Unified time analysis of photon and particle tunnelling

Olkhovsky, V. S.; Recami, Erasmo; Jakiel, J.

doi:10.1016/j.physrep.2004.06.001

Cited by 174 publications

(319 citation statements)

References 158 publications

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“…1, which increase in the tunneling region and have been obtained at different values of the energy of radiation E rad . From these figures one can see that the wave function satisfies the rules satisfied by the wave function inside the sub-barrier and in above-barrier regions (Olkhovsky & Recami, 1992;Olkhovsky et al, 2004;Zakhariev et al, 1990). Starting from very small a, the wave function has oscillations and its maxima increase monotonously with increasing of a.…”

Section: Wave Function Of Universe: Calculations and Analysismentioning

confidence: 71%

A Fully Quantum Model of Big Bang

Maydanyuk¹,

Popolo²,

Olkhovsky³

et al. 2012

Theoretical Concepts of Quantum Mechanics

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16www.intechopen.com 2 Will-be-set-by-IN-TECH (Vilenkin, 1994) could seem to be the most natural and clear description, where the wave function should represent an outgoing wave only in the enough large value of the scale factor a. However, is really such a wave free in the asymptotic region? In order to draw attention on the increase of the modulus of the potential with increasing value of the scale factor a and increasing magnitude of the gradient of such a potential, acting on this wave "through the barrier", then one come to a serious contradiction: the influence of the potential on this wave increases strongly with a! Now a new question has appeared: what should the wave represent in general in the cosmological problem? This problem connects with another and more general one in quantum physics -the real importance to define a "free" wave inside strong fields.T o this aim we need a mathematical stable tool to study it. It is unclear whether a connection between exact solutions for the wave function at turning point and "free" wave defined in the asymptotic region is correct. Note that the semiclassical formula of the penetrability of the barrier is constructed on the basis of wave which is defined concerning zero potential at infinity, i.e. this wave should be free outgoing in the asymptotic region. But in the cosmological problem we have opposite case, when the force acting on the wave increases up to infinity in the asymptotic region. At the same time, deformations of the shape of the potential outside the barrier cannot change the penetrability calculated in the framework of the semiclassical approach (up to the second order). An answer to such problem can be found in non-locality of definition of the penetrability in quantum mechanics, which is reduced to minimum in the semiclassical approach (i. e. this is so called "error" of the cosmological semiclassical approach). The problem of the correct definition of the wave in cosmology is reinforced else more, if one wants to calculate the incident and reflected waves in the internal region. Even with the known exact solution for the wave function there is uncertainty in determination of these waves! But, namely, the standard definition of the coefficients of penetrability and reflection is based on them. In particular, we have not found papers where the coefficient of reflection is defined and estimated in this problem (which differs essentially from unity at the energy of radiation close to the height of the barrier and, therefore, such a characteristics could be interesting from a physical point of view). Note that the semiclassical approximation put serious limits to the possibility of its definition at all (Landau & Lifshitz, 1989). Thus, in order to estimate probability of the formation of the Universe as accurately as possible, we need a fully quantum definition of the wave. Note that the non-semiclassical penetrability of the barrier in the cosmological problems has not been studied in detail and, therefore, a development of fully quantum methods for ...

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Section: Wave Function Of Universe: Calculations and Analysismentioning

confidence: 71%

A Fully Quantum Model of Big Bang

Maydanyuk¹,

Popolo²,

Olkhovsky³

et al. 2012

Theoretical Concepts of Quantum Mechanics

View full text Add to dashboard Cite

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“…One can suppose that it can be connected with some less visible physical effects or peculiarities of the proton-nucleus scattering process. Here, we can recall the hypothesis presented by Eremin, Olkhovsky and Giardina (see some related papers [76][77][78][79][80][81][82][83]) many years before about the possible connection of such oscillations in the bremsstrahlung spectra and tunneling time through the barrier. Adding our research in the α decay problem, we can now conclude that such a phenomenon is general enough for the nuclear reactions.…”

Section: Discussionmentioning

confidence: 84%

New approach to determine proton-nucleus interactions from experimental bremsstrahlung data

Maydanyuk

Zhang

2015

Phys. Rev. C

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A new approach is presented to determine the proton-nucleus interactions from the analysis of the accompanying photon bremsstrahlung. We study the scattering of p + 208 Pb at the proton incident energies of 140 and 145 MeV, and the scattering of p + 12 C, p + 58 Ni, p + 107 Ag and p + 197 Au at the proton incident energy of 190 MeV. The model determines contributions of the coherent emission (formed by an interaction between the scattering proton and nucleus as a whole without the internal many-nucleon structure), incoherent emission (formed by interactions between the scattering proton and nucleus with the internal many-nucleon structure), and transition between them in dependence on the photon energy. The radius-parameter of the proton-nucleus potential for these reactions is extracted from the experimental bremsstrahlung data analysis. We explain the hump-shaped plateau in the intermediate-and high-energy regions of the spectra by the essential presence of the incoherent emission, while at low energies the coherent emission predominates which produces the logarithmic shape spectrum. We provide our predictions (in absolute scale) for the angular distribution of the bremsstrahlung photons in order to test our model, results and analysis in further experiments.

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“…For a different shape of potentials, see for example the barrier, the stationary phase method, depending on the width of the potential and on the group velocity of the incoming particle, could break down. There is a rich number of articles leading with this problem in standard quantum mechanics [36][37][38][39][40][41][42].…”

Section: Introductionmentioning

confidence: 99%

“…In fact, in this limit new effects have to be considered and these effects cannot be obtained by simply using the stationary phase method [37,39,40].…”

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confidence: 99%

Quaternionic diffusion by a potential step

Ducati

2006

Journal of Mathematical Physics

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Abstract. In looking for qualitative differences between quaternionic and complex formulations of quantum physical theories, we provide a detailed discussion of the behavior of a wave packet in presence of a quaternionic time-independent potential step. In this paper, we restrict our attention to diffusion phenomena. For the group velocity of the wave packet moving in the potential region and for the reflection and transmission times, the study shows a striking difference between the complex and quaternionic formulations which could be matter of further theoretical discussions and could represent the starting point for a possible experimental investigation.

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Unified time analysis of photon and particle tunnelling

Cited by 174 publications

References 158 publications

A Fully Quantum Model of Big Bang

A Fully Quantum Model of Big Bang

New approach to determine proton-nucleus interactions from experimental bremsstrahlung data

Quaternionic diffusion by a potential step

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