Condensation and evolution of a space–time network

In this work, we try to propose in a novel way, using the Bose and Fermi quantum network approach, a framework studying condensation and evolution of a space–time network described by the Loop quantum gravity. Considering quantum network connectivity features in Loop quantum gravity, we introduce a link operator, and through extending the dynamical equation for the evolution of the quantum network posed by Ginestra Bianconi to an operator equation, we get the solution of the link operator. This solution is relevant to the Hamiltonian of the network, and then is related to the energy distribution of network nodes. Showing that tremendous energy distribution induces a huge curved space–time network may indicate space time condensation in high-energy nodes. For example, in the case of black holes, quantum energy distribution is related to the area, thus the eigenvalues of the link operator of the nodes can be related to the quantum number of the area, and the eigenvectors are just the spin network states. This reveals that the degree distribution of nodes for the space–time network is quantized, which can form space–time network condensation. The black hole is a sort of result of space–time network condensation, however there may be more extensive space–time network condensations, such as the universe singularity (big bang).     

Space–time fractional diffusion equations and asymptotic behaviors of a coupled continuous time random walk model

In this paper, we consider a type of continuous time random walk model where the jump length is correlated with the waiting time. The asymptotic behaviors of the coupled jump probability density function in the Fourier–Laplace domain are discussed. The corresponding fractional diffusion equations are derived from the given asymptotic behaviors. Corresponding to the asymptotic behaviors of the joint probability density function in the Fourier–Laplace space, the asymptotic behaviors of the waiting time probability density and the conditional probability density for jump length are also discussed.     

Spherically symmetric solution in a space–time with torsion

By using the method of group analysis, we obtain a new exact evolving and spherically symmetric solution of the Einstein–Cartan equations of motion, corresponding to a space–time threaded with a three-form Kalb–Ramond field strength. The solution describes in its more generic form, a space–time which scalar curvature vanishes for large distances and for large time. In static conditions, it reduces to a classical wormhole solution and to a exact solution with a localized scalar field and a torsion kink, already reported in literature. In the process we have found evidence towards the construction of more new solutions.     

Floquet scattering through a parity–time symmetric oscillating potential

We investigate the scattering of a particle from a trapping potential that is subjected to weak, parity–time symmetric periodic drivings. Using the Floquet theory, we derive the scattering matrix and calculate the transmittance of the incident particle. When the driving is purely coherent, our calculation recovers the known result and the transmission spectrum shows the familiar, bound-state-induced Fano resonances. When the driving is purely incoherent, we find the Fano resonances still occur, ...     

Once upon a time,in the Soviet Union …

Radiation reaction (but, more generally, fluctuations and dissipation) occurs when a system interacts with a heat bath, a particular case being the interaction of an electron with the radiation field. We have developed a general theory for the case of a quantum particle in a general potential (but, in more detail, an oscillator potential) coupled to an arbitrary heat bath at arbitrary temperature, and in an external time-dependent c-number field. The results may be applied to a large variety of problems in physics but we concentrate by showing in detail the application to the blackbody radiation heat bath, giving an exact result for the radiation reaction problem which has no unsatisfactory features such as the runaway solutions associated with the Abraham–Lorentz theory. In addition, we show how atomic energy and free energy shifts due to temperature may be calculated. Finally, we give a brief review of applications to Josephson junctions, quantum statistical mechanics, mesoscopic physics, quantum information, noise in gravitational wave detectors, Unruh radiation and the violation of the quantum regression theorem.     

Cosmic strings in a space–time with positive cosmological constant

We study Abelian strings in a fixed de Sitter background. We find that the gauge and Higgs fields extend smoothly across the cosmological horizon and that the string solutions have oscillating scalar fields outside the cosmological horizon for all currently accepted values of the cosmological constant. If the gauge to Higgs boson mass ratio is small enough, the gauge field function has a power-like behaviour, while it is oscillating outside the cosmological horizon if Higgs and gauge boson mass are comparable. Moreover, we observe that Abelian strings exist only up to a maximal value of the cosmological constant and that two branches of solutions exist that meet at this maximal value. We also construct radially excited solutions that only exist for non-vanishing values of the cosmological constant and are thus a novel feature as compared to flat space–time. Considering the effect of the de Sitter string on the space–time, we observe that the deficit angle increases with increasing cosmological constant. Lensed objects would thus be separated by a larger angle as compared to asymptotically flat space–time.     

α-relaxation near the glass transition — a local time process

The empirical Cole-Cole and Cole-Davidson expressions for the -relaxation part of the susceptibility (z)=o/[z ^b +1] ^a are analyzed within a general framework of diffusion processes. It is found that (z) represents a Green function for such a process, and the corresponding relaxation function can be expressed in terms of a local time processF(t)=1–E ₀[(t)]. This latter process describe an intermittent relaxation process occurring on a Cantor like visiting time-setJ _o. The exponentsa andb are fractal dimensions of such sets. It is argued that, in caseb1, the underlying diffusion process is related to the experimentally observed -process which then triggers the -process on the time-setJ _o.     

Relativistic spin-zero bosons in a Som–Raychaudhuri space–time

We investigate the Duffin–Kemmer–Petiau equation for spin-zero bosons in a (\(3+1\))-dimensional Som–Raychaudhuri space–time. We establish the covariant Duffin–Kemmer–Petiau equation in this curved space–time for the so-called oscillator and we include interaction with a scalar potential. We determine eigenfunctions and the corresponding eigenvalues for the oscillator with the Cornell potential. We investigate the effect of the space–time’s parameters, oscillator’s frequency and the Cornell potential’s parameters on the wave functions.     

Will a large complex system with time delays be stable?

In 1972 May showed that for a large linear system with random coupling the system size and the average coupling strength must together satisfy a simple inequality to ensure the stability of the equilibrium point. Here we extend the analysis to delay coupled systems. Our calculations establish that the same inequality obtained by May constrains the stability for systems randomly coupled through discrete and distributed delays.     

Noether symmetry and conserved quantity for a Hamilton system with time delay

In this paper, the Noether symmetries and the conserved quantities for a Hamilton system with time delay are discussed. Firstly, the variational principles with time delay for the Hamilton system are given, and the Hamilton canonical equations with time delay are established. Secondly, according to the invariance of the function under the infinitesimal transformations of the group, the basic formulas for the variational of the Hamilton action with time delay are discussed,the definitions and the criteria of the Noether symmetric transformations and quasi-symmetric transformations with time delay are obtained, and the relationship between the Noether symmetry and the conserved quantity with time delay is studied. In addition, examples are given to illustrate the application of the results.     

Multi-path propagation of acoustical wave and time reversal field in a solid plate

The multi-path effect of the acoustical wave in a solid plate is studied. The multireflection and wave conversion of the cylindrical compressional and shear waves, which are excited by an infinite strip on a free surface of the solid plate, are analyzed thoroughly by the far-field approximation method. The concise analytical representations of the cylindrical waves are obtained. The time reversal processing is then applied to the propagation of the cylindrical waves and analyzed theoretically and experimentally. It is shown that the waves coming from different array elements and different paths all arrive at the original place after the time reversal operation. It indicates that the time reversal can compensate automatically the wave aberration caused by the multi-path effect. The self-adaptive focusing of the time reversal field is also analyzed quantificationally by the focusing gain and the ratio of the principal to the second lobe. The effects of the focus position and the aperture of the transducer array on the focused field are also investigated. It shows that theoretical and experimental results are consistent to each other very well.     

Direct time domain observation of exciton–polariton oscillation in a semiconductor microcavity

We measured temporal evolution of the coherent emission from a semiconductor microcavity by an ac-balanced homodyne detector with high sensitivity and wide dynamic range. The experimental results can be well explained by the coupled exciton–photon model.