Magnetic operations: a little fuzzy mechanics?

Mielnik, Bogdan; Ramirez, A. D.

doi:10.1088/0031-8949/84/04/045008

Cited by 20 publications

(29 citation statements)

References 125 publications

(324 reference statements)

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“…For this reason, we confine ourselves in this paper with the simplified model of instantaneous changes of parameters. Although abrupt changes of parameters are idealizations of real processes, they are frequently used for the analysis of various physical processes [9][10][11][12][13][14][15][16][17]. Our plan is as follows.…”

Section: Introductionmentioning

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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Section: Introductionmentioning

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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“…They also occur in harmonic fields, though the results require a computer study [65,66,67]. Here, they can be given by the exact formula (43).…”

Section: Proposition 4 If β(T) = 0 In Some Intervalmentioning

confidence: 99%

Quantum operations: technical or fundamental challenge?

Mielnik¹

2013

J. Phys. A: Math. Theor.

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A class of unitary operations generated by idealized, semiclassical fields is studied. The operations implemented by sharp potential kicks are revisited and the possibility of performing them by softly varying external fields is examined. The possibility of using the ion traps as 'operation factories' transforming quantum states is discussed. The non-perturbative algorithms indicate that the results of abstract δ-pulses of oscillator potentials can become real. Some of them, if empirically achieved, could be essential to examine certain atypical quantum ideas. In particular, simple dynamical manipulations might contribute to the Aharonov-Bohm criticism of the time-energy uncertainty principle, and some others, to verify the existence of fundamental precision limits of the position measurements or the reality of 'non-commutative geometries'.

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“…It is worth to notice that the EL have been mainly studied for systems ruled by timedependent Hamiltonians, either in one or several dimensions [37,45,48,50,51,53,54] or for purely spin systems [39,40,44]. However, there are several works where the evolution loops are produced by time-independent Hamiltonians [30,33].…”

Section: Evolution Loopsmentioning

confidence: 99%

“…In the last decades there has been a growing interest in studying evolution loops (EL), which are circular dynamical processes such that the evolution operator of the system becomes the identity at a certain time [30,33,37,39,40,44,45,48,50,51,53,54]. They represent a natural generalization to what happens for the harmonic oscillator.…”

Section: Introductionmentioning

confidence: 99%

Harmonic Oscillator SUSY Partners and Evolution Loops

C.¹

2012

SIGMA

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Abstract. Supersymmetric quantum mechanics is a powerful tool for generating exactly solvable potentials departing from a given initial one. If applied to the harmonic oscillator, a family of Hamiltonians ruled by polynomial Heisenberg algebras is obtained. In this paper it will be shown that the SUSY partner Hamiltonians of the harmonic oscillator can produce evolution loops. The corresponding geometric phases will be as well studied.

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Magnetic operations: a little fuzzy mechanics?

Cited by 20 publications

References 125 publications

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

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

Quantum operations: technical or fundamental challenge?

Harmonic Oscillator SUSY Partners and Evolution Loops

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