Comment on “quantum formalism via signal analysis”

A recent attempt to derive the formalism of quantum mechanics from the properties of signals is criticized. One of the central conclusions reached by that attempt, namely that the Born statistical algorithm can be derived and is therefore not a postulate, is rejected.     

Response to “comment on ‘quantum formalism via signal analysis’”

A corrected demonstration of the statistical condition relating amplitudes and probabilities is presented.     

Quantum Hamiltonian formalism with constraints

A quantum system with constraints that does not necessarily correspond to a classical system with constraints is described in the Hamiltonian formalism.     

Quantum noise analysis of an amplifying TCRR using a continuous-modes formalism

A quantum-mechanical model of the amplifying two-coupler ring resonator based on the continuous-modes theory of quantum optics is used to show certain noise resonances of the output fields.     

Quantum mechanics in the K-field formalism: Field equation

The paper considers a field equation for representing a microparticle as an extended object constructed from that field (K field). It is shown that in contrast to the equation of an S field (i.e., Schrödinger equation), the boundary-value problem for the K-field equation cannot be used for a unique determination of the parameters of a microparticle in steady states. An auxiliary equation, therefore, is necessary to ensure that the solution of the K -field equation is unique. This is in complete agreement with the physical meaning of K field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 30–33, August, 1995.     

Quantum mechanics in theK-field formalism: The quantization problem

A system of two equations is examined in this work: theK-field equation (geometric analogue of the Schrödinger equation) and an additional equation that provides uniqueness of the solution of theK-field equation (theK-motion equation). It is shown that this system allows one to take Lyapunov stability of the solutions of theK-motion equations as the quantization criterion.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 38–41, January, 1996.     

Quantum theory: A Hilbert space formalism for probability theory

It is shown that the Hilbert space formalism of quantum mechanics can be derived as a corrected form of probability theory. These constructions yield the Schrödinger equation for a particle in an electromagnetic field and exhibit a relationship of this equation to Markov processes. The operator formalism for expectation values is shown to be related to anL ² representation of marginal distributions and a relationship of the commutation rules for canonically conjugate observables to a topological relationship of two manifolds is indicated.     

Quantum mechanics in theK-field formalism: Kepler's problem for spin particles

Using the well-known Kepler's problem, an attempt is made to demonstrate a procedure for constructing a nonrelativistic approximation of a quantum-mechanical model for steady states of hydrogen atoms in the K-field formalism. In this model, an electron is assumed to possess an intrinsic moment (spin) which, according to Frenkel, is comparable to the magnetic moment. It is shown that Lyapunov-stable trajectories of the K-particle (a test point particle representing the classical model of an electron in an atom) correspond to the conventional steady states of hydrogen atoms, with the trajectories being similar to those in the spin-zero particle model. The proposed model of the electronic structure in a hydrogen atom provides an insight into the physical cause of the atomic superfine structure and the physical meaning of the constant α=c/mc. Tomsk Polytechnical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 50–54, October, 1999.     

Continuous Variable Quantum Secret Sharing via Quantum Teleportation

A continuous variable quantum secret sharing (CVQSS) scheme is proposed by using quantum teleportation. In the scheme, the participants Bob and Charlie can recover the classical secret keys only when they cooperate. Meanwhile, the security of the CVQSS scheme is analyzed in detail by calculating the bit error rates (BERs) under different situations. It is shown that our proposed CVQSS scheme not only can resist the external attacks, but also can against the participant’s malicious attacks when the channel transmission efficiency η is above 50 %.     

Obtaining non-Abelian field theories via the Faddeev-Jackiw symplectic formalism

In this Letter we construct non-Abelian field theories employing the Faddeev-Jackiw symplectic formalism. The original Abelian fields were modified in order to introduce the non-Abelian algebra. We construct the SU(2) and SU(2)⊗U(1) Yang-Mills theories having as starting point the U(1) Maxwell electromagnetic theory.     

General formalism for quantitative Auger analysis

Auger electron spectroscopy can provide absolute, quantitative, analyses of surface chemical composition. The basic formalisms for treatment of the homogeneous surface and the layered structure are presented; their use and typical limitations are demonstrated by examining some applications.     

Quantum mechanics in theK-field formalism: Account of interactions with magnetic field

Using the K-field formalism, quantum equations are derived for a particle in a random stationary electromagnetic field. It is shown that this field can enter the K-field expression only via the |v(xⁱ)|² functions (the squared classical velocity of the K-particle). Tomsk Polytechnical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 55–57, October, 1999.     

Quantum games via search algorithms

We build new quantum games, similar to the spin flip game, where as a novelty the players perform measurements on a quantum system associated to a continuous time search algorithm. The measurements collapse the wave function into one of the two possible states. These games are characterized by a continuous space of strategies and the selection of a particular strategy is determined by the moments when the players measure.     

Global existence via Ginzburg-Landau formalism and pseudo-orbits of Ginzburg-Landau approximations

The so-called Ginzburg-Landau formalism applies for parabolic systems which are defined on cylindrical domains, which are, close to the threshold of instability, and for which the unstable Fourier modes belong to non-zero wave numbers. This formalism allows to describe an attracting set of solutions by a modulation equation, here the Ginzburg-Landau equation. If the coefficient in front of the cubic term of the formally derived Ginzburg-Landau equation has negative real part the method allows to show global existence in time in the original system of all solutions belonging to small initial conditions, inL . Another aim of this paper is to construct a pseudo-orbit of Ginzburg-Landau approximations which is close to a solution of the original system up tot=. We consider here as an example the socalled Kuramoto-Shivashinsky equation to explain the methods, but it applies also to a wide class of other problems, like e.g. hydrodynamical problems or reaction-diffusion equations, too.