Dynamical Invariants for Generalized Coherent States via Complex Quantum Hydrodynamics

Bonilla-Licea, Moise; Schuch, Dieter

doi:10.3390/dynamics1020009

Cited by 4 publications

(1 citation statement)

References 53 publications

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“…Defining a ”quantum potential”

in momentum space, in formal analogy with the one in position space (further details can be found in [ 28 , 29 ]), as

(where, this time, the expression ”potential” is, physically, actually correct), the position uncertainty in momentum space (which should not be confused with the position uncertainty in position space; more details in Section 4 ) can then, again, be written as the sum of contributions from phase and amplitude as

…”

Section: Quantum Fluctuations In Position and Momentum Spacementioning

confidence: 99%

Uncertainty Relations in the Madelung Picture

Bonilla-Licea

Schuch

2021

Entropy

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Madelung showed how the complex Schrödinger equation can be rewritten in terms of two real equations, one for the phase and one for the amplitude of the complex wave function, where both equations are not independent of each other, but coupled. Although these equations formally look like classical hydrodynamic equations, they contain all the information about the quantum system. Concerning the quantum mechanical uncertainties of position and momentum, however, this is not so obvious at first sight. We show how these uncertainties are related to the phase and amplitude of the wave function in position and momentum space and, particularly, that the contribution from the phase essentially depends on the position–momentum correlations. This will be illustrated explicitly using generalized coherent states as examples.

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“…Defining a ”quantum potential”

in momentum space, in formal analogy with the one in position space (further details can be found in [ 28 , 29 ]), as

…”

Section: Quantum Fluctuations In Position and Momentum Spacementioning

confidence: 99%

Uncertainty Relations in the Madelung Picture

Bonilla-Licea

Schuch

2021

Entropy

Self Cite

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Single-qubit gates designed by means of the Madelung picture

Bonilla–Licea,

Bonilla Estrada

2024

J. Phys.: Conf. Ser.

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In this work the Madelung picture is applied to the single qubit systems. The projective aspect of the Madelung quantities and the polar expression of the components of the quantum state allow one to obtain a general dynamical system of equations. Even though this dynamical system of equations is nonlinear, it offers the advantage of designing single quibt gates in a straightforward manner. It only requires the specification of the initial and final points on the Bloch sphere, as well as the gate operation time. This application of the Madelung picture is particularily illustrated for the nuclear magnetic resonance processor case. It turns the problem of specifying the magnetic fields into a simpler problem of substitution.

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Dynamical Invariant for Dissipative Systems via Complex Quantum Hydrodynamics

Schuch

Bonilla-Licea

2023

Dynamics

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For Hamiltonian systems with time-dependent potential, the Hamiltonian, and thus the energy, is no longer a constant of motion. However, for such systems as the parametric oscillator, i.e., an oscillator with time-dependent frequency ω(t), still, a dynamical invariant can be found that now has the dimension of action. The question, if such an invariant still exists after the addition of a dissipative friction force is analyzed for the classical as well as for the quantum mechanical case from different perspectives, particularly from that of a complex hydrodynamic formulation of quantum mechanics.

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Dynamical Invariants for Generalized Coherent States via Complex Quantum Hydrodynamics

Cited by 4 publications

References 53 publications

Uncertainty Relations in the Madelung Picture

Uncertainty Relations in the Madelung Picture

Single-qubit gates designed by means of the Madelung picture

Dynamical Invariant for Dissipative Systems via Complex Quantum Hydrodynamics

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