Quantum description of spin tunneling in magnetic molecules

Starting from a phenomenological Hamiltonian originally written in terms of angular momentum operators we derive a new quantum angle-based Hamiltonian that allows for a discussion on the quantum spin tunneling. The study of the applicability of the present approach, carried out in calculations with a soluble quasi-spin model, shows that we are allowed to use our method in the description of physical systems such as the Mn12-acetate molecule, as well as the octanuclear iron cluster, Fe8, in a reliable way. With the present description the interpretation of the spin tunneling is seen to be direct, the spectra and energy barriers of those systems are obtained, and it is shown that they agree with the experimental ones. (c) 2006 Elsevier B.V. All rights reserved.

Quantum spin tunneling in a soluble quasi-spin model: an angle-based potential description

We propose an approach which allows one to construct and use a potential function written in terms of an angle variable to describe interacting spin systems. We show how this can be implemented in the Lipkin-Meshkov-Glick, here considered a paradigmatic spin model. It is shown how some features of the energy gap can be interpreted in terms of a spin tunneling. A discrete Wigner function is constructed for a symmetric combination of two states of the model and its time evolution is obtained. The physical information extracted from that function reinforces our description of phase oscillations in a potential. (c) 2004 Elsevier B.V. All rights reserved.

A practical treatise on the combustion of coal : including description of various mechanical devices for the economic generation of heat by the combustion of fuel, whether solid, liquid or gaseous /

"Authors and books consulted or quoted from": p. [v]-vi.

Yorkshire, past and present: a history and a description of the three ridings of the great county of York, from the earliest ages to the year 1870; with an account of its manufactures, commerce, and civil and mechanical engineering.

Mode of access: Internet.

The mechanician, a treatise on the construction and manipulation of tools, for the use and instruction of young engineers and scientific amateurs; comprising the arts of blacksmithing and forging; the construction and manufacture of hand tools, and the various methods of using and grinding them; description of hand and machine processes; turning and screw cutting; and the various details of setting out work incidental to the mechanical engineer's and machinist's art.

Mode of access: Internet.

The complete cost-keeper: some original systems of shop cost-keeping or factory accounting, together with an exposition of the advantages of account keeping by means of cards instead of books, and a description of various mechanical aids to factory accounting,

Mode of access: Internet.

Experimental tests of quantum nonlinear dynamics in atom optics

Cold atoms in optical potentials provide an ideal test bed to explore quantum nonlinear dynamics. Atoms are prepared in a magneto-optic trap or as a dilute Bose-Einstein condensate and subjected to a far detuned optical standing wave that is modulated. They exhibit a wide range of dynamics, some of which can be explained by classical theory while other aspects show the underlying quantum nature of the system. The atoms have a mixed phase space containing regions of regular motion which appear as distinct peaks in the atomic momentum distribution embedded in a sea of chaos. The action of the atoms is of the order of Planck's constant, making quantum effects significant. This tutorial presents a detailed description of experiments measuring the evolution of atoms in time-dependent optical potentials. Experimental methods are developed providing means for the observation and selective loading of regions of regular motion. The dependence of the atomic dynamics on the system parameters is explored and distinct changes in the atomic momentum distribution are observed which are explained by the applicable quantum and classical theory. The observation of a bifurcation sequence is reported and explained using classical perturbation theory. Experimental methods for the accurate control of the momentum of an ensemble of atoms are developed. They use phase space resonances and chaotic transients providing novel ensemble atomic beamsplitters. The divergence between quantum and classical nonlinear dynamics is manifest in the experimental observation of dynamical tunnelling. It involves no potential barrier. However a constant of motion other than energy still forbids classically this quantum allowed motion. Atoms coherently tunnel back and forth between their initial state of oscillatory motion and the state 180 out of phase with the initial state.

Charge transport in a quantum electromechanical system

We describe a quantum electromechanical system comprising a single quantum dot harmonically bound between two electrodes and facilitating a tunneling current between them. An example of such a system is a fullerene molecule between two metal electrodes [Park et al., Nature 407, 57 (2000)]. The description is based on a quantum master equation for the density operator of the electronic and vibrational degrees of freedom and thus incorporates the dynamics of both diagonal (population) and off diagonal (coherence) terms. We derive coupled equations of motion for the electron occupation number of the dot and the vibrational degrees of freedom, including damping of the vibration and thermo-mechanical noise. This dynamical description is related to observable features of the system including the stationary current as a function of bias voltage

Quantum nondemolition measurement of Fock states of mesoscopic mechanical oscillators

We investigate a scheme that makes a quantum nondemolition (QND) measurement of the excitation level of a mesoscopic mechanical oscillator by utilizing the anharmonic coupling between two beam bending modes. The nonlinear coupling between the two modes shifts the resonant frequency of the readout oscillator in proportion to the excitation level of the system oscillator. This frequency shift may be detected as a phase shift of the readout oscillation when driven on resonance. We derive an equation for the reduced density matrix of the system oscillator, and use this to study the conditions under which discrete jumps in the excitation level occur. The appearance of jumps in the actual quantity measured is also studied using the method of quantum trajectories. We consider the feasibility of the scheme for experimentally accessible parameters.

Coupling of energy from quantum emitters to the plasmonic mode of V groove waveguides: A numerical study

This work is a theoretical investigation into the coupling of a single excited quantum emitter to the plasmon mode of a V groove waveguide. The V groove waveguide consists of a triangular channel milled in gold and the emitter is modeled as a dipole emitter, and could represent a quantum dot, nitrogen vacancy in diamond, or similar. In this work the dependence of coupling efficiency of emitter to plasmon mode is determined for various geometrical parameters of the emitter-waveguide system. Using the finite element method, the effect on coupling efficiency of the emitter position and orientation, groove angle, groove depth, and tip radius, is studied in detail. We demonstrate that all parameters, with the exception of groove depth, have a significant impact on the attainable coupling efficiency. Understanding the effect of various geometrical parameters on the coupling between emitters and the plasmonic mode of the waveguide is essential for the design and optimization of quantum dot–V groove devices.

Numerical Modelling of Mechanical Behaviour of Graphene

Graphene, one of the allotropes (diamond, carbon nanotube, and fullerene) of element carbon, is a monolayer of honeycomb lattice of carbon atoms, which was discovered in 2004. The Nobel Prize in Physics 2010 was awarded to Andre Geim and Konstantin Novoselov for their ground breaking work on the two-dimensional (2D) graphene [1]. Since its discovery, the research communities have shown a lot of interest in this novel material owing to its intriguing electrical, mechanical and thermal properties. It has been confirmed that grapheme possesses very peculiar electrical properties such as anomalous quantum hall effect, and high electron mobility at room temperature (250000 cm2/Vs). Graphene also has exceptional mechanical properties. It is one of the stiffest (modulus ~1 TPa) and strongest (strength ~100 GPa) materials. In addition, it has exceptional thermal conductivity (5000 Wm-1K-1). Due to these exceptional properties, graphene has demonstrated its potential for broad applications in micro and nano devices, various sensors, electrodes, solar cells and energy storage devices and nanocomposites. In particular, the excellent mechanical properties of graphene make it more attractive for development next generation nanocomposites and hybrid materials...

Multiscale coupling and multiphysics approaches in earth sciences : applications

Geoscientists are confronted with the challenge of assessing nonlinear phenomena that result from multiphysics coupling across multiple scales from the quantum level to the scale of the earth and from femtoseconds to the 4.5 Ga of history of our planet. We neglect in this review electromagnetic modelling of the processes in the Earth’s core, and focus on four types of couplings that underpin fundamental instabilities in the Earth. These are thermal (T), hydraulic (H), mechanical (M) and chemical (C) processes which are driven and controlled by the transfer of heat to the Earth’s surface. Instabilities appear as faults, folds, compaction bands, shear/fault zones, plate boundaries and convective patterns. Convective patterns emerge from buoyancy overcoming viscous drag at a critical Rayleigh number. All other processes emerge from non-conservative thermodynamic forces with a critical critical dissipative source term, which can be characterised by the modified Gruntfest number Gr. These dissipative processes reach a quasi-steady state when, at maximum dissipation, THMC diffusion (Fourier, Darcy, Biot, Fick) balance the source term. The emerging steady state dissipative patterns are defined by the respective diffusion length scales. These length scales provide a fundamental thermodynamic yardstick for measuring instabilities in the Earth. The implementation of a fully coupled THMC multiscale theoretical framework into an applied workflow is still in its early stages. This is largely owing to the four fundamentally different lengths of the THMC diffusion yardsticks spanning micro-metre to tens of kilometres compounded by the additional necessity to consider microstructure information in the formulation of enriched continua for THMC feedback simulations (i.e., micro-structure enriched continuum formulation). Another challenge is to consider the important factor time which implies that the geomaterial often is very far away from initial yield and flowing on a time scale that cannot be accessed in the laboratory. This leads to the requirement of adopting a thermodynamic framework in conjunction with flow theories of plasticity. This framework allows, unlike consistency plasticity, the description of both solid mechanical and fluid dynamic instabilities. In the applications we show the similarity of THMC feedback patterns across scales such as brittle and ductile folds and faults. A particular interesting case is discussed in detail, where out of the fluid dynamic solution, ductile compaction bands appear which are akin and can be confused with their brittle siblings. The main difference is that they require the factor time and also a much lower driving forces to emerge. These low stress solutions cannot be obtained on short laboratory time scales and they are therefore much more likely to appear in nature than in the laboratory. We finish with a multiscale description of a seminal structure in the Swiss Alps, the Glarus thrust, which puzzled geologists for more than 100 years. Along the Glarus thrust, a km-scale package of rocks (nappe) has been pushed 40 km over its footwall as a solid rock body. The thrust itself is a m-wide ductile shear zone, while in turn the centre of the thrust shows a mm-cm wide central slip zone experiencing periodic extreme deformation akin to a stick-slip event. The m-wide creeping zone is consistent with the THM feedback length scale of solid mechanics, while the ultralocalised central slip zones is most likely a fluid dynamic instability.

Response to “Comment on ‘Indications of energetic consequences of decoherence at short times for scattering from open quantum systems’” [AIP Advances 1, 049101 (2011)]

The Comment by Mayers and Reiter criticizes our work on two counts. Firstly, it is claimed that the quantum decoherence effects that we report in consequence of our experimental analysis of neutron Compton scattering from H in gaseous H2 are not, as we maintain, outside the framework of conventional neutron scatteringtheory. Secondly, it is claimed that we did not really observe such effects, owing to a faulty analysis of the experimental data, which are claimed to be in agreement with conventional theory. We focus in this response on the critical issue of the reliability of our experimental results and analysis. Using the same standard Vesuvio instrument programs used by Mayers et al., we show that, if the experimental results for H in gaseous H2 are in agreement with conventional theory, then those for D in gaseous D2 obtained in the same way cannot be, and vice-versa. We expose a flaw in the calibration methodology used by Mayers et al. that leads to the present disagreement over the behaviour of H, namely the ad hoc adjustment of the measured H peak positions in TOF during the calibration of Vesuvio so that agreement is obtained with the expectation of conventional theory. We briefly address the question of the necessity to apply the theory of open quantum systems.

Indications of energetic consequences of decoherence at short times for scattering from open quantum systems

Decoherence of quantum entangled particles is observed in most systems, and is usually caused by system-environment interactions. Disentangling two subsystems A and B of a quantum systemAB is tantamount to erasure of quantum phase relations between A and B. It is widely believed that this erasure is an innocuous process, which e.g. does not affect the energies of A and B. Surprisingly, recent theoretical investigations by different groups showed that disentangling two systems, i.e. their decoherence, can cause an increase of their energies. Applying this result to the context of neutronCompton scattering from H2 molecules, we provide for the first time experimental evidence which supports this prediction. The results reveal that the neutron-proton collision leading to the cleavage of the H-H bond in the sub-femtosecond timescale is accompanied by larger energy transfer (by about 3%) than conventional theory predicts. It is proposed to interpreted the results by considering the neutron-proton collisional system as an entangled open quantum system being subject to decoherence owing to the interactions with the “environment” (i.e., two electrons plus second proton of H2).