scholarly journals Four-dimensional quantum oscillator and magnetic monopole with U(1) dynamical group

2017 ◽  
Vol 32 (30) ◽  
pp. 1750161 ◽  
Author(s):  
Z. Bakhshi ◽  
H. Panahi ◽  
S. G. Golchehre
Keyword(s):  
Differential Equation ◽  
Charged Particle ◽  
Harmonic Oscillator ◽  
Quantum System ◽  
Magnetic Monopole ◽  
Group Representation ◽  
Quantum Oscillator ◽  
Dynamical Group ◽  
Oscillator Quantum ◽  
Dimensions Of Space

By using an appropriate transformation, it was shown that the quantum system of four-dimensional (4D) simple harmonic oscillator can describe the motion of a charged particle in the presence of a magnetic monopole field. It was shown that the Dirac magnetic monopole has the hidden algebra of U(1) symmetry and by reducing the dimensions of space, the U(1) × U(1) dynamical group for 4D harmonic oscillator quantum system was obtained. Using the group representation and based on explicit solution of the obtained differential equation, the spectrum of system was calculated.

Does a uniformly accelerated quantum oscillator radiate?

1991 ◽  
Vol 435 (1893) ◽  
pp. 205-215 ◽  
Keyword(s):  
Scalar Field ◽  
Harmonic Oscillator ◽  
Quantum System ◽  
Long Range ◽  
Heat Bath ◽  
Quantum Correlations ◽  
Quantum Oscillator ◽  
Range Interaction ◽  
Long Range Interaction

Does a quantum system, with no long-range interaction, which is uniformly accelerated through the Minkowski vacuum radiate as a result of excitation by the Unruh-Davies heat bath ? We address this question by considering the effect on an inertial harmonic oscillator (the ‘detector’) of a uniformly accelerated oscillator in the vacuum of a scalar field. We find that, contrary to the more prevalent view in the literature, if we take into account all the quantum correlations present in this experiment then no radiation will be detected.

Rosen-Chambers Variation Theory of Linearly-Damped Classic and Quantum Oscillator

2014 ◽  
Vol 4 (1) ◽  
pp. 404-426
Author(s):  
Vincze Gy. Szasz A.
Keyword(s):  
Harmonic Oscillator ◽  
Classical Mechanics ◽  
Universal Time ◽  
Variation Theory ◽  
Quantum Oscillator ◽  
Variation Principle ◽  
Poisson Brackets ◽  
Mathematical Meaning ◽  
Damped Harmonic Oscillator ◽  
Damped Oscillator

Phenomena of damped harmonic oscillator is important in the description of the elementary dissipative processes of linear responses in our physical world. Its classical description is clear and understood, however it is not so in the quantum physics, where it also has a basic role. Starting from the Rosen-Chambers restricted variation principle a Hamilton like variation approach to the damped harmonic oscillator will be given. The usual formalisms of classical mechanics, as Lagrangian, Hamiltonian, Poisson brackets, will be covered too. We shall introduce two Poisson brackets. The first one has only mathematical meaning and for the second, the so-called constitutive Poisson brackets, a physical interpretation will be presented. We shall show that only the fundamental constitutive Poisson brackets are not invariant throughout the motion of the damped oscillator, but these show a kind of universal time dependence in the universal time scale of the damped oscillator. The quantum mechanical Poisson brackets and commutation relations belonging to these fundamental time dependent classical brackets will be described. Our objective in this work is giving clearer view to the challenge of the dissipative quantum oscillator.

scholarly journals Reading a Qubit Quantum State with a Quantum Meter: Time Unfolding of Quantum Darwinism and Quantum Information Flux

2019 ◽  
Vol 26 (04) ◽  
pp. 1950023
Author(s):  
Salvatore Lorenzo ◽  
Mauro Paternostro ◽  
G. Massimo Palma
Keyword(s):  
Quantum Information ◽  
Harmonic Oscillator ◽  
Quantum System ◽  
Quantum State ◽  
Common Theme ◽  
Quantum Harmonic Oscillator ◽  
Collision Model ◽  
Single Qubit ◽  
Quantum Darwinism

Quantum non-Markovianity and quantum Darwinism are two phenomena linked by a common theme: the flux of quantum information between a quantum system and the quantum environment it interacts with. In this work, making use of a quantum collision model, a formalism initiated by Sudarshan and his school, we will analyse the efficiency with which the information about a single qubit gained by a quantum harmonic oscillator, acting as a meter, is transferred to a bosonic environment. We will show how, in some regimes, such quantum information flux is inefficient, leading to the simultaneous emergence of non-Markovian and non-darwinistic behaviours.

scholarly journals Klein–Gordon particle near RN black hole, generalized sl(2) algebra and harmonic oscillator energy

2019 ◽  
Vol 34 (31) ◽  
pp. 1950196
Author(s):  
J. Sadeghi ◽  
M. R. Alipour
Keyword(s):  
Differential Equation ◽  
Information Theory ◽  
Black Hole ◽  
Energy Spectrum ◽  
Harmonic Oscillator ◽  
Three Dimensional ◽  
The Other ◽  
Thermodynamical Properties ◽  
Heun Functions ◽  
Klein Gordon

In this paper, we consider Klein–Gordon particle near Reissner–Nordström black hole. The symmetry of such a background led us to compare the corresponding Laplace equation with the generalized Heun functions. Such relations help us achieve the generalized [Formula: see text] algebra and some suitable results for describing the above-mentioned symmetry. On the other hand, in case of [Formula: see text], which is near the proximity black hole, we obtain the energy spectrum. When we compare the equation of RN background with Laguerre differential equation, we show that the obtained energy spectrum is same as the three-dimensional harmonic oscillator. So, finally we take advantage of harmonic oscillator energy and make suitable partition function. Such function help us to obtain all thermodynamical properties of black hole. Also, the structure of obtained entropy lead us to have some bit and information theory in the RN black hole.

Solvability of the Caldeira–Leggett model

2020 ◽  
Vol 98 (7) ◽  
pp. 683-688
Author(s):  
Smail Bougouffa ◽  
Lazhar Bougoffa
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Differential Equations ◽  
Harmonic Oscillator ◽  
Master Equation ◽  
Wigner Distribution ◽  
Partial Differential ◽  
Coupled Differential Equations

In this paper, we illustrate the use of the method of the characteristics in various dissipative models of a single harmonic oscillator. The master equation governing the process can be transformed to a partial differential equation on the Wigner distribution, which in turn can be split to a system of coupled differential equations. We present a useful technique that can be used to separate the system without increasing the order and then the solutions can be obtained. The obtained solutions are used to calculate the average of energy observable of the system. This procedure can be extended to solve some other complex similar problems.

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