Relational Interpretation of the Wave Function and a Possible Way Around Bell’s Theorem

The famous “spooky action at a distance” in the EPR-scenario is shown to be a local interaction, once entanglement is interpreted as a kind of “nearest neighbor” relation among quantum systems. Furthermore, the wave function itself is interpreted as encoding the “nearest neighbor” relations between a quantum system and spatial points. This interpretation becomes natural, if we view space and distance in terms of relations among spatial points. Therefore, “position” becomes a purely relational concept. This relational picture leads to a new perspective onto the quantum mechanical formalism, where many of the “weird” aspects, like the particle-wave duality, the non-locality of entanglement, or the “mystery” of the double-slit experiment, disappear. Furthermore, this picture circumvents the restrictions set by Bell’s inequalities, i.e., a possible (realistic) hidden variable theory based on these concepts can be local and at the same time reproduce the results of quantum mechanics. PACS: 03.65.Ud, 04.60.Nc     

The carrier “antibinding” in quantum dots: a charge separation effect

We show that the carrier “antibinding” observed recently in semiconductor quantum dots, i.e., the fact that the ground state energy of two electron-hole pairs goes above twice the ground-state energy of one pair, can entirely be assigned to a charge separation effect, whatever its origin. In the absence of external electric field, this charge separation comes from different “spreading-out” of the electron and hole wavefunctions linked to the finite height of the barriers. When the dot size shrinks, the two-pair energy always stays below when the barriers are infinite. On the opposite, because barriers are less efficient for small dots, the energy of two-pairs in a dot with finite barriers, ends by behaving like the one in bulk, i.e., by going above twice the one-pair energy when the pairs get too close. For a full understanding of this “antibinding” effect, we have also reconsidered the case of one pair plus one carrier. We find that, while the carriers just have to spread out of the dot differently for the “antibinding” of two-pairs to appear, this “antibinding” for one pair plus one carrier only appears if this carrier is the one which spreads out the less. In addition a remarkable sum rule exists between the “binding energies” of two pairs and of one pair plus one carrier.     

On the Distribution of Surface Extrema in Several One- and Two-dimensional Random Landscapes

We study here a standard next-nearest-neighbor (NNN) model of ballistic growth on one-and two-dimensional substrates focusing our analysis on the probability distribution function P(M,L) of the number M of maximal points (i.e., local “peaks”) of growing surfaces. Our analysis is based on two central results: (i) the proof (presented here) of the fact that uniform one-dimensional ballistic growth process in the steady state can be mapped onto “rise-and-descent” sequences in the ensemble of random permutation matrices; and (ii) the fact, established in Ref. [G. Oshanin and R. Voituriez, J. Phys. A: Math. Gen. 37:6221 (2004)], that different characteristics of “rise-and-descent” patterns in random permutations can be interpreted in terms of a certain continuous-space Hammersley-type process. For one-dimensional system we compute P(M,L) exactly and also present explicit results for the correlation function characterizing the enveloping surface. For surfaces grown on 2d substrates, we pursue similar approach considering the ensemble of permutation matrices with long-ranged correlations. Determining exactly the first three cumulants of the corresponding distribution function, we define it in the scaling limit using an expansion in the Edgeworth series, and show that it converges to a Gaussian function as L → ∞.     

Anticipative control of switched queueing systems

The relevant dynamics of a queueing process can be anticipated by taking future arrivals into account. If the transport from one queue to another is associated with transportation delays, as it is typical for traffic or productions networks, future arrivals to a queue are known over some time horizon and, thus, can be used for an anticipative control of the corresponding flows. A queue is controlled by switching its outflow between “on” and “off” similar to green and red traffic lights, where switching to “on” requires a non-zero setup time. Due to the presence of both continuous and discrete state variables, the queueing process is described as a hybrid dynamical system. From this formulation, we derive one observable of fundamental importance: the green time required to clear the queue. This quantity allows to detect switching time points for serving platoons without delay, i.e., in a “green wave” manner. Moreover, we quantify the cost of delaying the start of a service period or its termination in terms of additional waiting time. Our findings may serve as a basis for strategic control decisions.     

Why the Initial Infinite Singularity of the Universe Is Not There

We “explain”, using a Classical approach, how the Universe was created out of “nothing”, i.e., with no input of initial energy. This is a Universe with no-initial infinite singularity of energy density.     

Total quantum-current yield in the soft x-ray region

The emission of slow secondary electrons excited in efficient photocathodes by fast internal x-ray electrons upon absorption of x-ray photons having energies in the range 1–10 keV is analyzed. Analytical expressions are derived for the quantum current yield of the x-ray photoelectric effect for a “point” model and a “non-point” model of energy exchange of fast internal x-ray electrons. We present some estimates for its parameters in a CsI photocathode. Fiz. Tverd. Tela (St. Petersburg) 40, 1042–1046 (June 1998)     

A short review of the magnetoelectric effect and related experimental techniques on single phase (multi-) ferroics

Whereas materials with intrinsic magnetoelectric (ME) effects have not yet made inroads in technology, the measurement of their tensor characteristics has become a precious tool for magnetic point group determination. Therefore, it is worthwhile to consider different measurement techniques. In particular techniques for determining the linear and bilinear ME effects will be discussed, essentially the quasi-static and dynamic magnetic field-induced methods will be evaluated. The measurement and application of ME “butterfly" loops for determining (weak) ferromagnetism and internal bias fields will be described. For the bilinear ME effect (with invariant EHH) a particularly sensitive measurement method with amplification effect will be highlighted, permitting, e.g., to detect subtle magnetic phase transitions. At least for the linear ME effect, we will stress that in the future only a dimensionless quantity should be used which is valid in all systems of units. Finally, the linear ME effect of TbPO₄ crystals is reexamined because in a former publication it was not clear which system of units was effectively used (“rationalized” or “not rationalized” Gaussian system of units). Effectively, this crystal has the largest linear ME effect known. At T = 1.50 K, in SI units: α _xy or α _yx = 730 ps/m, i.e., 0.220 in “not rationalized” Gaussian system of units.     

The renormalization group in the problem of turbulent convection of a passive scalar impurity with nonlinear diffusion

The problem of turbulent mixing of a passive scalar impurity is studied within the renormalization-group approach to the stochastic theory of developed turbulence for the case where the diffusion coefficient is an arbitrary function of the impurity concentration. Such a problem incorporates an infinite number of coupling constants (“charges”). A one-loop calculation shows that in the infinite-dimensional space of the charges there is a two-dimensional surface of fixed points of the renormalization-group equations. When the surface has an IR-stability region, the problem has scaling with universal critical dimensionalities, corresponding to the phenomenological laws of Kolmogorov and Richardson, but with nonuniversal (i.e., depending on the Prandtl number and the explicit form of the nonlinearity in the diffusion equation) scaling functions, amplitude factors in the power laws, and value of the “effective Prandtl turbulence number.” Zh. éksp. Teor. Fiz. 112, 1649–1663 (November 1997)     

Trapped rainbow techniques for spectroscopy on a chip and fluorescence enhancement

We report on the experimental demonstration of the broadband “trapped rainbow” in the visible range using arrays of adiabatically tapered optical nanowaveguides. Being a distinct case of the slow light phenomenon, the trapped rainbow effect could be applied to optical signal processing, sensing in such applications as spectroscopy on a chip, and to providing enhanced light-matter interactions. As an example of the latter applications, we have fabricated a large area array of tapered nanowaveguides, which exhibit broadband “trapped rainbow” effect. Considerable fluorescence enhancement due to slow light behavior in the array has been observed.     

Multifractal Nonrigidity of Topological Markov Chains

Given a multifractal spectrum, we consider the problem of whether it is possible to recover the potential that originates the spectrum. The affirmative solution of this problem would correspond to a “multifractal” classification of dynamical systems, i.e., a classification solely based on the information given by multifractal spectra. For the entropy spectrum on topological Markov chains we show that it is possible to have both multifractal rigidity and multifractal “nonrigidity”, by appropriately varying the Markov chain and the potential defining the spectrum. The “nonrigidity” even occurs in some generic sense. This strongly contrasts to the usual opinion among some experts that it should be possible to recover the potential up to some equivalence relation, at least in some generic sense. Supported by the Center for Mathematical Analysis, Geometry, and Dynamical Systems, through FCT by Program POCTI/FEDER and the grant SFRH/BD/10154/2002.     

Interactions in Noncommutative Dynamics

A mathematical notion of interaction is introduced for noncommutative dynamical systems, i.e., for one parameter groups of *-automorphisms of endowed with a certain causal structure. With any interaction there is a well-defined “state of the past” and a well-defined “state of the future”. We describe the construction of many interactions involving cocycle perturbations of the CAR/CCR flows and show that they are nontrivial. The proof of nontriviality is based on a new inequality, relating the eigenvalue lists of the “past” and “future” states to the norm of a linear functional on a certain C ^*-algebra. To the memory of Irving Segal Received: 12 October 1999 / Accepted: 21 October 1999     

Neutrino trapping in extremely compact objects described by the internal Schwarzschild-(anti-)de Sitter spacetimes

Extremely compact stars (ECS) (having radius R < 3GM/c ²) contain captured null geodesics. Certain part of neutrinos produced in their interior will be trapped, influencing thus their neutrino luminosity and thermal evolution. The trapping effect has been previously investigated for the internal Schwarzschild spacetimes with the uniform distribution of energy density. Here, we extend our earlier study considering the influence of the cosmological constant Λ on the trapping phenomena. Our model for the interior of ECS is based on the internal Schwarzschild-(anti-)de Sitter (S(a)dS) spacetimes with uniform distribution of energy density matched to the external vacuum S(a)dS spacetime with the same cosmological constant. Assuming uniform and isotropic distribution of local neutrino emissivity we determine behavior of the trapping coefficients, i.e., “global” one representing influence on the neutrino luminosity and “local” one representing influence on the cooling process. We demonstrate that the repulsive (attractive) cosmological constant has tendency to enhance (damp) the trapping phenomena.     

Cauchy—Riemann conditions and point singularities of solutions to linearized shallow-water equations

Singular solutions with algebraic “square-root” type singularity of two-dimensional equations of shallow-water theory are propagated along the trajectories of the external velocity field on which the field satisfies the Cauchy-Riemann conditions. In other words, the differential of the phase flow is proportional to an orthogonal operator on such a trajectory. It turns out that, in the linear approximation, this fact is closely related to the effect of “blurring” of solutions of hydrodynamical equations; namely, a singular solution of the Cauchy problem for the linearized shallow-water equations preserves its shape exactly (i.e., is not blurred) if and only if the Cauchy-Riemann conditions are satisfied on the trajectory (of the external field) along which the perturbation is propagated.     

The origin of thermal hadron production

Multihadron production in high energy collisions, from e⁺e^- annihilation to heavy ion interactions, shows remarkable thermal behaviour, specified by a universal “Hagedorn” temperature. We argue that this hadronic radiation is formed by tunneling through the event horizon of colour confinement, i.e., that it is the QCD counterpart of Hawking-Unruh radiation from black holes. It is shown to be emitted at a universal temperature T_H ≃ (σ/2 π)^1/2, where σ denotes the string tension. Since the event horizon does not allow information transfer, the radiation is thermal “at birth”.     

“Relationship” specification in Z-notation

Initially, relational model of data has been specified by E. F. Codd with the naming conventions to the attributes called “relationship”. It is something between relations and tables, i.e., between implementation and user view on data. In this paper, ideas for “relationship” are formally specified in Z-notation. The last one is an ISO standard now. The purpose of this paper is to reinvestigate ideas behind the “relationships” in a more formal way. This approach is useful for further research in extending relation model of data to capture multimedia data and data streams, which are, usually, generated by different kinds of sensors.     

Evolution of the dark matter halo in numerical models

Cosmological numerical models well reproduce many properties of a large-scale structure; however, there are a number of disagreements between simulation results and observations. Two most important inconsistencies are (i) the “cusp problem”, i.e., simulations show that the density in the inner halo regions tends to infinity at the center, and (ii) the problem of the number of halos, i.e., simulations show that the number of halos with small masses is larger than the number of observed dwarf Galaxies by a factor of 5–10. This paper is devoted to the study of these problems using rich statistical data, which is done for the first time. An extensive model catalog of halos was analyzed. It was shown that even a large sample of model halos contains no halo without “cusp”. Further possible ways for solving these problems are also discussed.     

Glimmers of a Pre-geometric Perspective

Spacetime measurements and gravitational experiments are made by using objects, matter fields or particles and their mutual relationships. As a consequence, any operationally meaningful assertion about spacetime is in fact an assertion about the degrees of freedom of the matter (i.e. non gravitational) fields; those, say for definiteness, of the Standard Model of particle physics. As for any quantum theory, the dynamics of the matter fields can be described in terms of a unitary evolution of a state vector in a Hilbert space. By writing the Hilbert space as a generic tensor product of “subsystems” we analyse the evolution of a state vector on an information theoretical basis and attempt to recover the usual spacetime relations from the information exchanges between these subsystems. We consider generic interacting second quantized models with a finite number of fermionic degrees of freedom and characterize on physical grounds the tensor product structure associated with the class of “localized systems” and therefore with “position”. We find that in the case of free theories no spacetime relation is operationally definable. On the contrary, by applying the same procedure to the simple interacting model of a one-dimensional Heisenberg spin chain we recover the tensor product structure usually associated with “position”. Finally, we discuss the possible role of gravity in this framework.     

A modified Jaynes-Cummings model for an atom interacting with a classical multifrequency field

An open quantum system, which consists of a “dressed” two-level atom, i.e., an atom interacting with a classical multifrequency field, and a single quantized mode of an electromagnetic field, is examined. It is shown that when the frequency of the quantized mode coincides with one of the transition frequencies between the quasienergy levels, two interaction mechanisms, which differ in the dynamics of the populations of the quasienergy states, can be realized. Zh. éksp. Teor. Fiz. 112, 818–827 (September 1997)     

Tense Operators on Basic Algebras

The concept of tense operators on a basic algebra is introduced. Since basic algebras can serve as an axiomatization of a many-valued quantum logic (see e.g. Chajda et al. in Algebra Univer. 60(1):63–90, 2009), these tense operators are considered to quantify time dimension, i.e. one expresses the quantification “it is always going to be the case that” and the other expresses “it has always been the case that”. We set up the axiomatization and basic properties of tense operators on basic algebras and involve a certain construction of these operators for left-monotonous basic algebras. Finally, we relate basic algebras with tense operators with another quantum structures which are the so-called dynamic effect algebras.