Relativistic kinematics is usually considered only as a manifestation of pseudo-Euclidean (Lorentzian) geometry of space-time. However, as it is explicitly stated in General Relativity, the geometry itself depends on dynamics, specifically, on the energy-momentum tensor. We discuss a few examples, which illustrate the dynamical aspect of the length-contraction effect within the framework of Special Relativity. We show some pitfalls associated with direct application of the length contraction formula in cases when an extended object is accelerated. Our analysis reveals intimate connections between length contraction and the dynamics of internal forces within the accelerated system. The developed approach is used to analyze the correlation between two congruent disks - one stationary and one rotating (the Ehrenfest paradox). Specifically, we consider the transition of a disk from the state of rest to a spinning state under the applied forces. It reveals the underlying physical mechanism in the corresponding transition from Euclidean geometry of stationary disk to Lobachevskys (hyperbolic) geometry of the spinning disk in the process of its rotational boost. A conclusion is made that the rest mass of a spinning disk or ring of a fixed radius must contain an additional term representing the potential energy of non-Euclidean circumferential deformation of its material. Possible experimentally observable manifestations of Lobachevskys geometry of rotating systems are discussed.
Experiments with acoustic waves guided along the mechanically free surface of an unconsolidated granular packed structure provide information on the elasticity of granular media at very low pressures that are naturally controlled by the gravitational acceleration and the depth beneath the surface. Comparison of the determined dispersion relations for guided surface acoustic modes with a theoretical model reveals the dependencies of the elastic moduli of the granular medium on pressure. The experiments confirm recent theoretical predictions that relaxation of the disordered granular packing through non-affine motion leads to a peculiar scaling of shear rigidity with pressure near the jamming transition corresponding to zero pressure. Unexpectedly, and in disagreement with the most of the available theories, the bulk modulus depends on pressure in a very similar way to the shear modulus.
Poisson bracket relations for generators of canonical transformations are derived directly from the Galilei and Poincare groups of changes of space-time coordinates. The method is simple but rigorous. The meaning of each step is clear because it corresponds to an operation in the group of changes of space-time coordinates. Only products and inverses are used; differences are not used. It is made explicitly clear why constants occur in some bracket relations but not in others, and how some constants can be removed, so that in the end there is a constant in the bracket relations for the Galilei group but not for the Poincare group. Each change of coordinates needs to be only to first order, so matrices are not needed for rotations or Lorentz transformations; simple three-vector descriptions are enough. Conversion to quantum mechanics is immediate. One result is a simpler derivation of the commutation relations for angular momentum directly from rotations. Problems are included.
We explore in the present work the near-field radiative heat transfer between two semi-infinite parallel nonlocal dielectric planes by means of fluctuational electrodynamics. We use atheory for the nonlocal dielectric permittivityfunction proposed byHalevi and Fuchs. This theory has the advantage to includedifferent models performed in the literature. According to this theory, the nonlocal dielectric function is described by a Lorenz-Drude like single oscillator model, in which the spatial dispersion effects are represented by an additional term depending on the square of the total wavevector k. The theory takes into account the scattering of the electromagneticexcitation at the surface of the dielectric material, which leads to the need of additional boundary conditions in order to solve Maxwells equations and treat the electromagnetic transmission problem. The additional boundary conditions appear as additional surface scattering parameters in the expressions of the surface impedances. It is shown that the nonlocal modeling deviates from the classical $1/d^2$ law in the nanometerrangeat distances still larger than the ones where quantum effects are expected to come into play.
We study in this work the near-field radiative heat transfer between two semi-infinite parallel planes of highly n-doped semiconductors. Using a nonlocal model of the dielectric permittivity, usually used for the case of metallic planes, we show that the radiative heat transfer coefficientsaturates as the separation distance is reduced for high doping concentration. These results replace the 1/d${}^2$ infinite divergence obtained in the local model case. Different features of the obtained results are shown to relate physically to the parameters of the materials, mainly the doping concentration and the plasmon frequency.
In this work, we have studied the peregrine rogue wave dynamics, with a solitons on finite background (SFB) ansatz, in the recently proposed (Phys. Rev. Lett. 110 (2013) 064105) continuous nonlinear Schrodinger system with parity-time symmetric Kerr nonlinearity. We have found that the continuous nonlinear Schrodinger system with PT-symmetric nonlinearity also admits Peregrine Soliton solution. Motivated by the fact that Peregrine solitons are regarded as prototypical solutions of rogue waves, we have studied Peregrine rogue wave dynamics in the c-PTNLSE model. Upon numerical computation, we observe the appearance of low-intense Kuznetsov-Ma (KM) soliton trains in the absence of transverse shift (unbroken PT-symmetry) and well-localized high-intense Peregrine Rogue waves in the presence of transverse shift (broken PT-symmetry) in a definite parametric regime.
By means of fluctuationnal electrodynamics, we calculate radiative heat flux between two pla-nar materials respectively made of SiC and SiO2. More specifically, we focus on a first (direct) situation where one of the two materials (for example SiC) is at ambient temperature whereas the second material is at a higher one, then we study a second (reverse) situation where the material temperatures are inverted. When the two fluxes corresponding to the two situations are different, the materials are said to exhibit a thermal rectification, a property with potential applications in thermal regulation. Rectification variations with temperature and separation distance are here reported. Calculations are performed using material optical data experimentally determined by Fourier transform emission spectrometry of heated materials between ambient temperature (around 300 K) and 1480 K. It is shown that rectification is much more important in the near-field domain, i.e. at separation distances smaller than the thermal wavelength. In addition, we see that the larger is the temperature difference, the larger is rectification. Large rectification is finally interpreted due to a weakening of the SiC surface polariton when temperature increases, a weakening which affects much less SiO2 resonances.
This paper brings further insight into the recently published N-body description of Debye shielding and Landau damping [Escande D F, Elskens Y and Doveil F 2014 Plasma Phys. Control. Fusion 57 025017]. Its fundamental equation for the electrostatic potential is derived in a simpler and more rigorous way. Various physical consequences of the new approach are discussed, and this approach is compared with the seminal one by Pines and Bohm [Pines D and Bohm D 1952 Phys. Rev. 85 338--353].
Retarded electromagnetic potentials are derived from Maxwells equations and the Lorenz condition. The difference found between these potentials and the conventional Li{e}nard-Wiechert ones is explained by neglect, for the latter, of the motion-dependence of the effective charge density. The corresponding retarded fields of a point-like charge in arbitary motion are compared with those given by the formulae of Heaviside, Feynman, Jefimenko and other authors. The fields of an accelerated charge given by the Feynman are the same as those derived from the Li{e}nard-Wiechert potentials but not those given by the Jefimenko formulae. A mathematical error concerning partial space and time derivatives in the derivation of the Jefimenko equations is pointed out.
The classical propagation of certain Lorentz-violating fermions is known to be governed by geodesics of a four-dimensional pseudo-Finsler $b$ space parametrized by a prescribed background covector field. This work identifies systems in classical physics that are governed by the three-dimensional version of Finsler $b$ space and constructs a geodesic for a sample non-constant choice for the background covector. The existence of these classical analogues demonstrates that Finsler $b$ spaces possess applications in conventional physics, which may yield insight into the propagation of SME fermions on curved manifolds.
