Charged particle in the presence of a variable magnetic field

Ms, Abdalla

doi:10.1103/physreva.37.4026

Cited by 25 publications

(12 citation statements)

References 11 publications

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“…For time-independent spring forces in the presence of a time-independent magnetic field, [25,26] gave the analytic wave function and energy spectrum, which, in terms of the Heisenberg picture we consider in this paper, means that analytic solutions of (68) were found. For the time-dependent case, [27,28] found analytic wave function for an isotropic harmonic oscillator. For the general case, finding the analytic solution of (68) is not an easy task and it is beyond the analysis presented in this paper.…”

Section: Quantizationmentioning

confidence: 99%

Scalar mode propagation in modified gravity with a scalar field

Felice¹,

Suyama²

2009

Phys. Rev. D

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We study the propagation of the scalar modes around a Friedmann-Lemaitre-Robertson-Walker universe for general modifications of gravity in the presence of a real scalar field. In general, there will be two propagating scalar perturbation fields, which will have in total four degrees of freedom. Two of these degrees will have a superluminal propagation--with k-dependent speed of propagation--whereas the other two will travel with the speed of light. Therefore, the scalar degrees of freedom do not modify the general feature of modified gravity models: the appearance of modes whose frequency depends on the second power of the modulus of the wave vector. Constraints are given and special cases are discussed.Comment: 13 pages, 1 figure, uses RevTe

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Section: Quantizationmentioning

confidence: 99%

Scalar mode propagation in modified gravity with a scalar field

Felice¹,

Suyama²

2009

Phys. Rev. D

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“…Instead, it can be modeled by two-dimensional time-dependent harmonic oscillator due to the existence of variable magnetic field B(t). Theoretical and experimental researches have been carried out extensively on the quantum properties of this system in the past several decades due to its importance not only in condensed matter physics but also in plasma physics [26][27][28][29][30][31][32][33][34][35][36]. Especially, the study of charged particle motion driven by external magnetic field is crucial in investigating magnetic confinement devices for fusion plasmas (whose subtopics are tokamaks, mirror machines, bumpy tori, and stellarators) and for space and astrophysical plasmas (whose subtopics are magnetospheric plasmas of earth and other planets like pulsar) [36].…”

Section: Introductionmentioning

confidence: 99%

An alternative approach to exact wave functions for time-dependent coupled oscillator model of charged particle in variable magnetic field

Maamache

Choi

2010

Annals of Physics

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The quantum states of time-dependent coupled oscillator model for charged particles subjected to variable magnetic field are investigated using the invariant operator methods. To do this, we have taken advantage of an alternative method, so-called unitary transformation approach, available in the framework of quantum mechanics, as well as a generalized canonical transformation method in the classical regime. The transformed quantum Hamiltonian is obtained using suitable unitary operators and is represented in terms of two independent harmonic oscillators which have the same frequencies as that of the classically transformed one. Starting from the wave functions in the transformed system, we have derived the full wave functions in the original system with the help of the unitary operators. One can easily take a complete description of how the charged particle behaves under the given Hamiltonian by taking advantage of these analytical wave functions.

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“…These states were used to calculate the propagators, transition amplitudes and transition probabilities between energy levels corresponding to the initial and final asymptotic magnetic fields. Several other aspects of the problem, where solutions to Equation (3) were used, were considered later, e.g., in papers [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] for α = 0. In particular, the problem of squeezing in the time dependent magnetic field with α = 0 was considered in [14,16,17,19,26] with respect to the canonical pairs of variables.…”

Section: Introductionmentioning

confidence: 99%

Energy and Magnetic Moment of a Quantum Charged Particle in Time-Dependent Magnetic and Electric Fields of Circular and Plane Solenoids

Dodonov

Horovits

2021

Entropy

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We consider a quantum spinless nonrelativistic charged particle moving in the xy plane under the action of a time-dependent magnetic field, described by means of the linear vector potential A=B(t)−y(1+α),x(1−α)/2, with two fixed values of the gauge parameter α: α=0 (the circular gauge) and α=1 (the Landau gauge). While the magnetic field is the same in all the cases, the systems with different values of the gauge parameter are not equivalent for nonstationary magnetic fields due to different structures of induced electric fields, whose lines of force are circles for α=0 and straight lines for α=1. We derive general formulas for the time-dependent mean values of the energy and magnetic moment, as well as for their variances, for an arbitrary function B(t). They are expressed in terms of solutions to the classical equation of motion ε¨+ωα2(t)ε=0, with ω1=2ω0. Explicit results are found in the cases of the sudden jump of magnetic field, the parametric resonance, the adiabatic evolution, and for several specific functions B(t), when solutions can be expressed in terms of elementary or hypergeometric functions. These examples show that the evolution of the mentioned mean values can be rather different for the two gauges, if the evolution is not adiabatic. It appears that the adiabatic approximation fails when the magnetic field goes to zero. Moreover, the sudden jump approximation can fail in this case as well. The case of a slowly varying field changing its sign seems especially interesting. In all the cases, fluctuations of the magnetic moment are very strong, frequently exceeding the square of the mean value.

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Charged particle in the presence of a variable magnetic field

Cited by 25 publications

References 11 publications

Scalar mode propagation in modified gravity with a scalar field

Scalar mode propagation in modified gravity with a scalar field

An alternative approach to exact wave functions for time-dependent coupled oscillator model of charged particle in variable magnetic field

Energy and Magnetic Moment of a Quantum Charged Particle in Time-Dependent Magnetic and Electric Fields of Circular and Plane Solenoids

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