An Exact Evolution Equation of the Curvature Perturbation for Closed Universe

As is well known, the exact evolution equation of the curvature perturbation plays a very important role in investigation of the inflaorresponding exacttion power spectrum of the flat universe. However, the c extension for the non-flat universes has not yet been given clearly. Interest in the non-flat, specially closed, universes has been aroused recently. The need for this extension is pressing. We start with the most elementary physical consideration and obtain finally this exact evolution equation of the curvature perturbation for the non-flat universes, as well as the evolutionary controlling parameter and the exact expression of the variable mass in this equation. We approximately perform a primitive and immature analysis on the power spectrum of non-flat universes. This analysis shows that the exact evolution equation of the curvature perturbation for the non-flat universes is very complicated, and we need to carry out many numerical and analytic works for this new equation in the future to judge whether the universe is fiat or closed by comparison of theories with observations.     

The Common Logic of Quantum Universe—Part I: The Case of Non-relativistic Quantum Mechanics

Foundations of Physics - The earliest formulation of the Higgs naturalness argument has been criticized on the grounds that it relies on a particular cutoff-based regularization scheme. One...     

Quantum Spectra of Hydrogen Atoms in Various Magnetic Fields with the Closed Orbit Theory

The quantum spectra of hydrogen atoms in various magnetic fields have been calculated with the closed orbit theory.The magnitude of the magnetic field decreases from 5.96 T to 0.56 T with a step of 0.6T.We demonstrate schematically that the closed orbits disappear with the decrease of the magnitude of the magnetic field when the corresponding finite resolution of experiment is fixed.This may give us a good way to control the shape and the number of the closed orbits in the system,and thus to control where a peak should exist in the Fourier transformation of the quantum spectra.     

Evolution of Quantum State for Mesoscopic Circuits with Dissipation

Based on the maximum entropy principle, we present a density matrix of mesoscopic RLC circuit to make it possible to analyze the connection of the initial condition with temperature. Our results show that the quantum state evolution is closely related to the initial condition, and that the system evolves to generalized coherent state if it is in ground state initially, and evolves to squeezed state if it is in excited state initially.     

The Foundations of Quantum Mechanics and the Evolution of the Cartan-Kähler Calculus

In 1960–1962, E. Kähler enriched É. Cartan’s exterior calculus, making it suitable for quantum mechanics (QM) and not only classical physics. His “Kähler-Dirac” (KD) equation reproduces the fine structure of the hydrogen atom. Its positron solutions correspond to the same sign of the energy as electrons. The Cartan-Kähler view of some basic concepts of differential geometry is presented, as it explains why the components of Kähler’s tensor-valued differential forms have three series of indices. We demonstrate the power of his calculus by developing for the electron’s and positron’s large components their standard Hamiltonian beyond the Pauli approximation, but without resort to Foldy-Wouthuysen transformations or ad hoc alternatives (positrons are not identified with small components in K ähler’s work). The emergence of negative energies for positrons in the Dirac theory is interpreted from the perspective of the KD equation. Hamiltonians in closed form (i.e. exact through a finite number of terms) are obtained for both large and small components when the potential is time-independent. A new but as yet modest new interpretation of QM starts to emerge from that calculus’ peculiarities, which are present even when the input differential form in the Kähler equation is scalar-valued. Examples are the presence of an extra spin term, the greater number of components of “wave functions” and the non-association of small components with antiparticles. Contact with geometry is made through a Kähler type equation pertaining to Clifford-valued differential forms.     

Revisiting “The Loophole of the Improved Secure Quantum Sealed-Bid Auction with Post-Confirmation and Solution”

Recently, Luo et al. make a detailed analysis on the security of quantum sealed-bid auction with post-confirmation protocol (Quantum Information Processing, Volume 11, Issue 6, pp 1359–1369, 2012) and present the corresponding improved strategy for its loophole. Unfortunately, we find their improved version is still not as secure as expected, since it is vulnerable to malicious bidders in collusion with the auctioneer. And there is an unreasonable suspicion in the honesty of the auctioneer for special situation. Then we propose an improved strategy, which can perfectly defeat kinds of attacks.     

Evolution of Bouncing Cosmological Models Due to the Self-Gravitational Corrections

A four-dimensional timelike brane with non-zero energy density is considered as the boundary of a five dimensional Schwarzschild anti de Sitter bulk background. The self-gravitational corrections to the first Friedmann equation act as a source of stiff matter contrary to standard FRW cosmology where the charge of the black hole plays this role. In a previous related paper (Setare in Eur. Phys. J. C 47:851, [2006]), bouncing cosmology was studied, from a holographic perspective, for the very special case of a brane that is void of any intrinsic matter sources. In this paper we extend the results of (Setare in Eur. Phys. J. C 47:851, [2006]). We consider the physically relevant case in which a perfect fluid with equation of state of radiation is present on the brane. Then, we describe solutions of the braneworld theory under investigation and also determine their stability. Specifically, if we do not consider the self-gravitational corrections, the AdS black hole with zero ADM mass, and open horizon is an attractor, while, if we consider, the AdS black hole with zero ADM mass and flat horizon, and D3-brane with non-zero energy density is a repeller.     

Projection Evolution of Quantum States—the Delayed Choice Puzzle

Physics of Atomic Nuclei - We discuss the problem of the time variable in the nearly standard formulation of the quantum mechanics. In order to be able to describe the outcome of some of the...     

Quantum Tunneling from Apparent Horizon of?Rainbow-FRW Universe

The quantum tunneling from the apparent horizon of rainbow-FRW universe is studied in this paper. We apply the semi-classical approximation, which is put forward by Parikh and Wilczek et al., to research on the scalar field particles tunneling from the apparent horizon of the rainbow-FRW universe, and then use the spin 1/2 Fermions tunneling theory, which brought forward by Kerner and Mann firstly, to research on the Fermions Hawking radiation via semi-classical approximation. Finally, we discuss the meanings of the quantum effect via Finsler geometry.     

The Quantum Treatment of the 5D-Warped Friedmann–Robertson–Walker Universe in Schrödinger Picture

The present paper is devoted to the time-evolving Schrödinger version of the Wheeler–De Witt equation, written for the five dimensional warped k=0—FRW Universe. For small values of the cosmological scale factor, a, the wave function of the Universe is expressed in terms of the Heun Double Confluent functions, which have been intensively worked out in the last years. As expected, for large a’s, one gets the well-known Hermite associated functions. Within the semiclassical approximation, valid for large n, the asymptotic representation of the Whittaker functions leads to the “free particle” behavior.     

Quantum Diffusion of the Random Schrödinger Evolution in the Scaling Limit II. The Recollision Diagrams

We consider random Schrödinger equations on \({\mathbb{R}^{d}}\) for d≥ 3 with a homogeneous Anderson-Poisson type random potential. Denote by λ the coupling constant and ψ _t the solution with initial data ψ₀. The space and time variables scale as \({x\sim \lambda^{-2 -\kappa/2}, t \sim \lambda^{-2 -\kappa}}\) with 0 < κ <  κ₀(d). We prove that, in the limit λ → 0, the expectation of the Wigner distribution of ψ _t converges weakly to the solution of a heat equation in the space variable x for arbitrary L ² initial data. The proof is based on a rigorous analysis of Feynman diagrams. In the companion paper [10] the analysis of the non-repetition diagrams was presented. In this paper we complete the proof by estimating the recollision diagrams and showing that the main terms, i.e. the ladder diagrams with renormalized propagator, converge to the heat equation.     

Quantum fluctuations of the “Copenhagen vacuum”

The effective energy of the approximate gauge-field configuration customarily known as the Copenhagen vacuum is calculated in the single-loop approximation. It is shown that this quantity is always positive and so it is impossible to make any statements about the spontaneous generation of such a field. The possibility of the temperature stabilization of a homogeneous chromomagnetic field is also discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 74–79, May, 1986.     

The Archaic Universe: Big Bang,Cosmological Term and the Quantum Origin of Time in Projective Cosmology

This article proposes some cosmological reflections at the qualitative and conjectural level, suggested by the Fantappié-Arcidiacono projective relativity theory. The difference will firstly be discussed between two types of singularity in this theory: geometric (de Sitter horizon) and physical (big bang, big crunch). The reasons for the existence of geometric singularities are deeply rooted in the principle of inertia and in the principle of relativity, while physical singularities are associated with the creation or destruction of matter. In this framework, quantum mechanics is introduced through a particular interpretation of Bohm’s holomovement. Finally, a possible mechanism is discussed for the genesis of the cosmological term. No form of inflation appears in the scenario described.     

Some Comments on “The Mathematical Universe”

I discuss some problems related to extreme mathematical realism, focusing on a recently proposed “shut-up-and-calculate” approach to physics (Tegmark in Found. Phys. 38:101, 2008; New Sci., September 15th, 2007). I offer arguments for a moderate alternative, the essence of which lies in the acceptance that mathematics is (at least in part) a human construction, and discuss concrete consequences of this—at first sight purely philosophical—difference in point of view.     

The Stochastic Limit of the Fröhlich Hamiltonian: Relations with the Quantum Hall Effect

We propose a model of an approximatively two-dimensional electron gas in a uniform electric and magnetic field and interacting with a positive background through the Fröhlich Hamiltonian. We consider the stochastic limit of this model and we find the quantum Langevin equation and the generator of the master equation. This allows us to calculate the explicit form of the conductivity and the resistivity tensors and to deduce a fine tuning condition (FTC) between the electric and the magnetic fields. This condition shows that the x-component of the current is zero unless a certain quotient, involving the physical parameters, takes values in a finite set of physically meaningful rational numbers. We argue that this behavior is quite similar to that observed in the quantum Hall effect. We also show that, under some conditions on the form factors entering in the definition of the model, also the plateaux and the almost linear behavior of the Hall resistivity can be recovered. Our FTC does not distinguish between fractional and integer values.     

Multiparty Quantum Secret Sharing of Quantum States with Quantum Registers

A quantum secret sharing scheme is proposed by making use of quantum registers. In the proposed scheme, secret message state is encoded into multipartite entangled states. Several identical multi-particle entanglement states are generated and each particle of the entanglement state is filled in different quantum registers which act as shares of the secret message. Two modes, i.e. the detecting mode and the message mode, are employed so that the eavesdropping can be detected easily and the secret message may be recovered. The security analysis shows that the proposed scheme is secure against eavesdropping of eavesdropper and cheating of participants.     

Accurate Determination of the Values of Fundamental Physical Constants: The Basis of the New “Quantum” SI Units

The metric system appeared as the system of units designed for macroscopic (laboratory scale) measurements. The progress in accurate determination of the values of quantum constants (such as the Planck constant) in SI units shows that the capabilities in high-precision measurement of microscopic and macroscopic quantities in terms of the same units have increased substantially recently. At the same time, relative microscopic measurements (for example, the comparison of atomic transition frequencies or atomic masses) are often much more accurate than relative measurements of macroscopic quantities. This is the basis for the strategy to define units in microscopic phenomena and then use them on the laboratory scale, which plays a crucial role in practical methodological applications determined by everyday life and technologies.The international CODATA task group on fundamental constants regularly performs an overall analysis of the precision world data (the so-called Adjustment of the Fundamental Constants) and publishes their recommended values. The most recent evaluation was based on the data published by the end of 2014; here, we review the corresponding data and results. The accuracy in determination of the Boltzmann constant has increased, the consistency of the data on determination of the Planck constant has improved; it is these two dimensional constants that will be used in near future as the basis for the new definition of the kelvin and kilogram, respectively. The contradictions in determination of the Rydberg constant and the proton charge radius remain. The accuracy of determination of the fine structure constant and relative atomic weight of the electron has improved.Overall, we give a detailed review of the state of the art in precision determination of the values of fundamental constants. The mathematical procedure of the Adjustment, the new data and results are considered in detail. The limitations due to macroscopic properties of material standards (such as the International prototype of the kilogram) and the isotopic composition of substances involved in precision studies in general (as standard measures for the triple point of water) and, in particular, in the determination of the fundamental constants are discussed. The perspectives of the introduction of the new quantum units, which will be free from the mentioned problems, are considered.Many physicists feel no sympathy for the International system of units (SI), believing that it does not properly reflect the character of physical laws. In fact, there are three parallel systems, namely the systems of quantities, system of their units and the related standards. The definition of the units, in particular, the SI units, above all, reflects our ability to perform precision measurements of physical values under certain conditions, in particular, to create appropriate standards. This requirement is not related to the beauty of fundamental laws of nature. More accurate determination of the fundamental constants is one of the areas where we accumulate such experience.