Search results for "Geometric"
showing 10 items of 652 documents
Liquid-liquid phase coexistence in gold clusters. 2D or not 2D?
2006
The thermodynamics of gold cluster anions (${\mathrm{Au}}_{N}^{\ensuremath{-}}$, $N=11,\dots{},14$) is investigated using quantum molecular dynamics. Our simulations suggest that ${\mathrm{Au}}_{N}^{\ensuremath{-}}$ may exhibit a novel, freestanding planar liquid phase which dynamically coexists with a normal three-dimensional liquid. Upon cooling with experimentally realizable cooling rates, the entropy-favored three-dimensional liquid clusters often supercool and solidify into the ``wrong'' dimensionality. This indicates that experimental validation of theoretically predicted ${\mathrm{Au}}_{N}^{\ensuremath{-}}$ ground states might be more complicated than hitherto expected.
Prospects of SPIN Gyroscopes Based on Nitrogen-Vacancy Centers in Diamond
2019
This project aims to develop solid-state gyroscopes based on ensembles of negatively charged nitrogen-vacancy (NV) centers in diamond [1], [2]. The NV center is a defect formed in diamond by one substitutional nitrogen atom and an adjacent vacancy. The NV- center features a ground state with electronic spin $\mathrm{S}=1$ , which can be initialized, manipulated, and detected via convenient optical, microwave and radiofrequency transitions (Fig. 1). Nuclear spins are appealing in the context of gyroscopes because they have much smaller gyromagnetic ratios than that of the electron (by a factor of about 1000), reducing the requirements on static magnetic-field stability and homogeneity. The l…
Exploring Gravitational Lensing
2019
In this article, we discuss the idea of gravitational lensing, from a systematic, historical and didactic point of view. We show how the basic lensing equation together with the concepts of geometrical optics opens a space of implications that can be explored along different dimensions. We argue that Einstein explored the idea along different pathways in this space of implication, and that these explorations are documented by different calculational manuscripts. The conceptualization of the idea of gravitational lensing as a space of exploration also shows the feasibility of discussing the idea in the classroom using some of Einstein's manuscripts.
Time-optimal control of the purification of a qubit in contact with a structured environment
2019
We investigate the time-optimal control of the purification of a qubit interacting with a structured environment, consisting of a strongly coupled two-level defect in interaction with a thermal bath. On the basis of a geometric analysis, we show for weak and strong interaction strengths that the optimal control strategy corresponds to a qubit in resonance with the reservoir mode. We investigate under which conditions qubit coherence and correlation between the qubit and the environment can speed up the control process.
Geometric phase in open systems.
2003
We calculate the geometric phase associated to the evolution of a system subjected to decoherence through a quantum-jump approach. The method is general and can be applied to many different physical systems. As examples, two main source of decoherence are considered: dephasing and spontaneous decay. We show that the geometric phase is completely insensitive to the former, i.e. it is independent of the number of jumps determined by the dephasing operator.
Regular packings on periodic lattices.
2011
We investigate the problem of packing identical hard objects on regular lattices in d dimensions. Restricting configuration space to parallel alignment of the objects, we study the densest packing at a given aspect ratio X. For rectangles and ellipses on the square lattice as well as for biaxial ellipsoids on a simple cubic lattice, we calculate the maximum packing fraction \phi_d(X). It is proved to be continuous with an infinite number of singular points X^{\rm min}_\nu, X^{\rm max}_\nu, \nu=0, \pm 1, \pm 2,... In two dimensions, all maxima have the same height, whereas there is a unique global maximum for the case of ellipsoids. The form of \phi_d(X) is discussed in the context of geomet…
Classical Geometric Phases: Foucault and Euler
2020
In the last chapter we saw how a quantum system can give rise to a Berry phase, by studying the adiabatic round trip of its quantum state on a certain parameter space. Rather than considering what happens to states in Hilbert space, we now turn to classical mechanics, where we are concerned instead with the evolution of the system in configuration space. As a first example, we are interested in the geometric phase of an oscillator that is constrained to a plane that is transported over some surface which moves along a certain path in three-dimensional space. Contrary to determining the Berry phase, there is no adiabatic approximation of the motion along the curve involved. The Foucault phas…
WIGNER TRANSFORM METHODS IN INCLUSIVE ELECTRON SCATTERING FROM NUCLEI
1984
A multiple scattering series for deep inelastic leptoninduced reactions is derived by using semiclassical Wigner transform methods. In contrast to the usual Glauber theory there is no limitation for the energy loss since a time-dependent formulation is used throughout. A simple parametrization of the generalized profile function yields a closed analytical expression for the longitudinal and transverse response function of p-shell nuclei. Comparison is made with the Saclay data for -'• C. I Introduction It is common knowledge that geometrical optics is valid if the wavelength of the scattering wave is small compared to the dimensions of the scatterer. Under these conditions the phase-space d…
Three-dimensional field distribution in the focal region of low-Fresnel-number axicons.
2006
Three-dimensional intensity and phase distributions generated by microaxicons are evaluated in the low-Fresnel-number regime. Apertured and nonapertured conical wavefronts may generate transverse patterns with notable deviations from the expected nondiffracting Bessel beam. First-order analytical expressions are proposed for the evaluation of the wave field produced by axicons of different Fresnel number in the focal region.
A geometric analysis of the effects of noise on Berry phase
2007
In this work we describe the effect of classical and quantum noise on the Berry phase. It is not a topical review article but rather an overview of our work in this field aiming at giving a simple pictorial intuition of our results.