abstract

Thermodynamics of the ideal Fermi gas trapped in an external generic power law potential \(U=\sum _{i=1} ^d c_i |\frac {x_i}{a_i}|^{n_i}\) is investigated systematically from the grand thermodynamic potential in \(d\)-dimensional space. These properties are explored carefully in the degenerate limit (\(\mu \gg K_{\rm B}T\)), where the thermodynamic properties are greatly dominated by the Pauli exclusion principle. Pressure and energy along with the isothermal compressibility are nonzero at \(T=0K\). The nonzero value of compressibility implies that zero point pressure is not a constant but depends on volume.

abstract

Thermodynamic properties of the ideal Bose gas trapped in an external generic power law potential are investigated systematically from the grand thermodynamic potential in \(d\)-dimensional space. In this manuscript, the most general conditions for Bose–Einstein condensate and the discontinuity conditions of heat capacity at the critical temperature in presence of generic power law potential are presented. The dependence of the physical quantities on external potential, particle characteristics and space dimensionality are discussed. The more general results obtained in this paper present an unified illustration of the Bose–Einstein condensation of ideal Bose systems as they reduce to the expressions and conclusions available in the literature with appropriate choice of power law exponent.

abstract

New rotation laws have been recently found for general-relativistic self-gravitating stationary fluids. It was not clear whether they apply to systems rotating with a constant linear velocity. In this paper, we fill this gap. The answer is positive. That means, in particular, that these systems should exhibit the recently discovered general-relativistic weak-field effects within rotating tori: the dynamic anti-dragging and the deviation from the Keplerian motion induced by the fluid selfgravity.

abstract

We present the joint helicity amplitudes for \(J/\psi \to {\mit \Lambda } \bar {\mit \Lambda }\), \({\mit \Lambda }(\bar {\mit \Lambda })\) decays to different final states in the helicity frame. Two observables to search for CP violation in \(J/\psi \to {\mit \Lambda }\bar {\mit \Lambda }\) can be expressed with the information of helicity angles of baryon and anti-baryon. Four decay parameters of \({\mit \Lambda }\) and \(\bar {\mit \Lambda }\), namely, \(\alpha _-,\,\alpha _+,\,\alpha _0\) and \(\bar \alpha _0\), can be obtained with the joint helicity amplitude equations by the likelihood fit method. With the data sample of \(10^{10}\) \(J/\psi \) decays accumulated by BESIII, the precision of the measurements is estimated to be about \(10^{-3}\).

abstract

In this article, we assume that the nonet scalar mesons above 1 GeV are \(\bar {q}q\) states and study the temperature dependence of the masses and decay constants of the \(a_0(1450)\) and \(K_0^*(1430)\) using the thermal QCD sum rules. We fit the numerical values into analytical functions, which have applications in phenomenological analysis of the thermal QCD and in interpreting the heavy-ion collision experiments.

abstract

The process of jet–gap–jet (JGJ) production is briefly described. The JGJ scattering amplitude parametrisation is discussed. On the basis of full amplitude calculations, the parametrisation formulas for the leading logarithmic (LL) and next-to-leading logarithmic (NLL) approximations are obtained. For each case, a sum over all conformal spins is considered. The obtained agreement is better than 0.25% for LL and 1% for NLL.

abstract

The complete spectrum of plasmons of the two interpenetrating plasma streams is found in a closed analytic form. The orientation of the wave vector with respect to the stream direction is arbitrary and the plasmas, which are assumed to be collisionless and spatially homogeneous, can be nonrelativistic, relativistic or even ultrarelativistic. Our results apply to the electromagnetic plasma of electrons and passive ions and to the quark–gluon plasma governed by QCD.

abstract

We review transverse momentum dependent (TMD) parton distribution functions, their application to topical issues in high-energy physics phenomenology, and their theoretical connections with QCD resummation, evolution and factorization theorems. We illustrate the use of TMDs via examples of multi-scale problems in hadronic collisions. These include transverse momentum \(q_{\rm T}\) spectra of Higgs and vector bosons for low \(q_{\rm T}\), and azimuthal correlations in the production of multiple jets associated with heavy bosons at large jet masses. We discuss computational tools for TMDs, and present the application of a new tool, TMDlib, to parton density fits and parameterizations.

abstract

Momentum transfer resulting from the interaction of two patches on the colloidal particle surfaces is, by nature, off-center and is responsible for particle’s rotations. We present how to compute exchange of momentum and angular momentum in the case when patches interact via a square well potential. Elements of the presented algorithm consist mostly of physical and geometrical conditions, partly requiring numerical calculations. The model has been applied to the two-dimensional system of spherical particles with three patches equally placed on the edge of the particles. An example of typical collisional frequencies resulting from molecular dynamics applied to a Monte Carlo equilibrated configuration and its comparison to the case with an unbonded hexagonal starting configuration have been given. It has been shown that at the agglomerated state, when particles are positionally arrested, the dynamics is dominated by the bounces with the borders of the potential well without hitting the cores of the particles.

abstract

The goal of this work is to construct a simplified model of the core-halo structures in binary systems, such as Thorne–Żytkov objects, hot Jupiters, protoplanets with large moons, red supergiants in binaries and globular clusters with central black hole. A generalized planar circular restricted three-body problem is investigated with one of the point masses, \(M\), replaced with a spherical body of finite size. The mechanical system under consideration includes two large masses \(m\) and \(M\), and a test body with small mass \(\mu \). Mass \(\mu \), initially, is placed at the geometric center of mass \(M\), and shares its orbital motion. Only gravitational interactions are considered and the extended mass \(M\) is assumed to be rigid with rotational degrees of freedom neglected. Equations of motion are presented, and linear instability criteria are derived using quantifier elimination. The motion of the test mass \(\mu \) is shown to be unstable due to the resonance between orbital and internal frequencies. In the framework of model, the central mass \(\mu \) can be ejected if resonance conditions are met during the evolution of the system. The above result is important for core-collapse supernova theory, with mass \(\mu \) identified with the helium core of the exploding massive star. The instability cause off-center supernova “ignition” relative to the center of mass of the hydrogen envelope. The instability is also inevitable during the protoplanet growth, with hypothetical ejection of the rocky core from gas giants and formation of the “puffy planets” due to resonance with orbital frequency. Hypothetical central intermediate black holes of the globular clusters are also in unstable position with respect to perturbations caused by the Galaxy. As an amusing example, we note that the Earth–Moon or the Earth–Sun systems are stable in the above sense, with the test body \(\mu \) being a hypothetical black hole created in the high-energy physics experiment.