scholarly journals Information and thermodynamics properties of a non-Hermitian particle ensemble

2020 ◽  
Author(s):  
Francisco Cleiton Lima ◽  
Allan Moreira ◽  
CARLOS ALBERTO ALMEIDA
Keyword(s):  
Magnetic Field ◽  
Information Theory ◽  
Quantum Mechanics ◽  
Thermodynamic Properties ◽  
Uniform Magnetic Field ◽  
Cyclotron Frequency ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Particle Ensemble ◽  
The Magnetic Field

In the context of non-relativistic quantum mechanics, we use information theory to study Shannon’s entropy of a non-Hermitian system and understand how the information is modified with the cyclotron frequency. Subsequently, we turn our attention to the construction of an ensemble of these spinless particles in the presence of a uniform magnetic field. Then, we study the thermodynamic properties of the model. Finally, we show how information and thermodynamic properties are modified with the action of the magnetic field.Keywords: Non-relativistic Quantum Mechanics; Quantum Information; Shannon Entropy.

scholarly journals Quantum Speed Limit for Relativistic Spin-0 and Spin-1 Bosons on Commutative and Noncommutative Planes

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Kang Wang ◽  
Yu-Fei Zhang ◽  
Qing Wang ◽  
Zheng-Wen Long ◽  
Jian Jing
Keyword(s):  
Magnetic Field ◽  
Lorentz Invariance ◽  
Wave Packets ◽  
Relativistic Quantum ◽  
Homogeneous Magnetic Field ◽  
Relativistic Quantum Mechanics ◽  
Speed Of Light ◽  
Initial State ◽  
The Magnetic Field ◽  
Noncommutative Plane

Quantum speed limits of relativistic charged spin-0 and spin-1 bosons in the background of a homogeneous magnetic field are studied on both commutative and noncommutative planes. We show that, on the commutative plane, the average speeds of wave packets along the radial direction during the interval in which a quantum state is evolving from an initial state to the orthogonal final one can not exceed the speed of light, regardless of the intensities of the magnetic field. However, due to the noncommutativity, the average speeds of the wave packets on noncommutative plane will exceed the speed of light in vacuum provided the intensity of the magnetic field is strong enough. It is a clear signature of violating Lorentz invariance in the relativistic quantum mechanics region.

Statistical properties of the q-deformed relativistic Dirac oscillator in minimal length quantum mechanics

2018 ◽  
Vol 96 (1) ◽  
pp. 25-29 ◽  
Author(s):  
S. Sargolzaeipor ◽  
H. Hassanabadi ◽  
W.S. Chung
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
External Magnetic Field ◽  
Relativistic Quantum ◽  
Two Dimensions ◽  
Minimal Length ◽  
Statistical Properties ◽  
Relativistic Quantum Mechanics ◽  
Two Dimensional ◽  
Dirac Oscillator

In this article, we introduce a two-dimensional Dirac oscillator in the presence of an external magnetic field in terms of q-deformed creation and annihilation operators in the framework of relativistic quantum mechanics with minimal length. We discuss the eigenvalues of q-deformed Dirac oscillator in two dimensions and report the statistical quantities of the system for a small real q.

scholarly journals Exact Solutions of the (2+1)-Dimensional Dirac Oscillator under a Magnetic Field in the Presence of a Minimal Length in the Non-commutative Phase Space

2015 ◽  
Vol 70 (8) ◽  
pp. 619-627 ◽  
Author(s):  
Abdelmalek Boumali ◽  
Hassan Hassanabadi
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
Phase Space ◽  
Hypergeometric Functions ◽  
Relativistic Quantum ◽  
Minimal Length ◽  
Wave Functions ◽  
Relativistic Quantum Mechanics ◽  
Two Dimensional ◽  
Dirac Oscillator

AbstractWe consider a two-dimensional Dirac oscillator in the presence of a magnetic field in non-commutative phase space in the framework of relativistic quantum mechanics with minimal length. The problem in question is identified with a Poschl–Teller potential. The eigenvalues are found, and the corresponding wave functions are calculated in terms of hypergeometric functions.

Stochastic microcausality in relativistic quantum mechanics

1984 ◽  
Vol 14 (9) ◽  
pp. 883-906 ◽  
Author(s):  
D. P. Greenwood ◽  
E. Prugovečki
Keyword(s):  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics

Relativistic Multiple Scattering Theory

1991 ◽  
Vol 253 ◽  
Author(s):  
B. L. Gyorffy
Keyword(s):  
Quantum Mechanics ◽  
Degrees Of Freedom ◽  
Relativistic Quantum ◽  
Schr6dinger Equation ◽  
Relativistic Effects ◽  
Relativistic Quantum Mechanics ◽  
Absolute Minimum ◽  
Crystalline Anisotropy ◽  
Symmetry Properties ◽  
Finite Set

The symmetry properties of the Dirac equation, which describes electrons in relativistic quantum mechanics, is rather different from that of the corresponding Schr6dinger equation. Consequently, even when the velocity of light, c, is much larger than the velocity of an electron Vk, with wave vector, k, relativistic effects may be important. For instance, while the exchange interaction is isotropic in non-relativistic quantum mechanics the coupling between spin and orbital degrees of freedom in relativistic quantum mechanics implies that the band structure of a spin polarized metal depends on the orientation of its magnetization with respect to the crystal axis. As a consequence there is a finite set of degenerate directions for which the total energy of the electrons is an absolute minimum. Evidently, the above effect is the principle mechanism of the magneto crystalline anisotropy [1]. The following session will focus on this and other qualitatively new relativistic effects, such as dichroism at x-ray frequencies [2] or Fano effects in photo-emission from non-polarized solids [3].

scholarly journals PROBABILITY IN RELATIVISTIC QUANTUM MECHANICS AND FOLIATION OF SPACE–TIME

2007 ◽  
Vol 22 (32) ◽  
pp. 6243-6251 ◽  
Author(s):  
HRVOJE NIKOLIĆ
Keyword(s):  
Quantum Mechanics ◽  
Wave Equations ◽  
Integral Curve ◽  
Relativistic Quantum ◽  
Space Time ◽  
Relativistic Quantum Mechanics ◽  
Relativistic Wave ◽  
Probability Densities ◽  
The Many ◽  
Conserved Currents

The conserved probability densities (attributed to the conserved currents derived from relativistic wave equations) should be nonnegative and the integral of them over an entire hypersurface should be equal to one. To satisfy these requirements in a covariant manner, the foliation of space–time must be such that each integral curve of the current crosses each hypersurface of the foliation once and only once. In some cases, it is necessary to use hypersurfaces that are not spacelike everywhere. The generalization to the many-particle case is also possible.

Sign in / Sign up

Export Citation Format

Share Document