A String Approximation for Cooper Pair in High-Tc_{\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

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

Entanglement condition via su(2) and su(1,1) algebra using Schr{\"o}dinger-Robertson uncertainty relation

The Schr{\"o}dinger-Robertson inequality generally provides a stronger bound on the product of uncertainties for two noncommuting observables than the Heisenberg uncertainty relation, and as such, it can yield a stricter separability condition in conjunction with partial transposition. In this paper, using the Schr{\"o}dinger-Robertson uncertainty relation, the separability condition previously derived from the su(2) and the su(1,1) algebra is made stricter and refined to a form invariant with respect to local phase shifts. Furthermore, a linear optical scheme is proposed to test this invariant separability condition.Comment: published version, 3.5 pages, 1 figur

Two-dimensional anyons and the temperature dependence of commutator anomalies

The temperature dependence of commutator anomalies is discussed on the explicit example of particular (anyonic) field operators in two dimensions. The correlation functions obtained show that effects of the non-zero temperature might manifest themselves not only globally but also locally.Comment: 11 pages, LaTe

Introduction to Quantum Thermodynamics: History and Prospects

Quantum Thermodynamics is a continuous dialogue between two independent theories: Thermodynamics and Quantum Mechanics. Whenever the two theories addressed the same phenomena new insight has emerged. We follow the dialogue from equilibrium Quantum Thermodynamics and the notion of entropy and entropy inequalities which are the base of the II-law. Dynamical considerations lead to non-equilibrium thermodynamics of quantum Open Systems. The central part played by completely positive maps is discussed leading to the Gorini-Kossakowski-Lindblad-Sudarshan GKLS equation. We address the connection to thermodynamics through the system-bath weak-coupling-limit WCL leading to dynamical versions of the I-law. The dialogue has developed through the analysis of quantum engines and refrigerators. Reciprocating and continuous engines are discussed. The autonomous quantum absorption refrigerator is employed to illustrate the III-law. Finally, we describe some open questions and perspectives

Dynamical F(R)F(R) gravities

It is offered that $F(R)-$modified gravities can be considered as nonperturbative quantum effects arising from Einstein gravity. It is assumed that nonperturbative quantum effects gives rise to the fact that the connection becomes incompatible with the metric, the metric factors and the square of the connection in Einstein - Hilbert Lagrangian have nonperturbative additions. In the simplest approximation both additions can be considered as functions of one scalar field. The scalar field can be excluded from the Lagrangian obtaining $F(R)-$gravity. The essence of quantum correction to the affine connection as a torsion is discussed.Comment: discussion on quantum corrections is adde

Unitary equivalence between ordinary intelligent states and generalized intelligent states

Ordinary intelligent states (OIS) hold equality in the Heisenberg uncertainty relation involving two noncommuting observables {A, B}, whereas generalized intelligent states (GIS) do so in the more generalized uncertainty relation, the Schrodinger-Robertson inequality. In general, OISs form a subset of GISs. However, if there exists a unitary evolution U that transforms the operators {A, B} to a new pair of operators in a rotation form, it is shown that an arbitrary GIS can be generated by applying the rotation operator U to a certain OIS. In this sense, the set of OISs is unitarily equivalent to the set of GISs. It is the case, for example, with the su(2) and the su(1,1) algebra that have been extensively studied particularly in quantum optics. When these algebras are represented by two bosonic operators (nondegenerate case), or by a single bosonic operator (degenerate case), the rotation, or pseudo-rotation, operator U corresponds to phase shift, beam splitting, or parametric amplification, depending on two observables {A, B}.Comment: published version, 4 page

Formulation of the Spinor Field in the Presence of a Minimal Length Based on the Quesne-Tkachuk Algebra

In 2006 Quesne and Tkachuk (J. Phys. A: Math. Gen. {\bf 39}, 10909, 2006) introduced a (D+1)-dimensional $(\beta,\beta')$-two-parameter Lorentz-covariant deformed algebra which leads to a nonzero minimal length. In this work, the Lagrangian formulation of the spinor field in a (3+1)-dimensional space-time described by Quesne-Tkachuk Lorentz-covariant deformed algebra is studied in the case where $\beta'=2\beta$ up to first order over deformation parameter $\beta$. It is shown that the modified Dirac equation which contains higher order derivative of the wave function describes two massive particles with different masses. We show that physically acceptable mass states can only exist for $\beta<\frac{1}{8m^{2}c^{2}}$. Applying the condition $\beta<\frac{1}{8m^{2}c^{2}}$ to an electron, the upper bound for the isotropic minimal length becomes about $3 \times 10^{-13}m$. This value is near to the reduced Compton wavelength of the electron $(\lambda_c = \frac{\hbar}{m_{e}c} = 3.86\times 10^{-13} m)$ and is not incompatible with the results obtained for the minimal length in previous investigations.Comment: 11 pages, no figur

Cosmological constant and Euclidean space from nonperturbative quantum torsion

Heisenberg's nonperturbative quantization technique is applied to the nonpertrubative quantization of gravity. An infinite set of equations for all Green's functions is obtained. An approximation is considered where: (a) the metric remains as a classical field; (b) the affine connection can be decomposed into classical and quantum parts; (c) the classical part of the affine connection are the Christoffel symbols; (d) the quantum part is the torsion. Using a scalar and vector fields approximation it is shown that nonperturbative quantum effects gives rise to a cosmological constant and an Euclidean solution.Comment: title is changed. arXiv admin note: text overlap with arXiv:1201.106