scholarly journals Two-Dimensional Klein–Gordon Oscillator in the Presence of a Minimal Length

2018 ◽  
Vol 15 (5) ◽  
pp. 473-477 ◽  
Author(s):  
A. Boumali ◽  
Z. Selama
Keyword(s):  
Minimal Length ◽  
Two Dimensional ◽  
Klein Gordon

scholarly journals Two-dimensional boson oscillator under a magnetic field in the presence of a minimal length in the non-commutative space

2021 ◽  
Vol 67 (2 Mar-Apr) ◽  
pp. 226
Author(s):  
Z. Selema ◽  
A. Boumal
Keyword(s):  
Magnetic Field ◽  
Schrödinger Equation ◽  
Momentum Space ◽  
Schrodinger Equation ◽  
Minimal Length ◽  
Wave Functions ◽  
Two Dimensional ◽  
Commutative Space ◽  
Klein Gordon

Minimal length in non-commutative space of a two-dimensional Klein-Gordon oscillator isinvestigated and illustrates the wave functions in the momentum space. The eigensolutionsare found and the system is mapping to the well-known Schrodinger equation in a Pöschl-Teller potential.

scholarly journals Thermal properties of a two-dimensional Duffin–Kemmer–Petiau oscillator under an external magnetic field in the presence of a minimal length

2020 ◽  
Vol 35 (33) ◽  
pp. 2050278
Author(s):  
H. Aounallah ◽  
B. C. Lütfüoğlu ◽  
J. Kříž
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Energy Eigenvalue ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Summation Formula ◽  
Minimal Length ◽  
Two Dimensional ◽  
Relativistic Limit ◽  
Ordinary Quantum

Generalized uncertainty principle puts forward the existence of the shortest distances and/or maximum momentum at the Planck scale for consideration. In this article, we investigate the solutions of a two-dimensional Duffin–Kemmer–Petiau (DKP) oscillator within an external magnetic field in a minimal length (ML) scale. First, we obtain the eigensolutions in ordinary quantum mechanics. Then, we examine the DKP oscillator in the presence of an ML for the spin-zero and spin-one sectors. We determine an energy eigenvalue equation in both cases with the corresponding eigenfunctions in the non-relativistic limit. We show that in the ordinary quantum mechanic limit, where the ML correction vanishes, the energy eigenvalue equations become identical with the habitual quantum mechanical ones. Finally, we employ the Euler–Mclaurin summation formula and obtain the thermodynamic functions of the DKP oscillator in the high-temperature scale.

Stable standing waves for the two-dimensional Klein–Gordon–Schrödinger system

2010 ◽  
Vol 140 (5) ◽  
pp. 1011-1039 ◽  
Author(s):  
Hiroaki Kikuchi
Keyword(s):  
General Theory ◽  
Perturbation Method ◽  
Ground State ◽  
Standing Waves ◽  
Orbital Stability ◽  
Two Dimensional ◽  
Spatial Dimensions ◽  
Klein Gordon ◽  
Linearized Operator ◽  
Schrödinger System

AbstractWe study the orbital stability of standing waves for the Klein–Gordon–Schrödinger system in two spatial dimensions. It is proved that the standing wave is stable if the frequency is sufficiently small. To prove this, we obtain the uniqueness of ground state and investigate the spectrum of the appropriate linearized operator by using the perturbation method developed by Genoud and Stuart and Lin and Wei. Then we apply to our system the general theory of Grillakis, Shatah and Strauss.

scholarly journals THE TWO-DIMENSIONAL STRINGY BLACK HOLE: A NEW APPROACH AND A NEW EFFECT

1996 ◽  
Vol 11 (08) ◽  
pp. 1463-1488
Author(s):  
H.J. DE VEGA ◽  
J. RAMÍREZ MITTELBRUN ◽  
M. RAMÓN MEDRANO ◽  
N. SÁNCHEZ
Keyword(s):  
Black Hole ◽  
Physical Phenomenon ◽  
Type Equation ◽  
Scalar Particle ◽  
Conformal Anomaly ◽  
Massless Scalar ◽  
Two Dimensional ◽  
New Approach ◽  
Klein Gordon ◽  
String Propagation

The string propagation in the two-dimensional stringy black hole is investigated from a new approach. We completely solve the classical and quantum string dynamics in the Lorentzian and Euclidean regimes. In the Lorentzian case all the physics reduces to a massless scalar particle described by a Klein-Gordon type equation with a singular effective potential. The scattering matrix is found and it reproduces the results obtained by coset CFT techniques. It factorizes into two pieces: an elastic Coulombian amplitude and an absorption part. In both parts, an infinite sequence of imaginary poles in the energy appears. The generic features of string propagation in curved D-dimensional backgrounds (string stretching, fall into space-time singularities) are analyzed in the present case. A new physical phenomenon specific to the present black hole is found: the quantum renormalization of the speed of light. We find that [Formula: see text] where k is the integer in front of the WZW action. Only for k→∞ does this new effect disappear (although the conformal anomaly is present). We analyze all the classical Euclidean string solutions and exactly compute the quantum partition function. No critical Hagedorn temperature appears here.

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