Related papers: Exact quantum revivals for the Dirac equation

Exact quantum revivals for the Dirac equation

URL: http://arxiv.org/abs/2309.12471v2
Date: Wed, 20 Dec 2023 09:13:57 GMT
Title: Exact quantum revivals for the Dirac equation
Authors: Fernando Chamizo and Osvaldo P. Santill\'an
Abstract summary: We generalize the Talbot effect and the revivals of the Schr"odinger equation to a relativistic situation with non zero mass. The revivals are exact, that is, are true revivals without taking any particular limit such as the non relativistic one. Several plots of the revivals are presented, which are useful for exemplifying the procedure proposed along the text.
Score: 55.2480439325792
License: http://creativecommons.org/licenses/by/4.0/
Abstract: In the present work, the results obtained in [1] about the revivals of a relativistic fermion wave function on a torus are considerably enlarged. In fact, all the possible quantum states exhibiting revivals are fully characterized. The revivals are exact, that is, are true revivals without taking any particular limit such as the non relativistic one. The present results are of interest since they generalize the Talbot effect and the revivals of the Schr\"odinger equation to a relativistic situation with non zero mass. This makes the problem nontrivial, as the dispersion relation is modified and is not linear. The present results are obtained by the use of arithmetic tools which are described in certain detail. In addition, several plots of the revivals are presented, which are useful for exemplifying the procedure proposed along the text.

Related papers

Generalization of exact operators of the Foldy-Wouthuysen transformation to arbitrary-spin particles in nonstationary fields [55.2480439325792]
We use the Foldy-Wouthuysen representation which allows one to obtain the Schr"odinger picture of relativistic quantum mechanics. We determine exact nonexponential and exponential operators of the Foldy-Wouthuysen transformation for arbitrary-spin particles in the nonstationary case.
arXiv Detail & Related papers (2024-10-27T18:41:50Z)
A Method Using Photon Collapse and Entanglement to Transmit Information [13.438312709072457]
We find that measurements cause quantum wave functions to collapse. By studying the overlooked phenomena of quantum wave function collapse, we find that quantum eigenstate sets may be artificially controlled. We propose an innovative method for direct information transmission utilizing photon wave function collapse and entanglement.
arXiv Detail & Related papers (2024-06-27T13:22:21Z)
Scalar field with a time-independent classical source, not trivial after all: from vacuum decay to scattering [0.0]
We solve exactly for the scattering amplitudes and find that a key ingredient is the production of particles from the unstable vacuum. We show that the trivial scattering found in the past is the byproduct of the adiabatic switching of the interaction.
arXiv Detail & Related papers (2024-03-22T18:00:00Z)
Real-time dynamics of false vacuum decay [49.1574468325115]
We investigate false vacuum decay of a relativistic scalar field in the metastable minimum of an asymmetric double-well potential. We employ the non-perturbative framework of the two-particle irreducible (2PI) quantum effective action at next-to-leading order in a large-N expansion.
arXiv Detail & Related papers (2023-10-06T12:44:48Z)
Beyond the light-cone propagation of relativistic wavefunctions: numerical results [0.0]
relativistic wavefunctions formally propagate beyond the light cone when the propagator is limited to the positive energy sector. By construction, this is the case for solutions of the Salpeter (or relativistic Schr"odinger) equation or for Klein-Gordon and Dirac wavefunctions defined in the Foldy-Wouthuysen representation.
arXiv Detail & Related papers (2022-12-16T10:48:38Z)
Fractional Quantum Zeno Effect Emerging from Non-Hermitian Physics [12.706932285002544]
We predict quantum non-Hermitian phenomena: the fractional quantum Zeno (FQZ) effect and FQZ-induced photon antibunching. We find FQZ-induced strong photon antibunching in the steady state of a driven emitter even for weak nonlinearities. Remarkably, we identify that the sub-Poissonian quantum statistics of photons, which has no classical analogs, stems here from the key role of non-Hermiticity.
arXiv Detail & Related papers (2022-07-07T17:41:24Z)
Nontrivial damping of quantum many-body dynamics [0.0]
We show that a nontrivial damping in the Schr"odinger picture can emerge if the dynamics in the unperturbed system possesses rich features. We substantiate our theoretical arguments by large-scale numerical simulations of charge transport in the extended Fermi-Hubbard chain.
arXiv Detail & Related papers (2021-03-11T12:58:39Z)
The Time-Evolution of States in Quantum Mechanics [77.34726150561087]
It is argued that the Schr"odinger equation does not yield a correct description of the quantum-mechanical time evolution of states of isolated (open) systems featuring events. A precise general law for the time evolution of states replacing the Schr"odinger equation is formulated within the so-called ETH-Approach to Quantum Mechanics.
arXiv Detail & Related papers (2021-01-04T16:09:10Z)
Gamow vectors formalism applied to the Loschmidt echo [0.0]
We use formalism to describe a phenomenon of irreversibility: the Loschmidt echo. We compare the characteristic decay times of this phenomenon with the decoherence ones. We conclude that the Loschmidt echo and the decoherence can be considered as two aspects of the same phenomenon.
arXiv Detail & Related papers (2020-09-23T04:32:00Z)
The Non-Hermitian quantum mechanics and its canonical structure [7.784991832712813]
The non-Hermitian Schr"odinger equation is re-expressed generally in the form of Hamilton's canonical equation without any approximation. The conventional difficulties in non-Hermitian quantum mechanics are totally overcome by the reformulation.
arXiv Detail & Related papers (2020-05-21T05:52:53Z)

This list is automatically generated from the titles and abstracts of the papers in this site.