Tachyon trajectories in Schwarzschild’s space-time

The motion of a tachyon in the empty Schwarzschild solution outside a massm is discussed. It is shown that a tachyon falling radially inwards never reaches the space-time singularity at the origin. Instead, it is bounced back at a point inside the Schwarzschild radius. The causal and non-causal aspects of such a bounce are considered. It is shown that a tachyon dropped from a radial co-ordinate <2.56m always airives before it went in whereas a tachyon dropped from a radial co-ordinate >3.27m always arrives later than its starting time. The more general case of a tachyon with a finite angular momentum is also analyzed. The possible astrophysical consequences of the presence of tachyons near condensed or collapsing objects and black holes are qualitatively discussed.     

Tachyonization of the ΛCDM cosmological model

In this work a tachyonization of the ΛCDM model for a spatially flat Friedmann–Robertson–Walker space–time is proposed. A tachyon field and a cosmological constant are considered as the sources of the gravitational field. Starting from a stability analysis and from the exact solutions for a standard tachyon field driven by a given potential, the search for a large set of cosmological models which contain the ΛCDM model is investigated. By the use of internal transformations two new kinds of tachyon fields are derived from the standard tachyon field, namely, a complementary and a phantom tachyon fields. Numerical solutions for the three kinds of tachyon fields are determined and it is shown that the standard and complementary tachyon fields reproduces the ΛCDM model as a limiting case. The standard tachyon field can also describe a transition from an accelerated to a decelerated regime, behaving as an inflationary field at early times and as a matter field at late times. The complementary tachyon field always behaves as a matter field. The phantom tachyon field is characterized by a rapid expansion where its energy density increases with time.     

Dispersionless Toda hierarchy and two-dimensional string theory

The dispersionless Toda hierarchy turns out to lie in the heart of a recently proposed Landau-Ginzburg formulation of two-dimensional string theory at self-dual compactification radius. The dynamics of massless tachyons with discrete momenta is shown to be encoded into the structure of a special solution of this integrable hierarchy. This solution is obtained by solving a Riemann-Hilbert problem. Equivalence to the tachyon dynamics is proven by deriving recursion relations of tachyon correlation functions in the machinery of the dispersionless Toda hierarchy. Fundamental ingredients of the Landau-Ginzburg formulation, such as Landau-Ginzburg potentials and tachyon Landau-Ginzburg fields, are translated into the language of the Lax formalism. Furthermore, a wedge algebra is pointed out to exist behind the Riemann-Hilbert problem, and speculations on its possible role as generators of extra states and fields are presented.     

Moving branes in the presence of background tachyon fields

We compute the boundary state associated with a moving Dp-brane in the presence of the open string tachyon field as a background field. The effect of the tachyon condensation on the boundary state is discussed. It leads to a boundary state associated with a lower-dimensional moving D-brane or a stationary instantonic D-brane. The former originates from condensation along the spatial directions and the latter comes from the temporal direction of the D-brane worldvolume. Using the boundary state, we also study the interaction amplitude between two arbitrary Dp ₁- and Dp ₂-branes. The long-range behavior of the amplitude is investigated, demonstrating an obvious deviation from the conventional form, due to the presence of the background tachyon field.     

Shape transition of semi-flexible macromolecules confined in channel and cavity

Stiff macromolecules entrapped in channels or in spherical cavities undergo a shape transition on increasing confinement as shown by our investigation using molecular simulations. In channels this weak-to-strong confinement transition leads to extended conformations without the hairpin-like back-folding. In cavities, on decrease of cavity radius, the semi-flexible chain in a disordered state starts to self-organize into the torus. As a common rule for both types of confinement the transition to the ordered structures is observed when the radius of cavity and cylindrical channel reaches the lower bound of macromolecular flexibility given by the average typical radius of curvature of the chain, which is approximately equal to the persistence length of the macromolecular chain. This simple geometric rule finds its application in various confinement situations of stiff bio-macromolecules either in micro-channel experiments or in real biophysical situation, such as DNA in viral capsid.     

Generic structure of externally driven tearing modes instabilities

A major limit to steady state and advanced high operation of tokamaks of reactor class is due to the onset of tearing modes that develop magnetic and may cause loss of energy confinement or a major disruption. Here the structure of a classical problem about the effects of external control helical fields is analysed and it is shown to offer a general paradigm of response of low order classical and neoclassical tearing modes to a wide class of external perturbations. New results of principle on the structural stability of the response model are obtained, leading to a clear interpretation of the role of “seed islands" in the onset of neo-classical tearing modes and the role of finite ion larmor radius corrections to Ohm's law. Received 12 November 2001 and Received in final form 4 January 2002     

Interaction Between Tachyon and Hessence (or Hantom) Dark Energies

In this work, we have considered that the universe is filled with tachyon and hessence (or hantom) dark energies. Subsequently we have investigated the interactions between tachyon and hessence (hantom) dark energies and calculated the potentials considering the power law form of the scale factor. It has been revealed that the tachyonic potential always decreases and hessence (or hantom) potential increases with corresponding fields. Furthermore, we have considered a correspondence between the hessence (or hantom) dark energy density and variable modified Chaplygin gas energy density. From this, we have found the expressions of the arbitrary positive constants B ₀ and C of variable modified Chaplygin gas.     

Tachyon field in cosmology

We study cosmological effects of homogeneous tachyon field as dark energy. We concentrate on two different scalar field potentials, the inverse square potential and the exponential potential. These models have a unique feature that the matter density parameter and the density parameter for tachyons remain comparable for a large range in red-shift. It is shown that there exists a range of parameters for which the universe undergoes an accelerated expansion and the evolution is consistent with structure formation requirements. For a viable model we require fine tuning of parameters comparable to that in ACDM or in quintessence models. For the exponential potential, the accelerated phase is followed by a phase witha(t) α t ^2/3 thus eliminating a future horizon.     

The Green's function of confined electrons in an external magnetic field: Analytical formulation

We derive the analytical form of the Green's function of 2-dimensional electrons with lateral confinement in a perpendicular magnetic field. The confinement potentials considered are infinite barriers at radius R (quantum dot) and at r and R (quantum ring).     

Dynamic Equations for Tachyon Gas

Dynamics of the tachyon gas is considered. It is interesting in the relation, that dark matter phenomenon is explained freely by existence of the tachyon gas. Tachyons have two unexpected properties: (1) a single tachyon cannot be detected and (2) the tachyon gas can be detected by its gravitational field. Although molecules (tachyons) of the tachyon gas moves with superluninal velocities, the mean motion of these molecules appears to be less, than the speed of the light. The tachyon gas properties differs from those of usual gas. The pressure of the tachyon gas is very high. It is not isotropic and depends on the gravitational potential. As a result the tachyon gas may form huge halos around galaxies. These halos have very large and almost constant density. This circumstance can explain the law of star velocities at the periphery of a galaxy. Properties of the tachyon gas admit one to consider it as a dark matter.     

Quantum-mechanical confinement with the robin condition

The energy spectrum of a nonrelativistic quantum particle in the confinement state in a closed spatial volume at general boundary confinement conditions (the Robin conditions) is investigated. It is shown that the properties of such a state are substantially more nontrivial compared with particle confinement using the potential barrier. It is also shown for a hydrogen-like atom arranged in a spherical cavity with radius R that if the surface layer with nonzero depth d plays the role of the boundary of the confinement region, all the energy levels of a discrete spectrum of the atom have a finite limit at R → 0, while the R-dependence of the lower layer at physically substantial parameters of the surface layer contains a deep well-pronounced minimum, in which the binding energy is considerably higher than for the lower 1s level of a free atom.     

CdxHg(1−x)Te Alloy Colloidal Quantum Dots: Tuning Optical Properties from the Visible to Near‐Infrared by Ion Exchange

The energy gap between valence and conduction levels in colloidal semiconductor quantum dots can be tuned via the nanoparticle diameter when this is comparable to or less than the Bohr radius. In materials such as cadmium mercury telluride, which readily forms a single phase ternary alloy, this quantum confinement tuning can also be augmented by compositional tuning, which brings a further degree of freedom in the bandgap engineering. Here it is shown that compositional control of 2.3 nm diameter Cd_xHg_(1?x)Te nanocrystals by exchange of Hg²⁺ in place of Cd²⁺ ions can be used to tune their optical properties across a technologically useful range, from 500 nm to almost 1200 nm. Data on composition‐dependent changes in the optical properties are provided, including bandgap, extinction coefficient, emission energy and spectral shape, Stokes shift, quantum efficiency, and radiative lifetimes as the exchange process occurs, which are highly relevant for those seeking to use these technologically important QD materials.     

Information flow,causality, and the classical theory of tachyons

Causal paradoxes arising in the tachyon theory have been systematically solved by using the reinterpretation principle as a consequence of which cause and effect no longer retain an absolute meaning. However, even in the tachyon theory, a cause is always seen to chronologically precede its effect, but this is obtained at the price of allowing cause and effect to be interchanged when required. A recent result has shown that this interchangeability of cause and effect must not be unlimited if heavy paradoxes are to be avoided. This partial recovery of the classical concept of causality has been expressed by the conjecture that transcendent tachyons cannot be absorbed by a tachyon detector. In this paper we analyze the directional properties of the flow of information between two observers in relative motion and its consequences on the logical self-consistency of the theory of superluminal particles. We show that the above conjecture does not provide a satisfactory solution to the problem because it implies that tachyons of any speed cannot be intercepted by the same detector.     

Sequential escapes: onset of slow domino regime via a saddle connection

We explore sequential escape behaviour of coupled bistable systems under the influence of stochastic perturbations. We consider transient escapes from a marginally stable “quiescent” equilibrium to a more stable “active” equilibrium. The presence of coupling introduces dependence between the escape processes: for diffusive coupling there is a strongly coupled limit (fast domino regime) where the escapes are strongly synchronised while for intermediate coupling (slow domino regime) without partially escaped stable states, there is still a delayed effect. These regimes can be associated with bifurcations of equilibria in the low-noise limit. In this paper, we consider a localized form of non-diffusive (i.e. pulse-like) coupling and find similar changes in the distribution of escape times with coupling strength. However, we find transition to a slow domino regime that is not associated with any bifurcations of equilibria. We show that this transition can be understood as a codimension-one saddle connection bifurcation for the low-noise limit. At transition, the most likely escape path from one attractor hits the escape saddle from the basin of another partially escaped attractor. After this bifurcation, we find increasing coefficient of variation of the subsequent escape times.     

Remarks on Black Hole Instabilities and Closed String Tachyons

Physical arguments stemming from the theory of black-hole thermodynamics are used to put constraints on the dynamics of closed-string tachyon condensation in Scherk–Schwarz compactifications. A geometrical interpretation of the tachyon condensation involves an effective capping of a noncontractible cycle, thus removing the very topology that supports the tachyons. A semiclassical regime is identified in which the matching between the tachyon condensation and the black-hole instability flow is possible. We formulate a generalized correspondence principle and illustrate it in several different circumstances: an Euclidean interpretation of the transition from strings to black holes across the Hagedorn temperature and instabilities in the brane-antibrane system.     

Non-archimedean string dynamics

Explicit formulas for the N-point tree amplitudes of the non-archimedean open string are derived. These amplitudes can be generated from a simple non-local lagrangian involving a single scalar field (the tachyon) in ambient space-time. This lagrangian is studied and is found to possess a tachyon free vacuum with no “particles” but with soliton solutions. The question of generalizing the adelic product formular to N-point amplitudes is taken up. The infinite product of 5-point amplitudes is shown to converge in a suitably chosen kinematic region whence it can be analytically continued. Though the precise form of the product formula for the 5-point (and N-point)amplitudes is not found, it is shown that the product is not equal to one as it is for the 4-point amplitudes but rather involves the famous zeros of the Riemann zeta function. Chan-Paton rules for non-archimedean open strings are given. A string over the (global) field of rational numbers is constructed. Other problems that are addressed are the introduction of supersymmetry, the nature of a p-adic string lagrangian, and the possibility of strings over other locally compact fields.     

Stability and electronic properties of carbon nanotubes doped with transition metal impurities

We apply first-principles method to investigate the effect of the diameter on the stability and electronic properties of zigzag carbon nanotubes doped with iron, nickel and manganese impurity atoms. In this contribution we follow the evolution of the electronic and structural properties as a function of the nanotube diameter. As a general result, we found that the binding energy decreases with the increasing nanotube radius. Additionally, depending on the interaction of transition metal impurity with the tubular carbon structure, it is observed that the total magnetization varies with the tube diameter due to hybridization and confinement effects. It is also shown that such magnetization varies with the curvature radius, increasing for manganese impurity atoms and decreasing for iron and nickel.     

Impurity related optical properties in tuned quantum dot/ring systems

In this paper, we explore the linear, third-order nonlinear, and total optical absorption coefficient (OAC) and refractive index change coefficient (RICC) of a GaAs doped quantum dot/quantum ring (QD/QR) with parabolic-inverse squared potential in conjunction with modified Gaussian confinement and taking into account the presence of on-centre shallow donor and or acceptor impurity. Calculations are done via the compact density matrix formalism and the iterative method. The two-dimensional parabolic QD/QR is subjected to uniform magnetic field oriented perpendicularly to the plane of the structure. The energy levels and wave function are derived within the framework of effective-mass and parabolic band approximation. The results exhibit that the OACs and RICC are clearly affected by different parameters of the applied confinement, strength of magnetic field, and the presence of impurity. The variation of confinement potential, nature of impurity, dot radius, cyclotron frequency of the parabolic confinement potential, and geometric parameter of the on-centre repulsive potential lead to either a red-shift or a blue-shift of the resonant peaks of the OACs and of the maximum and minimum of the RICC together with significant variations of the magnitudes of these resonant structures.     

Interaction of moving branes with background massless and tachyon fields in superstring theory

Using the boundary state formalism, we study a moving Dp-brane in a partially compact space-time in the presence of background fields: the Kalb-Ramond field B _μν, a U(1) gauge field A _α, and the tachyon field. The boundary state enables us to obtain the interaction amplitude of two branes with the above back-ground fields. The branes are parallel or perpendicular to each other. Because of the presence of background fields, compactification of some space-time directions, motion of the branes, and the arbitrariness of the dimensions of the branes, the system is rather general. Due to the tachyon fields and velocities of the branes, the behavior of the interaction amplitude reveals obvious differences from the conventional behavior.