We study a static dyonic black hole endowed with a global monopole and surrounded by a perfect fluid with an equation-of-state parameter ω. This parameter relates to distributions of radiation, dust, and dark matter. We use a modified lapse function to examine the horizon structure, thermodynamic properties, and phase transitions. The heat capacity shows critical behavior that divides stable and unstable phases. Curvature invariants confirm that the central singularity persists. Next, we calculate the photon sphere and shadow radius. We constrain the model parameters using observations from Sgr A*, which indicates that both the global monopole and surrounding matter significantly affect the shadow size. We analyze dynamical properties with the effective potential and quasi–normal modes using the WKB method. This shows that oscillation frequencies and damping rates are very sensitive to the matter distribution, and all modes indicate linear stability. Moreover, we investigate the greybody bound, emitted power spectrum, and partial absorption cross–section. These findings reveal that environmental effects change the potential barrier and the observable Hawking radiation spectrum. Finally, we conduct a topological analysis of the photon sphere and thermodynamic potentials to clarify the system’s stability properties. These results highlight how environmental matter and topological defects shape black hole physics.

Based on the framework established in a recent work (Ubriaco in Physica A 414:128, 2014), wherein a generalized bosonic model was formulated using the Dunkl operator formalism (DOF), we extend this approach to its different applications with introducing a statistical distribution—termed the Dunkl-deformed Bose–Einstein (DDBE) distribution—constructed by generalizing the usual Bose–Einstein distribution through the DOF. In this framework, we study further general thermodynamical and statistical properties of a gas model of the Dunkl-deformed bosons obeying the DDBE statistics. Emphasis is given to a careful analysis on the conditions under which the Bose–Einstein-like condensation would occur in the present Dunkl-deformed boson gas. It is shown that the critical temperature for such a system is higher than that of the usual (undeformed) Bose gas for values of the model deformation parameter θ in the range θ > 0 . As another application of the DDBE statistics, we investigate the thermostatistics of the Dunkl-deformed Debye solid and the effects of the deformation parameter θ on the high- and low-temperature behavior of the model specific heat are discussed. Our results obtained in this study could provide much physical insight for approaching not only in the treatment of interacting bosons theories including collective excitations, but also in the condensation characteristics of quantum systems beyond the standard formalism.

A q-deformed field theory at finite temperature is presented and its related thermo field dynamics is constructed. This enables us to introduce the quon field, whose Lagrangian leads to a q-deformed partition function. Accordingly, the general thermostatistical properties of a gas model of quon fields, such as the q-deformed statistical distribution function describing an intermediate-statistics behavior and the equation of state in two and three dimensions, are investigated. For low temperatures, the conditions under which Bose-Einstein-like condensation would occur in the quon gas model are discussed. It is shown that the critical temperature of such a gas is higher than that of the usual Bose gas for values of the model parameter q in the range q<1. For high temperatures, possible anyonic behavior of the present quon gas model in two spatial dimensions is studied through an analysis of the effect of deformation on the second and third virial coefficients in the equation of state. The results obtained in this work reveal the ability of the model for analyzing a parastatistical behavior of systems with quasiparticles and put forward it as a possible candidate for effectively modeling the properties of some exotic quantum states, such as in the case of dark matter constituents.

This study examines how q-deformation and adjustments to the Lane-Emden parameter influence the structural properties of white dwarfs, especially their radii. We start by deriving the Fermi energy for electrons confined in a three-dimensional box to establish the fundamental physics of white-dwarf interiors. The stellar radius is then calculated using the classical Lane-Emden equation and re-evaluated with a q-deformed and modified Lane-Emden formulation. Comparative analysis shows how q-deformation changes the governing equilibrium equations and, in turn, the predicted white-dwarf radii. The findings highlight the importance of q deformed statistics in shaping the internal structure of compact stars and offer deeper insights into potential deviations from standard models.

Having in mind the significance of parity (reflection) in various areas of physics, the single-mode and two-mode Wigner algebras are considered adding to them a reflection operator. The associated deformed sl(2, R) algebra, sl_ν(2,R) and the deformed so(3) algebra, so_ν(3), are constructed for the widely used Jordan-Schwinger and Holstein-Primakoff realizations, commenting on various aspects and ingredients of the formalism for both single-mode and two-mode cases. Finally, due to its potential application in the study of qubit and qutrit systems, the parity-deformed so_ν(3) representation is analyzed based on the isomorphy of so(3) and su(2). Related applications are discussed as well.

In this paper, inspired by Tsallis' probability distribution based on a q-deformed Boltzmann factor, we stipulate a new q-deformed quantum dynamics by applying the inverse Wick rotation beta - it to the Tsallis-deformed Boltzmann factor. We obtain a new time-dependent q-deformed Schr & ouml;dinger equation. The free time-evolution of a Gaussian wave packet and that induced by an harmonic interaction are studied within this q-deformed quantum mechanical framework.

In this paper, we construct a deformed Schwarzschild black hole from the de Sitter gauge theory of gravity within Dunkl generalization and we determine the metric coefficients versus Dunkl parameter and parity operators. Since the spacetime coordinates are not affected by the group transformations, only fields are allowed to change under the action of the symmetry group. A particular ansatz for the gauge fields is chosen and the components of the strength tensor are computed as well. Additionally, we analyze the modifications on the thermodynamic properties to a spherically symmetric black hole due to Dunkl parameters for even and odd parities. Finally, we verify a novel remark highlighted from heat capacity: the appearance of a phase transition when the odd parity is taken into account.

In this work, we explore both the ordinary q-Gaussian distribution and a new one defined here, determining both their mean and variance, and we use them to construct solutions of the q-deformed diffusion differential equation. This approach allows us to realize that the standard deviation of the distribution must be a function of time. In one case, we derive a linear Fokker-Planck equation within a finite region, revealing a new form of both the position- and time-dependent diffusion coefficient and the corresponding continuity equation. It is noteworthy that, in both cases, the conventional result is obtained when q tends to zero. Furthermore, we derive the deformed diffusion-decay equation in a finite region, also determining the position- and time-dependent decay coefficient. A discrete version of this diffusion-decay equation is addressed, in which the discrete times have a uniform interval, while for the discrete positions the interval is not uniform.

Most approaches towards a quantum theory of gravitation indicate the existence of a minimal length scale of the order of the Planck length. Quantum mechanical models incorporating such an intrinsic length scale call for a deformation of Heisenberg’s algebra resulting in a generalised uncertainty principle and constitute what is called gravitational quantum mechanics. Utilising the position representation of this deformed algebra, we study various models of gravitational quantum mechanics. The free time evolution of a Gaussian wave packet is investigated as well as the spectral properties of a particle bound by an external attractive potential. Here the cases of a box with infinite walls and an attractive potential well of finite depth are considered.

In this study, we explore the properties of a black hole model solved within the framework of loop quantum gravity, examining various aspects such as its thermodynamic behavior, quasi-normal modes, scattering, and topological characteristics. By determining the temperature and remnant mass, we establish a condition for the existence of the remnant mass. Additionally, using the shadow profile and fitting it to the EHT data, we derive upper and lower bounds for the model parameters. Our findings offer significant insight into the interplay between quantum effects and classical black hole physics. These results enhance our understanding of black hole thermodynamics and the nature of singularities, providing a valuable perspective on the potential unification of gravity and quantum mechanics.

In this paper, inspired by Tsallis' probability distribution based on a q-deformed Boltzmann factor, we stipulate a new q-deformed quantum dynamics by applying the inverse Wick rotation β→ i t to the Tsallis-deformed Boltzmann factor. We obtain a new time-dependent q-deformed Schrödinger equation. The free time-evolution of a Gaussian wave packet and that induced by an harmonic interaction are studied within this q-deformed quantum mechanical framework.

After introducing the algebraic and representative properties of the extended Weyl–Heisenberg algebra along with its special case containing the Wigner algebra, a new deformed boson algebra involving the reflection operator is proposed. Such an algebra differs from the other well-known deformed particle algebras in the literature so that its number operator spectrum constitutes a novel deformed number called ν -number, which is changed for both even n and odd n in its energy levels. As physical applications of the quantum algebra developed here, the thermostatistical properties of a gas model of the ν -deformed bosons and the blackbody radiation phenomena covering the ν -deformed photon gas are studied in detail. Another application is carried out onto lattice oscillations via the Debye crystal model containing the ν -deformed phonons. The effects of ν -deformation onto the low-temperature behavior of the model specific heat of the ν -deformed Debye solid are explored and are compared with the results of both the standard phonon gas and the ones with the non-extensive Tsallis statistics. Finally, possible implications of our results on other application areas of research such as strongly correlated quantum matter and star formation in cosmological systems are concisely discussed.

We introduce a specific deformed Bose gas model, whose underlying quasiparticle algebra is related to the κ-deformed bosonic oscillator algebra. We then develop the statistical distribution function of a gas model of the κ-deformed bosons containing finite and infinite dimensional cases. We investigate interpolating statistics behavior of this deformed model and apply it to lattice oscillations via the Debye crystal model. The effect of the deformation parameter κ onto the low-temperature behavior of the model specific heat is discussed and is compared with the results of both the standard phonon gas and the ones with the Tsallis non-extensive statistics. Another application is carried out onto the Bose-like condensation of this deformed model and the conditions under which the κ-deformed boson condensation would occur in such a system are discussed. It is shown that the critical temperature of the κ-deformed boson gas with the infinite dimensional case is higher than that of the ideal Bose gas, while it has lower values than those of the ideal Bose gas for the finite dimensional case. We consider that the results obtained in this work may provide much physical insight into further studies on strongly correlated quantum materials as well as interacting theories of bosons including collective excitations, where unconventional quantum statistics might have an important role.

We consider two strongly coupled harmonic oscillators (TSCHO) exposed by a bosonic bath in thermal non-equilibrium conditions (TNEC). To explain TNEC, we use the Tsallis statistics. To obtain the system's time evolution, we use the Liouville-von Neumann master equation. We find that the q-dependence of the entanglement of formation (EOF) gives EOFq<1 < EOFq=1 < EOFq>1. The effects of squeezing and coupling between two oscillators on EOF are analyzed. We apply our method to obtain the outputs of SWAP and CONT gates in TNEC exposed to the environment. We find that for different q-regions, the squeezing and hopping coefficients affect the amount of entanglement and its death slope after the CNOT-gate operation.

In this paper, we adopt q-deformed binary operations, such as q-addition, q-subtraction, q-multiplication, and q-division, to construct the q-deformed Schrödinger equation in one dimension. We explore the mathematics involving q-deformed binary operations. We q-deform the ordinary commutator and the definition of Fock space in q-deformed quantum mechanics. As examples, we discuss the particle in a box and the harmonic oscillator.

In this paper, the gravity with a deviation is considered. Modification of the Lane-Emden equation and Jeans’ instability condition is performed based on the gravity with a deviation. Some exact and numerical solutions are given for the modified Lane-Emden equation.

In this paper, we consider a system of the q-deformed bosonic Tamm-Dancoff oscillators, whose spectrum has some exponential cutoff factors at high energies. We first investigate the q-calculus in the Tamm-Dancoff (TD) boson algebra, and within this framework, the q-derivative, q-integral and q-exponential function are introduced. Using these properties, we construct a new formalism for the q-deformed quantum mechanics, which accordingly involve the q-adjoint operator and the q-Hermitian operator properties. We then derive the q-deformed Heisenberg relation, and develop the q-Hermitian momentum operator. The q-deformed Schrodinger equation is introduced, and as applications, we study the momentum eigenfunction and one-dimensional box problem. Another application of the TD type deformation onto lattice oscillations is also discussed through a model of the q-deformed Debye solid. Finally, other potential applications of the TD-oscillators gas model are concisely pointed out.

Starting on the basis of Fibonacci calculus and Fibonacci oscillator algebra, we introduce the main properties to develop a new formalism for the two-parameter (q_1,q_2) -deformed quantum mechanics, where q_1 and q_2 are real positive independent deformation parameters. As applications of such a two-parameter deformed formalism, we investigate the behavior of a quantum particle in some different physical phenomena covering the free particle and the inverse-harmonic potential case. The effect of two deformation parameters on the wave functions for these applications is studied. Another application is carried out onto the quantum statistics of lattice oscillations through a model of the (q_1,q_2) -deformed phonon gas, and it is shown that the high- and low-temperature behavior of the model specific heat differs notably from the classical theories for the interval 0<(q_1,q_2)<∞ . We also construct a two-parameter deformed non-extensive entropy based on some elements of the Fibonacci calculus and discuss its possible connection with the Tsallis entropy in non-extensive statistical mechanics. Finally, other possible application areas of the present two-parameter (q_1,q_2) -deformed construction on quantum mechanics are discussed.

In this article, gravity is considered with deviation and we solved the Lane-Emden equation using this deviation, first, we calculated the pressure and potential due to gravity, and considering the density resulting from solving this equation, we obtained the radius of the white dwarf in different states. We obtained the ordinary cases when the deformation parameter goes to zero.

We construct a momentum operator within the Wigner–Heisenberg algebra picture by means of a generalized derivative, a particular case of which is the Dunkl operator. The corresponding Hamiltonian is set up, and the Schrödinger equation is generated. We discuss properties of its bound state solutions and present an application involving a harmonic oscillator potential.