Quantum Holopedia Glossary

Doktor Habdank

Hamiltonian (quantum mechanics) & Quantization of the electromagnetic field
In quantum mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential energy. Its spectrum, the system’s energy spectrum or its set of energy eigenvalues, is the set of possible outcomes obtainable from a measurement of the system’s total energy. Due to its close relation to the energy spectrum and time-evolution of a system, it is of fundamental importance in most formulations of quantum theory.

Level spacing distribution follows Poisson or Wigner-Dyson distribution, indicates that they have found a signature for a
quantum integrable or chaotic system respectively.

Hiroki Nakayama, “Random Matrix Theory, Quantum Chaos, and Eigenstate Thermalization“, July 2, 2020

Quantum Transform’s Bimodal Distribution is analogous to the Schrodinger equation and is equal to the complex sum of the energy’s and order’s logarithmic distributions, where RLognormal(ΔE) is the real part and RLognormal(O) is the imaginary part.’

Written below we get the eqation for the Quantum Information Field Energy randomness observed at the bifurcation point of the spacetime:

\hat {H}[B]|\Psi (t)\rangle => RLognormal(\Delta E) + j \frac{\varphi(t)}{RLognormal(O)}

Doktor Habdank’s formula

Tachyonic fields bifurcation at the light speed

Luxons, in the special relativity, are the massless particles with the invariant light speed [1] and thus are bifurcation points for the tachyonic field. Beyond light speed, exist superluminal tachyon bifurcation vibrators. Exciton-polariton X-waves are the superluminal wave equivalent [2]

[1] Chashchina, Silagadze, BREAKING THE LIGHT SPEED BARRIER, ACTA PHYSICA POLONICA B, 2012

[2] Antonio Gianfrate, et al., Superluminal X-waves in a polariton quantum fluid, nature, 2017

In the classical case we are talking about the distribution of positions over time for one oscillator, whereas in the quantum case we are talking about the distribution over an ensemble of identically prepared systems.