Landau Diamagnetism from the Coherent States of an Electron in a Uniform Magnetic Field

Feldman, Albert; Kahn, Arnold H.

doi:10.1103/physrevb.1.4584

Cited by 136 publications

(135 citation statements)

References 8 publications

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“…This formulation allows the use of classical concepts to describe electron orbits, even containing all quantum effects [28]. In a previous effort, this approach was used to obtain the Wehrl entropy [21,22] and Fisher information [29] with the purpose of studying the thermodynamics of the Landau diamagnetism problem, namely, a free spinless charged particle in a uniform magnetic field [7].…”

Section: Landau Diamagnetism: Charged Particle In a Uniform Magnetic mentioning

confidence: 99%

“…In the past the appropriate partition function for this problem was calculated by Feldman and Kahn appealing to the concept of Glauber's coherent states as a set of basis states [28]. This formulation allows the use of classical concepts to describe electron orbits, even containing all quantum effects [28].…”

Section: Landau Diamagnetism: Charged Particle In a Uniform Magnetic mentioning

confidence: 99%

See 1 more Smart Citation

The Husimi Distribution: Development and Applications

Curilef¹,

Pennini²

2013

Advances in Quantum Mechanics

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Section: Landau Diamagnetism: Charged Particle In a Uniform Magnetic mentioning

confidence: 99%

Section: Landau Diamagnetism: Charged Particle In a Uniform Magnetic mentioning

confidence: 99%

The Husimi Distribution: Development and Applications

Curilef¹,

Pennini²

2013

Advances in Quantum Mechanics

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“…In order to find the motion of the classical FD system, we write the equations of motion for 19) which can be immediately integrated to give 20) where the integration constants are α ± (0), β ± (0) ∈ C. The classical Hamiltonian given in (4.6) is a constant of motion which, according to (4.20), takes the value…”

Section: Classical Motionmentioning

confidence: 99%

“…The coherent states associated to the the FD system have been studied under different conditions. The first contributions were due to Feldman and Mank'o [18,19,20], and more recent application have been given in [21,22,23]. Another important area where coherent states of FD type systems have been considered is in paraxial optics, where similar Hamiltonians are used to describe some optical waves (the so called Hermite-Gaussian and Laguerre-Gaussian modes) [24,25].…”

Section: Introductionmentioning

confidence: 99%

Superintegrability of the Fock–Darwin system

et al. 2017

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The Fock-Darwin system is analysed from the point of view of its symmetry properties in the quantum and classical frameworks. The quantum Fock-Darwin system is known to have two sets of ladder operators, a fact which guarantees its solvability. We show that for rational values of the quotient of two relevant frequencies, this system is superintegrable, the quantum symmetries being responsible for the degeneracy of the energy levels. These symmetries are of higher order and close a polynomial algebra. In the classical case, the ladder operators are replaced by ladder functions and the symmetries by constants of motion. We also prove that the rational classical system is superintegrable and its trajectories are closed. The constants of motion are also generators of symmetry transformations in the phase space that have been integrated for some special cases. These transformations connect different trajectories with the same energy. The coherent states of the quantum superintegrable system are found and they reproduce the closed trajectories of the classical one.

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“…[45], we exclude the coherent states with the mean coordinates outside the size and sum over the other states. Because R ≫ A, B and the exponential falls off rapidly with |z ′ y |, we can integrate |z ′ y | from zero to infinity safely.…”

Section: Thermodynamics On Nc Situationmentioning

confidence: 99%

Two-dimensional noncommutative atom gas with the Anandan interaction

Xiao-Min

2011

Phys. Rev. A

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Landau like quantization of the Anandan system in a special electromagnetic field is studied. Unlike the cases of the AC system and the HMW system, the torques of the system on the magnetic dipole and the electric dipole don't vanish. By constructing Heisenberg algebra, the Landau analog levels and eigenstates on commutative space, NC space and NC phase space are obtained respectively. By using the coherent state method, some statistical properties of such free atom gas are studied and the expressions of some thermodynamic quantities related to revolution direction are obtained. Two particular cases of temperature are discussed and the more simple expressions of the free energy on the three spaces are obtained. We give the relation between the value of σ and revolution direction clearly, and find Landau like levels of the Anandan system are invariant and the levels between the AC system and the HMW system are interchanged each other under Maxwell dual transformations on the three spaces. The two sets of eigenstates labelled by σ can be related by a supersymmetry transformation on commutative space, but the phenomenon don't occur on NC situation. We emphasize that some results relevant to Anandan interaction are suitable for the cases of AC interaction and HMW interaction under special conditions.

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Landau Diamagnetism from the Coherent States of an Electron in a Uniform Magnetic Field

Cited by 136 publications

References 8 publications

The Husimi Distribution: Development and Applications

The Husimi Distribution: Development and Applications

Superintegrability of the Fock–Darwin system

Two-dimensional noncommutative atom gas with the Anandan interaction

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