Closed Timelike Curves in Type Ⅱ Non-Vacuum Spacetime

Here we present a cyclicly symmetric non-vacuum spacetime, admitting closed timelike curves(CTCs) which appear after a certain instant of time,i.e.,a time-machine spacetime. The spacetime is asymptotically flat, freefrom curvature singularities and a four-dimensional extension of the Misner space in curved spacetime. The spacetime is of type Ⅱ in the Petrov classification scheme and the matter field pure radiation satisfy the energy condition.     

Closed orbits and limit cycles of second—order autonomous Birkhoff systems

In the paper,the existence of periodic orbits and the non-existence of limit cycles for the second-order autonomous Birkhoff system are studied.Further the existence of algebraic limit cycles for a generalized second-order autonomous Birkhoff system is studied.     

Open and Closed World Models in Kaluza-Klein-Theory with Variables G and Λ

The field equation of higher dimensions theory, have been applied in the area of cosmology. The resulting differential equations are solved for open and closed. We derive a relation between the Einstein constant G(t) and the cosmological constant Λ(t) from the conservation law T _μ ^ν _;ν =0. We give a specific form of Λ(t) to solve the non-linear differential equations. Some cosmological parameters are calculated and some relevant cosmological problems are discussed.     

Time and energy dependent dynamics of the STM tip — graphene system

Probability current and probability density of wave packets was calculated by solving the three dimensional time-dependent Schrödinger equation for a local potential model of the scanning tunneling microscope (STM) tip — graphene system. Geometrical and electronic structure effects of the three dimensional tunneling process are identified by studying three models of increasing complexity: a jellium half space, a narrow jellium sheet, and a local one electron pseudopotential. It was found that some of the key characteristics of the STM tip — graphene tunneling process are already present at the simple jellium models. In the STM tip — jellium half space system the direction of the momentum does not change during the tunneling event, hence this setup is characterised by introducing an effective distance. For the STM tip — narrow jellium sheet system the direction of the momentum is changed from vertical to horizontal during the tunneling event. The wave packet preferentially tunnels into the bound state of the jellium sheet. For the atomistic model of the graphene sheet an anisotropic spreading of the wave packet was found for hot electrons. This may open new opportunities to build carbon based nanoelectronic devices.     

Harper Operator,Fermi Curves and Picard–Fuchs Equation

This paper is a continuation of the work on the spectral problem of the Harper operator using algebraic geometry. We continue to discuss the local monodromy of algebraic Fermi curves based on Picard–Lefschetz formula. The density of states over approximating components of Fermi curves satisfies a Picard–Fuchs equation. By the property of Landen transformation, the density of states has a Lambert series as the quarter period. A q-expansion of the energy is derived from a mirror map as in the B-model.     

Time without clocks—An attempt

We try to define time intervals separating two states of systems of elementary particles and observers. The definition is founded on the notion of instant state of the system and uses no information connected with the use of a clock. Applying then the definition to a classical clock and to a sample of unstable particles, we obtain results in agreement with experiment. However, if the system contains few elementary particles, the properties of the time interval present some different features.     

Mesoscopic Persistent Currents,Aharonov—Bohm Magnetic Flux and Time Reversal Symmetry

We discuss the effect of Aharonov-Bohm magnetic flux on the time reversal symmetric properties of mesoscopic metallic ring systems.It is usually believed that AB flux causes time reversal symmetry breaking.We analyse the case of mesoscopic persistent currents and find out that AB flux does not break time reversal symmetry.our arguments are supported by the general theory of mesoscopic persistent currents.     

Quantum Curves for Hitchin Fibrations and the Eynard–Orantin Theory

We generalize the topological recursion of Eynard–Orantin (JHEP 0612:053, 2006; Commun Number Theory Phys 1:347–452, 2007) to the family of spectral curves of Hitchin fibrations. A spectral curve in the topological recursion, which is defined to be a complex plane curve, is replaced with a generic curve in the cotangent bundle T*C of an arbitrary smooth base curve C. We then prove that these spectral curves are quantizable, using the new formalism. More precisely, we construct the canonical generators of the formal ${\hbar}$ -deformation family of D modules over an arbitrary projective algebraic curve C of genus greater than 1, from the geometry of a prescribed family of smooth Hitchin spectral curves associated with the ${SL(2,\mathbb{C})}$ -character variety of the fundamental group π₁(C). We show that the semi-classical limit through the WKB approximation of these ${\hbar}$ -deformed D modules recovers the initial family of Hitchin spectral curves.     

Tritium Burn-up Depth and Tritium Break-Even Time

Similarly to but quite different from the xenon poisoning effects resulting from fission-produced iodine during the restart-up process of a fission reactor, we introduce a completely new concept of the tritium burn-up depth and tritium break-even time in the fusion energy research area. To show what the least required amount of tritium storage is used to start up a fusion reactor and how long a time the fusion reactor needs to be operated for achieving the tritium break-even during the initial start-up phase due to the finite tritium breeding time that is dependent on the tritium breeder, specific structure of breeding zone, layout of coolant flow pipe, tritium recovery scheme, extraction process, the tritium retention of reactor components, unrecoverable tritium fraction in breeder, leakage to the inertial gas container, and the natural decay etc., we describe this new phenomenon and answer this problem by setting up and by solving a set of equations, which express a dynamic subsystem model of the tritium inventory evolution in a fusion experimental breeder （FEB）. It is found that the tritium burn-up depth is 317g and the tritium break-even time is approximately 240 full power days for FEB designed detail configuration and it is also found that after one-year operation, the tritium storage reaches 1.18kg that is more than the least required amount of tritium storage to start up three of FEB-like fusion reactors.     

Time Variable Λ and the Accelerating Universe

We perform a deductive study of accelerating Universe and focus on the importance of variable time-dependent Λ in the Einstein’s field equations under the phenomenological assumption, Λ=αH ² for the full physical range of α. The relevance of variable Λ with regard to various key issues like dark matter, dark energy, geometry of the field, age of the Universe, deceleration parameter and barotropic equation of state has been trivially addressed. The deceleration parameter and the barotropic equation of state parameter obey a straight line relationship for a flat Universe described by Friedmann and Raychaudhuri equations. Both the parameters are found identical for α=1.     

Moments and Mean First—Passage Time of Parabolic—Bistable Potential System Driven by Colored Noise

A parabolic-bistable potential system driven by colored noise is studied.The exact analytical expressions of the stationary probability distribution (SPD) and the moments of the system are derived.Furthermore,the mean first-passage time is calculated by the use of two approximate methods,respectively.It is found that (i) the double peaks of SPD are rubbed-down into a flat single peak with the increasing of noise intensity;(ii) a minimum occurs on the curve of the second-order moment of the system vs.noise intensity at the point DΓ=0.025;(iii) the results obtained by our approximate approach are in good agreement with the numerical calculations for either small or large correlation time τ,while the conventional steepest descent approximation leads to poor results.     

Analytical Solution for Single—Mode Time—Dependent Oscillator

Based on the general theory of time-dependent quantum transformation,we use the “time evolution operator” method to solve the single-mode time-dependent oscillator.     

Virtual Black Holes and Space–Time Structure

In the standard formalism of quantum gravity, black holes appear to form statistical distributions of quantum states. Now, however, we can present a theory that yields pure quantum states. It shows how particles entering a black hole can generate firewalls, which however can be removed, replacing them by the ‘footprints’ they produce in the out-going particles. This procedure can preserve the quantum information stored inside and around the black hole. We then focus on a subtle but unavoidable modification of the topology of the Schwarzschild metric: antipodal identification of points on the horizon. If it is true that vacuum fluctuations include virtual black holes, then the structure of space-time is radically different from what is usually thought.     

Coherence Time Resolvable Diffraction and New Tunnelling Electronics

With the help of the perturbation method and the Feynman path integral technique,we analytically demonstrate that,when the electronic spectrum of a mesoscopic box is measured through two connecting leads,there exists a class of new diffraction phenomena in the coherence time domain,based on the new coherent tunnelling model,It is shown that the new diffraction effect determines the minimal resolvable coherence time to the Heisenberg limit.In particular,Fraunhofer optical phenomena,such as missing order and grating effects,can be reproduced in the meso-system,The predicted periodic oscillations as a function of voltage are in excellent agreement with experimental observations.     

Time—Resolved Photoluminescence Studies of AlInGaN Alloys

We study the two samples of AlInGaN,i.e.,1-μm Gan grown at 1030℃ on the buffer and followed by a 0.6μm-thick epilayer of AlInGaN under the low pressure of 76 Torr and the AlInGaN layer deposited diectly on the buffer layer without the high-temperature GaN layer,by temperature-dependent photoluminescence(PL) spectroscopy and picosecond time-resolved photoluminescence(TRPL) spectroscopy.The TRPL signals of both the samples were fitted well as a stretched exponential decay at all temperatures,indicating significant disorder in the material.We attribute the disorder to nanoscale quantum dots or discs of high indium concentration.Temperature dependence of dispersive exponent β shows that the stretched exponential decay of the two samples comes from dfferent mechanisms.The different depths of the localization potential account for the difference,which is illustrated by the results of temperature dependence of radiative recombination lifetime and PL peak energy.     

Classical and Quantum Mechanics via Supermetrics in Time

Koopman-von Neumann in the 30’s gave an operatorial formulation of Classical Mechanics. It was shown later on that this formulation could also be written in a path-integral form. We will label this functional approach as CPI (for classical path-integral) to distinguish it from the quantum mechanical one, which we will indicate with QPI. In the CPI two Grassmannian partners of time make their natural appearance and in this manner time becomes something like a three dimensional supermanifold. Next we introduce a metric in this supermanifold and show that a particular choice of the supermetric reproduces the CPI while a different one gives the QPI.