Quantum macroscopic equations from Bohm potential and propagation of waves

Bohm’s interpretation of Quantum Mechanics leads to the derivation of a Quantum Kinetic Equation. In the present work, moments of this kinetic equation are taken, thus deriving conservation equations. These macroscopic equations are then applied to study the propagation of longitudinal density perturbations in neutral gases and plasmas, of either fermions or bosons. The dispersion relation is derived and the effect of the Bohm potential shown; the speed of propagation calculated and the difference between fermions and bosons investigated. Pseudosonic waves in quantum plasmas are obtained including the effect of the Bohm potential.     

Spin-Statistics Transmutation in Quantum Field Theory

Spin-statistics transmutation is the phenomenon occurring when a “dressing” transformation introduced for physical reasons (e.g. gauge invariance) modifies the “bare” spin and statistics of particles or fields. Historically, it first appeared in Quantum Mechanics and in semiclassical approximation to Quantum Field Theory. After a brief historical introduction, we sketch how to describe such phenomenon in Quantum Field Theory beyond the semiclassical approximation, using a path-integral formulation of euclidean correlation functions, exemplifying with anyons, dyons and skyrmions.     

On the integral construction of the universal R-matrix for quantum current superalgebraUq (oŝp(1,2))

We discuss the problems in the construction of the universal R-matrix for the the Drinfeld current realization of quantum affine superalgebrasUq (oŝp(1,2)), where we try to present the universal R-matrix for the corresponding “Drinfeld” comultiplication in the form of certain integrals over current operators with specially chosen contours. Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June 2001. Author’s research is partially supported by the Summer Research Fellowship and the Taft Foundation at the University of Cincinnati.     

New Electroweak Formulation Fundamentally Accounting for the Effect Known as “Maximal Parity-Violation”

The electroweak scheme is wholly recast, in the framework of a relativistic quantum field formalism being a covariant fermion–antifermion extension of the usual one for massive spin- point fermions. The new formalism is able to reread the “maximal P-violation” effect in a way restoring P and C symmetries themselves: it provides a natural “chiral field” approach, which gives evidence of the existence of a pseudoscalar (extra) charge variety anticommuting with the scalar (ordinary) one and just underlying the “maximally P-violating” phenomenology. Its zero-mass limit leads to a strict “chiral” particle theory, which remodels any massless spin- fermion and corresponding antifermion as two mere pseudoscalar-charge eigenstates being the simple mirror images of each other. On such a basis, the (zero-mass) electroweak primary fermions are all redefined to be (only left-handed) “chiral” particles (with right-handed complements just standing for their antiparticles) and to carry at most scalar charges subjected as yet to a maximal uncertainty in sign: it is only by acquiring mass, and by gaining an extra helicity freedom degree, that they now may also manifest themselves as “Dirac” particles, with sharp scalar-charge eigenvalues. The fermion-mass appearance is thus made herein a dynamical condition strictly necessary to obtain actual superselected scalar-charge (and first, electric-charge) eigenstates. A pure “internal” mass-generating mechanism, relying only on would-be-Goldstone bosons (even to yield fermion masses) and no longer including an “external” Higgs contribution, is adopted accordingly. This is shown to be a self-consistent mechanism, which still maintains both renormalizability and unitarity. It involves a P-breaking in the neutral-weak-current sector (due to the Weinberg mixing) while it leaves the charged-current couplings truly P-invariant even in the presence of a (standardly parametrized) CP-violation.     

II. The standard model in the isotopic Foldy-Wouthuysen representation without higgs bosons in the fermion sector

The Standard Model with massive fermions is formulated in the isotopic Foldy-Wouthuysen representation. SU(1) × U(1) — invariance of the theory in this representation is independent of whether fermions possess mass or not, and, consequently, it is not necessary to introduce interactions between Higgs bosons and fermions. The study discusses a possible relation between spontaneous breaking of parity in the isotopic Foldy-Wouthuysen representation and the composition of elementary particles of “dark matter”.     

Complete Axiomatizations for Quantum Actions

We present two equivalent axiomatizations for a logic of quantum actions: one in terms of quantum transition systems, and the other in terms of quantum dynamic algebras. The main contribution of the paper is conceptual, offering a new view of quantum structures in terms of their underlying logical dynamics. We also prove Representation Theorems, showing these axiomatizations to be complete with respect to the natural Hilbert-space semantics. The advantages of this setting are many: (1) it provides a clear and intuitive dynamic-operational meaning to key postulates (e.g. Orthomodularity, Covering Law); (2) it reduces the complexity of the Solèr–Mayet axiomatization by replacing some of their key higher-order concepts (e.g. “automorphisms of the ortholattice”) by first-order objects (“actions”) in our structure; (3) it provides a link between traditional quantum logic and the needs of quantum computation. PACS: 02.10.-v Logic; set theory and algebra; 03.65.-w Quantum mechanics; 03.65.Fd Algebraic methods; 03.67.-a Quantum information.     

A Fast Algorithm for Wave Propagation from a Plane or a Cylindrical Surface

The newly developed Taylor-Interpolation-FFT (TI-FFT) algorithm dramatically increases the computational speeds for millimeter wave propagation from a planar (cylindrical) surface onto a “quasi-planar” (“quasi-cylindrical”) surface. Two different scenarios are considered in this article: the planar TI-FFT is for the computation of the wave propagation from a plane onto a “quasi-planar” surface and the cylindrical TI-FFT is for the computation of wave propagation from a cylindrical surface onto a “quasi-cylindrical” surface. Due to the use of the FFT, the TI-FFT algorithm has a computational complexity of O(N ² log₂  N ²) for an N × N computational grid, instead of N ⁴ for the direct integration method. The TI-FFT algorithm has a low sampling rate according to the Nyquist sampling theorem. The algorithm has accuracy down to −80 dB and it works particularly well for narrow-band fields and “quasi-planar” (“quasi-cylindrical”) surfaces.     

Structure theorem for covariant bundles on quantum homogeneous spaces

The natural generalization of the notion of bundle in quantum geometry is that of bimodule. If the base space has quantum group symmetries, one is particularly interested in bimodules covariant (equivariant) under these symmetries. Most attention has so far been focused on the case with maximal symmetry — where the base space is a quantum group and the bimodules are bicovariant. The structure of bicovariant bimodules is well understood through their correspondence with crossed modules. We investigate the “next best” case — where the base space is a quantum homogeneous space and the bimodules are covariant. We present a structure theorem that resembles the one for bicovariant bimodules. Thus, there is a correspondence between covariant bimodules and a new kind of “crossed” modules which we define. The latter are attached to the pair of quantum groups which defines the quantum homogeneous space. We apply our structure theorem to differential calculi on quantum homogeneous spaces and discuss a related notion of induced differential calculus. Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June 2001. This work was supported by a NATO fellowship grant.     

Quantum condensates in nuclear matter: Problems

In connection with the contribution “Quantum Condensates in Nuclear Matter” some problems are given to become more familiar with the techniques of many-particle physics. The text was submitted by the authors in English. This paper relates to Part 4: “Problems and Solutions” of materials of the Conference “Helmholtz International Summer School (HISS) on Dense Matter in Heavy-Ion Collisions and Astrophysics,” Dubna, August, 21–September 1, 2006, which were published in the issue 7, 2008.     

Anyonic lie algebras

We introduce anyonic Lie algebras in terms of structure constants. We provide the simplest examples and formulate some open problems. Presented at the 6th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 19–21 June 1997. This paper is in final form and no version of it will be published elsewhere.     

Bell,group and tangle

The “Bell” of the title refers to bipartite Bell states, and their extensions to, for example, tripartite systems. The “Group” of the title is the Braid Group in its various representations; while “Tangle” refers to the property of entanglement which is present in both of these scenarios. The objective of this note is to explore the relation between Quantum Entanglement and Topological Links, and to show that the use of the language of entanglement in both cases is more than one of linguistic analogy.     

Condensates in the Cosmos: Quantum Stabilization of the Collapse of Relativistic Degenerate Stars to Black Holes

According to prevailing theory, relativistic degenerate stars with masses beyond the Chandrasekhar and Oppenheimer–Volkoff (OV) limits cannot achieve hydrostatic equilibrium through either electron or neutron degeneracy pressure and must collapse to form stellar black holes. In such end states, all matter and energy within the Schwarzschild horizon descend into a central singularity. Avoidance of this fate is a hoped-for outcome of the quantization of gravity, an as-yet incomplete undertaking. Recent studies, however, suggest the possibility that known quantum processes may intervene to arrest complete collapse, thereby leading to equilibrium states of macroscopic size and finite density. I describe here one such process which entails pairing (or other even-numbered association) of neutrons (or constituent quarks in the event of nucleon disruption) to form a condensate of composite bosons in equilibrium with a core of degenerate fermions. This process is analogous to, but not identical with, the formation of hadron Cooper pairs that give rise to neutron superfluidity and proton superconductivity in neutron stars. Fermion condensation to composite bosons in a star otherwise destined to collapse to a black hole facilitates hydrostatic equilibrium in at least two ways: (1) removal of fermions results in a decrease in the Fermi level which stiffens the dependence of degeneracy pressure on fermion density, and (2) phase separation into a fermionic core surrounded by a self-gravitating condensate diminishes the weight which must be balanced by fermion degeneracy pressure. The outcome is neither a black hole nor a neutron star, but a novel end state, a “fermicon star,” with unusual physical properties.     

Three short distance structures from quantum algebras

We review known and we present new results on three types of short distance structures of observables which typically appear in studies of quantum group related algebras. In particular, one of the short distance structures is shown to suggest a new mechanism for the introduction of internal symmetries. Presented at the 6th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 19–21 June 1997.     

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.     

The modulation instability revisited

The modulational instability (or “Benjamin-Feir instability”) has been a fundamental principle of nonlinear wave propagation in systems without dissipation ever since it was discovered in the 1960s. It is often identified as a mechanism by which energy spreads from one dominant Fourier mode to neighboring modes. In recent work, we have explored how damping affects this instability, both mathematically and experimentally. Mathematically, the modulational instability changes fundamentally in the presence of damping: for waves of small or moderate amplitude, damping (of the right kind) stabilizes the instability. Experimentally, we observe wavetrains of small or moderate amplitude that are stable within the lengths of our wavetanks, and we find that the damped theory predicts the evolution of these wavetrains much more accurately than earlier theories. For waves of larger amplitude, neither the standard (undamped) theory nor the damped theory is accurate, because frequency downshifting affects the evolution in ways that are still poorly understood.     

Towardsψ-extension of rota calculus in mizar language

Some cases of extended Umbral calculus provide an underpining for deformed quantum oscillator models. The Umbral calculus has been already formulated in Maple package. We shall present the first stages of the Mizar System usage in formulating and checking the first principal statements of extended Umbral calculus. Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June 2001.