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 Physics , 2014, DOI: 10.1016/j.ultramic.2014.04.007 Abstract: Coherent electrons such as those in electron microscopes, exhibit wave phenomena and may be described by the paraxial wave equation. In analogy to light-waves, governed by the same equation, these electrons share many of the fundamental traits and dynamics of photons. Today, spatial manipulation of electron beams is achieved mainly using electrostatic and magnetic fields. Other demonstrations include simple phase-plates and holographic masks based on binary diffraction gratings. Altering the spatial profile of the beam may be proven useful in many fields incorporating phase microscopy, electron holography, and electron-matter interactions. These methods, however, are fundamentally limited due to energy distribution to undesired diffraction orders as well as by their binary construction. Here we present a new method in electron-optics for arbitrarily shaping of electron beams, by precisely controlling an engineered pattern of thicknesses on a thin-membrane, thereby molding the spatial phase of the electron wavefront. Aided by the past decade's monumental leap in nano-fabrication technology and armed with light-optic's vast experience and knowledge, one may now spatially manipulate an electron beam's phase in much the same way light waves are shaped simply by passing them through glass elements such as refractive and diffractive lenses. We show examples of binary and continuous phase-plates and demonstrate the ability to generate arbitrary shapes of the electron wave function using a holographic phase-mask. This opens exciting new possibilities for microscopic studies of materials using shaped electron beams and enables electron beam lithography without the need to move the electron beam or the sample, as well as high resolution inspection of electronic chips by structured electron illumination.
 Physics , 2003, DOI: 10.1103/PhysRevB.71.125313 Abstract: We determine the non-local in time and space current-current cross correlator $<\hat{I}(x_1,t_1) \hat{I}(x_2,t_2)>$ in a mesoscopic conductor with a scattering center at the origin. Its excess part appearing at finite voltage exhibits a unique dependence on the retarded variable $t_1-t_2-(|x_1|-|x_2|)/ v_{\rm\scriptscriptstyle F}$, with $v_{\rm\scriptscriptstyle F}$ the Fermi velocity. The non-monotonic dependence of the retardation on $x_1$ and its absence at the symmetric position $x_1 = -x_2$ is a signature of the wave function collapse, which thus becomes amenable to observation in a mesoscopic solid state device.
 Physics , 2006, DOI: 10.1088/1367-2630/7/1/239 Abstract: It is demonstrated that non-equilibrium vibrational effects are enhanced in molecular devices for which the effective potential for vibrations is sensitive to the charge state of the device. We calculate the electron tunneling current through a molecule accounting for the two simplest qualitative effects of the charging on the nuclear potential for vibrational motion: a shift (change in the equilibrium position) and a distortion (change in the vibrational frequency). The distortion has two important effects: firstly, it breaks the symmetry between the excitation spectra of the two charge states. This gives rise to new transport effects which map out changes in the current-induced non-equilibrium vibrational distribution with increasing bias voltage. Secondly, the distortion modifies the Franck-Condon factors for electron tunneling. Together with the spectral asymmetry this gives rise to pronounced nuclear wave function interference effects on the electron transport. For instance nuclear-parity forbidden transitions lead to differential conductance anti-resonances, which are stronger than those due to allowed transitions. For special distortion and shift combinations a coherent suppression of transport beyond a bias voltage threshold is possible.
 Physics , 2012, DOI: 10.1103/PhysRevLett.108.186806 Abstract: Electron transport in mesoscopic conductors has traditionally involved investigations of the mean current and the fluctuations of the current. A complementary view on charge transport is provided by the distribution of waiting times between charge carriers, but a proper theoretical framework for coherent electronic systems has so far been lacking. Here we develop a quantum theory of electron waiting times in mesoscopic conductors expressed by a compact determinant formula. We illustrate our methodology by calculating the waiting time distribution for a quantum point contact and find a cross-over from Wigner-Dyson statistics at full transmission to Poisson statistics close to pinch-off. Even when the low-frequency transport is noiseless, the electrons are not equally spaced in time due to their inherent wave nature. We discuss the implications for renewal theory in mesoscopic systems and point out several analogies with energy level statistics and random matrix theory.
 Gerd Bergmann ISRN Condensed Matter Physics , 2012, DOI: 10.5402/2012/391813 Abstract: The multielectron wave function of an interacting electron system depends on the size of the system, that is, the number of electrons. Here the question investigated is how the wave function changes for a symmetric Friedel-Anderson impurity when the volume is doubled. It turns out that for sufficiently large volume (when the level spacing is smaller than the resonance width) the change in the wave function can be expressed in terms of a universal single-electron state centered at the Fermi level. This electron state is independent of the number of electrons and independent of the parameters of the Friedel-Anderson impurity. It is even the same universal state for a Kondo impurity and a symmetric Friedel impurity independent of any parameter. The only requirement is that the impurity has a resonance exactly at the Fermi level and that the level spacing is smaller than the resonance width. This result clarifies recent fidelity calculations. 1. Introduction In the late 1960s Anderson [1] showed that the potential of a weak impurity in a metal host changes the total -electron wave function of the conduction electrons dramatically. Actually with increasing number of electron states (which is achieved by increasing the volume) the scalar product between the wave functions of the -electron host without and with the impurity approaches zero. This phenomenon is generally called the Anderson orthogonality catastrophe (AOC). In recent years this phenomenon has been somewhat generalized and decorated with the romantic name fidelity. The generalization is that one applies the AOC to an arbitrary system, which depends on one or several parameters . If the system consists of electrons then it is described by its Hamiltonian. The Hamiltonian may contain a term, which is proportional to a parameter . Suppose that one can calculate the ground state of the system for and for finite . Then the scalar product of the two wave functions is defined as the fidelity of the system. Here is the number of conduction electrons states, which is proportional to the volume. The fidelity depends on the size of the system and of particular interest is the limit for increasing towards infinity. If approaches zero in this limit (the thermodynamic limit), then one faces an AOC. Our group studied recently the fidelity of the Friedel-Anderson impurity. This is an electron system with a -atom as impurity. The energy of the -electron lies at below the Fermi level. If one removes a -electron, that is, creates a -hole, then the conduction electrons can hop into the empty -state with a hopping
 B. Barbiellini Physics , 2000, Abstract: Summary for the review talk on recent progress in the theoretical studies of electron momentum density distribution at the Sagamore XIII conference (Stare Jablonki, Poland; September 3-9, 2000).
 Physics , 2002, DOI: 10.1088/0953-4075/35/19/312 Abstract: A variation of the valence electron wave function inside a nucleus induced by a perturbative potential is expressed in terms of the potential momenta. As an application we consider QED vacuum polarization corrections due to the Uehling and Wichmann-Kroll potentials to the weak interaction matrix elements.
 Douglas M. Snyder Physics , 1995, Abstract: Generally a central role has been assigned to an unavoidable physical interaction between the measuring instrument and the physical entity measured in the change in the wave function that often occurs in measurement in quantum mechanics. A survey of textbooks on quantum mechanics by authors such as Dicke and Witke (1960), Eisberg and Resnick (1985), Gasiorowicz (1974), Goswami (1992), and Liboff (1993) supports this point. Furthermore, in line with the view of Bohr and Feynman, generally the unavoidable interaction between a measuring instrument and the physical entity measured is considered responsible for the uncertainty principle. A gedankenexperiment using Feynman's double-hole interference scenario shows that physical interaction is not necessary to effect the change in the wave function that occurs in measurement in quantum mechanics. Instead, the general case is that knowledge is linked to the change in the wave function, not a physical interaction between the physical existent measured and the measuring instrument. Empirical work on electron shelving that involves null measurements, or what Renninger called negative observations (Zeitschrift fur Physik, vol. 158, p. 417), supports these points. Work on electron shelving is reported by Dehmelt and his colleagues (Physical Review Letters, vol. 56, p. 2797), Wineland and his colleagues (Physical Review Letters, vol. 57, p. 1699), and Sauter, Neuhauser, Blatt, and Toschek (Physical Review Letters, vol. 57, p. 1696).
 Physics , 2010, DOI: 10.1143/JPSJ.80.044710 Abstract: By using analytical solution of a tight-binding model for armchair nanoribbons, it is confirmed that the solution represents the standing wave formed by intervalley scattering and that pseudospin is invariant under the scattering. The phase space of armchair nanoribbon which includes a single Dirac singularity is specified. By examining the effects of boundary perturbations on the wave function, we suggest that the existance of a strong boundary potential is inconsistent with the observation in a recent scanning tunneling microscopy. Some of the possible electron-density superstructure patterns near a step armchair edge located on top of graphite are presented. It is demonstrated that a selection rule for the G band in Raman spectroscopy can be most easily reproduced with the analytical solution.
 Physics , 2015, DOI: 10.1088/1367-2630/17/11/113048 Abstract: A technique is developed which allows for the detailed mapping of the electronic wave function in two-dimensional electron gases with low-temperature mobilities up to 15E6 cm^2/Vs. Thin ("delta") layers of aluminium are placed into the regions where the electrons reside. This causes electron scattering which depends very locally on the amplitude of the electron wave function at the position of the Al "delta"-layer. By changing the distance of this layer from the interface we map the shape of the wave function perpendicular to the interface. Despite having a profound effect on the electron mobiliy, the "delta"-layers do not cause a widening of the quantum Hall plateaus.
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