Properties of solutions of stochastic differential equations driven by the G-Brownian motion

In this paper, we study the differentiability of solutions of stochastic differential equations driven by the $G$-Brownian motion with respect to the initial data and the parameter. In addition, the stability of solutions of stochastic differential equations driven by the $G$-Brownian motion is obtained

Analysis of the Main Problems and Countermeasures of the Modern Apprenticeship Talents Training Model

The changes in our country’s economic development and the demand structure of talent have put forward higher requirements for personnel training in vocational education. The author starts from the present situation of the modern apprenticeship talent training mode, then compares and analyzes the hidden problems in modern Chinese apprenticeship talent training mode, and tries to propose solutions by reviewing literature, making surveys and combining with years of experience in vocational education teaching management.     Keywords: modern apprenticeship, literacy education, problems and countermeasure

Decoherence in Quantum Gravity: Issues and Critiques

An increasing number of papers have appeared in recent years on decoherence in quantum gravity at the Planck energy. We discuss the meaning of decoherence in quantum gravity starting from the common notion that quantum gravity is a theory for the microscopic structures of spacetime, and invoking some generic features of quantum decoherence from the open systems viewpoint. We dwell on a range of issues bearing on this process including the relation between statistical and quantum, noise from effective field theory, the meaning of stochasticity, the origin of non-unitarity and the nature of nonlocality in this and related contexts. To expound these issues we critique on two representative theories: One claims that decoherence in quantum gravity scale leads to the violation of CPT symmetry at sub-Planckian energy which is used to explain today's particle phenomenology. The other uses this process in place with the Brownian motion model to prove that spacetime foam behaves like a thermal bath.Comment: 25 pages, proceedings of DICE06 (Piombino

The Rotating-Wave Approximation: Consistency and Applicability from an Open Quantum System Analysis

We provide an in-depth and thorough treatment of the validity of the rotating-wave approximation (RWA) in an open quantum system. We find that when it is introduced after tracing out the environment, all timescales of the open system are correctly reproduced, but the details of the quantum state may not be. The RWA made before the trace is more problematic: it results in incorrect values for environmentally-induced shifts to system frequencies, and the resulting theory has no Markovian limit. We point out that great care must be taken when coupling two open systems together under the RWA. Though the RWA can yield a master equation of Lindblad form similar to what one might get in the Markovian limit with white noise, the master equation for the two coupled systems is not a simple combination of the master equation for each system, as is possible in the Markovian limit. Such a naive combination yields inaccurate dynamics. To obtain the correct master equation for the composite system a proper consideration of the non-Markovian dynamics is required.Comment: 17 pages, 0 figures

Stochastic Theory of Accelerated Detectors in a Quantum Field

We analyze the statistical mechanical properties of n-detectors in arbitrary states of motion interacting with each other via a quantum field. We use the open system concept and the influence functional method to calculate the influence of quantum fields on detectors in motion, and the mutual influence of detectors via fields. We discuss the difference between self and mutual impedance and advanced and retarded noise. The mutual effects of detectors on each other can be studied from the Langevin equations derived from the influence functional, as it contains the backreaction of the field on the system self-consistently. We show the existence of general fluctuation- dissipation relations, and for trajectories without event horizons, correlation-propagation relations, which succinctly encapsulate these quantum statistical phenomena. These findings serve to clarify some existing confusions in the accelerated detector problem. The general methodology presented here could also serve as a platform to explore the quantum statistical properties of particles and fields, with practical applications in atomic and optical physics problems.Comment: 32 pages, Late

Strain-induced magnetic phase transition in SrCoO3−δ_{3-\delta} thin films

It has been well established that both in bulk at ambient pressure and for films under modest strains, cubic SrCoO$_{3-\delta}$ ($\delta < 0.2$) is a ferromagnetic metal. Recent theoretical work, however, indicates that a magnetic phase transition to an antiferromagnetic structure could occur under large strain accompanied by a metal-insulator transition. We have observed a strain-induced ferromagnetic to antiferromagnetic phase transition in SrCoO$_{3-\delta}$ films grown on DyScO$_3$ substrates, which provide a large tensile epitaxial strain, as compared to ferromagnetic films under lower tensile strain on SrTiO$_3$ substrates. Magnetometry results demonstrate the existence of antiferromagnetic spin correlations and neutron diffraction experiments provide a direct evidence for a G-type antiferromagnetic structure with Ne\'el temperatures between $T_N \sim 135\,\pm\,10\,K$ and $\sim 325\,\pm\,10\,K$ depending on the oxygen content of the samples. Therefore, our data experimentally confirm the predicted strain-induced magnetic phase transition to an antiferromagnetic state for SrCoO$_{3-\delta}$ thin films under large epitaxial strain.Comment: 6 pages, 4 figure

Gravity and Nonequilibrium Thermodynamics of Classical Matter

Renewed interest in deriving gravity (more precisely, the Einstein equations) from thermodynamics considerations [1, 2] is stirred up by a recent proposal that 'gravity is an entropic force' [3] (see also [4]). Even though I find the arguments justifying such a claim in this latest proposal rather ad hoc and simplistic compared to the original one I would unreservedly support the call to explore deeper the relation between gravity and thermodynamics, this having the same spirit as my long-held view that general relativity is the hydrodynamic limit [5, 6] of some underlying theories for the microscopic structure of spacetime - all these proposals, together with that of [7, 8], attest to the emergent nature of gravity [9]. In this first paper of two we set the modest goal of studying the nonequilibrium thermodynamics of classical matter only, bringing afore some interesting prior results, without invoking any quantum considerations such as Bekenstein-Hawking entropy, holography or Unruh effect. This is for the sake of understanding the nonequilibrium nature of classical gravity which is at the root of many salient features of black hole physics. One important property of gravitational systems, from self-gravitating gas to black holes, is their negative heat capacity, which is the source of many out-of-the ordinary dynamical and thermodynamic features such as the non-existence in isolated systems of thermodynamically stable configurations, which actually provides the condition for gravitational stability. A related property is that, being systems with long range interaction, they are nonextensive and relax extremely slowly towards equilibrium. Here we explore how much of the known features of black hole thermodynamics can be derived from this classical nonequilibrium perspective. A sequel paper will address gravity and nonequilibrium thermodynamics of quantum fields [10].Comment: 25 pages essay. Invited Talk at Mariofest, March 2010, Rosario, Argentina. Festschrift to appear as an issue of IJMP

Quantum Field Effects on Cosmological Phase Transition in Anisotropic Spacetimes

The one-loop renormalized effective potentials for the massive $\phi^4$ theory on the spatially homogeneous models of Bianchi type I and Kantowski-Sachs type are evaluated. It is used to see how the quantum field affects the cosmological phase transition in the anisotropic spacetimes. For reasons of the mathematical technique it is assumed that the spacetimes are slowly varying or have specially metric forms. We obtain the analytic results and present detailed discussions about the quantum field corrections to the symmetry breaking or symmetry restoration in the model spacetimes.Comment: Latex 17 page