Thermal properties of the Dirac oscillator in Amelino-Camelia and Magueijo-Smolin DSR theories

In the language of creation and annihilation operators, we study a relativistic spin- $$\tfrac{1} {2}$$ fermion subject to a Dirac oscillator (DO) coupling and a constant magnetic field in both commutative and non-commutative (NC) spaces. All dynamical physical variables, in a two-dimensional complex formalism, are expressed in terms of the creation and annihilation operators via a z , $$\bar a_z$$ and a z , $$\bar a_z$$ in the commutative space, and d z , $$\bar d_z$$ and d z , $$\bar d_z$$ in the NC space. The eigensolutions of our problem have been determinated, and the exact connection with both Jaynes-Cummings (JC) and anti-Jaynes-Cummings (AJC) models has been established. In addition, we revealed the existence of the quantum phase transition in both commutative and NC spaces. The thermal properties of the Dirac oscillator under a magnetic field, calculated from the partition function, have been investigated, and the effect of the non-commutative parameters on these properties has been tested.

The effect of the minimal length on the thermal properties of a Dirac oscillator is considered. The canonical partition function is well determined by using the method based on Zeta Epstein function. Through this function, all thermodynamics properties, such as the free energy, the total energy, the entropy, and the specific heat, have been determined. Moreover, this study allows us to calculate the values of minimal length \triangle x=\hbar\sqrt{\beta} for some fermionic particles.

Comments on Superstatistical properties of the one-dimensional Dirac oscillator by Abdelmalek Boumali et al.

Superstatistical properties of the one-dimensional Dirac oscillator

Thermal properties of the one-dimensional space quantum fractional Dirac Oscillator

Statistical properties of the two-dimensional Dirac oscillator with spin–orbit coupling

Following the path integral approach and within in the context of nonrelativistic Snyder–de Sitter algebra, we formulate the Green function for Dirac oscillator particle in ([Formula: see text]) space-time dimension. Using the momentum space representation [Formula: see text], we determine the energy eigenvalues and the eigenfunctions, where the wave functions can be given in terms of Gegenbauer polynomials. In addition, the high-temperature thermodynamic properties of the relativistic harmonic oscillators are analyzed, which we found that the heat capacity is not equal two times greater than the heat capacity of the one-dimensional harmonic oscillator for higher temperatures in SdS model. The special cases are found and discussed.

An algebraic (representation-independent) analysis is presented for the Dirac oscillator in an angular momentum basis. The analysis is based on shift operators for energy and angular momentum, and it is similar to that for a non-relativistic isotropic harmonic oscillator. The shift operators generate all the eigenkets of the Dirac oscillator from a 'vacuum' ket. The shift operations yield energy eigenvalues and certain matrix elements. The relationship to the factorization method is discussed.

Using the momentum space representation, we determine the energy eigenvalues, eigenfunctions and the high-temperature thermodynamic properties of the Dirac oscillator in one dimension in the presence of a minimal length given by , where β is the deformation parameter of the modified commutation relation [X, P] = i(1 + βP2). The obtained results suggest that the effect of the minimal length could be detected in ultrarelativistic heavy-ion collisions.

Arbitrary spin Galilean oscillator

The study examined the solution of nonlinear oscillator and thermal properties of interacting system of real polyatomic molecules. A nonlinear oscillator potential was substituted into the radial part of the Schrodinger wave equation and solved using the Frobenius method to obtain the energy eigenvalues of the system. The partition function and the energy eigenvalues are used to determine three thermal properties for four polyatomic molecules which showed that added energy is required in the absence of the nonlinear term as the orbital and magnetic quantum numbers are increased and degeneracy completely removed. Other findings also reveal that as the virial coefficients of the four polyatomic molecules vary, the additive property of entropy is observed as well as the enhancement of the mean energy approximately proportional to the volume of the molecules. The four polyatomic molecules under consideration are environmentally impactful and are indispensable to man.

In this manuscript, we studied the thermal properties of hundred-watt fiber laser oscillator by real-time in-situ distributed temperature measurement. Optical frequency domain reflectometry (OFDR) was introduced to measure the temperature distribution of gain fiber core. The fiber laser oscillator operated at 1080 nm and the wavelength of detecting signal from OFDR was ~1550 nm. The maximum output power of this fiber oscillator was 100 W. The fiber core temperature distributions in experiment agree well with our theoretical simulation. The temperature measurement of gain fiber core in oscillator has always been a problem because the backward laser from the oscillator may reduce the signal-to-noise ratio in OFDR. To the best of our knowledge, this is the first temperature distribution measurement of fiber core in hundred-watt oscillator. By the experimental measurement and theoretical model, we also analyzed the thermal properties of laser oscillator respectively pumped by 915 nm and 976 nm LD sources. We found fiber laser oscillator pumped by 976 nm LD sources experienced not only higher maximum thermal load but also higher average thermal load than that pumped by 915 nm LD sources at the same level output power. We also analyzed the fiber core temperature of other components in system, such as combiners and fiber Bragg gratings (FBG). These results are meaningful for us to improve the thermal design and management in fiber lasers.

In this work, we have studied the thermal properties of Klein-Gordon oscillator (KGO) under the effect of a uniform magnetic field in noncommutative space, where the exact energy eigenvalues and normalized wave functions are obtained analytically. In this study, we found that the geometric spatial deformation of (KGO) is equivalent to the behavior of the Klein-Gordon equation in a commutative space describing the oscillatory motion of a spinless particle subjected to the action of a constant magnetic field, which means that the studied system has been influenced by the NC geometry.

Molecular dynamics simulations of Carbyne/Carbon nanotube gigahertz oscillators

The one-dimensional thermal properties of the Kemmer oscillator have been investigated. Firstly, we have found the spectrum of energy of the oscillator in question, and then we have calculated its thermal properties. A comparison of our results with those of the Dirac oscillator has been made.