Quantum particle across Grushin singularity
- URL: http://arxiv.org/abs/2011.13712v3
- Date: Mon, 24 May 2021 10:00:19 GMT
- Title: Quantum particle across Grushin singularity
- Authors: Matteo Gallone, Alessandro Michelangeli
- Abstract summary: We study the phenomenon of transmission across the singularity that separates the two half-cylinders.
All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection.
This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
- Score: 77.34726150561087
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: A class of models is considered for a quantum particle constrained on
degenerate Riemannian manifolds known as Grushin cylinders, and moving freely
subject only to the underlying geometry: the corresponding spectral analysis is
developed in detail in view of the phenomenon of transmission across the
singularity that separates the two half-cylinders. Whereas the classical
counterpart always consists of a particle falling in finite time along the
geodesics onto the metric's singularity locus, the quantum models may display
geometric confinement, or on the opposite partial transmission and reflection.
All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian
are examined as non-equivalent protocols of transmission/reflection and the
structure of their spectrum is characterised, including when applicable their
ground state and positivity. Besides, the stationary scattering analysis is
developed and transmission and reflection coefficients are calculated. This
allows to comprehend the distinguished status of the so-called `bridging'
transmission protocol previously identified in the literature, which we recover
and study within our systematic analysis.
Related papers
- Quantum Mechanics in Curved Space(time) with a Noncommutative Geometric Perspective [0.0]
We take seriously the noncommutative symplectic geometry corresponding to the quantum observable algebra.
The work points to a very different approach to quantum gravity.
arXiv Detail & Related papers (2024-06-20T10:44:06Z) - On reconstruction of states from evolution induced by quantum dynamical
semigroups perturbed by covariant measures [50.24983453990065]
We show the ability to restore states of quantum systems from evolution induced by quantum dynamical semigroups perturbed by covariant measures.
Our procedure describes reconstruction of quantum states transmitted via quantum channels and as a particular example can be applied to reconstruction of photonic states transmitted via optical fibers.
arXiv Detail & Related papers (2023-12-02T09:56:00Z) - Extracting the Quantum Geometric Tensor of an Optical Raman Lattice by
Bloch State Tomography [2.0758589947805572]
In Hilbert space, the geometry of the quantum state is identified by the quantum geometric tensor (QGT)
We propose and experimentally implement a complete Bloch state tomography to measure eigenfunction of an optical Raman lattice for ultracold atoms.
arXiv Detail & Related papers (2023-01-15T13:05:01Z) - Completing the quantum ontology with the electromagnetic zero-point
field [0.0]
This text begins with a series of critical considerations on the initial interpretation of quantum phenomena observed in atomic systems.
Arguments are given in favour of the random zero-point radiation field (ZPF) as the element needed to complete the quantum process.
The permanent presence of the field drastically affects the dynamics of the particle, which eventually falls under the control of the field.
arXiv Detail & Related papers (2022-07-13T23:11:48Z) - Localized non-relativistic quantum systems in curved spacetimes: a
general characterization of particle detector models [0.0]
We provide a consistent way of describing a localized non-relativistic quantum system undergoing a timelike trajectory in a curved spacetime.
This framework naturally provides a recipe for mapping a quantum theory defined in a non-relativistic background to a theory around a timelike trajectory in curved spacetimes.
We then apply our formalism to particle detector models, that is, to the case where the non-relativistic quantum system is coupled to a quantum field in a curved background.
arXiv Detail & Related papers (2022-06-02T18:00:31Z) - The appearance of particle tracks in detectors -- II: the semi-classical
realm [0.0]
We show how symmetries, such as spherical symmetry, of the initial state of a particle are broken by tracks consisting of infinitely many approximately measured particle positions.
In the semi-classical regime, which is reached when one considers highly energetic particles, we present a detailed, mathematically rigorous analysis of this phenomenon.
arXiv Detail & Related papers (2022-02-19T09:23:23Z) - Unraveling the topology of dissipative quantum systems [58.720142291102135]
We discuss topology in dissipative quantum systems from the perspective of quantum trajectories.
We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
arXiv Detail & Related papers (2020-07-12T11:26:02Z) - Quantum Geometric Confinement and Dynamical Transmission in Grushin
Cylinder [68.8204255655161]
We classify the self-adjoint realisations of the Laplace-Beltrami operator minimally defined on an infinite cylinder.
We retrieve those distinguished extensions previously identified in the recent literature, namely the most confining and the most transmitting.
arXiv Detail & Related papers (2020-03-16T11:37:23Z) - Bulk detection of time-dependent topological transitions in quenched
chiral models [48.7576911714538]
We show that the winding number of the Hamiltonian eigenstates can be read-out by measuring the mean chiral displacement of a single-particle wavefunction.
This implies that the mean chiral displacement can detect the winding number even when the underlying Hamiltonian is quenched between different topological phases.
arXiv Detail & Related papers (2020-01-16T17:44:52Z) - Probing chiral edge dynamics and bulk topology of a synthetic Hall
system [52.77024349608834]
Quantum Hall systems are characterized by the quantization of the Hall conductance -- a bulk property rooted in the topological structure of the underlying quantum states.
Here, we realize a quantum Hall system using ultracold dysprosium atoms, in a two-dimensional geometry formed by one spatial dimension.
We demonstrate that the large number of magnetic sublevels leads to distinct bulk and edge behaviors.
arXiv Detail & Related papers (2020-01-06T16:59:08Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.