Dirac Dynamics Research Articles

Minimal quantum walk simulation of Dirac fermions in curved space-times

The problem of simulating through quantum walks the curved space-time propagation of Dirac fermions is revisited, taking the $$(1 + 1)$$ D case as an example. New quantum walks are introduced which encode the space-time geometry, not in the mixing operators, but in new unitary shift operators which carry out a position-dependent translation of the wave function components. These walks simulate Dirac fermions in arbitrary curved space-times and coordinates. Contrary to previously proposed general alternatives, the wave functions of the new walks have as many components as usual Dirac spinors, and not twice that number. In particular, in $$(1 + 1)$$ D space-times, only one qubit is needed at each lattice point, which makes it easier to perform quantum simulations of the Dirac dynamics on current NISQs quantum devices. Numerical simulations of the Dirac dynamics in the post Newtonian, so-called Gravitoelectromagnetism regime are presented as an illustration. The possible usefulness of the new shift operators and quantum walks in other more general contexts is also discussed.

Majorana propagator on de Sitter space

We study the dynamics of Majorana fermions in an expanding de Sitter space and to that aim, by making use of the method of mode sums, we construct the vacuum Feynman propagator for Majorana fermions in de Sitter space. The Majorana condition implies nontrivial identities for the mode functions, which we carefully implement. We note that, under charge conjugation, the propagator transforms to minus itself, but do not discuss in detail the topological implications of this observation. We construct the propagator for a general complex mass and find that it is identical to the corresponding Dirac propagator, meaning that the coupling of fermions to the classical de Sitter gravitational background does not violate charge symmetry, i.e. it respects the Majorana condition. The complex mass propagator differs from its real mass counterpart in that the usual positive and negative energy projectors acquire a chiral rotation which depends on the phase of the mass term. We use our propagator to calculate the one-loop effective action for Majorana fermions, and find that it differs from that of Dirac fermions by a factor of 1/2, which accounts for the reduced number of degrees of freedom of the Majorana particle. Finally, we derive the Majorana and Dirac propagators for mixing n fermionic flavors and show that the number of CP-violating phases for Dirac fermions exceeds that of the Majorana fermions by {nleft( n-1right) }/{2}. This is vital for understanding how the dynamics of Dirac and Majorana fermions generate different CP-violating effects in the multi-flavor case.

Correction to: Relativistic density operators: Dirac dynamics, open quantum systems and non-standard neutrino interactions

Correction to: Relativistic density operators: Dirac dynamics, open quantum systems and non-standard neutrino interactions

Relativistic density operators: Dirac dynamics, open quantum systems and non-standard neutrino interactions

Relativistic density operators: Dirac dynamics, open quantum systems and non-standard neutrino interactions

Fast-Forward of Local-Phased-Regularized Spinor in Massless 2+1-Dimensions Adiabatic Dirac Dynamics

We discuss a method of controlling Dirac dynamics in (2+1)-dimensions using adiabatic fast-forward method proposed by Masuda-Nakamura. Due to infinitely large amount of time of adiabaticity, we have to use an infinitely large scaling factor to shorten the time interval. Thus, we need a regularization to remove this infinity. Our strategy is analogue to adiabatic fast-forward of Schrodinger equation. That is using an auxiliary Hamiltonian but now we use two phase factors applied to the components of spinor. We applied to a case where a system is controlled by uniform magnetic field.

Spatial Bloch oscillations in acoustic waveguide arrays

We designed a type of acoustic waveguide supported by spoof acoustic surface waves. The effective refractive index of acoustic waveguide can be effectively tuned by tailoring the waveguide width to control the propagation of spoof acoustic surface waves. Based on the advantage of the tunable refractive index, we construct a discrete waveguide array with transverse refractive index gradients to simulate the time evolution of the probability waves of electron in a tight-binding lattice under an external electric field. Based on numerical simulations and experiments, we discuss the relationship between the spatial Bloch oscillations period and the transverse refractive index gradient. Furthermore, we also investigate the influence of the interval between waveguides on the amplitude of the Bloch oscillations. Our acoustic waveguide array maybe provides a versatile testbed to explore analogous quantum mechanical effects, such as Zener tunneling, Anderson localization, and massless Dirac dynamics in acoustic system.

Time-Rescaling of Dirac Dynamics: Shortcuts to Adiabaticity in Ion Traps and Weyl Semimetals.

Only very recently, rescaling time has been recognized as a way to achieve adiabatic dynamics in fast processes. The advantage of time-rescaling over other shortcuts to adiabaticity is that it does not depend on the eigenspectrum and eigenstates of the Hamiltonian. However, time-rescaling requires that the original dynamics are adiabatic, and in the rescaled time frame, the Hamiltonian exhibits non-trivial time-dependence. In this work, we show how time-rescaling can be applied to Dirac dynamics, and we show that all time-dependence can be absorbed into the effective potentials through a judiciously chosen unitary transformation. This is demonstrated for two experimentally relevant scenarios, namely for ion traps and adiabatic creation of Weyl points.

Formation of nanostructures and optical analogues of massless Dirac particles via femtosecond lasers.

Subwavelength-scale surface structures have many important engineering and nanotechnology applications, e.g., superhydrophobicity and light-trapping. However, an effective and economic nanofabrication solution for general engineering materials, e.g., metals or silicon, is still not available to date. In this paper, we present an experimental and theoretical study of the nanostructure formation mechanism based on double time-delayed femtosecond laser beams and the coupled mode theory (CMT), demonstrating the use of an optical analogue of massless Dirac particles for high-throughput nanofabrication for the first time. In the experiments, a variety of complex periodic structures, including hexagonally arranged nanoholes, nano-square array, and periodic ripples, have been fabricated. The formation mechanisms of these nanostructures are explained by the CMT, where a transient plasmonic waveguide array (TPWA) is formed by the interference between the preceding laser and the induced surface plasmon polaritons (SPPs). The SPPs induced by the subsequent laser propagates through the TPWA, resulting in conical diffraction. This result shows the first practical application of the massless Dirac dynamics in nanofabrication.

Ballistic transport in disordered Dirac and Weyl semimetals

We study the dynamics of Dirac and Weyl electrons in disordered point-node semimetals. The ballistic feature of the transport is demonstrated by simulating the wave-packet dynamics on lattice models. We show that the ballistic transport survives under a considerable strength of disorder up to the semimetal-metal transition point, which indicates the robustness of point-node semimetals against disorder. We also visualize the robustness of the nodal points and linear dispersion under broken translational symmetry. The speed of the wave packets slows down with increasing disorder strength, and vanishes toward the critical strength of disorder, hence becoming the order parameter. The obtained critical behavior of the speed of the wave packets is consistent with that predicted by the scaling conjecture.

A comparison of the bremsstrahlung cross section in two frameworks: classical Lorentz–Abraham–Dirac dynamics and quantum field theory

In classical electromagnetic theory, the Lorentz–Abraham–Dirac (LAD) equation describes the dynamics of a charged particle, including radiation reaction. Though the LAD equation is derived from Maxwell’s equations, consistent with the conservation of energy and momentum, it admits unphysical solutions for point-like charged particles. By assuming small radiative effects, Landau and Lifshitz (LL) develop an approximation of the LAD equation that has no pathological solutions. Though the LL approximation is dynamically sound, it is the LAD equation that has firm theoretical underpinning. As such, the difficulties encountered in LAD dynamics suggest, in part, that an electrodynamic treatment of point-like particles lies outside the classical domain. Herein, we compute the cross section of a charged particle scattered by an attractive Coulombic potential using classical LAD and LL dynamics. We then compare this with the analogous cross section in quantum field theory (QFT). In particular, we compute the cross section for a charged scalar particle incident upon another extremely massive charged scalar with a single photon in the final state. We include the following -radiative corrections: scalar-photon vertex correction, infrared photon emission, vacuum polarization, and two-photon exchange. We find that the classical and quantum frameworks do not produce similar cross sections. Relative to the elastic cross section, the classical bremsstrahlung cross section vastly overestimates the relative QFT cross section; this is, in part, due to the fact that the additional radiative corrections in QFT do not have a classical analog in either the LAD or LL framework.

Spinor symmetries and underlying properties

By exploring a spinor space whose elements carry a spin 1/2 representation of the Lorentz group and satisfy the the Fierz–Pauli–Kofink identities we show that certain symmetries operations form a Lie group. Moreover, we discuss the reflex of the Dirac dynamics in the spinor space. In particular, we show that the usual dynamics for massless spinors in the spacetime is related to an incompressible fluid behavior in the spinor space.

Simulating the Majorana dynamics with ultracold atomic gases in a bilayer honeycomb lattice

The authors present theoretical results on the dynamical properties of General Majorana Quasiparticles and the unique Majorana Zitterbewegung. The results reveal the fidelity is a good observable to distinguish Majorana from Dirac or Weyl dynamics. Furthermore, a feasible method to detect the Majorana dynamics by using quench and quantum-state tomography has been provided in cold-atomic lattice system.

Higher gauge theories based on 3-groups

We study the categorical generalizations of a BF theory to 2BF and 3BF theories, corresponding to 2-groups and 3-groups, in the framework of higher gauge theory. In particular, we construct the constrained 3BF actions describing the correct dynamics of Yang-Mills, Klein-Gordon, Dirac, Weyl, and Majorana fields coupled to Einstein-Cartan gravity. The action is naturally split into a topological sector and a sector with simplicity constraints, adapted to the spinfoam quantization programme. In addition, the structure of the 3-group gives rise to a novel gauge group which specifies the spectrum of matter fields present in the theory, just like the ordinary gauge group specifies the spectrum of gauge bosons in the Yang-Mills theory. This allows us to rewrite the whole Standard Model coupled to gravity as a constrained 3BF action, facilitating the nonperturbative quantization of both gravity and matter fields. Moreover, the presence and the properties of this new gauge group open up a possibility of a nontrivial unification of all fields and a possible explanation of fermion families and all other structure in the matter spectrum of the theory.

Schrödinger and Dirac dynamics on time-dependent quantum graph

Quantum graphs with varying edges lengths are constructed. We deal with two types of operators on the graph edges: the Schrodinger and the Dirac operators. The dynamics of quantum particles for these two cases is compared. From the physical point of view, the Schrodinger dynamics corresponds to nonrelativistic particle and the Dirac dynamics to the relativistic one.

Local bosonization of massive fermions in three spatial dimensions with rotation invariance

In relativistic quantum field theory particles of half-integer spin must obey Fermi-Dirac statistics. Their quantum operators must anticommute at spacelike separation in contrast to commuting physical observables. We show that Fermi-Dirac spin $1/2$ operators can be emergent in a fully commuting field theory forming directed strings and loops of spin 0 and 1 constituents, reproducing massive Dirac dynamics with background fields. Such underlying description may violate relativistic invariance but there are no manifest interactions at a distance and rotation symmetry remains preserved. We show that under some constraints on the model there exists a well-defined ground state -- Fermi sea that it is stable -- fermions cannot convert to bosons.

Simulation of massless Dirac dynamics in plasmonic waveguide arrays.

The recent simulation of quantum behavior in condensed matter physics by well-designed photonic structures has opened unprecedented opportunities to steer the flow of light in novel manners. Here, we propose a design to simulate massless Dirac dynamics in evanescently coupled plasmonic ridge waveguide arrays with alternating positive and negative coupling coefficients. The coupling coefficients are carefully tailored by adjusting the geometric parameters of the waveguide in arrays, which are supposed to be feasible with advanced nanofabrication techniques. Further theoretical studies are also carried out based on the coupled mode theory to discuss the influence of excitation condition on beam propagation in this massless Dirac dynamics simulation case.

Similar ultrafast dynamics of several dissimilar Dirac and Weyl semimetals

Recent years have seen the rapid discovery of solids whose low-energy electrons have a massless, linear dispersion, such as Weyl, line-node, and Dirac semimetals. The remarkable optical properties predicted in these materials show their versatile potential for optoelectronic uses. However, little is known of their response in the picoseconds after absorbing a photon. Here, we measure the ultrafast dynamics of four materials that share non-trivial band structure topology but that differ chemically, structurally, and in their low-energy band structures: ZrSiS, which hosts a Dirac line node and Dirac points; TaAs and NbP, which are Weyl semimetals; and Sr1–yMn1–zSb2, in which Dirac fermions coexist with broken time-reversal symmetry. After photoexcitation by a short pulse, all four relax in two stages, first sub-picosecond and then few-picosecond. Their rapid relaxation suggests that these and related materials may be suited for optical switches and fast infrared detectors. The complex change of refractive index shows that photoexcited carrier populations persist for a few picoseconds.

Semiclassical dynamics of Dirac and Weyl particles in rotating coordinates

The semiclassical kinetic theory of Dirac particles in the presence of external electromagnetic fields and global rotation is established. To provide the Hamiltonian formulation of Dirac particles a symplectic two-form which is a matrix in spin indices is proposed. The particle number and current densities for the Dirac particles are acquired in the helicity basis. Following a similar procedure, semiclassical kinetic theory of the Weyl particles is accomplished. It is shown that the phase-space dynamics of the Weyl and Dirac particles is directly linked. The anomalous chiral effects due to the external electromagnetic fields and angular velocity of the frame are calculated.

Robust state preparation in quantum simulations of Dirac dynamics

A non-relativistic system such as an ultracold trapped ion may perform a quantum simulation of a Dirac equation dynamics under specific conditions. The resulting Hamiltonian and dynamics are highly controllable, but the coupling between momentum and internal levels poses some difficulties to manipulate the internal states accurately in wave packets. We use invariants of motion to inverse engineer robust population inversion processes with a homogeneous, time-dependent simulated electric field. This exemplifies the usefulness of inverse-engineering techniques to improve the performance of quantum simulation protocols.

The connection between Dirac dynamic and parity symmetry

Dirac spinors are important objects in the current literature, the algebraic structure presented in the text-books is a general method to write it, however, not unique. The purpose of the present work is to show an alternative approach to construct Dirac spinors, considering the interchange between the Lorentz representation space (1/2, 0) and (0, 1/2) made by the magic of Pauli matrices and not by parity, as was commonly thought. As is well known, the parity operator is related with the Dirac dynamics, as can be seen in Sperança L. D., Int. J. Mod. Phys. D, 2 (2014) 1444003. The major focus is to establish the relation between the Dirac dynamics with the parity operator, i.e., the reverse path shown in the paper by Sperança.