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Images of Ga+ -implanted amorphous silicon layers in a 110 n-type silicon substrate have been collected by a range of detectors in a scanning electron microscope and a helium ion microscope. The effects of the implantation dose and imaging parameters (beam energy, dwell time, etc.) on the image contrast were investigated. We demonstrate a similar relationship for both the helium ion microscope Everhart-Thornley and scanning electron microscope Inlens detectors between the contrast of the images and the Ga+ density and imaging parameters. These results also show that dynamic charging effects have a significant impact on the quantification of the helium ion microscope and scanning electron microscope contrast.

The preparation and analysis of Ni doped Co1–xNix(OH)2 (x = 0.6–0.8) nanorings are reported as produced using core–shell structured Co0.9Ni0.1(OH)2 nanodiscs as a starting template material. The resulting structure and elemental distribution were analyzed to investigate the transformation from discs to rings. A representative example involving the doping of Cu in the Co–Cu hydrate system is also presented.

First, we examine how spin is treated in special relativity and the necessity of introducing spin supplementary conditions (SSC) and how they are related to the choice of a center-of-mass of a spinning particle. Next, we discuss quantum electrodynamics and the Foldy−Wouthuysen transformation which we note is a position operator identical to the Pryce−Newton−Wigner position operator. The classical version of the operators are shown to be essential for the treatment of classical relativistic particles in general relativity, of special interest being the case of binary systems (black holes/neutron stars) which emit gravitational radiation.

The helium ion microscope (HelM) holds immense promise for nano-engineering and imaging with scope for in-situ chemical analysis. Here we will examine the potential of secondary electron hyperspectral imaging (SEHI) as a new route to exploring chemical variations in both two and three dimensions. We present a range of early applications in the context of image interpretation in wider materials science and process control in ion beam-based nano-engineering. Necessary steps for SEHI in the HelM to evolve into a reliable technique which can be fully embedded into nano-engineering workflows are considered.

We give a simple derivation and explanation of a recently proposed new relativistic interaction between the electron and the angular momentum of the electromagnetic field in quantum electrodynamics (QED). Our derivation is based on the work of Moller, who pointed out that, in special relativity, a particle with spin must always have a finite extension. We generalize Mollers classical result to the quantum regime and show that it leads to a new contribution to the energy, which is the special relativistic interaction term. In addition, we show that all spin terms arising from the Dirac equation may be obtained by this method., 3 pages

We outline an exact approach to decoherence and entanglement problems for continuous variable systems. The method is based on a construction of quantum distribution functions introduced by Ford and Lewis in which a system in thermal equilibrium is placed in an initial state by a measurement and then sampled by subsequent measurements. With the Langevin equation describing quantum Brownian motion, this method has proved to be a powerful tool for discussing such problems. After reviewing our previous work on decoherence and our recent work on disentanglement, we apply the method to the problem of a pair of particles in a correlated Gaussian state. The initial state and its time development are explicitly exhibited. For a single relaxation time bath at zero temperature exact numerical results are given. The criterion of Duan et al. for such states is used to prove that the state is initially entangled and becomes separable after a finite time (entanglement sudden death).

We consider the case of a pair of particles initially in a superposition state corresponding to a separated pair of wave packets. In contrast to a previous related work, we avoid a master equation approach and we calculate exactly the time development of this non-Gaussian state due to interaction with an arbitrary heat bath. We find that coherence decays continuously, as expected. We then investigate entanglement and find that at a finite time the system becomes separable (not entangled). Thus, we see that entanglement sudden death is also prevalent in continuous variable systems which should raise concern for the designers of entangled systems.

In the present paper we follow three major themes: (i) concepts of rotation in general relativity, (ii) effects induced by these generalized rotations, and (iii) their measurement using interferometry. Our journey takes us from the Foucault pendulum via the Sagnac interferometer to manifestations of gravito-magnetism in double binary pulsars and in Godel’s Universe. Throughout our article we emphasize the emerging role of matter wave interferometry based on cold atoms or Bose–Einstein condensates leading to superior inertial sensors. In particular, we advertise recent activities directed towards the operation of a coherent matter wave interferometer in an extended free fall.

We show that treating the black-body radiation field as a heat bath enables one to utilize powerful techniques from the realm of stochastic physics (such as the fluctuation–dissipation theorem and the related radiation damping) to treat problems that could not be treated rigorously by conventional methods. We illustrate our remarks by discussing specifically the effect of temperature on atomic spectral lines, and the solution to the problem of runaway solutions in the equation of motion of a radiating electron. We also present brief discussions relating to anomalous diffusion and wave-packet spreading in a radiation field and the influence of quantum effects on the laws of thermodynamics.PACS Nos.: 31.30.jg, 05.40.–a

Two-dimensional (2D) materials usually have a layer-dependent work function, which require fast and accurate detection for the evaluation of their device performance. A detection technique with high throughput and high spatial resolution has not yet been explored. Using a scanning electron microscope, we have developed and implemented a quantitative analytical technique which allows effective extraction of the work function of graphene. This technique uses the secondary electron contrast and has nanometre-resolved layer information. The measurement of few-layer graphene flakes shows the variation of work function between graphene layers with a precision of less than 10 meV. It is expected that this technique will prove extremely useful for researchers in a broad range of fields due to its revolutionary throughput and accuracy.

Cobalt hydrate and doped binary Co0.9M0.1OOH (M = Ni, Mn, Fe) nanorings of 100–300 nm were fabricated in solution through a facile ambient oxidation method. A transformation from Co0.9Ni0.1(OH)2 nanodiscs to hollow Co0.9Ni0.1OOH nanorings was observed with prolonged reaction time. Core-shell nanodiscs have elemental segregation with a Co(OH)2 core and Ni(OH)2 shell. Co0.9Ni0.1OOH nanorings displayed a higher electrochemical capacitance than Mn and Fe doped nanorings materials or materials with disc-like geometries.

The first in a long series of papers by John T. Lewis, G. W. Ford and the present author, considered the problem of the most general coupling of a quantum particle to a linear passive heat bath, in the course of which they derived an exact formula for the free energy of an oscillator coupled to a heat bath in thermal equilibrium at temperature T. This formula, and its later extension to three dimensions to incorporate a magnetic field, has proved to be invaluable in analyzing problems in quantum thermodynamics. Here, we address the question raised in our title viz. Nernst's third law of thermodynamics.

It is generally accepted that a system undergoing uniform acceleration with respect to zero-temperature vacuum will thermalize at a finite temperature (the so-called Unruh temperature) that is proportional to the acceleration. However, the question of whether or not the system actually radiates is highly controversial. Thus, we are motivated to present an exact calculation using a generalized quantum Langevin equation to describe an oscillator (the detector) moving under a constant force and coupled to a one-dimensional scalar field (scalar electrodynamics). Moreover, our analysis is simplified by using the oscillator as a detector. We show that this system does not radiate despite the fact that it does in fact thermalize at the Unruh temperature. We remark upon a differing opinion expressed regarding a system coupled to the electromagnetic field.

A previous paper analysed the experimental results of Myatt et al. (Nature, 403, 269 (2000)) on the decoherence of superposition states of Be ions confined in a harmonic potential by a linear Paul trap and subject to a random external electric field. Based on a rigorous derivation in the absence of an exter- nal force which had previously been obtained, a heuristic approach to the problem was presented. Whereas this approach was simple and physically appealing, a more rigorous analysis is clearly desirable, which is the content of this paper. It also makes clear that, for the case of a random force, decoherence is intrinsic to quantum mechanics and does not require a dissipative environment.

Decoherence phenomena are pervasive in the arena of nanostructures but perhaps even more so in the study of the fundamentals of quantum mechanics and quantum computation. Since there has been little overlap between the studies in both arenas, this is an attempt to bridge the gap. Topics stressed include (a) wave packet spreading in a dissipative environment, a key element in all arenas, (b) the definition of a quantitative measure of decoherence, (c) the near zero and zero temperature limit, and (d) the key role played by initial conditions: system and environment entangled at all times so that one must use the density matrix (or Wigner distribution) for the complete system or initially decoupled system and environment so that use of a reduced density matrix or reduced Wigner distribution is feasible. Our approach utilizes generalized quantum Langevin equations and Wigner distributions.

The claim by Rohrlich that the Abraham-Lorentz-Dirac equation is not the correct equation for a classical point charge is shown to be incorrect and it is pointed out that the equation which he proposes is the equation {\underline{derived}} by Ford and O'Connell for a charge with structure. The quantum-mechanical case is also discussed.

We first review the usefulness of the Wigner distribution functions (WDF), associated with Lindblad and pre-master equations, for analyzing a host of problems in Quantum Optics where dissipation plays a major role, an arena where weak coupling and long-time approximations are valid. However, we also show their limitations for the discussion of decoherence, which is generally a short-time phenomenon with decay rates typically much smaller than typical dissipative decay rates. We discuss two approaches to the problem both of which use a quantum Langevin equation (QLE) as a starting-point: (a) use of a reduced WDF but in the context of an exact master equation (b) use of a WDF for the complete system corresponding to entanglement at all times.

We use a multi-scale similarity analysis which gives specific relations between the velocity, amplitude and width of localized solutions of nonlinear differential equations, whose exact solutions are generally difficult to obtain.

We investigate the exact dynamics of the damped quantum harmonic oscillator under the (un)correlated initial conditions. We generalize the master equation to the cases of arbitrary factorized state and/or Gaussian state. For the factorized Gaussian state, we demonstrate that the effects of the initial oscillator-bath correlation are unnoticeable for the evolutions of variances, but can become remarkable for the evolutions of mean values even at high temperature. We also show that the initial dip during the purity evolution always shows up for the factorized initial state, but can disappear for some correlated non-factorizable initial state. Finally, we study the effects of repeated measurements on the time evolution of the damped oscillator. The comparison with the weak coupling results indicates that even for an intermediate coupling, they can give quite different transient behaviors.

Emphasis will be placed on unusual aspects of our derivation, particularly the use of techniques from the more developed realm of QED (quantum electrodynamics). We obtain explicit results for the precession of the spin (rotation) and orbital effects and we discuss the relatively recent (2008) verification of our spin precession result. Unusual features of our orbital precession analysis is the appearance of hidden momentum effects whose origins may be traced to a special relativistic effect.

Two particles of identical mass attract and repel each other even when there exist no classical external forces and their average relative momentum vanishes. This quantum force depends crucially on the number of dimensions of space.

In a letter to Nature (Ford G W and O'Connell R F 1996 Nature 380 113) we presented a formula for the derivative of the hyperbolic cotangent that differs from the standard one in the literature by an additional term proportional to the Dirac delta function. Since our letter was necessarily brief, shortly after its appearance we prepared a more extensive unpublished note giving a detailed explanation of our argument. Since this note has been referenced in a recent article (Estrada R and Fulling S A 2002 J. Phys. A: Math. Gen. 35 3079) we think it appropriate that it now appear in print. We have made no alteration to the original note.

We have completed the first stage of a two-stage genome wide screen designed to identify chromosomal regions that may harbour susceptibility genes for bipolar affective disorder. The first stage screening sample included 509 subjects from 151 nuclear families recruited within the United Kingdom and Republic of Ireland. This sample contained 154 narrowly defined affected sibling pairs (DSM-IV BPI) and 258 broadly defined affected sibling pairs (DSM-IV BPI, SABP, BPII, BPNOS or MDD(R)), approximately two thirds of all families contained at least one other additional typed individual. All individuals were genotyped using 398 highly polymorphic microsatellite markers from Applied Biosystems's Linkage Mapping Set Version 2. The average inter-marker distance was 9.6 cM and the mean heterozygosity was 0.78. Analysis of these data using non-parametric linkage methods (MAPMAKER/SIBS) found no evidence for loci of major effect and no regions reached genome-wide significance for either suggestive or significant linkage. We identified 19 points across the genome where the MLS exceeded a value set for follow up in our second stage screen (MLSor = 0.74 (equivalent to a nominal pointwise significance of 5%) under the narrowest diagnostic model). These points were on chromosomes 2, 3, 4, 6, 7, 9, 10, 12, 17, 18X. Some of these points overlapped with previous linkage reports both within bipolar affective disorder and other psychiatric illnesses. Under the narrowest diagnostic model, the single most significant multipoint linkage was on chromosome 18 at marker D18S452 (MLS=1.54). Overall the highest MLS was 1.70 on chromosome 2 at marker D2S125, under the broadest diagnostic model.

We provide a simple analytic formula in terms of elementary functions for the Laplace transform j_{l}(p) of the spherical Bessel function than that appearing in the literature, and we show that any such integral transform is a polynomial of order l in the variable p with constant coefficients for the first l-1 powers, and with an inverse tangent function of argument 1/p as the coefficient of the power l. We apply this formula for the Laplace transform of the memory function related to the Langevin equation in a one-dimensional Debye model., 5 pages LATEX, no figures. Accepted 2002, Physica Scripta

Surface organic residues inhibit the extraordinary electronic properties of graphene, hindering the development of graphene electronics. However, fundamental understanding of the residue morphology is still absent due to a lack of high-throughput and high-resolution surface characterization methods. Here, we demonstrate that secondary electron (SE) imaging in the scanning electron microscope (SEM) and helium ion microscope (HIM) can provide sub-nanometer information of a graphene surface and reveal the morphology of surface contaminants. Nanoscale polymethyl methacrylate (PMMA) residues are visible in the SE imaging, but their contrast, i.e. the apparent lateral dimension, varies with the imaging conditions. We have demonstrated a quantitative approach to readily obtain the physical size of the surface features regardless of the contrast variation. The fidelity of SE imaging is ultimately determined by the probe size of the primary beam. HIM is thus evaluated to be a superior SE imaging technique in terms of surface sensitivity and image fidelity. A highly efficient method to reveal the residues on a graphene surface has therefore been established.

The prototypical Schr\"{o}dinger cat state, i.e., an initial state corresponding to two widely separated Gaussian wave packets, is considered. The decoherence time is calculated solely within the framework of elementary quantum mechanics and equilibrium statistical mechanics. This is at variance with common lore that irreversible coupling to a dissipative environment is the mechanism of decoherence. Here, we show that, on the contrary, decoherence can in fact occur at high temperature even for vanishingly small dissipation.

One of the most widely used tools in quantum optics, the Lax formula for two-time correlations, is studied. The formula is then applied to two driven quantum systems: the oscillator and the two-level atom. Through a comparison with exact results for the oscillator, it is shown explicitly that the Lax formula is a weak coupling approximation that does not include quantum corrections to the Onsager regression hypothesis of classical statistical physics. For the two-level atom, the calculation of the well known Burshtein-Mollow spectrum of resonance fluorescence is extended to the case of non-zero temperature. q 2000 Elsevier Science B.V. All rights reserved.

We have previously pointed out (1996, Phys. Rev. Lett.77, 798) that in the calculation of a correlation function C(t) by means of the fluctuation–dissipation theorem, much insight could be gained by writing the Fourier transform of C(t) as of the Fourier transform of the relaxation function multiplying the universal power spectrum of quantum noise at temperature T. Here, we show how this factorization leads to an immediate simplifying approach in the weak coupling limit near resonance. In particular, the time decay dependencies which appear are those associated with the Onsager classical regression theorem. Also, we throw further light on our previous assertion that there is never a quantum regression theorem.

Efforts to achieve quantum computation, teleportation, and communication depend on minimizing decoherence, which is the destruction of a quantum interference pattern. Here, we examine effects arising from the universal zero-point (temperature T = 0) oscillations of the electromagnetic field on a free electron in a Schrodinger cat superposition state. A unique conclusion is that the spreading of an electron wavepacket and the rate of decay of decoherence depend on the bare mass m of the electron. However, only for m = 0 does decoherence occur and the fact that it occurs almost instantly is ruled out by electron interference experiments. For m ≠ 0, the electron essentially behaves as a free particle.

We present an analytical solution to the generalized discrete Poisson equation, a matrix equation which has a tridiagonal matrix with fringes having an arbitrary value for the diagonal elements. The results are of relevance to a variety of physical problems, which require the numerical solution of the Poisson equation. As examples, the formula has been applied to the solution of the electrostatic problem of tunnelling junction arrays with two and three rows.

For a quantum oscillator coupled to a reservoir, master equations obtained under the assumptions of weak coupling and use of a rotating-wave Hamiltonian (RWA) are known to give incorrect frequency shifts. Here, we show that a calculation which does not invoke the RWA gives results for the frequency shifts, which agree with exact results for Lamb-type (temperature T =0) shifts. However, for non-zero T , we point out that, in general, corresponding energy and free energy shifts for the system require exact treatments since off-resonant contributions (which are automatically excluded in weak coupling calculations) are important in the case of super-Ohmic reservoirs.

Here the problem considered is that of a pair of oscillators coupled to a common heat bath. Many, if not most, discussions of a single operator coupled to a bath have used the independent oscillator model of the bath. However, that model has no notion of separation, so the question of phenomena when the oscillators are near one another compared with when they are widely separated cannot be addressed. Here the Lamb model of an oscillator attached to a stretched string is generalized to illustrate some of these questions. The coupled Langevin equations for a pair of oscillators attached to the string at different points are derived and their limits for large and small separations obtained. Finally, as an illustration of a different phenomenon, the fluctuation force between a pair of masses attached to the string is calculated, with closed form expressions for the force at small and large separations.

We review of the Ford-O'Connell results on radiation reaction in electrodynamics and contrast them with the work of others. We conclude that the Ford-O'Connell results are the most complete and exact results .

Using a position operator obtained for spin 1 particles by the present author and Wigner, we obtain a quantum relativistic result for the hidden momentum force experienced by particles with structure. In particular, our result applies to the hidden magnetic forces manifest in some problems of electromagnetism. We also discuss spin and orbital angular momentum operators, as well as Wigner rotation., Proceedings of Wigner 111 Symposium to open the Wigner Research Institute, Budapest

The rotating wave approximation (RWA) is an integral part of the foundations of quantum optics and it is also used extensively in atomic and condensed-matter physics. Here we prove that the model has a serious defect, viz. the spectrum has no lower bound, for all models of physical interest. As a result, the reservoir is not passive (since energy can be extracted from it without limit) and hence the second law of thermodynamics is not satisfied. An alternative to the RWA is discussed.

clude dissipation by means of a self-consistent calculation, which considers not only the discrete charge transfer across the junction, but also the leads connecting the junction to external circuit. Our treatment is based on recent advances in the following two areas: ~a! the polaron problem where use has been made of both path integral and closed time-path Green’s function formulations; 10 ~b! single-electron tunneling by use of the path-integral method. 11‐14 This paper is organized as follows. In Sec. II, we present our model Hamiltonian for the environmental effects on single-electron tunneling. In Sec. III, we derive the selfconsistent equations of motion by using the path integral and the closed time-path Green’s-function formulation. In Sec. IV, we present our results where we focus on the weakcoupling regime. Our results are summarized in the concluding section.

The macroscopic description of a quantum oscillator with linear passive dissipation is formulated in terms of a master equation for the reduced density matrix. The procedure used is based on the asymptotic methods of nonlinear dynamics, which enables one to obtain an expression for the general term in the weak coupling expansion. For the special example of a charged oscillator interacting with the electromagnetic field, an explicit form of the master equation through third order in this expansion is obtained. This form differs from that generally obtained using the rotating wave approximation in that there is no electromagnetic (Lamb) shift and that an explicit expression is given for the decay rate. 1996 Academic Press, Inc.

We review recent theoretical work on an analytical approach to the charge dynamics of electron tunneling in single electron devices consisting of long arrays with equal stray capacitances and equal junction capacitances. Our approach to the problem has two basic steps. First, we find the exact solution for the potential profiles and the associated Gibbs free energy, based on a technique for diagonalizing a particular type of a tridiagonal matrix equation. Second, we study the change of the Gibbs free energy arising from single charge transfer. The method has been applied to one-dimensional long arrays, single electron traps, and single electron turnstiles, and the results are compared with that of the existing experiments. We point out the advantages of our method vis-à-vis other approaches used in the literature.

Based on the exact solution for the potential profile of the 2N turnstile with equal junction capacitances C, equal stray capacitances C0, and a coupling capacitance Cc, we obtain explicit expressions for the Gibbs free energy as well as the corresponding charging energy and the barrier height. In particular, we analyze the effects of the stray capacitances on the turnstile operation. In the C0=0 case, our results for the turnstile operation reduce to those of D. V. Averin, A. A. Odintsov, S. V. Vyshenskii [J. Appl. Phys. 73, 1297 (1993)]. In general, when C0/C is increased, the operable region of the turnstile decreases. Thus, in order to have a high quality turnstile, it is necessary to keep the stray capacitances small.

An exact solution for the potential profile of two coupled one-dimensional arrays each with m junctions with equal junction capacitances C, equal stray capacitances ${\mathit{C}}_{0}$, and equal coupling capacitances ${\mathit{C}}_{\mathit{c}}$ is presented. Analytical expressions for the total free energy as well as the injection threshold voltage ${\mathit{V}}_{\mathit{t}}$ of various charge solitons (an electron-hole pair, a single charge soliton, or a combined electron-hole pair and a single charge soliton) are derived. For m=3, we find that in the weak coupling regime (${\mathit{C}}_{\mathit{c}}$\ensuremath{\ll}C) single electron transport dominates, in contrast with existing results [D. V. Averin et al., Phys. Rev. Lett. 66, 2818 (1991)], and other differences are also found in the ${\mathit{C}}_{\mathit{c}}$\ensuremath{\gg}C limit. \textcopyright{} 1996 The American Physical Society.

We formulate, in the framework of the generalized quantum Langevin equation approach, the retarded Green's functions and the symmetrized position correlation functions for the motion of a charged quantum-mechanical particle in a spatial harmonic potential, coupled linearly to a passive heat bath, and subject to a constant homogeneous magnetic field. General conclusions can then be reached by using only those properties of the generalized susceptibility tensor imposed by fundamental physical principles. Explicit calculations are made for the Ohmic heat bath. We next investigate the Brownian motion of a charged particle in an external magnetic field. We continue by proving general relations between the retarded Green's functions and displacement correlation functions in the limit of long times at both absolute zero and nonzero temperatures, and further evaluate the long-time asymptotic behaviors of the two functions, for both the Ohmic and a rather general class of heat baths discussed extensively in the literature.

We present a simple calculation of the Lorentz transformation of the spectral distribution of blackbody radiation at temperature T. Here we emphasize that T is the temperature in the blackbody rest frame and does not change. We thus avoid the confused and confusing question of how temperature transforms. We show by explicit calculation that at zero temperature the spectral distribution is invariant. At finite temperature we find the well known result familiar in discussions of the the 2.7! K cosmic radiation., Comment: 6 pages

Quantum carpets—the spatio-temporal de Broglie density profiles—woven by an atom or an electron in the near-field region of a diffraction grating bring to light, in real time, the decoherence of each individual component of the interference term of the Wigner function characteristic of superposition states. The proposed experiments are feasible with present-day technology., publishedVersion

A heteroquantum‐dots (HQD) model for hydrogenated nanocrystalline silicon films (nc‐Si:H) is proposed. The main features of our model are as follows. (i) the nanocrystalline grains and the amorphous counterparts in which they are embedded have very different band gap and band structures. As a result, they form heterojunctionlike structures in the interface regions, where the band offset effects dramatically reduce the activation energy and the grains act like quantum dots. (ii) In the presence of an external field, the activated electrons in the quantum dots conduct via quantum tunneling through the interface barriers. By means of the HQD model, we have identified the conduction of nc‐Si:H as a thermal‐assisted tunneling process. Our results show that there are two distinct regimes for the conductivity of nc‐Si:H: (i) the low‐temperature regime, where there is a simple activation energy ΔE; (ii) the high‐temperature regime, where ΔE is effectively enhanced by the temperature effect of the electronic tunne...