Convergence properties of the cluster expansion for equal- time Green functions in scalar theories

We investigate the convergence properties of the cluster expansion of equal-time Green functions in scalar theories with quartic self-coupling in (0 + 1), (1 + 1), and (2 + 1) space-time dimensions. The computations are carried out within the equal-time correlation dynamics approach, which consists in a closed set of coupled equations of motion for connected Green functions as obtained by a truncation of the BBGKY hierarchy. We find that the cluster expansion shows good convergence as long as the system is in a localized state (single phase configuration) and that it breaks down in a non-localized state (two phase configuration), as one would naively expect. Furthermore, in the case of dynamical calculations with a time dependent Hamiltonian for the evaluation of the effective potential we find two timescales determining the adiabaticity of the propagation; these are the time required for adiabaticity in the single phase region and the time required for tunneling into the non-localized lowest energy state in the two phase region. Our calculations show a good convergence for the effective potentials in (1 + 1) and (2+1) space-time dimensions since tunneling is suppressed in higher space-time dimensions.     

Thermodynamics of de Sitter Black Holes in Massive Gravity

In this paper, by taking de Sitter space-time as a thermodynamic system, we study the effective thermodynamic quantities of de Sitter black holes in massive gravity, and furthermore obtain the effective thermodynamic quantities of the space-time. Our results show that the entropy of this type of space-time takes the same form as that in Reissner-Nordstr¨om-de Sitter space-time, which lays a solid foundation for deeply understanding the universal thermodynamic characteristics of de Sitter space-time in the future. Moreover, our analysis indicates that the effective thermodynamic quantities and relevant parameters play a very important role in the investigation of the stability and evolution of de Sitter space-time.     

Hamiltonian Chaos in Homogeneous ADM Cosmologies?

Chaos in dynamical systems has best been understood in terms of Hamiltonian systems. A primary method of diagnosis of chaos in these systems is the Lyapunov exponent. According to general relativity, space-time is itself a dynamical system. When the evolution of a model universe is expressed in the ADM form it can be described as a Hamiltonian system. Among the various model cosmologies, the Mixmaster or Bianchi IX cosmology has been extensively studied as a candidate to exhibit chaos. However, the Lyapunov exponents in this system have shown contradictory properties, including a seeming dependence on the coordinates used to describe space-time. Such dependencies, if true, would be surprising as the time coordinate of space-time is unrelated to the parameterization of phase space. Further, this sort of dependence would relegate chaos to a bad coordinate choice rather than a dynamic property of the system. The problem with the Lyapunov exponent lies in the ambiguities remaining in the ADM action integral. The current interpretation involves an arbitrary Lagrange multiplier—thought to be necessary for the coordinate invariance of space-time. An arbitrary multiplier turns out to be unnecessary for coordinate invariance, and in addition destroys the symplectic structure of phase space. In reality, the geometry selects the parameterization of phase space, and any change in the parameter results in a changed Hamiltonian system. It must be emphasized that the fixing of the phase space parameter does NOT impose a coordinate choice on space-time. The parameter is selected by the symplectic structure of phase space and full coordinate invariance of space-time is left intact. Once the demands of both geometries, space-time and phase space, have been satisfied, the Lyapunov exponent becomes independent of the coordinate imposed on space-time. Additionally, the correction of the phase space structure leads to a Hamiltonian that is more general, in that it describes a gravitational system with a cosmological constant, than is currently the case.     

Luminescence induced by spherically focused acoustic pulses in liquids

The determination of the phase of the bubble oscillation at the instant of light emission, which is a key issue for understanding the origin of cavitation luminescence of liquids, is discussed. The observation of luminescence in the course of the nucleation and growth of a bubble up to its collapse is performed in a bipolar wave consisting of a compression phase followed by a rarefaction phase in the regime of a two-fraction bubble cluster formation. The space-time distributions of the luminescence intensity and pressure and the dynamics of the cluster in water and a glycerin solution are investigated at the early stage of cavitation. A correlation between the maximal density of light flashes and the positive pressure pulses in the field of superposition of the initial and secondary cavitation compression waves is revealed. It is shown that the spherical focusing of acoustic pulses both away from the boundaries of the liquid and near its free surface makes it possible to compare the luminescence intensities for different rates of the pressure decrease.     

Some remarks on the dynamical origin of charge and space-time quantisation

It is argued here that the concept of dynamical origin of charge as formulated in a previous paper requires the quantisation of space-time. Indeed, in this scheme, it is pointed out that the quantisation of electric charge in unit ofe is a direct consequence of this space-time quantisation.     

Coleman-Weinberg approach in distorted space-time

The Coleman-Weinberg approach (renormalization-group improvement of the effective potential) is developed for an arbitrary renormalizable massless theory in distorted space-time. Some explicit examples are considered. It is proven that a phase transition induced by nonzero curvature may occur in an SU(5) inflationary universe.Tomsk Pedagogical Institute. Universal of Barcelona. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 28–32, January, 1994.     

Dynamical symmetries in mechanics

The object of this review is to discuss methods that enable one to trace the origin of symmetries and conservation laws in mechanics to geometrical symmetries of space-time. Starting with the basic Newtonian assumptions on absolute space and time classical mechanics is developed in configuration space and phase space independently together with the related structures such as force-less mechanics. Heuristic considerations on geometric symmetries in configuration space reveal their intimate relation to conservation laws. Using the methods of differential geometry this relationship is put on a formal footing and symmetry groups of all spherically symmetric single term potentials are classified. The method of infinitesimal canonical transformations is presented as an alternative method of deducing dynamical symmetries of an arbitrary system in phase space. These methods also apply to non-relativistic quantum theory. Possible extension to special and general relatively is also discussed.     

Space-time phase transitions in driven kinetically constrained lattice models

Kinetically constrained models (KCMs) have been widely used to study and understand the origin of glassy dynamics. These models show an ergodic-nonergodic first-order phase transition between phases of distinct dynamical “activity”. We introduce driven variants of two popular KCMs, the FA model and the (2)-TLG, as models for driven supercooled liquids. By classifying trajectories through their entropy production we prove that driven KCMs display an analogous first-order space-time transition between dynamical phases of finite and vanishing entropy production. We discuss how trajectories with rare values of entropy production can be realized as typical trajectories of a mapped system with modified forces.     

A self-consistent approach to quantum field theory for extended particles

A notion of quantum space-time is introduced, physically defined as the totality of all flows of quantum test particles in free fall. In quantum space-time the classical notion of deterministic inertial frames is replaced by that of stochastic frames marked by extended particles. The same particles are used both as markers of quantum space-time points as well as natural clocks, each species of quantum test particle thus providing a standard for space-time measurements. In the considered flat-space case, the fluctuations in coordinate values with respect to stochastic frames are described by coordinate probability amplitudes related to irreducible stochastic phase space representations of the Poincaré group. Lagrangian field theory on quantum space-time is formulated. The ensuing equations of motion for interacting fields contain no singularities in their nonlinear terms, and therefore can be handled by methods borrowed from classical nonlinear analysis.Supported in part by an NSERC grant.     

Spontaneous symmetry breaking in static Robertson-Walker space-time with background charge

The finite-temperature ⁴ theory of static Robertson-Walker (RW) space-time is extended to a case with background charge. In contrast to earlier work on static RW space-time, the curvature term is retained and its effect on the effective potential and phase transition are explicitly calculated. The spontaneous symmetry breaking aspects and its dependence on various factors are discussed.     

Solving Space-Time Fractional Differential Equations by Using Modified Simple Equation Method

In this article,we establish new and more general traveling wave solutions of space-time fractional Klein–Gordon equation with quadratic nonlinearity and the space-time fractional breaking soliton equations using the modified simple equation method.The proposed method is so powerful and effective to solve nonlinear space-time fractional differential equations by with modified Riemann–Liouville derivative.     

Kasner 时空中的中微子振荡相位

研究了质量中微子在 Kasner 时空特殊情况下的传播相位和振荡特征长度,得到了中微子的零短程线相位是短程线相位一半的关系.当参数a=0时,Kasner 时空中的传播相位和史瓦希时空中的相同.这一问题的研究在宇宙学中是有意义的^[1-3]. 关键词： 传播相位 Kasner 时空 质量中微子 振荡特征长度     

Spectral functions in the two-dimensional Hubbard model within a spin-charge rotating frame approach

We have performed electronic spectral function calculations for the Hubbard model on the square lattice using recently developed quantum SU(2) × U(1) rotor approach that enables a self-consistent treatment of the antiferromagnetic state. The collective variables for charge and spin are isolated in the form of the space-time fluctuating U(1) phase field and rotating spin quantization axis governed by the SU(2) symmetry, respectively. As a result interacting electrons appear as composite objects consisting of bare fermions with attached U(1) and SU(2) gauge fields. This allows us to write the fermion Green’s function in the space-time domain as a product of the SU(2) gauge fields, U(1) phase propagator and the pseudo-fermion correlation function. Consequently, the calculation of the spectral line shapes now reduces to performing the convolution of spin, charge and pseudo-fermion Green’s functions. The collective spin and charge fluctuations are governed by the effective actions that are derived from the Hubbard model for any value of the Coulomb interaction. The emergence of a sharp peak in the electron spectral function in the antiferromagnetic state indicates the decay of the electron into separate spin and charge carrying particle excitations.     

On the possibility of phase transitions in the geometric structure of space-time

It is shown that space-time may be not only in a state which is described by Riemann geometry but also in states which are described by Finsler geometry. Transitions between various metric states of space-time have the meaning of phase transitions in its geometric structure. These transitions together with the evolution of each of the possible metric states make up the general picture of space-time manifold dynamics.     

Estimate of the Maximal Energy Density and Space-Time Region of the Quark Matter in High Energy Heavy Ion Collisions

The Bjorken formula about maximal energy density in heavy ion collisions is modified,the effective way to increase the energy density is also analysed.The hydrodynamic equations and the equations of state in central and fragmental regions are discussed.It is pointed out that because of the energy diffusion caused by expansion of the system,it is lifficult to produce quark matter in fragmental region.For Au-Au collisions on the RHIC to be buict at BNL,the space-time region where phase transition occur d and the corresponding extent of impact parameter are predicted.     

Decay of cosmological constant in self-consistent inflation

The symmetric vacuum state in gauge theories with spontaneous symmetry breaking is symmetric in both internal and space-time variables. We consider this vacuum state as a Bose condensate of physical Higgs particles, defined over an asymmetric vacuum state, and identify the energy density of their self-interaction with the cosmological constant in the Einstein equation. In this picture, spontaneous symmetry breaking proceeds as decay. Decoherence of coherent oscillations of a scalar field in the course of decay provides the effective mechanism for damping of coherent oscillations, leading to the regime of slow evaporation of a Bose condensate. This mechanism is responsible for self-consistent inflation without fine-tuning of the potential parameters. The physical self-consistency in this model is provided by incorporating the origin of the cosmological constant in the dynamics of spontaneous breaking of particle symmetries. Received: 28 September 2000 / Revised version: 16 January 2001 / Published online: 25 April 2001     

Neutrino Oscillations in the de Sitter and the Anti-de Sitter Space-Time

General expressions of the neutrino oscillation phase in the generally static space-time with spherical symmetry are given. The effect of the gravitational field on the oscillation length is embodied in the gravitational red shift factor. We find that a blue shift of the oscillation length takes place when the neutrino travels out of the gravitational field. Then, we discuss the variation of the oscillation length influenced by the cosmological constant. In the de Sitter space-time, the positive cosmological constant prolongs the oscillation length. And, in the anti-de Sitter space-time, the negative cosmological constant shortens it as expected.     

Form-Preserving Transformations of Time-Dependent Schrödinger Equation with Time- and Position-Dependent Mass

We study space-time transformations of the time-dependent Schrödinger equation (TDSE) with time- and position-dependent (effective) mass. We obtain the most general space-time transformation that maps such a TDSE onto another one of its kind. The transformed potential is given in explicit form.     

Intermittency for coherent and incoherent current ensemble model

We investigate the origin of intermittency for multiparticle distribution in momentum space, following the idea that there is a kind of power law distribution of the space-time region of hadron emission. Using the formalism of current ensamble model to describe boson sources we discuss intermittency exponents for the coherent and incoherent (chaotic) particle production scheme.