Coherent States and Their Generalizations for a Charged Particle in a Magnetic Field

In this work, we construct coherent states for electrons in anisotropic 2D-Dirac materials immersed in a uniform magnetic field perpendicularly oriented to the sample. In order to describe the bidimensional effects on electron dynamics in a semiclassical approach, we adopt the symmetric gauge vector potential to describe the external magnetic field through a vector potential. By solving a Dirac-like equation with an anisotropic Fermi velocity, we identify two sets of scalar ladder operators that allow us to define generalized annihilation operators, which are generators of either the Heisenberg-Weyl or su(1, 1) algebra. We construct both bidimensional and su(1, 1) coherent states as eigenstates of such annihilation operators with complex eigenvalues. In order to illustrate the effects of the anisotropy on these states, we obtain their probability density and mean energy value. Depending upon the anisotropy, expressed by the ration between the Fermi velocities along the x-and y-axes, the shape of the probability density is modified on the xy-plane with respect to the isotropic case and according to the classical dynamics. * ediaz@fis.cinvestav.mx † moliva@fis.cinvestav.mx ‡ yconcha@umich.mx § raya@ifm.umich.mx arXiv:1907.06551v1 [quant-ph]

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“…In general, bidimensional states are a linear combination of all the stationary states Ψ m,n (x, y) [36]:…”

Section: Bidimensional Coherent States (2d-cs)mentioning

confidence: 99%

Coherent states in magnetized anisotropic 2D Dirac materials

Díaz-Bautista¹,

Oliva-Leyva²,

Concha‐Sánchez³

et al. 2020

J. Phys. A: Math. Theor.

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“…which are merely the coordinates of the center of a circle, which the particle rotates around with the cyclotron frequency ω 0 . The importance of these integrals of motion was emphasized by many authors during decades [4,17,[20][21][22][23][24][25].…”

Section: Main Equationsmentioning

confidence: 99%

A Quantum Charged Particle under Sudden Jumps of the Magnetic Field and Shape of Non-Circular Solenoids

Dodonov

Horovits

2019

Quantum Reports

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We consider a quantum charged particle moving in the x y plane under the action of a time-dependent magnetic field described by means of the linear vector potential of the form A = B ( t ) − y ( 1 + β ) , x ( 1 − β ) / 2 . Such potentials with β ≠ 0 exist inside infinite solenoids with non-circular cross sections. The systems with different values of β are not equivalent for nonstationary magnetic fields or time-dependent parameters β ( t ) , due to different structures of induced electric fields. Using the approximation of the stepwise variations of parameters, we obtain explicit formulas describing the change of the mean energy and magnetic moment. The generation of squeezing with respect to the relative and guiding center coordinates is also studied. The change of magnetic moment can be twice bigger for the Landau gauge than for the circular gauge, and this change can happen without any change of the angular momentum. A strong amplification of the magnetic moment can happen even for rapidly decreasing magnetic fields.

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“…This observation reflects the fact that the problem involving a moving stroboscopic soliton can be mapped onto the stationary problem via the gauge transformation, Eq. (8).…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…To date, the existence of nonspreading wave packets has been established in a wide range of physical systems and lies at the heart of a vibrant area of research on (generalized) coherent states, much of it reviewed in Refs. [5][6][7][8]. Here we briefly discuss two specific classes which are relevant for the central result of this work.…”

Section: Introductionmentioning

confidence: 99%

Overcoming dispersive spreading of quantum wave packets via periodic nonlinear kicking

et al. 2018

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We propose the suppression of dispersive spreading of wave packets governed by the free-space Schrödinger equation with a periodically pulsed nonlinear term. Using asymptotic analysis, we construct stroboscopically dispersionless quantum states that are physically reminiscent of, but mathematically different from, the well-known one-soliton solutions of the nonlinear Schrödinger equation with a constant (time-independent) nonlinearity. Our analytics are strongly supported by full numerical simulations. The predicted dispersionless wave packets can move with arbitrary velocity and can be realized in experiments involving ultracold atomic gases with temporally controlled interactions.

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Coherent States and Their Generalizations for a Charged Particle in a Magnetic Field

Cited by 18 publications

References 135 publications

Coherent states in magnetized anisotropic 2D Dirac materials

Coherent states in magnetized anisotropic 2D Dirac materials

A Quantum Charged Particle under Sudden Jumps of the Magnetic Field and Shape of Non-Circular Solenoids

Overcoming dispersive spreading of quantum wave packets via periodic nonlinear kicking

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