arXiv subjects

Minos Axenides

Publications and source records attributed to Minos Axenides.

At least 37 records · Page 2Linked to original sources

arXiv2011

Non Hamiltonian Chaos from Nambu Dynamics of Surfaces

We discuss recent work with E.Floratos (JHEP 1004:036,2010) on Nambu Dynamics of Intersecting Surfaces underlying Dissipative Chaos in $R^{3}$. We present our argument for the well studied Lorenz and Rössler strange attractors. We implement a flow decomposition to their equations of motion. Their volume preserving part preserves in time a family of two intersecting surfaces, the so called {\em Nambu Hamiltonians}. For dynamical systems with linear dissipative sector such as the Lorenz system, they are specified in terms of Intersecting Quadratic Surfaces. For the case of the Rössler system, with nonlinear dissipative part, they are given in terms of a Helicoid intersected by a Cylinder. In each case they foliate the entire phase space and get deformed by Dissipation, the irrotational component to their flow. It is given by the gradient of a surface in $R^{3}$ specified in terms of a scalar function. All three intersecting surfaces reproduce completely the dynamics of each strange attractor.

nlin.CD↗

arXiv2009

Strange Attractors in Dissipative Nambu Mechanics : Classical and Quantum Aspects

We extend the framework of Nambu-Hamiltonian Mechanics to include dissipation in $R^{3}$ phase space. We demonstrate that it accommodates the phase space dynamics of low dimensional dissipative systems such as the much studied Lorenz and Rössler Strange attractors, as well as the more recent constructions of Chen and Leipnik-Newton. The rotational, volume preserving part of the flow preserves in time a family of two intersecting surfaces, the so called {\em Nambu Hamiltonians}. They foliate the entire phase space and are, in turn, deformed in time by Dissipation which represents their irrotational part of the flow. It is given by the gradient of a scalar function and is responsible for the emergence of the Strange Attractors. Based on our recent work on Quantum Nambu Mechanics, we provide an explicit quantization of the Lorenz attractor through the introduction of Non-commutative phase space coordinates as Hermitian $ N \times N $ matrices in $ R^{3}$. They satisfy the commutation relations induced by one of the two Nambu Hamiltonians, the second one generating a unique time evolution. Dissipation is incorporated quantum mechanically in a self-consistent way having the correct classical limit without the introduction of external degrees of freedom. Due to its volume phase space contraction it violates the quantum commutation relations. We demonstrate that the Heisenberg-Nambu evolution equations for the Quantum Lorenz system give rise to an attracting ellipsoid in the $3 N^{2}$ dimensional phase space.

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arXiv2008

Nambu-Lie 3-Algebras on Fuzzy 3-Manifolds

We consider Nambu-Poisson 3-algebras on three dimensional manifolds $ {\cal M}_{3} $, such as the Euclidean 3-space $R^{3}$, the 3-sphere $S^{3}$ as well as the 3-torus $T^{3}$. We demonstrate that in the Clebsch-Monge gauge, the Lie algebra of volume preserving diffeomorphisms $SDiff({\cal M}_{3})$ is identical to the Nambu-Poisson algebra on ${\cal M}_{3}$. Moreover the fundamental identity for the Nambu 3-bracket is just the commutation relation of $ SDiff({\cal M}_{3})$. We propose a quantization prescription for the Nambu-Poisson algebra which provides us with the correct classical limit. As such it possesses all of the expected classical properties constituting, in effect, a concrete representation of Nambu-Lie 3-algebras.

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arXiv2007

Euler Top Dynamics of Nambu-Goto P-Branes

We propose a method to obtain new exact solutions of spinning p-branes in flat space-times for any p, which manifest themselves as higher dimensional Euler Tops and minimize their energy functional. We provide concrete examples for the case of spherical topology S^{2}, S^{3} and rotational symmetry \prod_{i}SO(q_{i}). In the case of toroidal topology T^{2}, T^{3} the rotational symmetry is \prod SU(q_{i}) and m target dimensions are compactified on the torus T^{m} . By double dimensional reduction the Light Cone Hamiltonians of T^{2}, T^{3} reduce to those of closed string S^{1} and T^{2} membranes respectively. The solutions are interpreted as non-perturbative spinning soliton states of type IIA-IIB superstrings.

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arXiv2006

Locked Quintessence and Cold Dark Matter

A supersymmetric hybrid potential model with low energy supersymmetry breaking scale ($ M_{S}\sim 1-10 Tev$) is presented for both dark matter and dark energy. Cold dark matter is associated with a light modulus field ($\sim 10-100 Mev$) undergoing coherent oscillations around a saddle point false vacuum with the presently observed energy density ($ρ_{0} \sim 10^{-12} eV^{4}$). The latter is generated by its coupling to a light dark energy scalar field ($ \sim 10^{-18} eV $) which is trapped at the origin ("locked quintessence"). Through naturally attained initial conditions the model is consistent with cosmic coincidence reproducing LCDM cosmology. An exit from the cosmic acceleration phase is estimated to occur within some eight Hubble times.

hep-ph↗

arXiv2004

Hybrid Dark Sector: Locked Quintessence and Dark Matter

We present a unified model of dark matter and dark energy. The dark matter field is a modulus corresponding to a flat direction of supersymmetry, which couples, in a hybrid type potential, with the dark energy field. The latter is a light scalar, whose direction is stabilized by non-renormalizable terms. This quintessence field is kept `locked' on top of a false vacuum due to the coupling with the oscillating dark matter field. It is shown that the model can satisfy the observations when we consider low-scale gauge-mediated supersymmetry breaking. The necessary initial conditions are naturally attained by the action of supergravity corrections on the potential, in the period following the end of primordial inflation.

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arXiv2003

SU(5) Unified Theories from Intersecting Branes

We discuss the first string theory examples of three generation non-supersymmetric SU(5) and {\em flipped} SU(5) GUTS, which break to the Standard model at low energy, without extra matter and/or gauge group factors. Our GUT examples are based on IIA $Z_3$ orientifolds with D6-branes intersecting at non-trivial angles. These theories necessarily satisfy RR tadpoles and are free of NSNS tadpoles as the complex structure moduli are frozen (even though a dilaton tadpole remains) to discrete values. We identify appropriately the bifundamental Higgses responsible for electroweak symmetry breaking. In this way, the neutrino see-saw mechanism get nicely realized in these constructions. Moreover, as baryon number is not a gauged symmetry gauge mediated dimension six operators do contribute to proton decay; however proton lifetime may be safely enhanced by appropriately choosing a high GUT scale. An accompanying natural doublet-triplet splitting guarantees the suppression of scalar mediated proton decay modes and the stability of triplet scalar masses against higher dimensional non-renormalizable operators.

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arXiv2003

Scaling Violations in Yang-Mills Theories and Strings in AdS_5

String solitons in AdS_5 contain information of N=4 SUSY Yang-Mills theories on the boundary. Recent proposals for rotating string solitons reproduce the spectrum for anomalous dimensions of Wilson operators for the boundary theory. There are possible extensions of this duality for lower supersymmetric and even for non-supesymmetric Yang-Mills theories. We explicitly demonstrate that the supersymmetric anomalous dimensions of Wilson operators in N=0,1 Yang-Mills theories behave, for large spin J, at the two-loop level in perturbation theory, like log J. We compile the analytic one- and two-loop results for the N=0 case which is known in the literature, as well as for the N=1 case which seems to be missing.

hep-th↗

arXiv2001

Semitopological Q-Rings

Semitopological Vortices (Q-Rings) are identified to be classical soliton configurations whose stability is attributed to both topological and nontopological charges. We discuss some recent work on the simplest possible realization of such a configuration in a scalar field theory with an unbroken U(1) global symmetry. We show that Q-Rings correspond to local minima of the energy, exhibit numerical solutions of their field configurations and derive virial theorems demonstrating their stability.

hep-ph↗

arXiv2000

Dynamics of Nontopological Solitons - Q Balls

We use numerical simulations and semi-analytical methods to investigate the stability and the interactions of nontopological stationary qball solutions. In the context of a simple model we map the parameter sectors of stability for a single qball and verify the result using numerical simulations of time evolution. The system of two interacting qballs is also studied in one and two space dimensions. We find that the system generically performs breather type oscillations with frequency equal to the difference of the internal qball frequencies. This result is shown to be consistent with the form of the qball interaction potential. Finally we perform simulations of qball scattering and show that the right angle scattering effect observed in topological soliton scattering in two dimensions, persists also in the case of qballs where no topologically conserved quantities are present. For relativistic collision velocities the qball charge is split into a forward and a right angle scattering component. As the collision velocity increases, the forward component gets amplified at the expense of the right angle component. The animated simulations of this study may be found on-line at the address http://leandros.chem.demokritos.gr/qballs/index.html

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arXiv1998

Phase Transitions in the Core of Global Embedded Defects

We demonstrate the existence of global monopole and vortex configurations whose core exhibits a phase structure. We determine the critical values of parameters for which the transition from the symmetric to the non-symmetric phase occurs and discuss the novel dynamics implied by the non-symmetric cores for defect interactions. We model phase transitions in the core of global embedded topological defects by identifying the relevant parameters with the vacuum expectation value of a dynamical scalar field. Finally, we argue that superheavy defects that undergo a core phase transition in the very early universe provide a novel realization for topological inflation.

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arXiv1997

Domain Walls and Vortices with Non-Symmetric Core

We review recent work on a new class of topological defects which possess a nonsymmetric core. They arise in scalar field theories with global symmetries, U(1) for domain walls and SU(2) for vortices, which are explicitly broken to $Z_2$ and U(1) respectively. Both of the latter symmetries are spontaneously broken. For a particular range of parameters both types of defect solutions are shown to become unstable and decay to the well known stable walls and vortices with symmetric cores.

hep-ph↗

arXiv1997

Topological Defects with Non-Symmetric Core

We demonstrate that field theories involving explicit breaking of continous symmetries, incorporate two generic classes of topological defects each of which is stable for a particular range of parameters. The first class includes defects of the usual type where the symmetry gets restored in the core and vacuum energy gets trapped there. We show however that these defect solutions become unstable for certain ranges of parameters and decay not to the vacuum but to another type of stable defect where the symmetry in not restored in the core. In the wall case, initially spherical, bubble-like configurations are simulated numerically and shown to evolve generically towards a planar collapse. In the string case, the decay of the symmetric core vortex resembles the decay of a semilocal string to a skyrmion with the important difference that while the skyrmion is unstable and decays to the vacuum, the resulting non-symmetric vortex is topologically stable.

hep-ph↗

arXiv1996

A ${\bf Z}_2$ Classification for 2D Fermion Level Crossing

We demonstrate that the number of fermionic zero modes of the static $2$-dimensional Dirac operator in the background of $SU(2)$ static gauge-Higgs field configurations is a topological invariant modulo four. Static configurations which are everywhere odd under parity with even-parity pure gauge behaviour at infinity admit $4n$, $n\in {\bf Z},$ zero modes of the Jackiw-Rebbi (JR) type. Odd-parity configurations with odd-parity pure gauge behaviour at infinity are topologically disconnected from the vacuum and admit $4 n + 2$ fermionic zero energy solutions. The classification implies the collapse of half of the fermion zero modes upon embedding a $2$-dimensional gauge-Higgs configuration (string) with odd-parity pure gauge behaviour at infinity into the $3$-dimensional Minkowski space.

hep-ph↗

arXiv1996

Baryon Number Non-Conservation and the Topology of Gauge Fields

An introduction to the subject of baryon number non-conservation in the electroweak theory at high temperatures or energies is followed by a summary of our discovery of an infinite surface of sphaleron-like configurations which play a key role in baryon-number non-conserving transitions in a hot electroweak plasma.

hep-ph↗

arXiv1996

Runaway Collapse of Witten Vortex Loops

We consider general properties of charged circular cosmic strings in a general family of world-sheet string models. We then specialize to a model recently proposed by Carter and Peter. This model was shown to give a good description of the features of the superconducting cosmic strings originally discovered by Witten. We derive an explicit expression for the potential determining the dynamics of the string and we present explicit expressions for the string tension and energy density as a function of string-loop radius. We also obtain explicit expressions for the wiggle and woggle speeds (speeds of transverse and longitudinal perturbations, respectively). We show that the contraction of the uniformly charged string is essentially governed by the string tension (for large loop radius) and by a {\it finite} Coulomb barrier (for small loop radius). We argue for the unobstructed contraction of a uniformly charged loop over the Coulombic barrier and its eventual collapse to a charged point. The implication of such an effect to the possible formation of naked singularities, in violation of the cosmic censorship hypothesis, is finally discussed.

hep-th↗

arXiv1995

$Z_2$ as the Topological Origin of B+L Violation in the Hot Electroweak Theory

The space of static finite-energy configurations in the electroweak theory admits a $Z_2$ topological structure. More precisely, we show that this space contains two disconnected sectors of unstable gauge-Higgs fields odd under a properly defined generalized parity. This classification extends the description of baryon and lepton number violating electroweak processes to the symmetric phase of the theory. Configurations with odd pure-gauge behaviour at spatial infinity, such as the sphaleron, multisphalerons, electroweak strings as well as an infinite surface of their equivalents, have half-integer Chern-Simons number and mediate B+L violating processes in the early universe. Finite-energy configurations with even pure-gauge behaviour, such as the $S^*$ new sphaleron and electroweak strings, are topologically equivalent to the vacuum and are irrelevant for B+L violation. We discuss the possible formation of B+L violating quark-lepton condensates in the symmetric high-temperature phase of the electroweak theory.

hep-ph↗

arXiv1995

A ${\bf Z}_2$ Origin for B+L Violation in the Hot Electroweak Theory

The space of static finite-energy configurations of the electroweak theory admits a ${\bf Z}_{2}$ topological structure. Odd-parity configurations with odd pure-gauge behavior at spatial infinity (S sphaleron, W-Z strings, multisphalerons) mediate rapid $B+L$ violation in the Early Universe. Configurations with even pure-gauge behavior (S$^{*}$ sphalerons, W-Z strings, multisphalerons) are trivial and topologically equivalent to the vacuum.

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