6,739 research outputs found

### A String Approximation for Cooper Pair in High-T$_{\bf c}$ superconductivity

It is assumed that in some sense the High-T$_c$ superconductivity is similar
to the quantum chromodynamics (QCD). This means that the phonons in High-T$_c$
superconductor have the strong interaction between themselves like to gluons in
the QCD. At the experimental level this means that in High-T$_c$ superconductor
exists the nonlinear sound waves. It is possible that the existence of the
strong phonon-phonon interaction leads to the confinement of phonons into a
phonon tube (PT) stretched between two Cooper electrons like a hypothesized
flux tube between quark and antiquark in the QCD. The flux tube in the QCD
brings to a very strong interaction between quark-antiquark, the similar
situation can be in the High-T$_c$ superconductor: the presence of the PT can
essentially increase the binding energy for the Cooper pair. In the first rough
approximation the PT can be approximated as a nonrelativistic string with
Cooper electrons at the ends. The BCS theory with such potential term is
considered. It is shown that Green's function method in the superconductivity
theory is a realization of discussed Heisenberg idea proposed by him for the
quantization of nonlinear spinor field. A possible experimental testing for the
string approximation of the Cooper pair is offered.Comment: Essential changes: (a) the section is added in which it is shown that
Green's function method in the superconductivity theory is a realization of
discussed Heisenberg quantization method; (b) Veneziano amplitude is
discussed as an approximation for the 4-point Green's function in High-T_c;
(c) it is shown that Eq.(53) has more natural solution on the layer rather
than on 3 dimensional spac

### On the pre-metric foundations of wave mechanics I: massless waves

The mechanics of wave motion in a medium are founded in conservation laws for
the physical quantities that the waves carry, combined with the constitutive
laws of the medium, and define Lorentzian structures only in degenerate cases
of the dispersion laws that follow from the field equations. It is suggested
that the transition from wave motion to point motion is best factored into an
intermediate step of extended matter motion, which then makes the
dimension-codimension duality of waves and trajectories a natural consequence
of the bicharacteristic (geodesic) foliation associated with the dispersion
law. This process is illustrated in the conventional case of quadratic
dispersion, as well as quartic ones, which include the Heisenberg-Euler
dispersion law. It is suggested that the contributions to geodesic motion from
the non-quadratic nature of a dispersion law might represent another source of
quantum fluctuations about classical extremals, in addition to the diffraction
effects that are left out by the geometrical optics approximation.Comment: 25 pages, 1 figur

### The actual content of quantum theoretical kinematics and mechanics

First, exact definitions are supplied for the terms: position, velocity, energy, etc. (of the electron, for instance), such that they are valid also in quantum mechanics. Canonically conjugated variables are determined simultaneously only with a characteristic uncertainty. This uncertainty is the intrinsic reason for the occurrence of statistical relations in quantum mechanics. Mathematical formulation is made possible by the Dirac-Jordan theory. Beginning from the basic principles thus obtained, macroscopic processes are understood from the viewpoint of quantum mechanics. Several imaginary experiments are discussed to elucidate the theory

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