String Phase Research Articles

Stability of BTZ black strings

We study the dynamical stability of the Banados-Teitelboim-Zanelli (BTZ) black string against fermionic and gravitational perturbations. The BTZ black string is not always stable against these perturbations. There exist threshold values for ${m}^{2}$ related to the compactification of the extra dimension for fermionic perturbation, the scalar part of the gravitational perturbation, and the tensor perturbation, respectively. Above the threshold values, perturbations are stable; while below these thresholds, perturbations can be unstable. We find that this nontrivial stability behavior qualitatively agrees with that predicted by a thermodynamical argument, showing that the BTZ black string phase is not the privileged stable phase.

Detection of sharing by descent, long-range phasing and haplotype imputation.

Uncertainty about the phase of strings of SNPs creates complications in genetic analysis, although methods have been developed for phasing population-based samples. However, these methods can only phase a small number of SNPs effectively and become unreliable when applied to SNPs spanning many linkage disequilibrium (LD) blocks. Here we show how to phase more than 1,000 SNPs simultaneously for a large fraction of the 35,528 Icelanders genotyped by Illumina chips. Moreover, haplotypes that are identical by descent (IBD) between close and distant relatives, for example, those separated by ten meioses or more, can often be reliably detected. This method is particularly powerful in studies of the inheritance of recurrent mutations and fine-scale recombinations in large sample sets. A further extension of the method allows us to impute long haplotypes for individuals who are not genotyped.

Can the Hagedorn phase transition be explained from matrix model for strings?

The partition function of BFSS matrix model is studied for two different classical backgrounds up to 1-loop level. One of the backgrounds correspond to a membrane wrapped around a compact direction and another to a localised cluster of D0-branes. It is shown that, there exist phase transitions between these two configurations - but only in presence of an IR cut-off. The low temperature phase corresponds to a string (wrapped membrane) phase and so we call this the Hagedorn phase transition. While the presence of an IR cut-off seemingly is only required for perturbative analysis to be valid, the physical necessity of such a cut-off can be seen in the dual super-gravity side. It has been argued from entropy considerations that a finite size horizon must develop even in an extremal configuration of D0-branes, from higher derivative O(gs) corrections to super-gravity. It can then be shown that the Hagedorn like transition exists in super-gravity also. Interestingly the perturbative analysis also shows a second phase transition back to a string phase. This is reminiscent of the Gregory-Laflamme instability.

Phase behavior of a simple dipolar fluid under shear flow in an electric field

Nonequilibrium molecular dynamics simulations are performed on a dense simple dipolar fluid under a planar Couette shear flow. Shear generates heat, which is removed by thermostatting terms added to the equations of motion of the fluid particles. The spatial structure of simple fluids at high shear rates is known to depend strongly on the thermostatting mechanism chosen. Kinetic thermostats are either biased or unbiased: biased thermostats neglect the existence of secondary flows that appear at high shear rates superimposed upon the linear velocity profile of the fluid. Simulations that employ a biased thermostat produce a string phase where particles align in strings with hexagonal symmetry along the direction of the flow. This phase is known to be a simulation artifact of biased thermostatting, and has not been observed by experiments on colloidal suspensions under shear flow. In this paper, we investigate the possibility of using a suitably directed electric field, which is coupled to the dipole moments of the fluid particles, to stabilize the string phase. We explore several thermostatting mechanisms where either the kinetic or configurational fluid degrees of freedom are thermostated. Some of these mechanisms do not yield a string phase, but rather a shear-thickening phase; in this case, we find the influence of the dipolar interactions and external field on the packing structure, and in turn their influence on the shear viscosity at the onset of this shear-thickening regime.

SEMICLASSICAL AND QUANTUM BLACK HOLES AND THEIR EVAPORATION, DE SITTER AND ANTI-DE SITTER REGIMES, GRAVITATIONAL AND STRING PHASE TRANSITIONS

An effective string theory in physically relevant cosmological and black hole space–times is reviewed. Explicit computations of the quantum string entropy, partition function and quantum string emission by black holes (Schwarzschild, rotating, charged, asymptotically flat, de Sitter dS and anti-de Sitter AdS space–times) in the framework of effective string theory in curved backgrounds provide an amount of new quantum gravity results as: (i) gravitational phase transitions appear with a distinctive universal feature: a square-root branch point singularity in any space–time dimensions. This is of the type of the de Vega–Sánchez transition for the thermal self-gravitating gas of point particles. (ii) There are no phase transitions in AdS alone. (iii) For dS background, upper bounds of the Hubble constant H are found, dictated by the quantum string phase transition. (iv) The Hawking temperature and the Hagedorn temperature are the same concept but in different (semiclassical and quantum) gravity regimes respectively. (v) The last stage of black hole evaporation is a microscopic string state with a finite string critical temperature which decays as usual quantum strings do in nonthermal pure quantum radiation (no information loss). (vi) New lower string bounds are given for the Kerr–Newman black hole angular momentum and charge, which are entirely different from the upper classical bounds. (vii) Semiclassical gravity states undergo a phase transition into quantum string states of the same system, these states are duals of each other in the precise sense of the usual classical–quantum (wave–particle) duality, which is universal irrespective of any symmetry or isommetry of the space–time and of the number or the kind of space–time dimensions.

Morphology and shear viscosity of aqueous two-phase biopolymer-surfactant mixtures

The relation between composition, rheology, and morphology in phase separated pullulan-sodium dodecyl sulphate systems containing sodium chloride has been investigated using rheo-optical methods. The rheological measurements showed that the apparent viscosity of these aqueous two-phase systems depends on the chemical composition of each phase, their volumetric composition, and the viscosity ratio of the separated phases. Optical observations revealed a droplet like morphology over a wide range of shear rates at low to moderate volume fractions of pullulan-rich phase. In some mixtures, string phases were observed at higher volume fractions of pullulan-rich phase and shear rates. Simultaneous analysis of the rheological data and observed structures at different shear rates/compositions indicates a close link between rheology and morphology of aqueous two-phase systems and provides a simple tool for predicting morphology on the basis of rheological data.

From Fundamental Strings to Small Black Holes

We give evidence in favour of a string/black hole transition in the case of BPS fundamental string states of the Heterotic string. Our analysis goes beyond the counting of degrees of freedom and considers the evolution of dynamical quantities in the process. As the coupling increases, the string states decrease their size up to the string scale when a small black hole is formed. We compute the absorption cross section for several fields in both the black hole and the perturbative string phases. At zero frequency, these cross sections can be seen as order parameters for the transition. In particular, for the scalars fixed at the horizon the cross section evolves to zero when the black hole is formed.

Sheared aqueous two-phase biopolymer–surfactant mixtures

Aqueous two-phase biopolymer–surfactant mixtures have so far received only little attention. Here, the behaviour of such mixtures was investigated adopting methods well established for aqueous two-phase biopolymer–biopolymer mixtures. The pullulan–sodium dodecyl sulphate (SDS) mixture, in which phase separation can be induced, and then enhanced by the addition of sodium chloride (NaCl), was chosen as a model system and its morphology and rheology under shear was analysed. Rheological measurements on phase-separated mixtures revealed that the viscosity depends on the chemical composition of the single phases, their viscosity ratio and volume fraction. Optical observations showed droplet-like morphology over a wide range of shear rates at low volume fractions of one phase, and co-continuous structures including string phases at high volume fractions and shear rates. For more concentrated systems, co-continuous structures were observed at all shear rates investigated, whereby in some cases string phases developed at high shear rates.

Generalized Statistical Models of Voids and Hierarchical Structure in Cosmology

Generalized statistical models of voids and hierarchical structure in cosmology are developed. The often quoted negative binomial model and frequently used thermodynamic model are shown to be special cases of a more general distribution which contains a parameter a. The parameter is related to the Levy index alpha and the Fisher critical exponent tau, the latter describing the power law fall off of clumps of matter around a phase transition. The parametera, exponent tau, or index alpha can be obtained from properties of a void scaling function. A stochastic probability variable is introduced into a statistical model which represent the adhesive growth of galaxy structure. For p 1/2, an adhesive growth can go on indefinitely thereby forming an infinite supercluster. At p=1/2 a scale free power law distribution for the galaxy count distribution is present. The stochastic description also leads to consequences that have some parallels with cosmic string results, percolation theory and phase transitions.

New stable phase of non-uniform charged black strings

Non-uniform black strings coupled to a gauge field are constructed by a perturbative method in a wide range of spacetime dimensions. At the linear order of perturbations, we see that the Gregory-Laflamme instability vanishes at the point where the background solution becomes thermodynamically stable. The emergence/vanishing of the static mode resembles phase transitions, and in fact we find that its critical exponent is nearly 1/2, which means a second-order transition. By employing higher-order perturbations, the physical properties of the non-uniform black strings are investigated in detail. For fixed spacetime dimensions, we find the critical charges at which the stability of non-uniform states changes. For some range of charge, non-uniform black strings are entropically favored over uniform ones. The gauge charge works as a control parameter that controls not only the stability of uniform black strings but also the non-uniform states. In addition, we find that for a fixed background charge the uniform state is not necessarily the state carrying the largest tension. The phase diagram and a comparison with the critical dimension are also discussed.

From fundamental strings to small black holes

We give evidence in favour of a string/black hole transition in the case of BPS fundamental string states of the Heterotic string. Our analysis goes beyond the counting of degrees of freedom and considers the evolution of dynamical quantities in the process. As the coupling increases, the string states decrease their size up to the string scale when a small black hole is formed. We compute the absorption cross section for several fields in both the black hole and the perturbative string phases. At zero frequency, these cross sections can be seen as order parameters for the transition. In particular, for the scalars fixed at the horizon the cross section evolves to zero when the black hole is formed.

A microscopic model for the black hole: Black string phase transition

Computations in general relativity have revealed an interesting phase diagram for the black hole–black string phase transition, with three different black objects present for a range of mass values. We can add charges to this system by ‘boosting’ plus dualities; this makes only kinematic changes in the gravity computation but has the virtue of bringing the system into the near-extremal domain where a microscopic model can be conjectured. When the compactification radius is very large or very small then we get the microscopic models of ( 4 + 1 )-dimensional near-extremal holes and ( 3 + 1 )-dimensional near-extremal holes respectively (the latter is a uniform black string in 4 + 1 dimensions). We propose a simple model that interpolates between these limits and reproduces most of the features of the phase diagram. These results should help us understand how ‘fractionation’ of branes works in general situations.

Configurational temperature and pressure molecular dynamics: review of current methodology and applications to the shear flow of a simple fluid

Recently developed configurational methods for controlling the temperature and pressure in a molecular dynamics simulation are reviewed [C. Braga and K. P. Travis, J. Chem. Phys. 123, 134101 (2005); ibid. 124, 104102 (2006)]. Results from equilibrium molecular dynamics simulations of a WCA fluid are used to demonstrate that at equilibrium, these new methods are at least as good as their kinetic counterparts, and in some applications, may be advantageous. A finite difference based numerical scheme is presented for calculating the configurational temperature and pressure. This approach is advantageous in cases where the potential energy function may have many terms such as the kind used in general simulation codes like DL_POLY. Equilibrium molecular dynamics simulations are conducted in the isothermal–isobaric ensemble in which these numerical estimates of the pressure and temperature are used in the Nosé–Hoover feedback schemes. The results obtained demonstrate the validity of the numerical method. Non-equilibrium molecular dynamics (NEMD) simulations have been conducted at constant volume and constant pressure in order to compare kinetic and configurational methods of controlling temperature and a combination of temperature and pressure. We demonstrate that the new configurational thermostat does not give rise to a spurious string phase, unlike its kinetic temperature counterpart, but gives results in line with those obtained using a previously developed configurational thermostat. Furthermore we find that at constant pressure, there is no evidence for a string phase with our new configurational isothermal–isobaric method but a string phase is observed, albeit at a higher strain rate, using kinetic temperature and pressure control.

Notes on Fast Moving Strings

We review the recent work on the mechanics of fast moving strings in anti-de Sitter space times a sphere and discuss the role of conserved charges. An interesting relation between the local conserved charges of rigid solutions was found in the earlier work. We propose a generalization of this relation for arbitrary solutions, not necessarily rigid. We conjecture that an infinite combination of local conserved charges is an action variable generating periodic trajectories in the classical string phase space. It corresponds to the length of the operator on the field theory side.

Stringy effects during inflation and reheating

We consider inflationary cosmology in the context of string compactifications with multiple throats. In scenarios where the warping differs significantly between throats, string and Kaluza-Klein physics can generate potentially observable corrections to the cosmology of inflation and reheating. First we demonstrate that a very low string scale in the ground state compactification is incompatible with a high Hubble scale during inflation, and we propose that the compactification geometry is altered during inflation. In this configuration, the lowest scale is just above the Hubble scale, which is compatible with the effective field theory but still leads to potentially observable cosmic microwave background corrections. Also in the appropriate region of parameter space, we find that reheating leads to a phase of long open strings in the standard model sector (before the usual radiation-dominated phase). We sketch the cosmology of the long string phase and we discuss possible observational consequences.

The charged black hole/string transition

We generalize the discussion of hep-th/0509170 to charged black holes. For the two dimensional charged black hole, which is described by an exactly solvable worldsheet theory, a transition from the black hole to the string phase occurs when the Hawking temperature of the black hole reaches a limiting value, the temperature of free strings with the same mass and charge. At this point a tachyon winding around Euclidean time in the Euclidean black hole geometry, which has a non-zero condensate, becomes massless at infinity, and the horizon of the black hole is infinitely smeared. For Reissner-Nordstrom black holes in d\ge 4 dimensions, the exact worldsheet CFT is not known, but we propose that it has similar properties. We check that the leading order solution is in good agreement with this proposal, and discuss the expected form of \alpha' corrections.

SIMPLE SOLUTIONS TO THE EINSTEIN EQUATIONS IN SPACES WITH UNUSUAL TOPOLOGY

We discuss simple vacuum solutions to the Einstein Equations in five-dimensional space–times compactified in two different ways. In such spaces, one black hole phase and more than one black string phase may exist. Several old metrics are adapted to new background topologies to yield new solutions to the Einstein Equations. We then briefly talk about the angular momentum they may carry, the horizon topology and phase transitions that may occur.

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.

Nonequilibrium Molecular Dynamics Simulations of Molten Sodium Chloride

The main problems arising in all far-from-equilibrium simulations come from temperature control. When local flows become important, it is not a simple matter to distinguish between the flow velocity and thermal motion. A way to bypass this problem is to control the temperature given by the “configurational expression”, which does not depend on velocity. The responses of molten NaCl to strong shear and strong constant and oscillating electric fields using kinetic and configurational thermostats are compared. The differences in response increase with the increase in the external perturbation, and in very strong fields one can observe striking structural differences. In the case of shear flow, the differences are of a general nature seen in all liquids (the appearance of a string phase with kinetic thermostats), while in an electric field they are peculiar to ionic fluids and are related to the degree of dissociation. Some structural properties can be deduced by evaluating the configurational temperature expression.

Searching for a connection between matroid theory and string theory

We make a number of observations about matter-ghost string phase, which may eventually lead to a formal connection between matroid theory and string theory. In particular, in order to take advantage of the already established connection between matroid theory and Chern–Simons theory, we propose a generalization of string theory in terms of some kind of Kahler metric. We show that this generalization is closely related to the Kahler–Chern–Simons action due to Nair and Schiff. In addition, we discuss matroid/string connection via matroid bundles and a Schild type action, and we add new information about the relationship between matroid theory, D=11 supergravity and Chern–Simons formalism.