Converse spectral problem in the relativistic quasiclassical approximation

The problem of quasipotential reconstruction from a given two-particle composite system energy spectrum is solved in the relativistic quasiclassical approximation. The nonrelativistic and ultrarelativistic asymptotes of the expressions obtained are studied.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 63–68, April, 1984.The authors thank Yu. S. Vernov, V. G. Kadyshevskii, and N. B. Skachkov for their interest in the study and valuable discussion of the results obtained.     

Converse KAM: Theory and practice

We unify, extend, reinterpret and apply criteria of Birkhoff [1], Herman [9], Mather [2, 3], Aubry et al. [4, 5], and Newman and Percival [6] for the nonexistence of invariant circles for area preserving twist maps. The criteria enable one to establish regions of phase space through which no rotational invariant circles pass. For families of maps the same can be done for regions of the combined space of phase points and parameters. The criteria can be implemented rigorously on a computer, and give a practical method of proving quite strong results. As an example, we present a computer program which proved that the standard map has no rotational invariant circles for any parameter value |k|63/64.     

Converse flexoelectric effect in the SrTiO3 single crystal

The converse flexoelectric effect in the SrTiO₃ single crystal as a response of inhomogeneous strain (bending strain) to an applied electric field has been studied. The temperature dependence of the effect in the temperature range of 77–450 K has been obtained.     

Converse flexoelectric effect in comb electrode piezoelectric microbeam

We demonstrate the converse flexoelectric effect in a lead zirconate titanate microbeam. The fringe electric field of a comb electrode induces converse flexoelectric responses in uniformly poled and depoled beams. The simulated electric field distribution shows that bending of the beam is induced by piezoelectric and _μ11${\mu }_{11}$, _μ12${\mu }_{12}$ flexoelectric coefficients. Simulations indicate that piezoelectric displacement occurs in different directions in the two opposite poled samples while flexoelectric displacement remains the same. This finding is verified by the displacement measurement results.     

Brillouin's theorem and the Hellmann-Feynman theorem for Hartree-Fock wave functions

It is shown that there is an intimate relation between the Hellmann-Feynman theorem and Brillouin's theorem. A more general form of Brillouin's theorem is provided, which applies to excited states of arbitrary symmetry and multiplicity. This new form leads to a simple proof of the Hellmann-Feynman theorem. This theorem is valid when all the orbitals that occur in the wave function are determined by a complete, and not a partial, variational procedure. Arguing in the opposite direction it is shown that the complete satisfaction of the generalized Brillouin's theorem provides an alternative scheme for obtaining the Hartree-Fock orbitals.     

Geometry of the Saxon-Hutner theorem

Making use of the fact that any real localized potential of both the Dirac and Schrödinger equations on the line can be viewed either as a vector in the three-dimensional vector space or as a point on the single-sheeted hyperboloid we are able to derive a fairly general condition which ensures the validity of the Saxon-Hutner theorem that is spelled out in purely geometrical terms.     

Extension of the fluctuation theorem

Heat fluctuations are studied in a dissipative system with both deterministic and stochastic components for a simple model: a Brownian particle dragged through water by a moving potential. An extension of the stationary state fluctuation theorem is derived. For infinite time, this reduces to the conventional fluctuation theorem only for small fluctuations; for large fluctuations, it gives a much larger ratio of the probabilities of the particle to absorb rather than supply heat. This persists for finite times and should be observable in experiments similar to a recent one carried out by Wang et al.     

Generalization of the Hellmann-Feynman theorem

The well-known Hellmann-Feynman theorem of quantum mechanics connected with the derivative of the eigenvalues with respect to a parameter upon which the Hamiltonian depends, is generalized to include cases in which the domain of definition of the Hamiltonian of the system also depends on that parameter.     

Evading the Goldstone theorem

Peter W. Higgs describes in detail his interest from 1960 in the work of Nambu and Goldstone and the background events leading to the papers of 1964 that showed how one can evade the Goldstone theorem using a gauge theory. He also discusses how these ideas have been developed by others to culminate in the electroweak theory of the Standard Model. 1     

New forms of the Pomeranchuk theorem

A new mathematical technique is developed and used to obtain a series of new forms of the Pomeranchuk theorem. Particular ones of these forms are expedient for use in high-energy physics, depending on the experimental situation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 26–32, July, 1984.It remains to thank Prof. Yu. M. Lomsadze for valuable comments.     

A test of the optical theorem

Forward differential cross sections for π^?p elastic scattering at 1.0, 1.5 and 2.0 GeV/c show that the square of the imaginary parts of the nuclear scattering agrees with the optical theorem prediction within ±3%, when averaged over the three momenta.     

Heisenberg proof of the Balian-Low theorem

We give an alternate proof of the fact that a function generating a basis of coherent states must have an infinitely long tail in either position space or momentum space. Our argument is a very natural one in which the Heisenberg Uncertainty Principle enters directly.Supported in part by the National Science Foundation under Grant No. DMS 8603795.     

Experimental test of the no-signaling theorem

In 1981 N. Herbert proposed a gedanken experiment in order to achieve by the "First Laser-Amplified Superluminal Hookup" (FLASH) a faster-than-light (FTL) communication by quantum nonlocality. The present work reports the first experimental realization of that proposal by the optical parametric amplification of a single photon belonging to an entangled EPR pair into an output field involving N=5 x 10{3} photons. A theoretical and experimental analysis explains in general and conclusive terms the precise reasons for the failure of the FLASH program as well as of any similar FTL proposals.     

On the discovery of Birkhoff's theorem

Birkhoff showed in 1923 that the Schwarzschild solution for the metric from a point particle was also valid in the a priori non-static case as long as the spherical symmetry was maintained. This theorem was actually discovered and published two years earlier by an unknown Norwegian physicist, J.T. Jebsen. His life and scientific career is briefly chronicled.     

A proof of the Nielsen-Ninomiya theorem

The Nielsen-Ninomiya theorem asserts the impossibility of constructing lattice models of non-selfinteracting chiral fermions. A new proof is given here. This proof fills a technical gap in the two proofs presented by the authors of the theorem. It also serves as prelude to an investigation of the chiral properties of the general lattice model.     

On the van Cittert-Zernike theorem

The van Cittert-Zernike theorem states that the spatial coherence over a space illuminated by an incoherent extended source is described by the Fourier transform of the intensity distribution over the source. The theorem is usually used in a restricted case of the spatial coherence in a plane parallel to the source plane and illuminated by an incoherent extended source of uniform intensity distribution. In this paper we re-examine the van Cittert-Zernike theorem by reviewing it in an original formulation and extend the theorem to the spatial coherence at any two points of a light field illuminated by an incoherent extended source having a non-uniform intensity distribution.     

Hydrodynamics and the fluctuation theorem

The fluctuation theorem is a pivotal result of statistical physics. It quantifies the probability of observing fluctuations which are in violation of the second law of thermodynamics. More specifically, it quantifies the ratio of the probabilities of observing entropy-producing and entropy-consuming fluctuations measured over a finite volume and time span in terms of the rate of entropy production in the system, the measurement volume, and time. We study the fluctuation theorem in computer simulations of planar shear flow. The simulations are performed by employing the method of multiparticle collision dynamics, which captures both thermal fluctuations and hydrodynamic interactions. The main outcome of our analysis is that the fluctuation theorem is verified at any averaging time provided that the measurement volume exhibits a specific dependence on a hydrodynamic time scale.