The Role of Myelin in Malfunctions of Neuron Transmittance.

Because of different mechanism of electro-signaling in myelinated axons than in dendrites or unmyelinated axons, the role of the myelin needs to be reconsidered upon new premises in distinction to conventional cable model. It occurs that the latter model is inapplicable for so-called saltatory conduction in myelinated axons and the former imagination on the role of the myelin based on the cable model is confusing. We show how the myelin sheath of axons controls the electro-signaling in myelinated neurons upon a wave-type ionic oscillation model of electro-signaling, ion plasmon-polariton model, in close agreement with observations of the saltatory conduction not reachable within traditional cable model approach. This is of particular importance for better understanding of malfunctions of neuron communication due to demyelination diseases and for the strategy of future therapy methods at paralysis and at demyelination syndromes. The new mechanism of signaling in myelinated neurons is also supported by recent advances in recognition of so-called micro-saltatory conduction in C-fibers of pain sensation, also exceeding the range of applicability of the conventional cable model.

Formal derivation of the Laughlin function and its generalization for other topological phases of FQHE.

Using the braid symmetry we demonstrate the derivation of the Laughlin function for the main hierarchy 1/q of FQHE in the lowest Landau level of two-dimensional electron system with a mathematical rigour. This proves that the derivation of Laughlin function unavoidably requires some topological elements and cannot be completed within a local quantum mechanics, i.e., without global topological constraints imposed. The method shows the way for the generalization of this function onto other fractions from the general quantum Hall hierarchy. A generalization of the Laughlin function is here formulated.

Limits of Applicability of the Composite Fermion Model.

The popular model of composite fermions, proposed in order to rationalize FQHE, were insufficient in view of recent experimental observations in graphene monolayer and bilayer, in higher Landau levels in GaAs and in so-called enigmatic FQHE states in the lowest Landau level of GaAs. The specific FQHE hierarchy in double Hall systems of GaAs 2DES and graphene also cannot be explained in the framework of composite fermions. We identify the limits of the usability of the composite fermion model by means of topological methods, which elucidate the phenomenological assumptions in composite fermion structure and admit further development of FQHE understanding. We demonstrate how to generalize these ideas in order to explain experimentally observed FQHE phenomena, going beyond the explanation ability of the conventional composite fermion model.

Quantum generators of random numbers.

Generation of random numbers is a central problem for many applications in the field of information processing, including, e.g., cryptography, in classical and quantum regime, but also mathematical modeling, Monte Carlo methods, gambling and many others. Both, the quality of the randomness and efficiency of the random numbers generation process are crucial for the most of these applications. Software produced pseudorandom bit sequences, though sufficiently quick, do not fulfill required randomness quality demands. Hence, the physical hardware methods are intensively developed to generate truly random number sequences for information processing and electronic security application. In the present paper we discuss the idea of the quantum random number generators. We also present a variety of tests utilized to assess the quality of randomness of generated bit sequences. In the experimental part we apply such tests to assess and compare two quantum random number generators, PQ4000KSI (of company ComScire US) and JUR01 (constructed in Wroclaw University of Science and Technology upon the project of The National Center for Research and Development) as well as a pseudorandom generator from the Mathematica Wolfram package. Finally, we present our new prototype of fully operative miniaturized quantum random generator JUR02 producing a random bit sequence with velocity of 1 Mb/s, which successfully passed standard tests of randomness quality (like NIST and Dieharder tests). We also shortly discuss our former concept of an entanglement-based quantum random number generator protocol with unconditionally secure public randomness verification.

Topological Classification of Correlations in 2D Electron Systems in Magnetic or Berry Fields.

Recent topology classification of 2D electron states induced by different homotopy classes of mappings of the planar Brillouin zone into Bloch space can be supplemented by a homotopy classification of various phases of multi-electron homotopy patterns induced by Coulomb interaction between electrons. The general classification of such type is presented. It explains the topologically protected correlations responsible for integer and fractional Hall effects in 2D multi-electron systems in the presence of perpendicular quantizing magnetic field or Berry field, the latter in topological Chern insulators. The long-range quantum entanglement is essential for homotopy correlated phases in contrast to local binary entanglement for conventional phases with local order parameters. The classification of homotopy long-range correlated phases induced by the Coulomb interaction of electrons has been derived in terms of homotopy invariants and illustrated by experimental observations in GaAs 2DES, graphene monolayer, and bilayer and in Chern topological insulators. The homotopy phases are demonstrated to be topologically protected and immune to the local crystal field, local disorder, and variation of the electron interaction strength. The nonzero interaction between electrons is shown, however, to be essential for the definition of the homotopy invariants, which disappear in gaseous systems.

Author Correction: Quantum random number generators with entanglement for public randomness testing.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Quantum random number generators with entanglement for public randomness testing.

We discuss a simple idealistic quantum entanglement based protocol for quantum random number generation allowing a trusted third party to publicly perform arbitrarily complex tests of randomness without any violation of the secrecy of the generated bit sequences. The protocol diminishes also an average time of the randomness testing (thus enabling arbitrary shortening of this time with increasing number of entangled qubits).

Explanation of an unexpected occurrence of [Formula: see text] fractional quantum Hall effect states in monolayer graphene.

Recent experiment reveals the appearance of incompressible fractional quantum Hall effect states in monolayer graphene at [Formula: see text] and [Formula: see text] [Formula: see text], [Formula: see text] [Formula: see text] substituting the compressible Hall metal states at these fillings in the lowest Landau level in a narrow magnetic field window depending on the sample parameters. Simultaneously, none such behavior has been observed either for [Formula: see text] or [Formula: see text] [Formula: see text], [Formula: see text] [Formula: see text]. We propose an explanation of these observations in terms of homotopy of monolayer graphene in consistence with a general theory of correlated states in planar Hall systems.