Exploring the Implications of the Deformation Parameter and Minimal Length in the Generalized Uncertainty Principle

The breakdown of the Heisenberg Uncertainty Principle occurs when energies approach the Planck scale, and the corresponding Schwarzschild radius becomes similar to the Compton wavelength. Both of these quantities are approximately equal to the Planck length. In this context, we have introduced a model that utilizes a combination of Schwarzschild’s radius and Compton length to quantify the gravitational length of an object. This model has provided a novel perspective in generalizing the uncertainty principle. Furthermore, it has elucidated the significance of the deforming linear parameter β and its range of variation from unity to its maximum value.

Exact solution of the one-dimensional Klein-Gordon equation with scalar and vector linear potentials in the presence of a minimal length

Using the momentum space representation, we solve the Klein--Gordon equation in one spatial dimension for the case of mixed scalar and vector linear potentials in the context of deformed quantum mechanics characterized by a finite minimal uncertainty in position. The expressions of bound state energies and the associated wave functions are exactly obtained.

Maximum Momentum,Minimal Length and Quantum Gravity Effects of Compact Star Cores

Based on the generalized uncertainty principle with maximum momentum arid minimal length, we discuss the equation of state of ideal ultra-relativistic Fermi gases at zero temperature. Maximum momentum avoids the problem that the Fermi degenerate pressure blows up since the increase of the Fermi energy is not limited. Applying this equation of state to the Tolman-Oppenheimer Volkoff （TOV） equation, the quantum gravitational effects on the cores of compact stars are discussed. In the center of compact stars, we obtain the singularity-free solution of the metric component, gtt ～-（1 ＋ 0.2185×r^2）. By numerically solving the TOV equation, we find that quantum gravity plays an important role in the region r～10^4α0（△x）min. Current observed masses of neutron stars indicate that the dimensionless parameter α0 cannot exceed 10^19.

Minimal Length Quantum Mechanics of Dirac Particles in Noncommutative Space

We study the two-dimensional harmonic oscillator in commutative and noncommutative space within the framework of minimal length quantum mechanics for spin-l^2 particles. The energy spectra and the eigenfunction are obtained in both cases. Special cases are also deduced.

Solution of the spin-one DKP oscillator under an external magnetic field in noncommutative space with minimal length

The spin-one Duffin-Kemmer-Petiau （DKP） oscillator under a magnetic field in the presence of Ihe minimal length in the noncommutative coordinate space is studied by using the momentum space representation. The explicit form of energy eigenvalues is found, and the eigenfunctions are obtained in terms of the Jacobi polynomials. It shows that for the same azimuthal quantum number, the energy E increases monotonically with respect to the noncomnmtative parameter and the minimal length parameter. Additionally, we also report some special cases aiming to discuss the effect of the noncommutative coordinate space and the minimal length in the energy spectrum.

Exact Solution of D-Dimensional Klein-Gordon Oscillator with Minimal Length

Specific modifications of the usual canonical commutation relations between position and momentumoperators have been proposed in the literature in order to implement the idea of the existence of a minimal observablelength. Here, we study a consequence of this proposal in relativistic quantum mechanics by solving in the momentumspace representation the Klein-Gordon oscillator in arbitrary dimensions. The exact bound states spectrum and thecorresponding momentum space wave function are obtained. Following Chang et al. (Phys. Rev. D 65 (2002) 125027),we discuss constraint that can be placed on the minimal length by measuring the energy levels of an electron in a penningtrap.

Minimal Length Effects on Schwinger Mechanism

In this paper, we investigate effects of the minimal length on the Schwinger mechanism using the quantum field theory （QFT） incorporating the minimal length. We first study the Schwinger mechanism for scalar fields in both usual QFT and the deformed QFT. The same calculations are then performed in the case of Dirac particles. Finally, we discuss how our results imply for the corrections to the Unruh temperature and the Hawking temperature due to the minimal length.

Quantum Field Theory with a Minimal Length Induced from Noncommutative Space

From the inspection of noncommutative quantum mechanics, we obtain an approximate equivalent relation for the energy dependence of the Planck constant in the noncommutative space, which means a minimal length of the space. We find that this relation is reasonable and it can inherit the main properties of the noncommutative space.Based on this relation, we derive the modified Klein–Gordon equation and Dirac equation. We investigate the scalar field and φ4model and then quantum electrodynamics in our theory, and derive the corresponding Feynman rules. These results may be considered as reasonable approximations to those of noncommutative quantum field theory. Our theory also shows a connection between the space with a minimal length and the noncommutative space.

Quantization of Space in the Presence of a Minimal Length

In this article, we apply the Generalized Uncertainty Principle （GUP）, which is consistent with quantum gravity theories to an elementary particle in a finite potential well, and study the quantum behavior in this system. The generalized Hamiltonian contains two additional terms, which are proportional to ap3 （the result of the maximum momentum assumption） and a2p4 （the result of the minimum length assumption）, where a - 1/MpIc is the GUP parameter. On the basis of the work by Ali et al., we solve the generaiized Schrodinger equation which is extended to include the a2 correction term, and find that the length L of the finite potentiai well must be quantized. Then a generalization to the double-square-well potential is discussed. The result shows that all the measurable lengths especially the distance between the two potential wells are quantized in units of aolp1 in GUP scenario.

Minimal length effects on motion of a particle in Rindler space

Various quantum theories of gravity predict the existence of a minimal measurable length.In this paper,we study effects of the minimal length on the motion of a particle in the Rindler space under a harmonic potential.This toy model captures key features of particle dynamics near a black hole horizon and allows us to make three observations.First,we find that chaotic behavior becomes stronger with increases in minimal length effects,leading predominantly to growth in the maximum Lyapunov characteristic exponents,while the KAM curves on Poincarésurfaces of a section tend to disintegrate into chaotic layers.Second,in the presence of the minimal length effects,it can take a finite amount of Rindler time for a particle to cross the Rindler horizon,which implies a shorter scrambling time of black holes.Finally,the model shows that some Lyapunov characteristic exponents can be greater than the surface gravity of the horizon,violating the recently conjectured universal upper bound.In short,our results reveal that quantum gravity effects may make black holes prone to more chaos and faster scrambling.

Maximal sequence length of exact match between members from a gene family during early evolution

Mutation (substitution, deletion, insertion, etc.) in nucleotide acid causes the maximal sequence lengths of exact match (MALE) between paralogous members from a duplicate event to become shorter during evolution. In this work, MALE changes between members of 26 gene families from four representative species (Arabidopsis thaliana, Oryza sativa, Mus mus- culus and Homo sapiens) were investigated. Comparative study of paralogous’ MALE and amino acid substitution rate (dA<0.5) indicated that a close relationship existed between them. The results suggested that MALE could be a sound evolutionary scale for the divergent time for paralogous genes during their early evolution. A reference table between MALE and divergent time for the four species was set up, which would be useful widely, for large-scale genome alignment and comparison. As an example, de- tection of large-scale duplication events of rice genome based on the table was illustrated.

A fuzzy adaptive smoothing approach to robust endpoint detection based on MDL using sub-band speech

To develop a more robust endpoint detection algorithm, this paper first proposes a fuzzy adaptive smoothing algorithm. The general idea underlying adaptive smoothing is to adapt the short-term sub-band mean of the amplitude to the local attributes of speech on the basis of discontinuity measures. The adaptive smoothing algorithm in this paper utilizes a scale-space framework through the minimal description length （MDL）. We recommend using the fuzzy muhi-attribute decision making approach to select the proper sub-bands where the word boundary can be more reliably detected. The process and simulation of the fuzzy adaptive smoothing algorithm are given. The parameters utilize the mean amplitude of the audible frequency range （300 -3 700 Hz） and the sub-band mean of the amplitude （16 band filter-bank）. We selected the audible band energy because of its usefulness in detecting high-energy regions and making the distinction between speech and noise. Otherwise, the fuzzy adaptive smoothing algorithm is processed in sub-band speech to utilize the full range of frequency information.

Length minimization of uniform linear antenna array for millimeter wave communications with maximum capacity

For uniform linear antenna array （ULA） based millimeter wave communications, the maximum capacity can be achieved by the optimal antenna separation product （ASP）. However, due to the practical size limitation, it is necessary to decrease the ULA length. In this paper, an optimization problem is formulated to minimize the ULA length for millimeter wave communications with maximum capacity. We decompose the problem into two subproblems： length selection optimization and orientation deployment optimization. The optimal length selection can be obtained when the transmit and receive ULAs have equal length. By using the property of trigonometric function, we derive the optimal orientation deployment and study the influence of orientation deviation on ULA length. Simulation results are presented to validate the analyses.

Time-dependent Aharonov–Casher effect on noncommutative space

In this paper,we study the time-dependent Aharonov-Casher effect and its corrections due to spatial noncommutativity.Given that the charge of the infinite line in the Aharonov-Casher effect can adiabatically vary with time,we show that the original Aharonov-Casher phase receives an adiabatic correction,which is characterized by the time-dependent charge density.Based on Seiberg-Witten map,we show that noncommutative corrections to the time-dependent Aharonov-Casher phase contains not only an adiabatic term but also a constant contribution depending on the frequency of the varying electric field.