On geometric interpretation of the Aharonov–Bohm effect

A geometric interpretation of the Aharonov–Bohm effect is given in terms of connections on principal fiber bundles. It is demonstrated that the principal fiber bundle can be trivial while the connection and its holonomy group are nontrivial. Therefore, the main role is played by geometric rather than topological effects.     

Parity effect of the initial capital based on Parrondo’s games and the quantum interpretation

In our previous study [Zhu et al., Quantum game interpretation for a special case of Parrondo’s paradox, Physica A 390 (2011) 579], the capital-dependent Parrondo’s game where one game depends on the capital modulus $M=4$ was shown not to have a definite stationary probability distribution and that payoffs of the game depended on the parity of the initial capital. This paper presents a generalization of these results to even $M$ greater than 4. An intuitive explanation for producing this phenomenon is that the discrete-time Markov chain of the game is divided into two completely unrelated inner and outer rings. The process taking the inner ring or outer ring of the game is determined by the initial capital of parity and then a win or loss of the game is determined. Quantum game theory is used to further analyze the phenomenon. The results show that the explanation of the game corresponding to a stationary probability distribution is that the probability of the initial capital has reached parity.     

On the effect of electric potential on resistance of metals’ surface to microindentation

The effect of electric potential on the microindentation resistance is investigated experimentally for aluminum and zirconium samples. The effects of the electric potential proper applied to a sample and of the potential arising due to contact potential difference between metals with different electron work functions are compared. A qualitative equivalence of these two types of electrical action is revealed. A possibility of a significant (over 10%) change in the metal microhardness due to the above nentioned actions is established.     

Harrison’s interpretation of the cosmological redshift revisited

Harrison’s argument against the interpretation of the cosmological redshift as a Doppler effect is revisited, exaggerated, and discussed. The context, purpose, and limitations of the interpretations of this phenomenon are clarified.     

On determination of the Grüneisen parameter from experimental data

It is shown that the localization criterion for the crystal-liquid phase transition introduced earlier for macrostructures is also valid for nanocrystals. The variation of the parameters of activation processes (formation of vacancies and self-diffusion) with a decrease in the nanocrystal size is investigated. It is shown that the lattice of a nanocrystal is more perfect than that of a macrocrystal at low temperatures, while at high temperatures, the nanocrystal is activated by mobile vacancies to a greater extent than the macrocrystal.     

New experimental tests of the photon’s indivisibility

We consider the old foundational problem of quantum/classical optics ?C indivisibility of photon. Quantum theory predicts that in experiments on coincidence detection double clicks are impossible (up to noise); on the other hand, the known semiclassical and classical models predict a relatively high rate of coincidence. We present a model of the classical (random) wave type which predicts that in the same way as in quantum optics coincidence of clicks is a rare event. However, this model has a new prediction compared to quantum optics, namely, that the rate of double clicks depends substantially on the discrimination threshold of a detector. We propose to perform new detailed tests to check the discrimination threshold dependence predicted by our model. In experiments on coincidence detection performed to date, for example, the Grangier experiment does not contain statistical data on the threshold dependence.     

On hydrodynamic interpretation of folding of an α-helical protein

Using the method of molecular dynamics, the simulation of folding of an α-helical protein from the unfolded to compact and functional (native) state is performed. The protein folding is interpreted as a stationary motion of a compressible “folding fluid”. It is shown that the densities of folding fluxes obey the same similarity relations as the velocities of an incompressible fluid in the Kolmogorov’s turbulence theory, except that instead of the rate of change of kinetic energy per mass unit, the rate of change of flux variance per volume unit plays the role of the key parameter.     

First experimental observation of the conical effect in Smith–Purcell radiation

The conical effect in Smith–Purcell radiation arising from electrons moving at non-zero angle to the direction of grating periodicity has been observed for the first time. It was found that the maximum of radiation intensity for ψ ≠ 0 shifts in both polar and azimuth angles. The experimental and theoretical results were compared, and the good agreement was shown. The experiment has been performed for 6 MeV electrons and at millimeter wavelengths.     

On estimating nanoparticle size with the help of the Mössbauer effect

A method for estimating nanoparticle size by determining the distribution function p(H _n ) of hyperfine magnetic fields from data on the Mössbauer spectrum of ⁵⁷Fe nuclei is described. The idea of the method stems from the fact that, owing to the breaking of exchange bonds for surface atoms, their contribution to the total area bounded by the p(H _n ) curve can be singled out. The potentialities of the method are illustrated using the data obtained in experiments with nanoparticles of magnetite.     

Comparison of different experimental methods for the assessment of the room’s acoustics

The paper presents the acoustics analysis of three different enclosed spaces. These spaces (rooms) have different geometrical shapes and sizes and serve for different purposes. The early decay time, reverberation time, clarity and center time are evaluated with Dirac, WinMLS, Aurora and Caracad software using simple, low-cost equipment. The listed acoustic parameters were determined using linear sine sweep and impulsive sources. Comparisons between experimental measurements, simulations and analytic results were done. The room impulse response measurement proved to be the most reliable method to evaluate the properties of different rooms even if the measurements are perturbed by non-idealities of the low-cost equipment.     

On the fictitious nonlinearity of the surface impedance of the Earth’s crust

The observations of Alfvén oscillations of the magnetosphere are used to study the Earth’s crust and upper mantle by the magnetotelluric sounding method. The sounding procedure involves the measurement of the horizontal components of the electromagnetic field at a given point on the ground, the calculation of the surface impedance, and the determination of the conductivity of rocks from these data. It has been shown that the anharmonicity of the oscillations of the magnetosphere in combination with the nonlocality of the boundary condition on the ground gives rise to the amplitude dependence of the impedance calculated using the classical magnetotelluric sounding method. This apparent nonlinearity of the impedance can be manifested in the sounding of the Earth’s interior with intense electromagnetic pulsations, which appear when the Earth’s magnetosphere is embedded in the highspeed solar wind flow.     

On the impossibility of using the longitude of the ascending node of GP-B for measuring the Lense–Thirring effect

The possibility of analyzing the node of the GP-B satellite in order to measure also the Lense–Thirring effect on its orbit is examined. This feature is induced by the general relativistic gravitomagnetic component of the Earth gravitational field. The GP-B mission has been launched in April 2004 and is aimed mainly to the measurement of the gravitomagnetic precession of four gyroscopes carried onboard at a claimed accuracy of 1%. of better. The aliasing effect of the solid Earth and ocean components of the solar K₁ tidal perturbations would make the measurement of the Lense–Thirring effect on the orbit unfeasible. Indeed, the science period of the GP-B mission amounts to almost one year. During this time span the Lense–Thirring shift on the GP-B node would be 164 milliarcseconds (mas), while the tidal perturbations on its node would have a period of the order of 10³ years and amplitudes of the order of 10⁵ mas.     

On the Geodesic Nature of Wegner’s Flow

Wegner’s method of flow equations offers a useful tool for diagonalizing a given Hamiltonian and is widely used in various branches of quantum physics. Here, generalizing this method, a condition is derived, under which the corresponding flow of a quantum state becomes geodesic in a submanifold of the projective Hilbert space, independently of specific initial conditions. This implies the geometric optimality of the present method as an algorithm of generating stationary states. The result is illustrated by analyzing some physical examples.     

On Zurek’s Derivation of the Born Rule

Recently, W. H. Zurek presented a novel derivation of the Born rule based on a mechanism termed environment-assisted invariance, or envariance [W. H. Zurek, Phys. Rev. Lett. 90(2), 120404 (2003)]. We review this approach and identify fundamental assumptions that have implicitly entered into it, emphasizing issues that any such derivation is likely to face.     

On the CHSH Form of Bell’s Inequalities

A common mistake present in the derivation of the usually known as the CHSH form of Bell’s inequalities is pointed out. References and comments to the correct approach are given. This error does not alter the final result and only affects the logical consistency of the derivation, but since it seems to be a widespread misconception regarding the roll and interpretation of the of use of hidden variables in Bell’s theorem it is considered to be of general interest.     

On the Road Map of Vogel’s Plane

We define “population” of Vogel’s plane as points for which universal character of adjoint representation is regular in the finite plane of its argument. It is shown that they are given exactly by all solutions of seven Diophantine equations of third order on three variables. We find all their solutions: classical series of simple Lie algebras (including an “odd symplectic” one), \({D_{2,1,\lambda}}\) superalgebra, the line of sl(2) algebras, and a number of isolated solutions, including exceptional simple Lie algebras. One of these Diophantine equations, namely \({knm=4k+4n+2m+12,}\) contains all simple Lie algebras, except so\({(2N+1).}\) Among isolated solutions are, besides exceptional simple Lie algebras, so called \({\mathfrak{e}_{7\frac{1}{2}}}\) algebra and also two other similar unidentified objects with positive dimensions. In addition, there are 47 isolated solutions in “unphysical semiplane” with negative dimensions. Isolated solutions mainly belong to the few lines in Vogel plane, including some rows of Freudenthal magic square. Universal dimension formulae have an integer values on all these solutions at least for first three symmetric powers of adjoint representation.     

Bosonic mode interpretation of novel scanning tunnelling microscopy and related experimental results,within boson–fermion modelling of cuprate high-temperature superconductivity

This paper seeks to synthesize much recent work on the cuprate high-temperature superconductors around the latest energy-resolved scanning tunnelling microscopy (STM) results from Davis and co-workers. The STM conductance diffuse scattering results in particular are employed as point of entry to discuss bosonic modes, of both condensed and uncondensed form. The bosonic mode picture is essential to understanding an ever-growing range of observations within the high-temperature superconductivity field (HTSC). The work is expounded within the context of the site-inhomogeneous negative-U boson–fermion modelling long advocated by the present author. This general approach is at present seeing much theoretical development, into which I have looked to couple many of the experimental advances. While this formal theory is not yet sufficiently detailed to cover adequately all the experimental complexities presented by the real cuprate systems, it is clear that it affords very appreciable support to the line taken. An attempt is made throughout to clarify why and how it is that these novel circumstances and phenomena are tied so very closely to this particular set of materials.     

Isotopic shift of the ground state of neon from the experimental results concerning the absorption of 0.63-μm laser radiation

Isotopic shifts of the 3s[3/2] ₁ ⁰ –2р ⁶(¹ S ₀) and 3s'–2р ⁶(¹ S ₀) transitions, equal, respectively, to 417 ± 20 and–98 ± 20 MHz, have been measured using the 0.63-μm radiation of a helium–neon laser and opto-magnetic resonances induced by the interference of the reactive components of fields in overlapping areas of the emissions of isotopic atoms. Combining these results with the absolute specific mass shift of the 3p[5/2]₂ level (–647 MHz), the isotopic mass shift of the ground state of neon equal to 3223 ± 30 MHz, and its specific mass shift equal to–9782 ± 30 MHz have been determined.