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Gennady N. Nikolaev

Publications and source records attributed to Gennady N. Nikolaev.

4 recordsLinked to original sources
arXiv2017

Paradox of Photons Disconnected Trajectories Being Located by Means of "Weak Measurements" in the Nested Mach-Zehnder Interferometer

Recently, a scheme based on the method of weak measurements to register the trajectories of photons passing through a nested Mach-Zehnder interferometer was proposed [L. Vaidman, Phys. Rev. A \textbf{87}, 052104 (2013)] and then realized [A. Danan, D. Farfurnik, S. Bar-Ad, et al., Phys. Rev. Lett. \textbf{111}, 240402 (2013)]. Interpreting the results of the experiment, the authors concluded that "the photons do not always follow continuous trajectories". It is shown in this work that these results can be easily and clearly explained in terms of traditional classical electrodynamics or quantum mechanics implying the continuity of all possible paths of photons. Consequently, a new concept of disconnected trajectories proposed by the authors of work [Phys. Rev. Lett. \textbf{111}, 240402 (2013)] is unnecessary.

quant-ph↗
arXiv2017

Response to the Comment on "Paradox of Photons Disconnected Trajectories Being Located by Means of "Weak Measurements" in the Nested Mach-Zehnder Interferometer" (JETP Letters 105, 152 (2017))

In [JETP Lett. 105(3), 152 (2017)], a clear and comprehensive analysis of the paradoxical results of experiment [Phys. Rev. Lett. 111, 240402 (2013)] was carried out on the basis of the classical wave theory of light, which presupposes the continuity of possible of light paths. It was shown that the paradoxical results of the experiment are due not to the discontinuity of the trajectories of light, as claimed in [Phys. Rev. Lett. 111, 240402 (2013)], but to the used way of detecting the path of photons. The experiment modification proposed in [JETP Lett. 105(3), 152 (2017)] allows us to eliminate the seeming discontinuity of the light trajectories. In Comment [arXiv:1705.02137 (2017)] to the article such modification is declared unreasonable. This Response to the Comment shows that this statement is not based on clear and logical arguments. Instead, it is only asserted that the proposed modification "violates the faithfulness indication of the trace" of photons. Therefore, the Comment's criticism can not be considered as well-founded. Consequently, the conclusion of [JETP Lett. 105(3), 152 (2017)] that a new concept of disconnected trajectories proposed by the authors of work [Phys. Rev. Lett. 111, 240402 (2013)] is unnecessary, remains valid.

quant-ph↗
arXiv2004

Renormgroup Invariants and Approximations of Mappings

The relationship between mappings of sets and renormalization group transformations is established, and renormalization group invariants of such mappings are found. These results are valid both for continuous and discrete mappings and for various dimensionality of image and preimage of the mappings too. It is suggested a number of mapping approximations improved in comparison with an ordinary power expansion. The approximations take into account the global one-to-one character of the mappings. The method is illustrated by a number of examples: by reconstructing of some analytical functions, calculating the integral of the typical partition function of statistical mechanics and the ground state energy for the quartic anharmonic oscillator. In the whole range of nonlinearity parameter varying from zero up to infinity the accuracy of the RG approximation based on a few terms of divergent series is about 0.06% in the next to last case and 0.004% in the last one.

math-ph↗