Search results for "Two degrees of freedom"
showing 4 items of 4 documents
A simple quantum gate with atom chips
2005
We present a simple scheme for implementing an atomic phase gate using two degrees of freedom for each atom and discuss its realization with cold rubidium atoms on atom chips. We investigate the performance of this collisional phase gate and show that gate operations with high fidelity can be realized in magnetic traps that are currently available on atom chips.
Poincaré Surface of Sections, Mappings
2001
We consider a system with two degrees of freedom, which we describe in four-dimensional phase space. In this (finite) space we define an (oriented) two-dimensional surface. If we then consider the trajectory in phase space, we are interested primarily in its piercing points through this surface. This piercing can occur repeatedly in the same direction. If the motion of the trajectory is determined by the Hamiltonian equations, then the n + 1-th piercing point depends only on the nth. The Hamiltonian thus induces a mapping n → n + 1 in the “Poincare surface of section” (PSS). The mapping transforms points of the PSS into other (or the same) points of the PSS. In the following we shall limit …
The KAM Theorem
2016
This theorem guarantees that, under certain assumptions, in the case of a perturbation \(\varepsilon H_{1}(\boldsymbol{J},\boldsymbol{\theta })\) with small enough ɛ, the iterated series for the generator W(θ i 0, J i ) converges (according to Newton’s procedure) and thus the invariant tori are not destroyed. The KAM theorem is valid for systems with two and more degrees of freedom. However, in the following, we shall deal exclusively with the case of two degrees of freedom.
(H,ρ)-induced dynamics and large time behaviors
2018
Abstract In some recent papers, the so called ( H , ρ ) -induced dynamics of a system S whose time evolution is deduced adopting an operatorial approach, borrowed in part from quantum mechanics, has been introduced. Here, H is the Hamiltonian for S , while ρ is a certain rule applied periodically (or not) on S . The analysis carried on throughout this paper shows that, replacing the Heisenberg dynamics with the ( H , ρ ) -induced one, we obtain a simple, and somehow natural, way to prove that some relevant dynamical variables of S may converge, for large t , to certain asymptotic values. This cannot be so, for finite dimensional systems, if no rule is considered. In this case, in fact, any …