Universal tunneling time for all fields

Nimtz, G.; Stahlhofen, A. A.

doi:10.1002/andp.200810293

Cited by 25 publications

(25 citation statements)

References 23 publications

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“…Electrons which are tunneling do not need a material type of pathway or file, nor a conductive polymer chain for tunneling through even insulating or empty spaces. As Nimtz has shown later, moreover, electrons do not spend any time within the barrier but arrive at the other side at the same time as they begin tunneling [11].…”

Section: Open Accessmentioning

confidence: 81%

New Insight into Organic Metal Polyaniline Morphology and Structure

Weßling

2010

Polymers

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Abstract:Polyaniline is known to be a true metal, though a nanometal. Previous experimental and theoretical evidence is reviewed. Two important structural features are presented, which have not publicly been discussed so far: (a) The formation of complexes between polyaniline and metals (Cu, Fe, Zn, In, etc.) which are crucial for most practical applications of the organic metal, polyaniline; and (b) a model for the polyaniline chain structure within the smallest morphological unit, the roughly 10 nm primary particle.

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Section: Open Accessmentioning

confidence: 81%

New Insight into Organic Metal Polyaniline Morphology and Structure

Weßling

2010

Polymers

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“…Contrary to the amplitude (see the inset where the phase time saturates to a constant value for a sufficiently barrier's thickness. This phenomenon has been observed experimentally [108] and explained theoretically [109][110][111] in 1D photonic crystals. For a frequency lying in the allowed bands, the phase time (not shown here) increases linearly as a function of N.…”

Section: Transmission Enhancement Assisted By Surface Resonancementioning

confidence: 77%

One-Dimensional Phononic Crystals

Boudouti¹,

Djafari‐Rouhani²

2012

Springer Series in Solid-State Sciences

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In this chapter, we discuss the vibrational properties of one-dimensional (1D) phononic crystals of both discrete and continuous media. These properties include the dispersion curves of infinite crystals as well as the confined modes and localized (surface, cavity) modes of finite and semi-infinite crystals. A general rule about the existence of localized surface modes in finite and semi-infinite superlattices with free surfaces is presented. We also present the calculations of reflection and transmission coefficients, particularly in view of selective filtering through localized modes. Most of the results presented in this chapter deal with waves propagating along the axis of the superlattice. However, in the last part of the chapter, we also discuss wave propagation out of the normal incidence and, more particularly, we demonstrate the possibility of omnidirectional transmission gap and selective filtering for any incidence angle. A comparison of the theoretical results with experimental data available in the literature is also presented and the reliability of the theoretical predictions is indicated. IntroductionThe one-dimensional (1D) phononic crystals called superlattices (SLs) are of great importance in material science. These structures are, in general, composed of two or several layers repeated periodically along the direction of growth. The layers constituting each cell of the SL can be made of a combination of solid-solid or solid-fluid-layered media. These materials enter now in the category of so-called phononic crystals (see the first chapter of this book and references therein) [1][2][3] constituted by inclusions (spheres, cylinders, etc.) arranged in a host matrix along two-dimensional (2D) and three-dimensional (3D) of the space. After the proposal of SLs by Esaki [4], the study of elementary excitations in multilayered systems has been very active. Among these excitations, acoustic phonons have received increased attention after the first observation by Colvard et al.[5] of a doublet associated to folded longitudinal acoustic phonons by means of Raman scattering. The essential property of these structures is the existence of forbidden frequency bands induced by the difference in acoustic properties of the constituents and the periodicity of these systems leading to unusual physical phenomena in these heterostructures in comparison with bulk materials [6][7][8].With regard to acoustic waves in solid-solid SLs, a number of theoretical and experimental works have been devoted to the study of the band gap structures of periodic SLs [6-10] composed of crystalline, amorphous semi-conductors, or metallic multilayers at the nanometric scale. The theoretical models used are essentially the transfer matrix [7,[11][12][13] and the Green's function methods [6,[14][15][16], whereas the experimental techniques include Raman scattering [5,17,18], ultrasonics [19][20][21][22][23][24][25][26][27][28][29], and time-resolved X-ray diffraction [30]. Besides the existence of the band-gap structures in perfe...

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“…Recent experimental data on phonon and electron tunneling have pointed to a similar barrier traversal time relation ship 21,22 .…”

Section: Tunneling Barriermentioning

confidence: 86%

On Virtual Phonons, Photons, and Electrons

Nimtz

2009

Found Phys

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A macroscopic realization of the strange virtual particles is presented. The classical Helmholtz and the quantum mechanical Schrödinger equations are analogous differential equations. Their imaginary solutions are called evanescent modes in the case of elastic and electromagnetic fields. In the case of non-relativistic quantum mechanical fields they are called tunneling solutions. The imaginary solutions of this differential equation point to strange consequences: They are non local, they are not observable, and they described as virtual particles. During the last two decades QED calculations of the imaginary solutions have been experimentally confirmed for phonons, photons, and for electrons. The experimental proofs of the predictions of the non-relativistic quantum mechanics and of the Wigner phase time approach for the elastic, the electromagnetic and the Schrödinger fields will be presented in this article. The results are zero tunneling time and an interaction time (i.e. a phase shift) at the barrier interfaces. The measured barrier interaction time (i.e. the barrier transmission time) scales approximately inversely with the particle energy.

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Universal tunneling time for all fields

Cited by 25 publications

References 23 publications

New Insight into Organic Metal Polyaniline Morphology and Structure

New Insight into Organic Metal Polyaniline Morphology and Structure

One-Dimensional Phononic Crystals

On Virtual Phonons, Photons, and Electrons

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