Dynamical dimensional reduction

We propose to call a dynamical dimensional reduction effective if the corresponding dynamical system possesses a single attracting critical point representing expanding physical space-time and static internal space. We show that theBV × T ^D multidimensional cosmological model with a hydrodynamic energy-momentum tensor provides an example of effective dimensional reduction. We also study the dynamics of the multidimensional cosmological model of typeBI × T ^D with an energy-momentum tensor representing low temperature quantum effects, monopole contribution and the cosmological constant. It turns out that anisotropy and the cosmological constant are crucial for the process of dimensional reduction to be effective. We argue that this is the general property of homogeneous multidimensional cosmological models.     

Ultrametricity in three-dimensional edwards-anderson spin glasses

We perform an accurate test of ultrametricity in the aging dynamics of the three-dimensional Edwards-Anderson spin glass. Our method consists in considering the evolution in parallel of two identical systems constrained to have fixed overlap. This turns out to be a particularly efficient way to study the geometrical relations between configurations at distant large times. Our findings strongly hint towards dynamical ultrametricity in spin glasses, while this is absent in simpler aging systems with domain growth dynamics. A recently developed theory of linear response in glassy systems allows us to infer that dynamical ultrametricity implies the same property at the level of equilibrium states.     

Optimized Lower Bounds for Five-Body Hamiltonians

A methodology recently proposed for deriving optimized lower bounds for the energies of the ground states of N-body systems is applied to the five-body case. Such lower bounds result from an optimization process over a certain number of parameters. The so-called universal dynamical constraints, i.e., relations between the values of the parameters corresponding to the optimized lower bound and which have the properties to be of dynamical nature and to be independent of the particular form of the potential, are computed in their totality and great calculational details are given. The optimized lower bound obtained in this way proves to be saturated, i.e., identical to the exact result, in the harmonic oscillator case. Particular mass configurations are considered with the corresponding simplifications in the universal dynamical constraints. In relation to the property of saturability in the case of harmonic interactions, particular attention is devoted to five-body systems with harmonic interactions. Various mass configurations are considered and for each case the corresponding ground state energy is derived.     

Spatially Homogeneous Bianchi Type-I Universes with Variable G and Λ

In this paper, we have studied the cosmological models of Bianchi type-I universes in a different basic form filled with bulk viscous fluid, in the presence of time-dependent gravitational as well as cosmological constants. A set of new exact cosmological solutions have been obtained in both full and truncated causal theories. These solutions are suitable for describing the evolution of the universe in its early stages. The physical and dynamical consequences have been discussed in detail.     

Nonsingular global string compactifications

We consider an exotic "compactification" of spacetime in which there are two infinite extra dimensions, using a global string instead of a domain wall. By having a negative cosmological constant we prove the existence of a nonsingular static solution using a dynamical systems argument. A nonsingular solution also exists in the absence of a cosmological constant with a time-dependent metric. We compare and contrast this solution with the Randall-Sundrum universe and the Cohen-Kaplan spacetime and consider the options of using such a model as a realistic resolution of the hierarchy problem.     

The time-dependent quantum harmonic oscillator revisited: Applications to quantum field theory

In this article, we formulate the study of the unitary time evolution of systems consisting of an infinite number of uncoupled time-dependent harmonic oscillators in mathematically rigorous terms. We base this analysis on the theory of a single one-dimensional time-dependent oscillator, for which we first summarize some basic results concerning the unitary implementability of the dynamics. This is done by employing techniques different from those used so far to derive the Feynman propagator. In particular, we calculate the transition amplitudes for the usual harmonic oscillator eigenstates and define suitable semiclassical states for some physically relevant models. We then explore the possible extension of this study to infinite dimensional dynamical systems. Specifically, we construct Schrödinger functional representations in terms of appropriate probability spaces, analyze the unitarity of the time evolution, and probe the existence of semiclassical states for a wide range of physical systems, particularly, the well-known Minkowskian free scalar fields and Gowdy cosmological models.     

Real‐time three‐dimensional single‐particle tracking spectroscopy for complex systems

Complex systems are characterized by dynamical processes spread over multiple time and length scales. At a given instant, these systems can display spatial heterogeneities in which the local physical and chemical properties are nonuniform, depending on the location. They can also exhibit dynamical heterogeneities in which the local dynamical characteristics vary with time. These types of systems pose unique experimental challenges for their characterization and test of theoretical ideas. Recently, real‐time three‐dimensional (3D) single‐particle tracking spectroscopy has been developed to address these kinds of problems. With this approach, in principle, one can follow how a system evolves spatially as well as temporally. This article attempts to provide an introduction to this promising new technique by discussing the aims of studying a complex system and recent experimental advances towards this goal.     

Conformal Invariance, Accelerating Universe and the Cosmological Constant Problem

We investigate a conformal invariant gravitational model which is taken to hold at early universe. The conformal invariance allows us to make a dynamical distinction between the two unit systems (or conformal frames) usually used in cosmology and elementary particle physics. In this model we argue that when the universe suffers phase transition, the resulting mass scale introduced by particle physics should have a variable contribution to vacuum energy density. This variation is controlled by the conformal factor which is taken as a dynamical field. We then deal with the cosmological consequences of this model. In particular, we shall show that there is an inationary phase at early times. At late times, on the other hand, it provides a mechanism which makes a large effective cosmological constant relax to a sufficiently small value. Moreover, we shall show that the conformal factor acts as a quintessence field that leads the universe to accelerate at late times.     

Duality and the cosmological constant

A dynamical theory is studied in which a scalar field ϕ in Einstein-Minkowski space is coupled to the four-velocityN _μ of a preferred inertial observer in that space. As a consistent requirement on this coupling we study a principle of duality invariance of the dynamical mass term of ϕ at some universal length in the small-distance regime. In the large-distance regime duality breaking can be introduced by giving a background value to ϕ and a background direction toN _μ. It is shown that, in an appropriate approximation, duality breaking can be related to the emergence of a characteristic phase in which the condensation of the ground state allows massive excitations with a characteristic scale of squared mass which agrees with the present observational bound for the cosmological constant.     

Gravitational coupling and dynamical reduction of the cosmological constant

We introduce a dynamical model to reduce a large cosmological constant to a sufficiently small value. The basic ingredient in this model is a distinction which has been made between the two unit systems used in cosmology and particle physics. We have used a conformal invariant gravitational model to define a particular conformal frame in terms of large scale properties of the universe. It is then argued that the contributions of mass scales in particle physics to the vacuum energy density should be considered in a different conformal frame. In this manner, a decaying mechanism is presented in which the conformal factor appears as a dynamical field and plays a key role to relax a large effective cosmological constant. Moreover, we argue that this model also provides a possible explanation for the coincidence problem.     

Surrounded Vaidya black holes: apparent horizon properties

We study the thermodynamical features and dynamical evolutions of various apparent horizons associated with the Vaidya evaporating black hole surrounded by the cosmological fields of dust, radiation, quintessence, cosmological constant-like and phantom. In this regard, we address in detail how do these surrounding fields contribute to the characteristic features of a surrounded dynamical black hole in comparison to a dynamical black hole in an empty background.     

Gravitational coupling,dynamical changes of units and the cosmological constant problem

A spacetime interval connecting two neighbouring points can be measured in different unit systems.For instance,it can be measured in atomic unit defined in terms of fundamental constants existing in quantum theories.It is also possible to use a gravitational unit which is defined by the use of properties of macroscopic objects.These two unit systems are usually regarded as indistinguishable up to a constant conversion factor.Here we consider the possibility that these two units are related by an epoch-dependent conversion factor.This is a dynamical changes of units.Regarding a conformal transformation as a local unit transformation,we use a gravitational model in which the gravitational and the matter sectors are given in different conformal frames(or unit systems).It is relevant to the cosmological constant problem,namely the huge discrepancy between the estimated and the observational values of the cosmological constant in particle physics and cosmology,respectively.We argue that the problem arises when one ignores evolution of the conversion factor relating the two units during expansion of the Universe.Connection of the model with violation of equivalence principle and possible variation of fundamental constants are also discussed.     

A dust-filled Kantowski-Sachs universe with Λ#62;0

A new solution of Einstein's field equations is found. It describes a dust-filled Kantowski-Sachs universe with positive cosmological constant. The mass density of the dust is positive. This cosmological model develops from a point singularity towards an infinite barrel singularity.     

Cosmological Model Based on Gauge Theory of Gravity

A cosmological model based on gauge theory of gravity is proposed in this paper. Combining cosmological principle and field equation of gravitational gauge field, dynamical equations of the scale factor R(t) of our universe can be obtained. This set of equations has three different solutions. A prediction of the present model is that, if the energy density of the universe is not zero and the universe is expanding, the universe must be space-flat, the total energy density must be the critical density ρ_c of the universe. For space-flat case, this model gives the same solution as that of the Friedmann model. In other words, though they have different dynamics of gravitational interactions, general relativity and gauge theory of gravity give the same cosmological model.     

Hamiltonian cosmology of bigravity

This article is written as a review of the Hamiltonian formalism for the bigravity with de Rham–Gabadadze–Tolley (dRGT) potential, and also of applications of this formalism to the derivation of the background cosmological equations. It is demonstrated that the cosmological scenarios are close to the standard ΛCDM model, but they also uncover the dynamical behavior of the cosmological term. This term arises in bigravity regardless on the choice of the dRGT potential parameters, and its scale is given by the graviton mass. Various matter couplings are considered.     

Brans-dicke vacuum solutions and the cosmological constant: A qualitative analysis

We investigate Brans-Dicke vacuum solutions in the presence of a cosmological constant A from the point of view of dynamical system theory. Assuming a Friedmann-Robertson-Walker metric we plot the phase diagrams corresponding to all values of. The analysis of the diagrams allows us to determine several physical properties of the solutions as well as their global dynamical behaviour.     

Scaling behavior in a Fibonacci-sequenced system

The rudiments of dynamical systems theory are employed to analyze the transmission of light through a two-element medium in which the elements are arranged in a Fibonacci sequence. A dynamical map, introduced by previous authors, is extended so that the enlarged map generates direct predictions about the behavior of the transmission coefficient for phases in the neighborhood of certain critical values. These values correspond to unique periodic orbits of the map. Lowest-order calculations are performed analytically to study the properties of scaling near the critical phases. A scale factor is defined to describe this behavior. The study examines three cases in which the map has a fixed point, a 3-cycle, and a 6-cycle. The first two cases have the property that their scale factors are given by exactly the same Fibonacci number. In contrast, the third case has the property that its scale factor depends explicitly on a parameter of the physical system. Speculative remarks are added in conclusion to argue for the occurrence of a type of scaling whose features originate in the abstract structure of the Fibonacci sequence and are independent of the particular choice of physical system.     

On the stochasticity in relativistic cosmology

It was shown earlier by I. M. Lifshitz and two of us that the evolution of the relativistic cosmological models towards the singularity undergoes spontaneous stochastization.⁽¹⁾ In the present paper it is shown that the statistical parameters of this evolution can be calculated in an exact manner. From the point of view of the general ergodic theory we deal here with a specific mode of stochastization of a deterministic dynamical system with a five-dimensional phase space. The knowledge of the source of stochasticity makes it possible to develop a quantitative statistical theory with appreciable completeness.