Showing papers on "Winding number published in 1996"
TL;DR: In this paper, the authors describe spinor fields with nonvanishing winding number on a truncated (fuzzy) sphere, and the corresponding field theory actions conserve all basic symmetries of the standard commutative version (space isometries and global chiral symmetry).
Abstract: In the framework of noncommutative geometry we describe spinor fields with nonvanishing winding number on a truncated (fuzzy) sphere. The corresponding field theory actions conserve all basic symmetries of the standard commutative version (space isometries and global chiral symmetry), but due to the noncommutativity of the space the fields are regularized and they contain only a finite number of modes.
184 citations
TL;DR: In this article, the BPS and low energy non-BPS excitations of the D-string in terms of open strings that travel on the Dstring were examined, and the energy thresholds for exciting a long D string, for arbitrary winding number, were studied.
127 citations
TL;DR: In this paper, the BPS and low energy non-BPS excitations of the D-string were examined in terms of open strings that travel on the D string, for arbitrary winding number.
Abstract: We examine the BPS and low energy non-BPS excitations of the D-string, in terms of open strings that travel on the D-string. We use this to study the energy thresholds for exciting a long D-string, for arbitrary winding number. We also compute the leading correction to the entropy from non-BPS states for a long D-string, and observe the relation of all these quantities with the corresponding quantities for the elementary string.
101 citations
TL;DR: In this paper, the Dirichlet p-branes in type II string theory on a space which has been toroidally compactified in d dimensions were considered and an explicit construction of the field theory description of this system by putting a countably infinite number of copies of each brane on the noncompact covering space, and modding out the resulting gauge theory by Z^d.
Abstract: We consider Dirichlet p-branes in type II string theory on a space which has been toroidally compactified in d dimensions. We give an explicit construction of the field theory description of this system by putting a countably infinite number of copies of each brane on the noncompact covering space, and modding out the resulting gauge theory by Z^d. The resulting theory is a gauge theory with graded fields corresponding to strings winding around the torus an arbitrary number of times. In accordance with T-duality, this theory is equivalent to the gauge theory for the dual system of (d + p)-branes wrapped around the compact directions, where the winding number is exchanged for momentum in the compact direction.
32 citations
TL;DR: In this article, the existence of topological defects within the spin-exciton energy band of a 2D electron gas under a strong magnetic field at filling factor of 1 was investigated within the Hartree-Fock (HF) approximation.
Abstract: The existence of topological defects, known as Skyrmions, within the spin-exciton energy band of a two-dimensional (2D) electron gas under a strong magnetic field at filling factor $\ensuremath{
u}=1$, is investigated within the Hartree-Fock (HF) approximation. Using the linear momentum representation, developed previously for the description of magnetoexcitons in 2D electron systems, it is shown that the inhomogeneity created in the system by a charged Skyrmion can be described by a nonuniform rotation of the spin-density operators in a condensate of spin excitons. In the limit when the spatial dependence of the rotation angles is very smooth on the magnetic length scale, it is found that the winding number of a created Skyrmion is equal to the number of particles injected to, or removed from the system. The minimum HF energy level of a neutral topological defect, i.e., a widely separated Skyrmion-anti-Skyrmion pair with a unit winding number, is found to lay exactly in the middle of the spin-exciton energy band.
27 citations
TL;DR: It is found that states with winding number larger than a critical one are unstable, in the sense that they decay to states with smaller winding number.
Abstract: We give a statistical characterization of states with nonzero winding number in the Phase Turbulence (PT) regime of the one-dimensional Complex Ginzburg-Landau equation. We find that states with winding number larger than a critical one are unstable, in the sense that they decay to states with smaller winding number. The transition from Phase to Defect Turbulence is interpreted as an ergodicity breaking transition which occurs when the range of stable winding numbers vanishes. Asymptotically stable states which are not spatio-temporally chaotic are described within the PT regime of nonzero winding number.
27 citations
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11 Mar 1996
TL;DR: In this paper, the existence of anti-zeros for the tetrahedral 3-monopole and other SU(2) BPS monopoles with the symmetries of the Platonic solids has been proved.
Abstract: Recently the existence of certain SU(2) BPS monopoles with the symmetries of the Platonic solids has been proved Numerical results in an earlier paper suggest that one of these new monopoles, the tetrahedral 3-monopole, has a remarkable new property, in that the number of zeros of the Higgs field is greater than the topological charge (number of monopoles) As a consequence, zeros of the Higgs field exist (called anti-zeros) around which the local winding number has opposite sign to that of the total winding In this letter we investigate the presence of anti-zeros for the other Platonic monopoles Other aspects of anti-zeros are also discussed
16 citations
TL;DR: In this paper, the Dirichlet problem for the semilinear equation of the vibrating string uxx uyy +f(x;y;u) = 0 in bounded domain with corner points was discussed.
Abstract: Using Mawhin’s coincidence topological degree arguments and xed point theory for non-expansive mappings results, we discuss the solvability of the Dirichlet problem for the semilinear equation of the vibrating string uxx uyy +f(x;y;u) = 0 in bounded domain with corner points. When the winding number associated to the domain is rational, we improve and extend some results of Lyashenko [8] and Lyashenko{Smiley [9]. The case where the winding number is irrational is also examined.
11 citations
TL;DR: In this article, the authors investigated the spectrum of D-branes and their interactions with closed strings and showed that a collection of many D-strings behaves, at large dilaton values, as a single multiply wound string, and they used this result and T-duality transformations to show that a similar phenomenon occurs for effective strings produced by wrapping pbranes on a small p-1-dimensional torus, for suitable coupling.
Abstract: We investigate some aspects of the spectrum of D-branes and their interactions with closed strings. As argued earlier, a collection of many D-strings behaves, at large dilaton values, as a single multiply wound string. We use this result and T-duality transformations to show that a similar phenomenon occurs for effective strings produced by wrapping p-branes on a small (p-1)-dimensional torus, for suitable coupling. To understand the decay of an excited D-string at large dilaton values, we study the decay of an elementary string at small dilaton values. A long string, multiply wound on a circle, with a small excitation energy is found to predominantly decay into another string with the same winding number and an unwound closed string (rather than two wound strings). This decay amplitude agrees, under duality, with the decay amplitude computed using the Born-Infeld action for the D-string. We compute the absorption cross section for the D-brane model studied by Callan and Maldacena. The absorption cross section for the dilaton equals that for the scalars obtained by reduction of the graviton, and both agree with the cross section expected from a classical hole with the same charges.
9 citations
TL;DR: The spectrum of the fermion zero modes in the vicinity of a vortex with fractional winding number is discussed in this article, inspired by the observation of the 1/2vortex in high-temperature superconductors made by [J.R. Kirtley, C.C. Tsuei, M. Rupp et al., Phys. Rev. Lett.
Abstract: The spectrum of the fermion zero modes in the vicinity of a vortex with fractional winding number is discussed. This is inspired by the observation of the 1/2-vortex in high-temperature superconductors made by [J.R. Kirtley, C.C. Tsuei, M. Rupp et al., Phys. Rev. Lett. 76, 1336 (1996)]. The fractional value of the winding number leads to a frac-tional value of the invariant which describes the topology of the energy spectrum of fermions. This results in the phenomenon of the “half-crossing:” the spectrum approaches zero but does not cross it, being captured at the zero energy level. The similarity with the phenomenon of fermion condensation is discussed.
9 citations
TL;DR: The spectrum of the fermion zero modes with fractional winding number is discussed in this article, which is inspired by the observation of the 1/2 vortex in high-temperature superconductors.
Abstract: The spectrum of the fermion zero modes in the vicinity of the vortex with fractional winding number is discussed. This is inspired by the observation of the 1/2 vortex in high-temperature superconductors (Kirtley, et al, Phys. Rev. Lett. 76 (1996) 1336). The fractional value of the winding number leads to the fractional value of the invariant, which describes the topology of the energy spectrum of fermions. This results in the phenomenon of the "half-crossing": the spectrum approaches zero but does not cross it, being captured at the zero energy level. The similarity with the phenomenon of the fermion condensation is discussed.
TL;DR: A detailed quantitative analysis of the transition process mediated by a sphaleron type non-Abelian gauge field configuration in a static Einstein universe and a closed analytical expression for the transition rate at the one-loop level is derived.
Abstract: A detailed quantitative analysis of the transition process mediated by a sphaleron type non-Abelian gauge field configuration in a static Einstein universe is carried out. By examining spectra of the fluctuation operators and applying the zeta function regularization scheme, a closed analytical expression for the transition rate at the one-loop level is derived. This is a unique example of an exact solution for a sphaleron model in $3+1$ spacetime dimensions.
Patent•
10 Dec 1996
TL;DR: In this paper, the effective winding part height of a post-deformation coil spring measured with an element line as a center that is divided by a coil average diameter is defined as the ratio of lateral force to up and down load.
Abstract: PURPOSE: To reduce lateral force acting on a compression coil spring by setting an effective winding number at a specific value within the range of the effective winding number being a specific number. CONSTITUTION: In the case of a graph showing how lateral force is changed due to spring specifications, an (x) axis shows a coil effective winding number, and a (y) axis shows the ratio of lateral force to up and down load, and a (z) axis shows a value (hereinafter called an effective winding part lengthwise and lateral ratio λ) which is the effective winding part height of a post-deformation coil spring measured with an element line as a center that is divided by a coil average diameter. From this drawing, it is evident that lateral force is changed periodically due to an effective winding line and the smaller the effective winding number becomes or the larger the effective winding part lengthwise and lateral ratio λ becomes, it tends to become the larger. Also, a minimum value is realized when the effective winding number is (n) (an integral number), and when it is 1.5n, a maximum value is indicated. Therefore, in the case of a compression coil spring to be used for a coil spring for suspension or the like, within the range of the effective winding number being from 2 to 5, the effective winding line is set at n±0.125 (n = an integral number). As a result, the lateral force of a compression coil spring can be reduced drastically.
TL;DR: In this article, the authors describe the dynamics of a resonant non-integrable Hamiltonian, where the term with behaves as a perturbation to the remaining integrable part (call it ) of the Hamiltonian.
Abstract: The purpose of this article is the description of the classical dynamics of a resonant non-integrable Hamiltonian, which is written in the form and where the term with behaves as a perturbation to the remaining integrable part (call it ) of the Hamiltonian. Apart from the chaotic region around the separatrix of , the dynamics of H is clearly different from that of only in the neighbourhood of low-order periodic orbits of , where coupling-induced resonance islands are seen to emerge. In order to model these resonance islands, is Taylor expanded in terms of its action integrals (thanks to recent exact analytical calculations) and the perturbation with is Fourier expanded in terms of the angles conjugate to the actions of . Retaining in the expansion only the term which is almost secular (because of the vicinity of the periodic orbit) leads to a local single resonance form of H. The classical frequencies and action integrals, which can be calculated analytically for this local expression of H, are shown to be in excellent agreement with `exact' numerical values deduced from power spectra and Poincare surfaces of section. It is pointed out in the discussion that all the trajectories inside coupling-induced resonance islands share one almost degenerate classical frequency, and that the width of the coupling-induced island grows as the square root of the perturbation parameter , but is inversely proportional to the square root of the slow classical frequency at the periodic orbit and to the square root of the derivative, with respect to the first action integral, of the winding number.
TL;DR: In this paper, the authors consider the case of the punctured plane for which the prepotential solution is of the form V=αθ+Φ(θ).
Abstract: We reconsider quantum mechanical systems based on the classical action being the period of a one-form over a cycle and elucidate three main points. First we show that the prepotential V is no longer completely arbitrary but obeys a consistency integral equation. That is the one-form dV defines the same period as the classical action. We then apply this to the case of the punctured plane for which the prepotential solution is of the form V=αθ+Φ(θ). The function Φ is any but a periodic function of the polar angle. For the topological information to be preserved, we require further that Φ be even. Second we point out the existence of a hidden scale which comes from the regularization of the infrared behavior of the solutions. This will then be used to eliminate certain invariants preselected on dimensional counting grounds. Then by discarding nonperiodic solutions as being nonphysical, we compute the expectation values of the BRST-exact observables with the general form of the prepotential using only the orthonormality of the solutions (periodic). Third we give topological interpretations of the invariants in terms of the topological invariants which live naturally on the punctured plane as the winding number and the fundamental group of homotopy, but this requires a priori twisting of the homotopy structure.
TL;DR: It is shown that, in the authors' approximation, the emerging population of long/infinite string is produced by the classical dynamics of the fields alone, being essentially unaffected by field fluctuations.
Abstract: We develop winding number correlation functions that allow us to assess the role of field fluctuations on vortex formation in an Abelian gauge theory. We compute the behavior of these correlation functions in simple circumstances and show how fluctuations are important in the vicinity of the phase transition. We further show that, in our approximation, the emerging population of long or infinite string is produced by the classical dynamics of the fields alone, being essentially unaffected by field fluctuations. \textcopyright{} 1996 The American Physical Society.
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TL;DR: In this article, the phase diagram of the minimum enthalpy configurations exhibits the structure of a complete $d$-dimensional devil's staircase, where the winding number of a minimum enthymeme configuration is locked to rational values, while the fraction of atoms in each sub-well is sub-commensurable with the winding.
Abstract: We solve exactly a class of Frenkel-Kontorova models with piecewise parabolic potential, which has $d$ sub-wells in a period. With careful analysis, we show that the phase diagram of the minimum enthalpy configurations exhibits the structure of a complete $d$-dimensional devil's staircase. The winding number of a minimum enthalpy configuration is locked to rational values, while the fraction of atoms in each sub-well is locked to values which are sub-commensurable with the winding number.
TL;DR: In this article, the statistical mechanics of a 1-dimensional gas of both adjoint and fundamental representation quarks were examined using large-N expansion and it was shown that, when the density of fundamental quarks is small, there is a first order phase transition at a critical temperature and adjoint quark density which can be interpreted as deconfinement.
Abstract: We examine the statistical mechanics of a 1-dimensional gas of both adjoint and fundamental representation quarks which interact with each other through 1+1-dimensional U(N) gauge fields. Using large-N expansion we show that, when the density of fundamental quarks is small, there is a first order phase transition at a critical temperature and adjoint quark density which can be interpreted as deconfinement. When the fundamental quark density is comparable to the adjoint quark density, the phase transition becomes a third order one. We formulate a way to distinguish the phases by considering the expectation values of high winding number Polyakov loop operators.
TL;DR: It is shown that the recent proof of the vanishing of the {theta} parameter when gauge transformations of arbitrary fractional winding numbers are allowed breaks down in precisely those cases where the representability condition is obeyed.
Abstract: The role which gauge transformations of noninteger winding numbers might play in non-Abelian gauge theories is studied. The phase factor acquired by the semiclassical physical states in an arbitrary background gauge field when they undergo a gauge transformation of an arbitrary real winding number is calculated in the path integral formalism assuming that a {theta}{ital F{tilde F}} term added to the Lagrangian plays the same role as in the case of integer winding numbers. Requiring that these states provide a representation of the group of {open_quote}{open_quote}large{close_quote}{close_quote} gauge transformations, a condition on the allowed backgrounds is obtained. It is shown that this representability condition is only satisfied in the monopole sector of a spontaneously broken gauge theory, but not in the vacuum sector of an unbroken or a spontaneously broken non-Abelian gauge theory. It is further shown that the recent proof of the vanishing of the {theta} parameter when gauge transformations of arbitrary fractional winding numbers are allowed breaks down in precisely those cases where the representability condition is obeyed because certain gauge transformations needed for the proof, and whose existence is assumed, are either spontaneously broken or cannot be globally defined as a result of a topological obstruction. {copyright} {italmore » 1996 The American Physical Society.}« less
TL;DR: In this article, the authors define the topological winding number for unimodal maps that share the essential properties of that of winding numbers for forced oscillators exhibiting period-doubling cascades.
Abstract: We define the topological winding number for unimodal maps that share the essential properties of that of winding numbers for forced oscillators exhibiting period-doubling cascades. It is demonstrated how this number can be computed for any of the periodic orbits in the first period-doubling cascade. The limiting winding number at the accumulation point of the first period-doubling cascade is also derived. It is shown that the limiting value for the winding number ω∞ can be computed as the Farey sum of any two neighbouring topological winding numbers in the period-doubling cascade. The derivations are all based on symbolic dynamics and simple combinatorics.
TL;DR: A model where a Chern-Simons term is coupled to the three-dimensional x-y model and this term endows vortices with an internal angular momentum and thus they acquire arbitrary statistical character is introduced.
Abstract: We introduce a model where a Chern-Simons term is coupled to the three-dimensional x-y model. This term endows vortices with an internal angular momentum and thus they acquire arbitrary statistical character. In our interpretation of the Chern-Simons term in the three-dimensional x-y model, it takes an integer value that can be written as a sum over all vortex lines of the product of the vortex charge and the winding number of the internal phase angle along that vortex line. We have used the Monte Carlo method to study the three-dimensional x-y model with the Chern-Simons term. Our findings suggest that this model belongs to the x-y universality class with the critical temperature growing with increasing internal angular momentum. \textcopyright{} 1996 The American Physical Society.
TL;DR: In this paper, an algebra of operators for the toroidal bosonic string is defined and its representations are constructed, and it is shown that there exist an infinite number of inequivalent quantizations, which are parametrized by two parameters 0≤s, t < 1.
Abstract: Target space duality is reconsidered from the viewpoint of quantization in a space with nontrivial topology. An algebra of operators for the toroidal bosonic string is defined and its representations are constructed. It is shown that there exist an infinite number of inequivalent quantizations, which are parametrized by two parameters 0≤s, t<1. The spectrum exhibits the duality only when s=t or –t (mod 1). A deformation of the algebra by a central extension is also introduced. It leads to a kind of twisted relation between the zero mode quantum number and the topological winding number.
TL;DR: In this paper, an algebra of operators for the toroidal bosonic string is defined and its representations are constructed, which leads to a kind of twisted relation between the zero mode quantum number and the topological winding number.
Abstract: Target space duality is reconsidered from the viewpoint of quantization in a space with nontrivial topology. An algebra of operators for the toroidal bosonic string is defined and its representations are constructed. It is shown that there exist an infinite number of inequivalent quantizations, which are parametrized by two parameters $ 0 \le s, t < 1 $. The spectrum exhibits the duality only when $ s = t $ or $ -t $ (mod 1). A deformation of the algebra by a central extension is also introduced. It leads to a kind of twisted relation between the zero mode quantum number and the topological winding number.
TL;DR: In this paper, the authors constructed sequences of axially symmetric multisphaleron solutions in SU(2) Yang-Mills-dilaton theory, which correspond to abelian magnetic monopoles.
Abstract: We construct sequences of axially symmetric multisphaleron solutions in SU(2) Yang-Mills-dilaton theory. The sequences are labelled by a winding number $n>1$. For $n=1$ the known sequence of spherically symmetric sphaleron solutions is obtained. The solutions within each sequence are labelled by the number of nodes $k$ of the gauge field functions. The limiting solutions of the sequences correspond to abelian magnetic monopoles with $n$ units of charge and energy $E \propto n$.