Levy stability for anisotropic dynamical fluctuation in high energy multiparticle production

The behaviour of Levy index?? in various phase space dimensions is studied. The reason for the violation of Levy stable condition at three-dimension observed in experiment is investigated. It is shown that the apparent violation of Levy stable condition may be due to the wrong isotropic analysis for the highly anisotropic phase space of multiparticle production.     

Levy stability for anisotropic dynamical fluctuation in high energy multiparticle production

The behaviour of Levy indexμ in various phase space dimensions is studied. The reason for the violation of Levy stable condition at three-dimension observed in experiment is investigated. It is shown that the apparent violation of Levy stable condition may be due to the wrong isotropic analysis for the highly anisotropic phase space of multiparticle production.     

Levy Stability Analysis of Random Cascade Model

The Levy stable analysis for random cascade model is performed. The Levy stable index μ ofa-model is obtained by both Monte-Carlo simulation and analytical calculation. It is foundthat μ is increasing when the fluctuation becomes weaker, and vice versa, just as expected.It is shown that the Levy stable index of α-model depends mainly upon the model parameter α. Its weak dependence on the number λ of branches in each elementary splitting is due tothe normalization of probability in each step. The possible reason of the Levy stable indexgreater than 2 found experimentally is briefly discussed.     

EPR correlations and EPW distributions revisited

It is shown that Bell's proof of the violation of local realism in phase space is incorrect. Bell's experiment is based upon position measurements of free particles. A violation can be derived even for a nonnegative Wigner distribution, which in this case acts as a local classical model.     

Target excitation dependence of self-similar cascading rate in multihadron production process at 350 GeV

In the present work target excitation dependence of the self-similar cascading rate has been studied in detail in the framework of Levy stable law using the experimental data of pions obtained from π ^?-AgBr interactions at 350 GeV/c. TheLevy indices µ measured from the analysis fulfill the requirement of the Levy stable region 0 ? µ ? 2. The study gives an evidence of self-similar cascading mechanism responsible for multiparticle production. The different values of µ indicate different rates of cascading for different degrees of target excitation. Moreover, the values of universal scaling exponent (ν) obtained from Ginzburg-Landau theory indicate that no clear evidence of second-order phase transition has been found in the interaction.     

Lorentz-violating effects on topological defects generated by two real scalar fields

The influence of a Lorentz violation on soliton solutions generated by a system of two coupled scalar fields is investigated. Lorentz violation is induced by a fixed tensor coefficient that couples the two fields. The Bogomol’nyi method is applied and first-order differential equations are obtained whose solutions minimize the energy and are also solutions of the equations of motion. The analysis of the solutions in phase space shows how the stability is modified with the Lorentz violation. It is shown explicitly that the solutions preserve linear stability despite the presence of Lorentz violation. Considering Lorentz violation as a small perturbation, an analytical method is employed to yield analytical solutions.     

Revisiting black hole thermodynamics in massive gravity: charged particle absorption and infalling shell of dust

In this study, we apply two methods to consider the variation of massive black holes in both normal and extended thermodynamic phase spaces. The first method considers a charged particle being absorbed by the black hole, whereas the second considers a shell of dust falling into it. With the former method, the first and second laws of thermodynamics are always satisfied in the normal phase space; however, in the extended phase space, the first law is satisfied but the validity of the second law?of?thermodynamics depends upon the model parameters. With the latter method, both laws are valid. We argue that the former method's violation of the second law of thermodynamics may be attributable to the assumption that the change of internal energy of the black hole is equal to the energy of the particle. Finally, we demonstrate that the event horizon always ensures the validity of weak cosmic censorship in both phase spaces; this means that the violation of the second law of thermodynamics, arising under the aforementioned assumption, does not affect the weak cosmic censorship conjecture. This further supports our argument that the assumption in the first method is responsible for the violation and requires deeper treatment.     

The refined inviscid stability condition and cellular instability of viscous shock waves

Combining the work of Serre and Zumbrun, Benzoni-Gavage, Serre, and Zumbrun, and Texier and Zumbrun, we propose as a mechanism for the onset of cellular instability of viscous shock and detonation waves in a finite-cross-section duct, the violation of the refined planar stability condition of Zumbrun-Serre, a viscous correction of the inviscid planar stability condition of Majda. More precisely, we show for a model problem involving flow in a rectangular duct with artificial periodic boundary conditions that transition to multidimensional instability through violation of the refined stability condition of planar viscous shock waves on the whole space generically implies for a duct of sufficiently large cross-section, a cascade of Hopf bifurcations involving more and more complicated cellular instabilities. The refined condition is numerically calculable as described by Benzoni-Gavage-Serre-Zumbrun.     

Explicit CP violation in the Dine–Seiberg–Thomas model

The possibility of explicit CP violation is studied in a supersymmetric model proposed by Dine, Seiberg, and Thomas, with two effective dimension-five operators. The explicit CP violation may be triggered by complex phases in the coefficients for the dimension-five operators in the Higgs potential, and by a complex phase in the scalar top quark masses. Although the scenario of explicit CP violation is found to be inconsistent with the experimental data at LEP2 at tree level, it may be possible at the one-loop level. For a reasonable parameter space, the masses of the neutral Higgs bosons and their couplings to a pair of Z bosons are consistent with the LEP2 data, at the one-loop level.     

Linear relaxation processes governed by fractional symmetric kinetic equations

The fractional symmetric Fokker-Planck and Einstein-Smoluchowski kinetic equations that describe the evolution of systems influenced by stochastic forces distributed with stable probability laws are derived. These equations generalize the known kinetic equations of the Brownian motion theory and involve symmetric fractional derivatives with respect to velocity and space variables. With the help of these equations, the linear relaxation processes in the force-free case and for the linear oscillator is analytically studied. For a weakly damped oscillator, a kinetic equation for the distribution in slow variables is obtained. Linear relaxation processes are also studied numerically by solving the corresponding Langevin equations with the source given by a discrete-time approximation to white Levy noise. Numerical and analytical results agree quantitatively.     

Chaos bound in Kerr-Newman-Taub-NUT black holes via circular motions

In this study, we investigate the influence of the angular momentum of a charged particle around Kerr-Newman-Taub-NUT black holes on the Lyapunov exponent and find spatial regions where the chaos bound is violated. The exponent is obtained by solving the determination of the eigenvalues of a Jacobian matrix in the phase space. Equilibrium positions are obtained by fixing the charge-to-mass ratio of the particle and changing its angular momentum. For certain values of the black holes' electric charge, the NUT charge and rotational parameter, a small angular momentum of the particle, even with zero angular momentum, causes violation of the bound. This violation disappears at a certain distance from the event horizon of the non-extremal Kerr-Newman-Taub-NUT black hole when the angular momentum increases to a certain value. When the black hole is extremal, the violation always exists no matter how the angular momentum changes. The ranges of the angular momentum and spatial regions for the violation are found. The black holes and particle rotating in the same and opposite directions are discussed.     

Postselective measurement of the electronic entanglement in the system of two Mach-Zehnder interferometers with coulomb interaction

The parameters at which the maximally entangled two-particle state appears in the system of two ideal electronic Mach-Zehnder interferometers are known. In this work, the operation of nonideal devices with finite scattering in splitters and with reflection in the region of the Coulomb Interaction has been considered. It has been shown that, under the condition of postselection of experimental results, these factors can increase the observed Bell parameter to values exceeding Cirel’son’s (or Tsirelson’s) bound equal to 2√2 up to the mathematical limit equal to 4. A simple postselective measurement scheme providing B = 4 has been described. Although the results of such measurements are not as fundamental as the observation of the violation of Bell’s inequality, they can indirectly indicate the existence of an entangled state in the system. The measurement system is more stable against fluctuations of the phase than a system without postselection. Furthermore, it has been found that the proposed system is optimal for investigation of cross correlations between interferometers in the dc regime (beyond the paradigm of the violation of Bell’s inequality) because they cannot be generated by coordinated fluctuations of Aharonov-Bohm phases.     

Chaotic jets with multifractal space-time random walk

The problem of normal and anomalous diffusion is examined for the four-dimensional (4-D) map that arises from the problem of particle motion in a constant magnetic field and electrostatic wave packet. This 4-D map consists of two coupled 2-D maps: a standard map and a web map. The case of a weak chaos is considered. It is shown that due to the finite observation time, the particle diffusion possesses strong nonhomogeneous properties. Existence of long-living bundles of orbits with coherent propagation property is checked. These bundles are named "chaotic jets." The same name is used for a part of the trajectory if this part corresponds to long-living trapping or flight. The existence of chaotic jets depends on the topological properties of the phase space and influences the asymptotic law of transport. The particle transport can be considered as a random walk in the multifractal space-time that is produced by flights and trappings of a test particle in some area of its phase space. Levy random walk theory and its generalization for the multifractal space-time situation is considered and asymptotic laws for displacements are derived. Different intermediate asymptotics are discussed.     

(P)arity violation in QCD motivated hadronic models at extreme conditions

We investigate the possibility of parity being spontaneously violated in QCD at finite baryon density and temperature. QCD is approximated by a generalized σ model with two isomultiplets of scalars and pseudoscalars. The mechanism of parity violation is based on interplay between lightest and heavier degrees of freedom and it cannot be understood in simple models retaining the pion and nucleon sectors solely. We argue that, in the dense and hot nuclear matter of a few normal densities and moderate temperatures, parity violation may arise due to a second-order phase transition and its occurrence is well compatible with the existence of stable bound state of normal nuclear matter.     

Stable single-photon interference in a 1 km fiber-optic Mach-Zehnder interferometer with continuous phase adjustment

We experimentally demonstrate stable and user-adjustable single-photon interference in a 1 km long fiber-optic Mach-Zehnder interferometer, using an active phase control system with the feedback provided by a classical laser. We are able to continuously tune the single-photon phase difference between the interferometer arms using a phase modulator, which is synchronized with the gate window of the single-photon detectors. The phase control system employs a piezoelectric fiber stretcher to stabilize the phase drift in the interferometer. A single-photon net visibility of 0.97 is obtained, yielding future possibilities for experimental realizations of quantum repeaters in optical fibers and violation of Bell's inequalities using genuine energy-time entanglement.     

A proposal to test Bell’s inequalities with mesoscopic non-local states in cavity QED

We propose a cavity quantum electrodynamics (CQED) experiment to test the violation of a Bell-type inequality using non-local mesoscopic states (NLMS). These states involve coherent field superpositions stored in two spatially-separated high-Q cavities. The inequality is expressed in terms of the measured Wigner function of the entangled two-field-mode system at four points in phase space, as proposed in [Banaszek and Wódkiewicz, Phys. Rev. Lett. 82, 2009 (1999)]. We examine the production of these entangled NLMS and the measurement of their Wigner function. The experiment involves circular Rydberg atoms and superconducting millimeter-wave cavities. We present a detailed numerical study of the optimal inequality violation and of the effect of decoherence. We discuss the range of experimental parameters making it possible to observe a locality violation and show that they correspond to realistic, albeit demanding, conditions.     

Chaotic transmission of waves and "cooling" of signals

Ray dynamics in waveguide media exhibits chaotic motion. For a finite length of propagation, the large distance asymptotics is not uniform and represents a complicated combination of bunches of rays with different intermediate asymptotics. The origin of the phenomena that we call "chaotic transmission," lies in the nonuniformity of the phase space with sticky domains near the boundary of islands. We demonstrate different fractal properties of ray propagation using underwater acoustics as an example. The phenomenon of the kind of Levy flights can occur and it can be used as a mechanism of cooling of signals when the width of spatial spectra dispersion is significantly reduced. (c) 1997 American Institute of Physics.     

Energy diffusion in hard-point systems

We investigate the diffusive properties of energy fluctuations in a one-dimensional diatomic chain of hard-point particles interacting through a square-well potential. The evolution of initially localized infinitesimal and finite perturbations is numerically investigated for different density values. All cases belong to the same universality class which can be also interpreted as a Levy walk of the energy with scaling exponent γ=3/5. The zero-pressure limit is nevertheless exceptional in that normal diffusion is found in tangent space and yet anomalous diffusion with a different rate for perturbations of finite amplitude. The different behaviour of the two classes of perturbations is traced back to the “stable chaos" type of dynamics exhibited by this model. Finally, the effect of an additional internal degree of freedom is investigated, finding that it does not modify the overall scenario.