Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userQuantum walking in curved spacetime: discrete metric
85
0
0.0
(
0
)
Added by
Giuseppe Di Molfetta Prof.
Publication date
2017
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
A discrete-time quantum walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs have familiar physics PDEs as their continuum limit. Some slight generalization of them (allowing for prior encoding and larger neighbourhoods) even have the curved spacetime Dirac equation, as their continuum limit. In the $(1+1)-$dimensional massless case, this equation decouples as scalar transport equations with tunable speeds. We characterise and construct all those QWs that lead to scalar transport with tunable speeds. The local coin operator dictates that speed; we provide concrete techniques to tune the speed of propagation, by making use only of a finite number of coin operators---differently from previous models, in which the speed of propagation depends upon a continuous parameter of the quantum coin. The interest of such a discretization is twofold : to allow for easier experimental implementations on the one hand, and to evaluate ways of quantizing the metric field, on the other.
rate research
Read More
A boundary undergoing relativistic motion can create particles from quantum vacuum fluctuations in a phenomenon known as the dynamical Casimir effect. We examine the creation of particles, and more generally the transformation of quantum field states, due to boundary motion in curved spacetime. We provide a novel method enabling the calculation of the effect for a wide range of trajectories and spacetimes. We apply this to the experimental scenario used to detect the dynamical Casimir effect, now adopting the Schwarzschild metric, and find novel resonances in particle creation as a result of the spacetime curvature. Finally, we discuss a potential enhancement of the effect for the phonon field of a Bose-Einstein condensate.
Gravity induced neutrino-antineutrino oscillations are studied in the context of one and two flavor scenarios. This allows one to investigate the particle-antiparticle correlations in two and four level systems, respectively. Flavor entropy is used to probe the entanglement in the system. The well known witnesses of non-classicality such as Mermin and Svetlichly inequalities are investigated. Since the extent of neutrino-antineutrino oscillation is governed by the strength of the gravitational field, the behavior of non-classicality shows interesting features as one varies the strength of the gravitational field. Specifically, the suppression of the entanglement with the increase of the gravitational field is observed which is witnessed in the form of decrease in the flavor entropy of the system. The features of the Mermin and the Svetlichny inequalities allow one to make statements about the degeneracy of neutrino mass eigenstates.
We introduce an exact mapping between the Dirac equation in (1+1)-dimensional curved spacetime (DCS) and a multiphoton quantum Rabi model (QRM). A background of a (1+1)-dimensional black hole requires a QRM with one- and two-photon terms that can be implemented in a trapped ion for the quantum simulation of Dirac particles in curved spacetime. We illustrate our proposal with a numerical analysis of the free fall of a Dirac particle into a (1+1)-dimensional black hole, and find that the Zitterbewegung effect, measurable via the oscillatory trajectory of the Dirac particle, persists in the presence of gravity. From the duality between the squeezing term in the multiphoton QRM and the metric coupling in the DCS, we show that gravity generates squeezing of the Dirac particle wave function.
We describe a new mechanism - radiatively-induced gravitational leptogenesis - for generating the matter-antimatter asymmetry of the Universe. We show how quantum loop effects in C and CP violating theories cause matter and antimatter to propagate differently in the presence of gravity, and prove this is forbidden in flat space by CPT and translation symmetry. This generates a curvature-dependent chemical potential for leptons, allowing a matter-antimatter asymmetry to be generated in thermal equilibrium in the early Universe. The time-dependent dynamics necessary for leptogenesis is provided by the interaction of the virtual self-energy cloud of the leptons with the expanding curved spacetime background, which violates the strong equivalence principle and allows a distinction between matter and antimatter. We show here how this mechanism is realised in a particular BSM theory, the see-saw model, where the quantum loops involve the heavy sterile neutrinos responsible for light neutrino masses. We demonstrate by explicit computation of the relevant two-loop Feynman diagrams how these radiative corrections display the necessary dependence on the sterile neutrino masses to generate an asymmetry, and show how the induced lepton asymmetry may be sufficiently large to play an important role in determining the baryon-to-photon ratio of the Universe.
We give an upper bound of the relative entanglement entropy of the ground state of a massive Dirac-Majorana field across two widely separated regions $A$ and $B$ in a static slice of an ultrastatic Lorentzian spacetime. Our bound decays exponentially in $dist (A, B)$, at a rate set by the Compton wavelength and the spatial scalar curvature. The physical interpretation our result is that, on a manifold with positive spatial scalar curvature, one cannot use the entanglement of the vacuum state to teleport one classical bit from $A$ to $B$ if their distance is of the order of the maximum of the curvature radius and the Compton wave length or greater.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
