Minimum Time in Quantum State Transitions: Dynamical Foundations and Applications

Lisboa, Alexandre Coutinho; Piqueira, José Roberto Castilho

doi:10.5772/63025

Cited by 1 publication

(2 citation statements)

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“…Namely, this approach gives a sufficient signature that a gravitational field can be quantized. Further, the problem of the minimum time evolution between two quantum states is also presented and discussed [2]. The quantum transition, time dependent perturbation theory, Fermi-Golden rule and impurity scattering are presented in [3].…”

Section: Introductionmentioning

confidence: 99%

“…In some applications of quantum theory, like quantum computing, we want to know what is the shortest physically possible time for a quantum state to evolve to another one? This is closely linked to dynamical characterization derived from the time-energy uncertainty relations [2]. In order to develop the algorithm for solution of the mentioned problem in quantum dynamics, one should use the time-energy uncertainty relation and generalize it in the case of a time-dependent Hamiltonian operator [18].…”

Section: Introductionmentioning

confidence: 99%

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Minimum Time Transition Between Quantum States in Gravitational Field

Novaković¹

2021

AJMP

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Here it is started with the proportionality between Planck's and related gravitational parameters. Using the ratio between Planck mass and related minimal gravitational radius (half of Planck length) we obtain maximal radial density (kg/m) in gravitational field. On the other hand, minimal radial density one obtains using the ratio between Planck mass and related maximal radius in gravitational field. It is based on new Relativistic Alpha Field Theory (RAFT) that predicts the existence of minimal and maximal gravitational radius in a gravitational field. Thus, no singularity at the minimal gravitational radius and no infinity at the maximal gravitational radius. It is shown that the maximal radial density is constant and is valid for all amounts of masses. Also, minimal radial density is constant and is valid for all amounts of masses. Using Planck parameters, it is calculated the energy conservation constant k = 0.999934. Since this constant is less from unity and grater from zero, the minimal gravitational radius cannot be zero (no singularity in a gravitational field) and maximal gravitational radius cannot be infinitive (no infinity in gravitational field). Here quantization of a gravitational field is based on the multiplication of the minimal gravitational length (twice of minimal radius) by parameter n =1, 2,… The calculation of the minimum time transition between two quantum state for the proton gives 0.413466×10 -62 seconds. The minimal expansion time from minimal to maximal radius of proton is equal to 1.253992×10 -58 sec. This is in accordance with recently observation, revealing nano big bang: the first millisecond of crystal formation. The calculation of the minimum time transition between two quantum state for Universe is 13.948503×10 9 years. The minimal expansion time from minimal to maximal radius of Universe is equal to 422,151.136168×10 9 years. Previous calculation is based on the velocity equal to the speed of light. Since the real transition velocity is less than the speed of light, the real transition and expansion times are greater compare to the previous calculation. Following the previous results, one can understand why the quantum approach has only sense for the small mases i.e. particles.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%