Presence Of Minimal Length Research Articles

Relativistic quantum heat engine with the presence of minimal length

The presence of a minimal length has a significant effect on relativistic physical systems. This paper discusses how minimal length affects the efficiency of a relativistic quantum heat engine. The working substance chosen is a Dirac particle trapped in a one-dimensional infinite potential well. In this paper, we calculate the efficiency of a quantum heat engine in three thermodynamic cycles, namely the Carnot, Otto, and Brayton cycles. The engine efficiency is calculated analytically and numerically. In this research, the minimal length is a correction factor for the relativistic energy. The result is that the minimal length could increase or decrease the efficiency of the relativistic quantum heat engine on the small potential width according to the particle mass, the expansion parameter, and the thermodynamic cycle.

Quantum Lenoir engine in the presence of minimal length

The effect of minimal length for quantum heat engine systems is proposed. We use a system of trapped Fermi particles in an infinite potential well. The thermodynamic cycle chosen is the reversible Lenoir cycle. We use both a single particle case and a multiparticle case. The result is that the minimum length increases the efficiency of the engine if the width of the potential well is infinitely small, and the maximum value is obtained when the width of the potential well is close to zero.

Analytical solution of the Bohr-Mottelson equation in the presence of minimal length for yukawa potential using hypergeometric method

The relativistic energy and wave function of the Bohr-Mottelson equation in the presence of minimal length are investigated by the hypergeometric method. The Bohr-Mottelson equation in the presence of minimal length is influenced by Yukawa potential. The energy relativistic is calculated by using Matlab software, and the wave function is expressed in the Hypergeometric term. The existence of minimal length caused increased of the energy relativistic of Bohr-Mottelson equation.

Analysis of minimal length effect on the non-relativistic energy and wave function for the exponential type potential using Supersymmetric Quantum Mechanics

In this research, the minimal length effect was analysed on the energy and wave functions of the non-relativistic mechanical quantum system by studying the Schrodinger equation. The three dimensional Schrodinger equation with minimal length for the exponential type potential was solved by using supersymmetric quantum mechanics. To get the solution, the exponential type potential was reduced to the Morse potential. The non-relativistic energy was calculated numerically for diatomic molecules, LiH and HCl by using the Matlab software. From the results were shown that the presence of minimal length gives effect to the non-relativistic energy, it was seen clearly in the higher value of angular momentum l and quantum number n.

Lorentz force and ponderomotive force in the presence of a minimal length

In this work, according to the electromagnetic field tensor in the framework of generalized uncertainty principle (GUP), we obtain the Lorentz force and Faraday’s law of induction in the presence of a minimal length. Also, the ponderomotive force and ponderomotive pressure in the presence of a measurable minimal length are found. It is shown that in the limit [Formula: see text], the generalized Lorentz force and ponderomotive force become the usual forms. The upper bound on the isotropic minimal length is estimated.

Klein Paradox for the Bosonic Equation in the Presence of Minimal Length

We present an exact solution of the one-dimensional modified Klein Gordon and Duffin Kemmer Petiau (for spins 0 and 1) equations with a step potential in the presence of minimal length in the uncertainty relation, where the expressions of the new transmission and reflection coefficients are determined for all cases. As an application, the Klein paradox in the presence of minimal length is discussed for all equations.

Quantum Carnot Heat Engine Efficiency with Minimal Length

In this paper, the effects of the minimum lengths () to the efficiency of a quantum heat engine are considered. A particle in infinite one-dimensional potential well is used as the “working substance”. We obtain quantized energy of particle in the presence of minimal length, and then we do the isoenergetic cycle. We calculate heat exchanged between the system and reservoir, and then we get the efficiency of the engine. We observe that the minimum length increases efficiency of the engine at the small width of the potential well.

Novel characteristics of energy spectrum for 3D Dirac oscillator analyzed via Lorentz covariant deformed algebra

We investigate the Lorentz-covariant deformed algebra for Dirac oscillator problem, which is a generalization of Kempf deformed algebra in 3 + 1 dimension of space-time, where Lorentz symmetry are preserved. The energy spectrum of the system is analyzed by taking advantage of the corresponding wave functions with explicit spin state. We obtained entirely new results from our development based on Kempf algebra in comparison to the studies carried out with the non-Lorentz-covariant deformed one. A novel result of this research is that the quantized relativistic energy of the system in the presence of minimal length cannot grow indefinitely as quantum number n increases, but converges to a finite value, where c is the speed of light and β is a parameter that determines the scale of noncommutativity in space. If we consider the fact that the energy levels of ordinary oscillator is equally spaced, which leads to monotonic growth of quantized energy with the increment of n, this result is very interesting. The physical meaning of this consequence is discussed in detail.

Some Aspects of Supersymmetric Field Theories with Minimal Length and Maximal Momentum

We consider a real scalar field and a Majorana fermion field to construct a supersymmetric quantum theory of free fermion fields based on the deformed Heisenberg algebra[x,p] = iℏ(1−βp+2β2p2), whereβis a deformation parameter. We present a deformed supersymmetric algebra in the presence of minimal length and maximal momentum.

Dirac oscillator with minimal lengths and free particle on AdS2 and S2

We use two different types of laddering equations which are realized by the associated Gegenbauer functions. We show that the Dirac oscillator equation with minimal lengths can be written to form associated Gegenbauer functions. This leads us to write the Dirac oscillator equation in terms of first order equations. By changing some variable in two types of equations, we have some u(1,1) and u(2) algebras. These algebras correspond to AdS2 and S2. Finally, we conclude that all quantum states from the Dirac oscillator (presence of minimal lengths) correspond to the quantum states of free particle on AdS2 and S2.

Pauli-Hamiltonian in the presence of minimal lengths

We construct the Pauli-Hamiltonian on a space where the position and momentum operators obey generalized commutation relations leading to the appearance of a minimal length. Using the momentum space representation we determine exactly the energy eigenvalues and eigenfunctions for a charged particle of spin half moving under the action of a constant magnetic field. The thermal properties of the system in the regime of high temperatures are also investigated, showing a magnetic behavior in terms of the minimal length.

An exact solution of the one-dimensional Dirac oscillator in the presence of minimal lengths

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.

Casimir effect in the presence of minimal lengths

It is expected that the implementation of minimal length in quantum models leads to a consequent lowering of Planck's scale. In this paper, using the quantum model with minimal length of Kempf et al (1994 J. Math. Phys. 35 4483; 1995 Phys. Rev. D 52 1108; 1997 J. Phys. A 30 2093; 1996 J. Math. Phys. 37 2121), we examine the effect of the minimal length on the Casimir force between parallel plates.