Linux environment, thanks to the use of the Ardupilot controller and the Gazebo simulator. Finally, starting from the results obtained from the simulation, it is possible to evaluate the error made in the est…
Wind gust estimation for precise quasi-hovering control of quadrotor aircraft
2021
Abstract This paper focuses on the control of quadrotor vehicles without wind sensors that are required to accurately track low-speed trajectories in the presence of moderate yet unknown wind gusts. By modeling the wind disturbance as exogenous inputs, and assuming that compensation of its effects can be achieved through quasi-static vehicle motions, this paper proposes an innovative estimation and control scheme comprising a linear dynamic filter for the estimation of such unknown inputs and requiring only position and attitude information. The filter is built upon results from Unknown Input Observer theory and allows estimation of wind and vehicle state without measurement of the wind its…
Quantum walk on the line through potential barriers
2015
Quantum walks are well-known for their ballistic dispersion, traveling $\Theta(t)$ away in $t$ steps, which is quadratically faster than a classical random walk's diffusive spreading. In physical implementations of the walk, however, the particle may need to tunnel through a potential barrier to hop, and a naive calculation suggests this could eliminate the ballistic transport. We show by explicit calculation, however, that such a loss does not occur. Rather, the $\Theta(t)$ dispersion is retained, with only the coefficient changing, which additionally gives a way to detect and quantify the hopping errors in experiments.