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P. Olesen

Publications and source records attributed to P. Olesen.

At least 19 recordsLinked to original sources
arXiv2016

A center vortex representaton of the classical SU(2) vacuum

The classical massless SU(2) field theory has an infinite number of gauge equivalent representations of the vacuum. We show that among these there exists a non-perturbative center vortex representation with some similarity to the quantum vacuum of the same theory. This classical SU(2) vacuum consists of a lattice of center vortex pairs combining to triviality. However, this triviality can be broken by perturbations, for example by adding a mass term, or by considering the electroweak theory where the Higgs field does the breaking, or by quantum fluctuations like in QCD.

hep-th↗
arXiv2015

Dimensional reduction in freely decaying turbulent non-helical magnetic fields

We show that the self-similarity property of decaying turbulent non-helical magnetic fields is the same in all dimensions. It is shown that these fields produce an inverse transfer in all dimensions. It is also shown that this phenomenon in a certain gauge can be assigned to a time independent value of the squared vector potential. This mechanism is similar to what happens in the well known inverse cascade in two dimensional magnetohydrodynamics.

astro-ph.CO↗
arXiv2015

Inverse transfer of self-similar decaying turbulent non-helical magnetic field

We show that decaying turbulent non-helical magnetic fields satisfy a self-similarity relation according to which the relevant scales increase as time passes (inverse cascade or inverse transfer). We compute analytically quantities which have previously been determined by numerical calculations, for example the average energy and the integral scale which are proportional to 1/t and the square root of t,respectively, where t is the time. We also briefly discuss self-similarity for the helical case.

astro-ph.CO↗
arXiv2013

Anti-screening ferromagnetic superconductivity

We consider the Ginzburg-Landau mean field theory of ferromagnetic superconductors with complex order parameter $ψ_i, i=1,2,3$. Below the critical temperature superconductivity is generated by means of a tachyonic term in the free energy $-α|ψ_i|^2$ $(α>0)$, stabilized by a $ψ^4$-term. However, we show that when $α$ becomes negative superconductivity can also be generated spontaneously by the magnetic field through the Zeeman like coupling between the field and the spin of the order parameter, in analogy with what happens in W-meson condensation. We also show that this mechanism leads to a vortex lattice which has anti-screening currents, enhancing the magnetic field instead of counteracting it. The lattice of vortices is a collective phenomenon where the individual elements do not exist in isolated form. If the parameter $α$ vanishes it is possible to obtain an explicit form of the vortex lattice in terms of Weierstrass' p-function.

hep-th↗
arXiv2012

W condensation at the LHC?

We discuss the possibility of the generation and subsequent decay of a W and Z condensate in LHC collisions. We point out that a process like $h\rightarrowγγ$, which involves a virtual W loop, may have an enhancement if the condensate exists. Even if this is not the case, the W propagator is influenced by the strong, but short lived magnetic field generated in proton-proton collisions. This will influence the di-gamma decay of the Higgs particle.

hep-ph↗
arXiv2012

The QCD scattering amplitude from area behaved Wilson loops

We explicitly construct the dominant saddle-point trajectory in the sum-over-path representation of meson scattering amplitudes in large $N$ QCD for area-behaved Wilson loops and show that it dominates in the Regge regime. The graphic representation of the leading trajectory is very similar to the diagrams widely used to illustrate meson scattering.

hep-th↗
arXiv2007

On the zero viscosity limit

The question of whether the zero viscosity limit $ν\to 0$ is identical to the no viscosity $ν\equiv 0$ case is investigated in a simple shell (GOY) model with only three shells. We find that it is possible to express two velocities in terms of Bessel functions. The third velocity function acts as a background. The relevant Bessel functions are infinitely oscillating as $ν\to 0$ and do not have a limiting value. Therefore two of the velocity functions of this three-shell model are not analytic functions of $ν$ at the point $ν=0$. We also mention a perturbative method which may be used to improve the model.

hep-th↗
arXiv2003

An Integrable Version of Burgers Equation in "Magnetohydrodynamics"

It is pointed out that for the case of (compressible) magnetohydrodynamics (MHD) with the fields $v_y(y,t)$ and $B_x(y,t)$ one can have equations of the Burgers type which are integrable. We discuss the solutions. It turns out that the propagation of the non-linear effects is governed by the initial velocity (as in Burgers case) as well as by the initial Alfvén velocity. Many results previously obtained for the Burgers equation can be transferred to the MHD case. We also discuss equipartition $v_y=\pm B_x$. It is shown that an initial localized small scale magnetic field will end up in fields moving to the left and the right, thus transporting energy from smaller to larger distances.

nlin.SI↗
arXiv2002

Proceedings to the Workshops ''What comes beyond the Standard model'' 2000,2001, VOLUME 1: Festschrift dedicated to the 60th birthday of Holger Bech Nielsen

The present volume is the collection of contributions by friends of Holger Bech Nielsen for his 60th birthday. Contents: 1.Unified internal space of spins and charges (N. Mankoc Borstnik) 2.Semitopological Q-Rings (M. Axenides) 3.Non-local axial anomalies in the Standard model (D. Melikhov, B. Stech) 4.Could there be a fourth generation? (C.D. Froggatt) 5.Another complex Bateman equation (D.B. Fairlie) 6.Non-associative loops for Holger Bech Nielsen (P.H. Frampton) 7.Particles, fluids and vortices (J.W. van Holten) 8.Results on 2D current algebras (J.L. Petersen) 9.Phase transition in gauge theories and the Planck scale physics (L.V. Laperashvili and D.A. Ryzhikh) 10.Some remarks on the 'classical' large N limit (P. Olesen) 11.String theory and the size of hadrons (L. Susskind) 12.Relativity and $c/sqrt3$ (S.I. Blinnikov, L.B. Okun and M.I. Vysotsky) 13.Vortices (Jeff Greensite)

hep-ph↗
arXiv2002

Scaling and the prediction of energy spectra in decaying hydrodynamic turbulence

Few rigorous results are derived for fully developed turbulence. By applying the scaling properties of the Navier-Stokes equation we have derived a relation for the energy spectrum valid for unforced or decaying isotropic turbulence. We find the existence of a scaling function $ψ$. The energy spectrum can at any time by a suitable rescaling be mapped onto this function. This indicates that the initial (primordial) energy spectrum is in principle retained in the energy spectrum observed at any later time, and the principle of permanence of large eddies is derived. The result can be seen as a restoration of the determinism of the Navier-Stokes equation in the mean. We compare our results with a windtunnel experiment and find good agreement.

nlin.CD↗
arXiv2001

Noncommutative String Worldsheets from Matrix Models

We study dynamical effects of introducing noncommutativity on string worldsheets by using a matrix model obtained from the zero-volume limit of four-dimensional SU($N$) Yang-Mills theory. Although the dimensionless noncommutativity parameter is of order 1/N, its effect is found to be non-negligible even in the large $N$ limit due to the existence of higher Fourier modes. We find that the Poisson bracket grows much faster than the Moyal bracket as we increase $N$, which means in particular that the two quantities do not coincide in the large $N$ limit. The well-known instability of bosonic worldsheets due to long spikes is shown to be cured by the noncommutativity. The extrinsic geometry of the worldsheet is described by a crumpled surface with a large Hausdorff dimension.

hep-th↗
arXiv2000

Broadening of the QCD3 flux tube from the AdS/CFT correspondence

We use the finite temperature AdS/CFT approach to demonstrate logarithmic broadening of the confining QCD3 flux tube as a function of quark separation. This behavior indicates that, unlike lattice QCD, there is no roughening transition in the AdS/CFT formulation, which raises the interesting possibility of extrapolating strong coupling results to weak couplings by the use of resummation techniques. In the zero-temperature non-confining limit, we find that this logarithmic broadening of the field strength distribution is absent. Our results are obtained numerically at strong couplings, in the supergravity approximation.

hep-th↗
arXiv2000

Phase transition in Wilson loop correlator from AdS/CFT correspondence

A previous calculation of the phase transition in the Wilson loop correlator in the zero temperature AdS/CFT correspondence is extended to the case where the loops are concentric circles of unequal radii. This phase transition occurs due to the instability of the classical string stretched between the loops. We compute the string action and its expansion in the distance h between the loops for small h. We also find that the connected minimal surface is subleading or does not even exist when h=0 and the radii are considerably different. This feature has no analogue in flat space.

hep-th↗
arXiv1999

Pulses in the Zero-Spacing Limit of the GOY Model

We study the propagation of localised disturbances in a turbulent, but momentarily quiescent and unforced shell model (an approximation of the Navier-Stokes equations on a set of exponentially spaced momentum shells). These disturbances represent bursts of turbulence travelling down the inertial range, which is thought to be responsible for the intermittency observed in turbulence. Starting from the GOY shell model, we go to the limit where the distance between succeeding shells approaches zero (``the zero spacing limit'') and helicity conservation is retained. We obtain a discrete field theory which is numerically shown to have pulse solutions travelling with constant speed and with unchanged form. We give numerical evidence that the model might even be exactly integrable, although the continuum limit seems to be singular and the pulses show an unusual super exponential decay to zero as $\exp(- \mathrm{const} σ^n)$ when $n \to \infty$, where $σ$ is the {\em golden mean}. For finite momentum shell spacing, we argue that the pulses should accelerate, moving to infinity in a finite time. Finally we show that the maximal Lyapunov exponent of the GOY model approaches zero in this limit.

chao-dyn↗
arXiv1999

Some Speculations on the Gauge Coupling in the AdS/CFT Approach

We propose the principle that the scale of the glueball masses in the AdS/CFT approach to QCD should be set by the square root of the string tension. It then turns out that the strong bare coupling runs logarithmically with the ultraviolet cutoff T if first order world sheet fluctuations are included. We also point out that in the end, when all corrections are included, one should obtain an equation for the coupling running with T which has some similarity with the equation for the strong bare coupling.

hep-th↗
arXiv1999

Worldsheet Fluctuations and the Heavy Quark Potential in the AdS/CFT Approach

We consider contributions to the heavy quark potential, in the AdS/CFT approach to SU(N) gauge theory, which arise from first order fluctuations of the associated worldsheet in anti-deSitter space. The gaussian fluctuations occur around a classical worldsheet configuration resembling an infinite square well, with the bottom of the well lying at the AdS horizon. The eigenvalues of the corresponding Laplacian operators can be shown numerically to be very close to those in flat space. We find that two of the transverse world sheet fields become massive, which may have implications for the existence of a L{ü}scher term in the heavy quark potential. It is also suggested that these massive degrees of freedom may relate to extrinsic curvature in an effective D=4 string theory.

hep-th↗
arXiv1998

Remarks on the Heavy Quark Potential in the Supergravity Approach

We point out certain unexpected features of the planar QCD3 confining potential, as computed from a classical worldsheet action in an AdS metric via the Maldacena conjecture. We show that there is no Luscher c/R term in the static-quark potential, which is contrary to both the prediction of various effective string models, and the results of some recent lattice Monte Carlo studies. It is also noted that the glueball masses extracted from classical supergravity tend to finite, coupling-independent constants in the strong coupling limit, even as the string tension tends to infinity in the same limit; this is a counter-intuitive result.

hep-th↗