String Density Research Articles

SCENARIOS OF COSMIC STRING WITH A VARIABLE COSMOLOGICAL CONSTANT

Exact solutions to the Einstein field equations with cosmic string and a space-varying cosmological constant, viz. Λ = Λ(r), in the energy–momentum tensors are presented. Three cases have been studied: the variable cosmological constant (1) has power law dependence, (2) is proportional to the string fluid density, and (3) is purely a constant. Some cases of interesting physical consequences have been found where (i) the variable cosmological constant can be represented by a power law of the type Λ = 3r-2, (ii) the variable cosmological constant and the cosmic string density are interdependent according to the relation Λ = -8πρs, and (iii) the cosmic string density can be scaled by a power law of the type ρs= r-2. It is also shown that several known solutions can be recovered from the general form of the solutions obtained here.

Worldsheet analysis of gauge/gravity dualities

Gauge/gravity dualities are investigated from the worldsheet point of view. In [H. Kawai, T. Suyama, AdS/CFT correspondence as a consequence of scale invariance, Nucl. Phys. B 789 (2008) 209, arXiv:0706.1163 [hep-th]; H. Kawai, T. Suyama, Some implications of perturbative approach to AdS/CFT correspondence, Nucl. Phys. B 794 (2008) 1, arXiv:0708.2463 [hep-th]], a duality between 4d SYM and supergravity on AdS 5 × S 5 has been partly explained by using an anisotropic scale invariance of worldsheet theory. In this paper, we refine the argument and generalize it to lower dimensional cases. We show the correspondence between the Wilson loops in ( p + 1 ) -d SYM and the minimal surface in the black p-brane background. Although the scale invariance does not exist in these cases, the generalized scale transformation can be utilized. We also find that the energy density of open strings can be related to the ADM mass of the p-brane without relying on this symmetry.

Long spatio-temporally stationary filaments in air using short pulse UV laser Bessel beams

The formation of long stationary filaments resulting in uniform high density plasma strings in air using short pulse UV laser Bessel beams is shown. The length and the electron density of the plasma strings can be easily tuned by adjusting the conical Bessel wavefront angle. It is shown that in this regime the length of the plasma string can be extended over meter-long scales without any compromise in the string uniformity or any temporal evolution of the filamented laser pulse.

Velocity-dependent models for non-Abelian/entangled string networks

We develop velocity-dependent models describing the evolution of string networks that involve several types of interacting strings, each with a different tension. These incorporate the formation of Y-type junctions with links stretching between colliding strings, while always ensuring energy conservation. These models can be used to describe network evolution for non-Abelian strings as well as cosmic superstrings. The application to ${Z}_{N}$ strings in which interactions are topologically constrained, demonstrates that a scaling regime is generally reached which involves a hierarchy of string densities with the lightest most abundant. We also study hybrid networks of cosmic superstrings, where energetic considerations are more important in determining interaction outcomes. We again find that networks tend towards scaling, with the three lightest network components being dominant and having comparable number densities, while the heavier string states are suppressed. A more quantitative analysis depends on the precise calculation of the string interaction matrix using the underlying string or field theory. Nevertheless, these results provide further evidence that the presence of junctions in a string network does not obstruct scaling.

On string solutions of the Bethe equations in the % MathType!MTEF!2!1!+- % feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBqj3BWbIqubWexLMBb50ujbqegm0B % 1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqr % Ffpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0F % irpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaa % GcbaWefv3ySLgznfgDOfdarCqr1ngBPrginfgDObYtUvgaiuaacqWF % neVtryqr1ngBPrgaiyaacqGF9aqpcqGF0aanaaa!4928! $$ \mathcal{N} = 4 $$ supersymmetric Yang-Mills theory

The Bethe equations which arise in description of the spectrum of the dilatation operator for the su(2) sector of the $$ \mathcal{N} = 4 $$ supersymmetric Yang-Mills theory are considered in the anti-ferromagnetic regime. These equations are a deformation of those for the Heisenberg XXX magnet. We prove that in the thermodynamic limit, roots of the deformed equations group into strings. We prove that the corresponding Yang's action is convex, which implies the uniqueness of a solution for centers of the strings. The state formed by strings of length (2n+1) is considered, and the density of their distribution is found. It is shown that the energy of such a state decreases as n grows. It is observed that the nonanalyticity of the left-hand sides of the Bethe equations leads to an additional contribution to the density and energy of strings of even length. We conclude that the structure of the anti-ferromagnetic vacuum is determined by the behavior of exponential corrections to string solutions in the thermodynamic limit and, possibly, involves strings of length 2. Bibliography: 14 titles.

Microlensing by cosmic strings

We consider the signature and detectability of gravitational microlensing of distant quasars by cosmic strings. Because of the simple image configuration such events will have a characteristic lightcurve, in which a source would appear to brighten by exactly a factor of 2, before reverting to its original apparent brightness. We calculate the optical depth and event rate, and conclude that current predictions and limits on the total length of strings on the sky imply optical depths of 10 −8 and event rates of fewer than one event per 10 9 sources per year. Disregarding those predictions but replacing them with limits on the density of cosmic strings from the cosmic microwave background fluctuation spectrum, leaves only a small region of parameter space (in which the sky contains about 3 × 10 5 strings with deficit angle of the order of 0.3 milli-seconds) for which a microlensing survey of exposure 10 7 source years, spanning a 20–40-year period, might reveal the presence of cosmic strings.

Direct observation of cosmic strings via their strong gravitational lensing effect – I. Predictions for high-resolution imaging surveys

We use current theoretical estimates for the density of long cosmic strings to predict the number of strong gravitational lensing events in astronomical imaging surveys as a function of angular resolution and survey area. We show that angular resolution is the single most important factor, and that interesting limits on the dimensionless string tension G{mu}/c{sup 2} can be obtained by existing and planned surveys. At the resolution of the Hubble Space Telescope (0'.14), it is sufficient to survey of order a square degree -- well within reach of the current HST archive -- to probe the regime G{mu}/c{sup 2} {approx} 10{sup -8}. If lensing by cosmic strings is not detected, such a survey would improve the limit on the string tension by an order of magnitude on that available from the cosmic microwave background. At the resolution (0'.028) attainable with the next generation of large ground based instruments, both in the radio and the infra-red with adaptive optics, surveying a sky area of order ten square degrees will allow us to probe the G{mu}/c{sup 2} {approx} 10{sup -9} regime. These limits will not be improved significantly by increasing the solid angle of the survey.

Five-dimensional axially symmetric string cosmological model in Lyra manifold

In this paper we constructed five dimensional axially symmetric cosmological model generated by a cloud of strings with particles attached to them in Lyra manifold. Out of the two different cases obtained one case leads to the five dimensional vacuum universe in general theory of relativity while the other case yields a string cosmological model in Lyra manifold. In the cosmic string model we observed that the sum of tension density and rest energy density of strings vanishes and this model is also inflationary.

Physical modelling of the piano string scale

Several stages of physics-based mathematical modelling are described for the design of the piano string scale. Strings are assumed to be perfectly flexible, and piano hammers are described by a nonlinear hysteretic model. It is also assumed that the parameters of the hammers for the whole hammer set are determined experimentally beforehand. Simulation procedures are used to systematically adjust the structure of the piano scale to its optimal value. The efficiency of the piano scale is improved by the analysis of the numerically simulated string motion and spectra of the string vibrations excited by the impact of the hammer. The set of variables to be optimized includes the linear mass density and tension of the piano strings and the position of the striking point. In addition, the problem of choosing appropriate tensions for neighbouring strings terminated on separate bass and treble bridges is considered.

ENERGY AND SYSTEM SIZE DEPENDENCE STUDY OF THE PERCOLATION PHASE TRANSITION

Multiparticle production at high energies is described in terms of color strings stretched between the projectile and target. As the string density increases, overlap in the transverse plane leads to cluster formation. At some critical density a macroscopic cluster appears, spanning the entire system. This marks the percolation phase transition. Data from [Formula: see text] p + p , d + Au and Au + Au collisions at RHIC has been analyzed using the STAR detector to obtain the percolation density parameter, η. The particle pT spectrum from 200 GeV p + p data is parametrized using a power law. Values of the fit parameters are used in the d + Au and Au + Au analysis. For 200 GeV Au + Au collisions, the value of η is found to lie above the critical percolation threshold, while for other collision systems and energies, it is below the critical value. This supports the idea of string percolation, which at high enough string density is a possible mechanism to explore the hadronic phase transition to a quark-gluon plasma.

SEMICLASSICAL (QUANTUM FIELD THEORY) AND QUANTUM (STRING) DE SITTER REGIMES: NEW RESULTS

We compute the quantum string entropy S s (m, H) from the microscopic string density of states ρ s (m, H) of mass m in de Sitter space–time. We find for high m (high Hm → c/α') a new phase transition at the critical string temperature T s = (1/2πk B )L cl c2/α', higher than the flat space (Hagedorn) temperature t s (L cl = c/H, the Hubble constant H acts at the transition, producing a smaller string constant α' and thus, a higher tension). T s is the precise quantum dual of the semiclassical (QFT Hawking–Gibbons) de Sitter temperature T sem = ħ c/(2πk B L cl ). By precisely identifying the semiclassical and quantum (string) de Sitter regimes, we find a new formula for the full de Sitter entropy S sem (H), as a function of the usual Bekenstein–Hawking entropy [Formula: see text]. For L cl ≫ ℓ Planck , i.e. for low [Formula: see text] is the leading term, but for high H near c/ℓ Planck , a new phase transition operates and the whole entropy S sem (H) is drastically different from the Bekenstein–Hawking entropy [Formula: see text]. We compute the string quantum emission cross-section σ string by a black hole in de Sitter (or asymptotically de Sitter) space–time (bhdS). For T sem bhdS ℓ T s (early evaporation stage), it shows the QFT Hawking emission with temperature T sem bhdS (semiclassical regime). For T sem bhdS → T s , σ string exhibits a phase transition into a string de Sitter state of size [Formula: see text], [Formula: see text], and string de Sitter temperature T s . Instead of featuring a single pole singularity in the temperature (Carlitz transition), it features a square root branch point (de Vega–Sanchez transition). New bounds on the black hole radius r g emerge in the bhdS string regime: it can become r g = L s /2, or it can reach a more quantum value, r g = 0.365 ℓ s .

SEMICLASSICAL (QFT) AND QUANTUM (STRING) ROTATING BLACK HOLES AND THEIR EVAPORATION: NEW RESULTS

Combination of both quantum field theory (QFT) and string theory in curved backgrounds in a consistent framework, the string analogue model, allows us to provide a full picture of the Kerr–Newman black hole and its evaporation going beyond the current picture. We compute the quantum emission cross-section of strings by a Kerr–Newman black hole (KNbh). It shows the black hole emission at the Hawking temperature T sem in the early stage of evaporation and the new string emission featuring a Hagedorn transition into a string state of temperature Ts at the last stages. New bounds on J and Q emerge in the quantum string regime (besides the known ones of the classical/semiclassical QFT regime). The last state of evaporation of a semiclassical Kerr–Newman black hole with mass M > m Pl , angular momentum J and charge Q is a string state of temperature Ts, string mass Ms, J = 0 and Q = 0, decaying as usual quantum strings do into all kinds of particles. (Naturally, in this framework, there is no loss of information, (there is no paradox at all).) We compute the string entropy Ss(m, j) from the microscopic string density of states of mass m and spin mode j, ρ(m, j). (Besides the Hagedorn transition at Ts) we find for high j (extremal string states j → m2α′c), a new phase transition at a temperature [Formula: see text], higher than Ts. By precisely identifying the semiclassical and quantum (string) gravity regimes, we find a new formula for the Kerr black hole entropy S sem (M, J), as a function of the usual Bekenstein–Hawking entropy [Formula: see text]. For M ≫ m Pl and J < GM2/c, [Formula: see text] is the leading term, but for high angular momentum, (nearly extremal case J = GM2/c), a gravitational phase transition operates and the whole entropy S sem is drastically different from the Bekenstein–Hawking entropy [Formula: see text]. This new extremal black hole transition occurs at a temperature T sem J = (J/ℏ)T sem , higher than the Hawking temperature T sem .

SEMICLASSICAL (QFT) AND QUANTUM (STRING) ANTI-DE SITTER REGIMES: NEW RESULTS

We compute the quantum string entropy Ss(m, H) from the microscopic string density of states ρs(m, H) of mass m in Anti-de Sitter space–time. For high m, (high Hm → c/α′), no phase transition occurs at the Anti-de Sitter string temperature Ts = (1/2πkB)L cl c2/α′, which is higher than the flat space (Hagedorn) temperature ts. (L cl = c/H, the Hubble constant H acts as producing a smaller string constant α′ and thus, a higher tension). Ts is the precise quantum dual of the semiclassical (QFT) Anti-de Sitter temperature scale T sem = ℏc/(2πkBL cl ). We compute the quantum string emission σ string by a black hole in Anti-de Sitter (or asymptotically Anti-de Sitter) space–time (bhAdS). For T sem bhAdS ≪ Ts (early evaporation stage), it shows the QFT Hawking emission with temperature T sem bhAdS (semiclassical regime). For T sem bhAdS → Ts, it exhibits a phase transition into a Anti-de Sitter string state of size [Formula: see text], and Anti-de Sitter string temperature Ts. New string bounds on the black hole emerge in the bhAdS string regime. The bhAdS string regime determines a maximal value for H : H max = 0.841c/ls. The minimal black hole radius in Anti-de Sitter space–time turns out to be rg min = 0.841ls, and is larger than the minimal black hole radius in de Sitter space–time by a numerical factor equal to 2.304. We find a new formula for the full AdS entropy S sem (H), as a function of the usual Bekenstein–Hawking entropy [Formula: see text]. For L cl ≫ ℓ Planck , i.e. for low H ≪ c/ℓ Planck , or classical regime, [Formula: see text] is the leading term with its logarithmic correction, but for high H ≥ c/ℓ Planck or quantum regime, no phase transition operates, in contrast to de Sitter space, and the entropy S sem (H) is very different from the Bekenstein–Hawking term [Formula: see text].

The string density problem and the Camassa–Holm equation

Recently, the string density problem, considered in the pioneering work of M. G. Kreĭn, has arisen naturally in connection with the Camassa-Holm equation for shallow water waves. In this paper we review the forward and inverse string density problems, with some numerical examples, and relate it to the Camassa-Holm equation, with special reference to multi-peakon/anti-peakon solutions. Under stronger assumptions, the Camassa-Holm spectral problem and the string density problem can be transformed to the Schrödinger spectral problem and its inverse problem. Recent results exploiting this transformation are reviewed briefly.

Nonequilibrium relaxations within the ground-state manifold in the antiferromagnetic Ising model on a triangular lattice

We present an extensive Monte Carlo simulation study on the nonequilibrium kinetics of triangular antiferromagnetic Ising model within the ground state ensemble which consists of sectors, each of which is characterized by a unique value of the string density p through a dimer covering method. Building upon our recent work [Phys. Rev. E 68, 066127 (2003)] where we considered the nonequilibrium relaxation observed within the dominant sector with p=2/3, we here focus on the nonequilibrium kinetics within the minor sectors with p<2/3. The initial configurations are chosen as those in which the strings are straight and evenly distributed. In the minor sectors, we observe a characteristic spatial anisotropy in both equilibrium and nonequilibrium spatial correlations. We observe emergence of a critical relaxation region (in the spatial and temporal domain) which grows as p deviates from p=2/3. Spatial anisotropy appears in the equilibrium spatial correlation with the characteristic length scale xi(e,V)(p) diverging with vanishing string density as xi(e,V)(p) approximately p(-2) along the vertical direction, while along the horizontal direction the spatial length scale diverges as xi(e,H) approximately p(-1). Analytic forms for the anisotropic equilibrium correlation functions are given. We also find that the spin autocorrelation function A(t) shows a simple scaling behavior A(t)=A(t/tau(A)(p)), where the time scale tau(A)(p) shows a power-law divergence with vanishing p as tau(A)(p) approximately p(-phi) with phi approximately or equal to 4. These features can be understood in terms of random walk nature of the fluctuations of the strings within the typical separation between neighboring strings.

Effect of reconnection probability on cosmic (super)string network density

We perform numerical simulations of cosmic string evolution with intercommuting probability $P$ in the range $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\ensuremath{\le}P\ensuremath{\le}1$, both in the matter and radiation eras. We find that the dependence of the scaling density on $P$ is significantly different than the suggested $\ensuremath{\rho}\ensuremath{\propto}{P}^{\ensuremath{-}1}$ form. In particular, for probabilities greater than $P\ensuremath{\simeq}0.1$, $\ensuremath{\rho}(1/P)$ is approximately flat, but for $P$ less than this value it is well-fitted by a power-law with exponent ${0.6}_{\ensuremath{-}0.12}^{+0.15}$. This shows that the enhancement of string densities due to a small intercommuting probability is much less prominent than initially anticipated. We interpret the flat part of $\ensuremath{\rho}(1/P)$ in terms of multiple opportunities for string reconnections during one crossing time, due to small-scale wiggles. We also propose a two-scale model, which satisfactorily fits our results over the whole range of $P$ covered by the simulations.

Model-generated lexical activity predicts graded ERP amplitudes in lexical decision

Recent neurocognitive studies of visual word recognition provide information about neuronal networks correlated with processes involved in lexical access and their time course (e.g., [Holcomb, Ph.J., Grainger J. and O'Rourke, T. (2002). An Electrophysiological Study of the Effects of Orthographic Neighborhood Size on Printed Word Perception, J. of Cogn. Neurosci. 14 938–950; Binder, J.R., McKiernan, K.A., Parsons, M.E., Westbury, C.F., Possing, E.T., Kaufman, J.N. and Buchanan, L. (2003). Neural Correlates of Lexical Access during Visual Word Recognition, J. Cogn. Neurosci. 15 372–393.]). These studies relate the orthographic neighborhood density of letter strings to the amount of global lexical activity in the brain, generated by a hypothetical mental lexicon as speculated in an early paper by [Jacobs, A.M. and Carr, T.H. (1995). Mind mappers and cognitive modelers: Toward cross-fertilization, Behav. Brain. Sci. 18 362–363]. The present study uses model-generated stimuli theoretically eliciting graded global lexical activity and relates this activity to activation of lexical processing networks using event-related potentials (ERPs). The results from a lexical decision task provide evidence for an effect of lexicality around 350 ms post-stimulus and also a graded effect of global lexical activity for nonwords around 500 ms post-stimulus. The data are interpreted as reflecting two different decision processes: an identification process based on local lexical activity underlying the ‘yes’ response to words and a temporal deadline process underlying the ‘no’ response to nonwords based on global lexical activity.

On the stability of the primordial closed string gas

We recast the study of a closed string gas in a toroidal container in the physical situation in which the single string density of states is independent of the volume because energy density is very high. This includes the gas for the well known Brandenberger-Vafa cosmological scenario. We describe the gas in the grand canonical and microcanonical ensembles. In the microcanonical description, we find a result that clearly confronts the Brandenberger-Vafa calculation to get the specific heat of the system. The important point is that we use the same approach to the problem but a different regularization. By the way, we show that, in the complex temperature formalism, at the Hagedorn singularity, the analytic structure obtained from the so-called F-representation of the free energy coincides with the one computed using the S-representation.

Cosmological evolution of cosmic strings with time-dependent tension

We discuss the cosmological evolution of cosmic strings with time-dependent tension. We show that, in the case that the tension changes as a power of time, the cosmic string network obeys the scaling solution: the characteristic scale of the string network grows with the time. But due to the time dependence of the tension, the ratio of the energy density of infinite strings to that of the background universe is {\it not} necessarily constant.

CONCEPTUAL UNIFICATION OF ELEMENTARY PARTICLES, BLACK HOLES, QUANTUM DE SITTER AND ANTI-DE SITTER STRING STATES

We provide a conceptual unified description of the quantum properties of black holes (BH), elementary particles, de Sitter (dS) and Anti-de Sitter (AdS) string states.The conducting line of argument is the classical–quantum (de Broglie, Compton) duality here extended to the quantum gravity (string) regime (wave–particle–string duality). The semiclassical (QFT) and quantum (string) gravity regimes are respectively characterized and related: sizes, masses, accelerations and temperatures. The Hawking temperature, elementary particle and string temperatures are shown to be the same concept in different energy regimes and turn out the precise classical–quantum duals of each other; similarly, this result holds for the BH decay rate, heavy particle and string decay rates; BH evaporation ends as quantum string decay into pure (nonmixed) radiation. Microscopic density of states and entropies in the two (semiclassical and quantum) gravity regimes are derived and related, an unifying formula for BH, dS and AdS states is provided in the two regimes. A string phase transition towards the dS string temperature (which is shown to be the precise quantum dual of the semiclassical (Hawking–Gibbons) dS temperature) is found and characterized; such phase transition does not occurs in AdS alone. High string masses (temperatures) show a further (square root temperature behavior) sector in AdS. From the string mass spectrum and string density of states in curved backgrounds, quantum properties of the backgrounds themselves are extracted and the quantum mass spectrum of BH, dS and AdS radii obtained.