A Geometrical Representation of Entanglement as Internal Constraint

We study a system of two entangled spin 1/2, were the spin's are represented by a sphere model developed within the hidden measurement approach which is a generalization of the Bloch sphere representation, such that also the measurements are represented. We show how an arbitrary tensor product state can be described in a complete way by a specific internal constraint between the ray or density states of the two spin 1/2. We derive a geometrical view of entanglement as a “rotation” and “stretching” of the sphere representing the states of the second particle as measurements are performed on the first particle. In the case of the singlet state entanglement can be represented by a real physical constraint, namely by means of a rigid rod.     

Probability distribution of inherent states in models of granular media and glasses

The present paper develops a Statistical Mechanics approach to the inherent states of glassy systems and granular materials by following the original ideas proposed by Edwards for granular media. We consider three lattice models (a diluted spin glass, a system of hard spheres under gravity and a hard-spheres binary mixture under gravity) introduced to describe glassy and granular systems. They are evolved using a “tap dynamics” analogous to that of experiments on granular media. We show that the asymptotic states reached in such a dynamics are not dependent on the particular sample history and are characterized by a few thermodynamical parameters. We assume that under stationarity these systems are distributed in their inherent states satisfying the principle of maximum entropy. This leads to a generalized Gibbs distribution characterized by new “thermodynamical” parameters, called “configurational temperatures” (related to Edwards compactivity for granular materials). Finally, we show by Monte Carlo calculations that the average of macroscopic quantities over the tap dynamics and over such distribution indeed coincide. In particular, in the diluted spin glass and in the system of hard spheres under gravity, the asymptotic states reached by the system are found to be described by a single “configurational temperature”. Whereas in the hard-spheres binary mixture under gravity the asymptotic states reached by the system are found to be described by two thermodynamic parameters, coinciding with the two configurational temperatures which characterize the distribution among the inherent states when the principle of maximum entropy is satisfied under the constraint that the energies of the two species are independently fixed. Received 19 March 2002 and Received in final form 14 June 2002     

Dark matter and dark energy of the universe

A possibility of existing spheres filled with a uniform constant scalar field in the Universe is shown. These spheres can act as “dark matter” and can be responsible for a decreasing behavior of the “ rotational” curved galaxies observed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 9–19, April, 2006.     

Differential calculus on quantum Euclidean spheres

We study covariant differential calculus on the quantum Euclidean spheres S _q ^N−1 which are quantum homogeneous spaces with coactions of the quantum groups O _q (N). First order differential calculi on the quantum Euclidean spheres satisfying a dimension constraint are found and classified: ForN≥6, there exist exactly two such calculi one of which is closely related to the classical differential calculus in the commutative case. Higher order differential forms and symmetry are discussed. Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000.     

Einstein’s “Zur Elektrodynamik...” (1905) Revisited, With Some Consequences

Einstein, in his “Zur Elektrodynamik bewegter K?rper”, gave a physical (operational) meaning to “time” of a remote event in describing “motion” by introducing the concept of “synchronous stationary clocks located at different places”. But with regard to “place” in describing motion, he assumed without analysis the concept of a system of co-ordinates.In the present paper, we propose a way of giving physical (operational) meaning to the concepts of “place” and “co-ordinate system”, and show how the observer can define both the place and time of a remote event. Following Einstein, we consider another system “in uniform motion of translation relatively to the former”. Without assuming “the properties of homogeneity which we attribute to space and time”, we show that the definitions of space and time in the two systems are linearly related. We deduce some novel consequences of our approach regarding faster-than-light observers and particles, “one-way” and “two-way” velocities of light, symmetry, the “group property” of inertial reference frames, length contraction and time dilatation, and the “twin paradox”. Finally, we point out a flaw in Einstein’s argument in the “Electrodynamical Part” of his paper and show that the Lorentz force formula and Einstein’s formula for transformation of field quantities are mutually consistent. We show that for faster-than-light bodies, a simple modification of Planck’s formula for mass suffices. (Except for the reference to Planck’s formula, we restrict ourselves to Physics of 1905.)     

Hysteresis Phenomenon in Deterministic Traffic Flows

We study phase transitions of a system of particles on the one-dimensional integer lattice moving with constant acceleration, with a collision law respecting slower particles. This simple deterministic “particle-hopping” traffic flow model being a straightforward generalization to the well known Nagel–Schreckenberg model covers also a more recent slow-to-start model as a special case. The model has two distinct ergodic (unmixed) phases with two critical values. When traffic density is below the lowest critical value, the steady state of the model corresponds to the “free-flowing” (or “gaseous”) phase. When the density exceeds the second critical value the model produces large, persistent, well-defined traffic jams, which correspond to the “jammed” (or “liquid”) phase. Between the two critical values each of these phases may take place, which can be interpreted as an “overcooled gas” phase when a small perturbation can change drastically gas into liquid. Mathematical analysis is accomplished in part by the exact derivation of the life-time of individual traffic jams for a given configuration of particles. This research has been partially supported by Russian Foundation for Fundamental Research and French Ministry of Education grants.     

Nonlocal charges in susy integrable models

We study systematically the general properties of theB-extension of any integrable model and its properties as Hamiltonian structures etc. We clarify the origin of “exotic” changes in such models. We show that in such models there exist at least two sets of non-local conserved charges and that the “exotic” charges are part of this non-local charge hierarchy. Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000.     

“Elastic” fluctuation-induced effects in smectic wetting films

The Li-Kardar field theory approach is generalized to wetting smectic films and the “elastic” fluctuation-induced interaction is obtained between the external flat bounding surface and distorted IA (isotropic liquid-smectic A) interface acting as an “internal” (bulk) boundary of the wetting smectic film under the assumption that the IA interface is essentially “softer” than the surface smectic layer. This field theory approach allows calculating the fluctuation-induced corrections in Hamiltonians of the so-called “correlated” liquids confined by two surfaces, in the case where one of the bounding surfaces is “rough” and with different types of surface smectic layer anchoring. We obtain that in practice, the account of thermal displacements of the smectic layers in a wetting smectic film reduces to the addition of two contributions to the IA interface Hamiltonian. The first, so-called local contribution describes the long-range thermal “elastic” repulsion of the fluctuating IA interface from the flat bounding surface. The second, so-called nonlocal contribution is connected with the occurrence of an “elastic” fluctuation-induced correction to the stiffness of the IA interface. An analytic expression for this correction is obtained.     

Integrable Evolution Equations on Spaces of Tensor Densities and Their Peakon Solutions

We study a family of equations defined on the space of tensor densities of weight λ on the circle and introduce two integrable PDE. One of the equations turns out to be closely related to the inviscid Burgers equation while the other has not been identified in any form before. We present their Lax pair formulations and describe their bihamiltonian structures. We prove local wellposedness of the corresponding Cauchy problem and include results on blow-up as well as global existence of solutions. Moreover, we construct “peakon” and “multi-peakon” solutions for all λ ≠ 0, 1, and “shock-peakons” for λ = 3. We argue that there is a natural geometric framework for these equations that includes other well-known integrable equations and which is based on V. Arnold’s approach to Euler equations on Lie groups.     

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.     

The optical sum rule in strongly correlated systems

We discuss the problem of a possible “violation” of the optical sum rule in the normal (nonsuperconducting) state of strongly correlated electronic systems, using our recently proposed DMFT + Σ approach applied to two typical models: the “hot spot” model of the pseudogap state and the disordered Anderson-Hubbard model. We explicitly demonstrate that the general Kubo single-band sum rule is satisfied for both models, but the optical integral itself is in general dependent on temperature and characteristic parameters, such as the pseudogap width, correlation strength, and disorder scattering, leading to an effective “violation” of the optical sum rule, which may be observed in experiments. The text was submitted by the authors in English.     

An explicitly solvable model of the spontaneous <Emphasis Type="Italic">PT</Emphasis>-symmetry breaking

We contemplate the pair of the purely imaginary delta-function potentials on a finite interval with Dirichlet boundary conditions. The two parameter model exhibits nicely the expected quantitative features of the unavoided level crossing and of a “phase-transition” complexification of the energies. Combining analytic and numerical techniques we investigate strength- and position-dependence of spectrum. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.     

Detecting hidden spatial and spatio-temporal structures in glasses and complex physical systems by multiresolution network clustering

We elaborate on a general method that we recently introduced for characterizing the “natural” structures in complex physical systems via multi-scale network analysis. The method is based on “community detection” wherein interacting particles are partitioned into an “ideal gas” of optimally decoupled groups of particles. Specifically, we construct a set of network representations (“replicas”) of the physical system based on interatomic potentials and apply a multiscale clustering (“multiresolution community detection”) analysis using information-based correlations among the replicas. Replicas may i) be different representations of an identical static system, ii) embody dynamics by considering replicas to be time separated snapshots of the system (with a tunable time separation), or iii) encode general correlations when different replicas correspond to different representations of the entire history of the system as it evolves in space-time. Inputs for our method are the inter-particle potentials or experimentally measured two (or higher order) particle correlations. We apply our method to computer simulations of a binary Kob-Andersen Lennard-Jones system in a mixture ratio of A₈₀B₂₀ , a ternary model system with components “A”, “B”, and “C” in ratios of A₈₈B₇C₅ (as in Al₈₈Y₇Fe₅ , and to atomic coordinates in a Zr₈₀Pt₂₀ system as gleaned by reverse Monte Carlo analysis of experimentally determined structure factors. We identify the dominant structures (disjoint or overlapping) and general length scales by analyzing extrema of the information theory measures. We speculate on possible links between i) physical transitions or crossovers and ii) changes in structures found by this method as well as phase transitions associated with the computational complexity of the community detection problem. We also briefly consider continuum approaches and discuss rigidity and the shear penetration depth in amorphous systems; this latter length scale increases as the system becomes progressively rigid.     

Regular exact models for a nonstatic gas sphere in general relativity

Some new exact models for an expanding or a contracting gaseous sphere (i.e., the density is to vanish at the outer boundary together with the pressurep) are given. The physical properties of the models are investigated, and it is found that both the pressure and the density are positive inside the outer boundary of the sphere, and their respective gradients are negative. The density is increasing for contracting spheres, and it is decreasing for expanding spheres. It is also shown that this is the case for the pressure at any moment for the layers close to the boundary of the spheres. For these layers it is further shown that the adiabatic speed of sound is less than the speed of light, and the trace of the energy-momentum tensor is positive. The rate of change of the circumference as measured by an observer riding on the boundary of the sphere is increasing for expanding spheres and it is decreasing for collapsing spheres. We also find that the physical radius is an increasing function of comoving radial coordinate. The mass function is further shown to be positive.     

Proton magnetic relaxation in a disperse “dry water” nanosystem

We have studied the characteristic features of proton magnetic relaxation in a disperse “dry water” nanosystem. We have determined the effect of the microstructure of the “dry water” on its NMR relaxation parameters.     

Spontaneous symmetry breaking in a system of strongly interacting multicomponent fermions (electrons with spin and conducting nanotubes)

We calculate the ground-state wave functions for a system of multicomponent strongly interacting fermions. We show that it is a state with spontaneously broken chiral symmetry that describes a phase with a finite density of chiral complexes. The number of particles constituting a complex depends on the number of fermion components. For example, in the case of two-component electrons (spin), the condensate is built of four-particle complexes consisting of two “right” electrons and two “left” holes with the opposite spins. The article is published in the original.     

PIV Web Visualization System toward PIV visualization grid

To visualize the simulation and experimental data, the fluid dynamics scientists and engineers have to possess a powerful visualization engine with CG package in their laboratories. We developed a Problem Solving Environment (PSE) system called “PIV Web Visualization System” to solve this obstacle, using computational grid common service tool “Globus”, programming language Java and Java Servlet. This system has “Grid Portal” which enables us to view the visualization resources on the networks as a unified whole and can be accessed around the world through the Internet, and it combines PIV engine “KMU-PIV” on visualization server in Korea Maritime University with a nonlinear video editing system on Kanazawa University as a real application.     

Paradoxes of neutrino oscillations

Despite the theory of neutrino oscillations being rather old, some of its basic issues are still being debated in the literature. We discuss a number of such issues, including the relevance of the “same energy” and “same momentum” assumptions, the role of quantum-mechanical uncertainty relations in neutrino oscillations, the dependence of the coherence and localization conditions that ensure the observability of neutrino oscillations on neutrino energy and momentum uncertainties, the question of (in)dependence of the oscillation probabilities on the neutrino production and detection processes, and the applicability limits of the stationary-source approximation. We also develop a novel approach to calculation of the oscillation probability in the wave-packet approach, based on the summation/integration conventions different from the standard one, which allows a new insight into the “same energy” vs. “same momentum” problem. We also discuss a number of apparently paradoxical features of the theory of neutrino oscillations. The text was submitted by the authors in English.     

Reality in quantum mechanics,Extended Everett Concept,and consciousness

Conceptual problems in quantum mechanics result from the specific quantum concept of reality and require, for their solution, including the observer’s consciousness into the quantum theory of measurements. Most naturally, this is achieved in the framework of Everett’s “many-world interpretation” of quantum mechanics. According to this interpretation, various classical alternatives are perceived by consciousness separately from each other. In the Extended Everett Concept (EEC) proposed by the present author, the separation of the alternatives is identified with the phenomenon of consciousness. This explains the classical character of the alternatives and unusual manifestations of consciousness arising “at the edge of consciousness” (i.e., in sleep or trance) when its access to “other alternative classical realities” (other Everett’s worlds) becomes feasible. Because of reversibility of quantum evolution in EEC, all time moments in the quantum world are equivalent, while the impression of flow of time appears only in consciousness. If it is assumed that consciousness may influence the probabilities of alternatives (which is consistent in case of infinitely many Everett’s worlds), EEC explains free will, “probabilistic miracles” (observing low-probability events), and decreasing entropy in the sphere of life. The text was submitted by the author in English.