International Journal of Modern Physics A

In this paper, the Feynman path integral approach within three parameters Dunkl derivative is investigated in the one-dimensional case of nonrelativistic quantum mechanics. We successfully derive the propagator in Cartesian coordinates and give its exact expression for the free particle, inverse square, harmonic oscillator and pure Coulomb potentials. The energy eigenvalues and their corresponding wave functions are determined.

The effective field theory of the Calogero–Sutherland model represents a universality class of quantum hydrodynamic fluids in one spatial dimension. It describes quantum compressible fluids involving both chiralities in which the chiral density field obeys the quantum Benjamin–Ono equation. An extension of this theory to describe a laminar flow of the Calogero–Sutherland fluids in a rectangular geometry with small transverse width and the topology of a ribbon, is considered here. The physical picture is based on the edge states in the hierarchical quantum Hall effect, which may be seen as a collection of parallel one-dimensional quantum incompressible fluids moving along but confined within the transverse microscopic width of the edge of the sample. The effective theory is thus defined as the direct product of two one-dimensional theories of the Calogero–Sutherland class so that one involves motion while the other is confining. Charge transport may be induced by coupling the system to an external electromagnetic field that yields a global translation of the ground state. The effective theory describes quantum solitonic excitations along the direction of the flow and possesses a two-dimensional electric current density which shows a Wigner semicircle law profile in the transverse direction, suggesting a Poiseuille-like behavior but without dissipative viscous effects since the velocity of the fluid is not a well-defined quantum field. This simple physical picture predicts interesting phenomena with distinctive signatures that may be tested in real samples.

We study warm inflation in the framework of $f(\varphi )T$ gravity, where $\varphi$ is the inflaton and T is the trace of the energy–momentum tensor. The inflaton field is assumed to roll on the natural inflaton potential and the result is analyzed in light of Planck 2018 and BICEP/Keck 2021 data. We start by obtaining the field equations under slow-roll approximations. The scalar and tensor power spectra and their corresponding spectral index and tensor-to-scalar ratio with a temperature-dependent form of the dissipation coefficient during the inflationary era are then evaluated. It is found that the warm inflation model in $f(\varphi )T$ gravity is compatible with observational bands.

In this paper, we present a three-parameter model for the distributions of “dark matter” around local spherically symmetric and static distributions of normal matter, usually referred to as “dark matter halos”. The model is based on the assumption that the spontaneous symmetry breaking mechanism involving the Higgs field in the standard model of elementary particle physics leads to the existence of a constant distribution of vacuum energy throughout space–time. This is to be interpreted as a constant distribution of proper energy, as measured by local observers in their proper reference frames. Due to the presence of this universal distribution of vacuum energy, the model requires the introduction of the cosmological term in the Einstein field equations, in order to regulate the behavior of the resulting geometry at cosmologically large distances. By implementing the model on galactic scales, we are able to establish the gravitational consequences of such a homogeneous distribution of proper energy density at these scales. This results in equivalent halo masses and orbital velocity curves that, at least qualitatively, match the observations for galactic “dark matter” halos. Although the detailed realization of the model presented and calculated here cannot be construed as a precise representation of galactic structure, given that most of the actual structure of the galaxy, such as the galactic disk itself, is ignored, and replaced by a single spherically symmetric bulge, in this paper we do introduce the conceptual framework that may be used to construct a more complete galactic model in the future.

Compared to the minimal supersymmetric standard model (MSSM), $\mu$ from $\nu$ Supersymmetric Standard Model ($\mu \nu$SSM) introduces three singlet right-handed neutrino superfields, which lead to the mixing of the Higgs doublets with the sneutrinos. This mixing affects the Standard Model (SM)-like Higgs boson mass. In this work, we separately give the mixing of the CP-even and CP-odd neutral scalar mass matrices with the explicit CP violation, and analyze how the phases impact the SM-like Higgs boson mass and the signal strengths. At the same time, we give the radiative corrections for the Higgs boson mass with effective potential methods.

Recent research has shown that generalized entropies are suitable for describing the thermodynamic properties of gravitational systems. In 2016, Giddings proposed that the spectrum of Hawking radiation, which characterizes evaporating semiclassical black holes, originates from a quantum “atmosphere” that lies beyond a black hole’s horizon. Subsequent studies confirmed that this proposal is possible if the Bekenstein–Hawking entropy of the Schwarzschild black hole is taken to be the Tsallis entropy, and that this result is also compatible with the generalization of the Tsallis entropy to the Rényi entropy. In our paper, we show that the Sharma–Mittal entropy, which is another generalization of the Tsallis entropy, rejects the possibility of Hawking’s proposal but can be compatible with Giddings’ suggestion. So, in this paper, we consider the Sharma–Mittal entropy and study its behavior related to Giddings’ suggestion. So we specify a range for the upper limit of the $(\delta -R)$ parameter, which enables Giddings’ suggestion in the presence of the Sharma–Mittal entropy. We also understood that the Sharma–Mittal entropy, similar to the Tsallis and Rényi entropies, exhibits the same behavior under some approximation of its parameters, in accordance with Giddings’ suggestion.

In this paper, we study nonclassical inflaton, which is minimally coupled to the semi-classical gravity in FRW universe in Coherent Squeezed Vacuum State (CSVS). We have determined the Oscillatory phase of inflaton, power-law expansion, scale factor, density fluctuations, quantum fluctuations and particle production for CSVS. We have obtained an estimated leading solution of scale factor in CSVS and found it proportional to $t^{2/3}$ and showing similar diversification as demonstrated by Semi-classical Einstein Equation (SCEE) of gravity in matter dominated universe. We have also studied the validity of SCEE in CSVS. We have computed validity of uncertainty relation for FRW Universe by determining the quantum fluctuation for CSVS. Our results show that Quantum fluctuations don’t depend on coherent parameter $\mathbf{\Upsilon }$ as the uncertainty relation doesn’t effect by the displacement of $\mathbf{\Upsilon }$ in phase space. We have also studied the production of particles in CSVS for oscillating massive inflaton in flat FRW universe.

The study of the effective potential for nonrenormalizable scalar $SO(N)$ symmetric theories leads to recurrence relations for the coefficients of the leading logarithms due to the Bogoliubov–Parasiuk theorem. These relations can be transformed into generalized renormalization-group (RG) equation which can be solved exactly in the large-N limit.

Proton therapy is an advanced particle radiotherapy technology. Lanzhou University recently designed a new linear accelerator system for proton therapy. In the system, a 750MHz radio frequency quadrupole (RFQ) accelerator was used to complete the initial acceleration of particles. The RFQ can accelerate a proton beam intensity of 1mA from 30keV to 3MeV kinetic energy within a length of 2m. This paper aims to complete the physical design of this high-frequency RFQ, including beam dynamics design, radio frequency (RF) design, and multiphysics analysis. In the dynamics design, a novel design strategy for controlling the longitudinal emittance was adopted to improve the output beam quality of the RFQ. The simulation results showed that the RFQ outlet longitudinal emittance was controlled below 0.1 $\pi$ mm mrad. In the RF design, the pi-mold rod structure was applied to RFQ at such high frequencies for the first time. After the whole cavity simulation, it was found that the separation between the operating frequency of the RFQ cavity and its closest dipole mode reached 58.3MHz, and its quality factor reached 6352. Finally, a multiphysics analysis was performed. The analysis showed that the maximum temperature rise of the RFQ cavity was less than $2.5^{\circ }$C and the frequency drift due to heating was 18kHz. This paper presents the current status of the design of this new linear accelerator. Compared with previous RFQs, the new RFQ has a very high transmission efficiency and higher RF stability.

In this paper, we show the existence of an invariant minimum speed in space–time by forming the basis of a deformed special relativity so-called symmetrical special relativity (SSR). Such observer-independent minimum speed emerges from Dirac’s large number hypothesis (LNH), which leads us to build SSR-theory. This allows us to understand that the hydrogen atom represents the most stable bound state in the universe as being a fundamental structure of the symmetrical space–time with two limits of speed, namely the speed of light c and a minimum speed V. Such minimum speed is associated with a background reference frame for representing the vacuum energy related to the cosmological constant. So the symmetry in space–time given by the invariant minimum speed, which has origin in the electrical and gravitational bound states in hydrogen atom is able to provide a deeper understanding of the proton-electron mass ratio, i.e. $m_p∕m_e=1836.15267343(11)$ given in terms of the universal minimum speed V. Furthermore, we investigate how the minimum speed in space–time plays a fundamental role in the quantization of energy in hydrogen atom.