Approximate Solutions of the Dirac Equation for?the?Manning-Rosen Potential Including the?Spin-Orbit Coupling Term

The bound-state solutions of the Dirac equation for the Manning-Rosen potential are presented approximately for arbitrary spin-orbit quantum number κ. The energy eigenvalues and corresponding two-component spinors of the two Dirac particles are obtained in the closed form by using the framework of the spin symmetry and pseudospin symmetry concept. Two special cases κ=±1 and the Hulthén potential are briefly investigated.     

Wigner Functions and Tomograms of?the?Klauder-Perelomov Coherent States for?the?Pseudoharmonic Oscillator

Using the coherent state representation of Wigner operator and the technique of integration within an ordered product (IWOP) of operators, the Wigner functions of the Klauder-Perelomov coherent states (KP-CSs) for the pseudoharmonic oscillator (PHO) are obtained and the variations of the Wigner functions with the parameters k and z are discussed. Moreover, the tomograms of the KP-CSs for the PHO are calculated by virtue of intermediate coordinate-momentum representation in quantum optics. Project 10574060 supported by the National Natural Science Foundation of China and project X071049 supported by Science Foundation of Liaocheng University.     

Can the CMB reveal the topology of the universe?

This article summarizes recent progress in the development of tools to study the topology of the universe with the cosmic microwave background. The different signatures of the topology and observational constraints are described. The ability of future experiments to reveal the topological structure of our universe is then discussed. To cite this article: J.P. Uzan, A. Riazuelo, C. R. Physique 4 (2003).     

Does the market maker stabilize the market?

The market maker plays an important role in price formation, but his/her behavior and stabilizing impact on the market are relatively unclear, in particular in speculative markets. This paper develops a financial market model that examines the impact on market stability of the market maker, who acts as both a liquidity provider and an active investor in a market consisting of two types of boundedly rational speculative investors—the fundamentalists and trend followers. We show that the market maker does not necessarily stabilize the market when he/she actively manages the inventory to maximize profits, and that rather the market maker’s impact depends on the behavior of the speculators. Numerical simulations show that the model is able to generate outcomes for asset returns and market inventories that are consistent with empirical findings.     

Can the LHC rule out the MSSM?

If supersymmetry (SUSY) exists in nature and is a solution to the hierarchy problem then it should be detectable at the TeV energy scale which the large hadron collider (LHC) is now exploring. One of the main goals of the LHC is the discovery or exclusion of the R-parity conserving minimal supersymmetric standard model (MSSM). So far, the SUSY search results are presented in the context of the constrained MSSM and other specific simplified SUSY models. A model-independent analysis necessarily relies on the trigger-system of the LHC detectors. By using the posterior samples of a 20-parameter MSSM, the phenomenological MSSM, from a fit to indirect collider and cosmological data we find that there is a significant volume in the MSSM parameter space that would escape the standard trigger-systems of the detectors. As such, in the absence of discovery in the current and future LHC runs, it would be difficult if not impossible to exclude the MSSM unless some dedicated and special triggers are commissioned or a Higgs boson with mass as predicted by the supersymmetric models is not found.     

Whence the Minkowski momentum?

Electromagnetic waves carry the Abraham momentum, whose density is given by p_EM = S(r,t) / c². Here S(r,t) = E(r,t) × H(r,t) is the Poynting vector at point r in space and instant t in time, E and H are the local electromagnetic fields, and c is the speed of light in vacuum. The above statement is true irrespective of whether the waves reside in vacuum or within a ponderable medium, which medium may or may not be homogeneous, isotropic, transparent, linear, magnetic, etc. When a light pulse enters an absorbing medium, the force experienced by the medium is only partly due to the absorbed Abraham momentum. This absorbed momentum, of course, is manifested as Lorentz force (while the pulse is being extinguished within the absorber), but not all the Lorentz force experienced by the medium is attributable to the absorbed Abraham momentum. We consider an absorptive/reflective medium having the complex refractive index n₂ + iκ₂, submerged in a transparent dielectric of refractive index n₁, through which light must travel to reach the absorber/reflector. Depending on the impedance-mismatch between the two media, which mismatch is dependent on n₁, n₂, κ₂, either more or less light will be coupled into the absorber/reflector. The dependence of this impedance-mismatch on n₁ is entirely responsible for the appearance of the Minkowski momentum in certain radiation pressure experiments that involve submerged objects.     

The More the Merrier?

The trade-off between traits in life-history strategies has been widely studied for sexual and parthenogenetic organisms, but relatively little is known about the reproduction strategies of asexual animals. Here, we investigate clonal reproduction in the freshwater planarian Schmidtea mediterranea, an important model organism for regeneration and stem cell research. We find that these flatworms adopt a randomized reproduction strategy that comprises both asymmetric binary fission and fragmentation (generation of multiple offspring during a reproduction cycle). Fragmentation in planarians has primarily been regarded as an abnormal behavior in the past; using a large-scale experimental approach, we now show that about one third of the reproduction events in S. mediterranea are fragmentations, implying that fragmentation is part of their normal reproductive behavior. Our analysis further suggests that certain characteristic aspects of the reproduction statistics can be explained in terms of a maximum relative entropy principle.     

Is the CNMSSM more credible than the CMSSM?

“Post-sphaleron baryogenesis”, a fresh and profound mechanism of baryogenesis accounts for the matter–antimatter asymmetry of our present universe in a framework of Pati–Salam symmetry. We attempt here to embed this mechanism in a non-SUSY SO(10) grand unified theory by reviving a novel symmetry breaking chain with Pati–Salam symmetry as an intermediate symmetry breaking step and as well to address post-sphaleron baryogenesis and neutron–antineutron oscillation in a rational manner. The Pati–Salam symmetry based on the gauge group \(\mathrm{SU}(2)_L \times \mathrm{SU}(2)_{R} \times \mathrm{SU}(4)_C\) is realized in our model at \(10^{5}\) – \(10^{6}\)  GeV and the mixing time for the neutron–antineutron oscillation process having \(\Delta B=2\) is found to be \(\tau _{n-\bar{n}} \simeq 10^{8}\) – \(10^{10}\)  s with the model parameters, which is within the reach of forthcoming experiments. Other novel features of the model include low scale right-handed \(W^{\pm }_R\) , \(Z_R\) gauge bosons, explanation for neutrino oscillation data via the gauged inverse (or extended) seesaw mechanism and most importantly TeV scale color sextet scalar particles responsible for an observable \(n\) – \(\bar{n}\) oscillation which may be accessible to LHC. We also look after gauge coupling unification and an estimation of the proton lifetime with and without the addition of color sextet scalars.     

Can EMMA solve the puzzle of the knee?

The knee is a change in the slope of the cosmic ray spectrum at approximate energy of 3 PeV. There are multiple competing models for the knee giving conflicting predictions about this change for different masses of the primary particle. Accurate mass measurements of cosmic rays spectra around 3 PeV would be able to exclude some of these models. Cosmic-ray experiment EMMA uses a new method for studying the composition of cosmic rays at the knee area. It is able to determine the multiplicity, the lateral distribution, and the arrival direction of incoming muons produced early in the shower evolution on an event-by-event basis and deduce from these measurements the mass and the energy of the primary particle. EMMA is situated at the depth of 75 m in the Pyhäsalmi mine, Finland. This rock overburden, which corresponds to 210 m of water equivalent, gives EMMA a cut-off energy of 50 GeV for vertical muons. Since the simulations using different air-shower models give similar predictions for the lateral distribution of these high energy muons, we are confident that EMMA should yield a reliable and an air-shower model independent data on the composition of cosmic rays around the knee region.     

Why is the Euclidean Line the Same as the Real Line?

This paper investigates whether the differential structure of space-time follows from accepted laws of physics, or is a mathematical invention. In view of the results of [7], it suffices to consider whether the assumed identity of the Euclidean line E—the line of the geometers of ancient Greece—and the real line R of modern analysis, follows from any known law of nature (i.e., one that can be falsified empirically). Since the totality of empirical data is finite, one is forced to conclude that the completeness of R cannot be falsified empirically—and therefore, according to Popper's criterion, the real line must be an invention, and not a discovery. It then becomes difficult to tell whether Newton's second law of motion (expressed as the differential equation is an invention or a discovery! Finally, some alternatives to the above analysis are briefly analysed.     

Is the derivation of the Langevin formula correct?

The derivation of the Langevin formula is analyzed. It is shown that a basic assumption in it is incorrect. A more correct derivation of a similar formula is proposed.     

What is the problem in the locality problem?

In connection with my previous paper Locality, Reflection, and Wave-Particle Duality [Found. Phys. 17, 813 (1987)], in this paper I distinguish explicitly, in the locality problem, between assertions, deductively established results, interpretations, intuitions, and facts. This clarifies the structure of the problem.     

Demise of the Cosmic Censor?

Initial data for general relativity may be such that there are trapped surfaces on a spatial initial data surface. Penrose has proposed that if the cosmic censorship hypothesis is true, the ADM mass M of asymptotically flat initial data and the area A of the outermost apparent horizon surface should satisfy the inequality A 16M². Initial data which does not satisfy this inequality may be viewed as providing a counterexample of the cosmic censorship conjecture. We describe initial data that appears to violate this inequality.     

Does the Gaussian thermostat maximize the phase-space compression factor?

A recent hypothesis of D. J. Evans and A. Baranyai according to which the Gaussian thermostat maximizes the average phase-space compression factor in nonequilibrium steady states is analyzed for a dilute gas under uniform shear flow. Three routes have been followed: (i) an exact solution of the Bhatnagar-Gross-Krook kinetic equation for arbitrary shear rate, (ii) an exact solution of the Boltzmann equation through super-Burnett order, and (iii) a numerical solution of the Boltzmann equation for finite shear rates. The results show that the above hypothesis does not exactly hold for arbitrary shear rates, although the thermostat that maximizes is close to the Gaussian one. In addition, the influence of the thermostat considered on the nonlinear shear viscosity is also analyzed.     

Does the planck mass run on the cosmological-horizon scale?

Einstein's theory of general relativity contains a universal value of the Planck mass. However, one may envisage that in alternative theories of gravity the effective value of the Planck mass (or Newton's constant), which quantifies the coupling of matter to metric perturbations, can run on the cosmological-horizon scale. In this Letter, we study the consequences of a glitch in the Planck mass from subhorizon to superhorizon scales. We show that current cosmological observations severely constrain this glitch to less than 1.2%.     

Can the Past Be Changed?

The paper shows that the past, history in a non-technical sense, can be changed in quantum mechanics. The first part of the paper reviews Deutsch's analysis in his paper of 1991. It is demonstrated that Deutsch assumes the existence of a multiplicity of essentially classical worlds. Such a multiplicity of worlds would allow the past to be changed in classical mechanics. It is argued that the existence of multiple classical worlds is not required by quantum mechanics. It is then shown that it is possible to change the past in conventional quantum mechanics even without the assumption of a multiplicity of worlds.     

Is the Devil in h?

This note is a part of my effort to rid quantum mechanics (QM) nonlocality. Quantum nonlocality is a two faced Janus: one face is a genuine quantum mechanical nonlocality (defined by the Lüders’ projection postulate). Another face is the nonlocality of the hidden variables model that was invented by Bell. This paper is devoted the deconstruction of the latter. The main casualty of Bell’s model is that it straightforwardly contradicts Heisenberg’s uncertainty and Bohr’s complementarity principles generally. Thus, we do not criticize the derivation or interpretation of the Bell inequality (as was done by numerous authors). Our critique is directed against the model as such. The original Einstein-Podolsky-Rosen (EPR) argument assumed the Heisenberg’s principle without questioning its validity. Hence, the arguments of EPR and Bell differ crucially, and it is necessary to establish the physical ground of the aforementioned principles. This is the quantum postulate: the existence of an indivisible quantum of action given by the Planck constant. Bell’s approach with hidden variables implicitly implies rejection of the quantum postulate, since the latter is the basis of the reference principles.