Related papers: A massless interacting Fermionic Cellular Automato…
We investigate the mean dimension of a cellular automaton (CA for short) with a compact non-discrete space of states. A formula for the mean dimension is established for (near) strongly permutative, permutative algebraic and unit…
The Thirring Quantum Cellular Automaton (QCA) describes the discrete time dynamics of local fermionic modes that evolve according to one step of the Dirac cellular automaton followed by the most general on-site number-preserving…
In a recent paper [arXiv:1506.06649 [nlin.CG]], we presented an example of a 3-state cellular automaton which exhibits behaviour analogous to degenerate hyperbolicity often observed in finite-dimensional dynamical systems. We also…
The existence of multiple radial solutions to the elliptic equation modeling fermionic cloud of interacting particles is proved for the limiting Planck constant and intermediate values of mass parameters. It is achieved by considering the…
Lattice proposals for a nonperturbative formulation of the Standard Model easily lead to a global U(1) symmetry corresponding to exactly conserved fermion number. The absence of an anomaly in the fermion current would then appear to inhibit…
A Drude-Sommerfeld topological model (DSTM) is proposed to describe Weyl fermions under residual collisions. They are nearly free and dressed by their own weak magnetic field that breaks the reflection and time symmetries around a layer.…
The bound states of fermions in the external field of an Abelian dyon are studied here both analytically and numerically. Their existence is due to the dyon's electric charge resulting from a polarization of the fermionic vacuum. The…
We study the entanglement Hamiltonian of an interval for the massless Dirac field in an inhomogeneous background on a segment where the same boundary condition at both its endpoints is imposed, and in its ground state. We focus on a class…
It is argued that the specific heat of $N$ massless Dirac fermions in 2 spatial dimensions interacting with 1/r Coulomb interactions is suppressed logarithmically relative to its non-interacting counterpart. The (dimensionless) coefficient…
A natural architecture for nanoscale quantum computation is that of a quantum cellular automaton. Motivated by this observation, in this paper we begin an investigation of exactly unitary cellular automata. After proving that there can be…
The properties of two-state nearest-neighbour cellular automata (CA) that are capable of density classification are discussed. It is shown that these CA actually conserve the total density, rather than merely classifying it. This is also…
Weyl and Dirac (semi)metals in three dimensions have robust gapless electronic band structures. Their massless single-body energy spectra are protected by symmetries such as lattice translation, (screw) rotation and time reversal. In this…
We study the effects of strong $1/r$ long-range Coulomb interactions in a Weyl semimetal. We consider a three-dimensional (3D) Dirac fermion system on a lattice with a time-reversal symmetry breaking term, and take into account $1/r$…
In 2+1 dimensions the global U($2N$) symmetry associated with massless Dirac fermions is broken to U($N)\otimes$U($N$) by a parity-invariant mass. I will show how to adapt the domain wall formulation to recover the U($2N$)-invariant limit…
A fermion node is subset of fermionic configurations for which a real wave function vanishes due to the antisymmetry and the node divides the configurations space into compact nodal cells (domains). We analyze the properties of fermion…
We consider a quantum massless fermionic field in (1+1) dimensions in the case of moving boundaries. We work in the canonical approach in order to find a Hamiltonian describing the dynamics of the field. Thus, we study the statistics of…
The scattering of Dirac fermions on the sine-Gordon kink is studied both analytically and numerically. To achieve invariance with respect to a discrete symmetry, the sine-Gordon model is treated as a nonlinear $\sigma$-model with a circular…
We study the self-interaction effects for the Dirac particle moving in an external field created by static charges in (1+1)-dimensions. Assuming that the total electric charge of the system vanishes, we show that the asymptotically linearly…
A map on finitely many fermionic modes represents a unitary evolution if and only if it preserves canonical anti-commutation relations. We use this condition for the classification of fermionic cellu- lar automata (FCA) on Cayley graphs of…
Relativistic massless Weyl and Dirac fermions have isotropic and linear dispersion relations to maintain Poincar\'{e} symmetry, which is the most basic symmetry in high-energy physics. The situation in condensed matter physics is less…