Discrete Time Quantum Walk in a QCD Chiral Condensate Lattice

We propose a chiral condensate lattice with Pmmm space group symmetry (No. 47, D2h, order 8) and a cubic unit cell built from the four light quarks and antiquarks hypothesized to serve as the fundamental building blocks of the chiral condensate lattice and of baryonic and leptonic matter. The proposed Pmmm chiral condensate lattice arises from spontaneous symmetry breaking of the parent Pm3̄m space group (No. 221, Oh, order 48), with the 40 broken symmetry operations generating the three pions π⁺, π⁻, π⁰ as Goldstone bosons, and is proposed as an alternative structural description of the instanton liquid QCD chiral condensate. Electrons and positrons are embedded within the chiral condensate lattice and perform discrete-time quantum walks (DTQW) driven by underlying quark and antiquark permutations between the highly symmetric Wyckoff positions of the Pmmm unit cell, analogous to quark hopping in the instanton liquid. We assume that quark permutations occur at the Zitterbewegung frequency, ensuring that the embedded electron is never bare and generating a confined electron cloud within the chiral condensate lattice. The spin and helicity states of the embedded electrons are structurally defined by the chiral condensate structure and dynamics: the quantum walker type, matter or antimatter, determines the spin state, while the helicity state depends on whether the motion of the larger quark charge is parallel or antiparallel to the motion of the embedded electron charge. We assume that an electron undergoing a DTQW embedded within the chiral condensate lattice produces a coherent wave packet, in contrast to the wave packet dispersion found by Schrödinger and Darwin in 1927, which may provide indirect evidence for the existence of the proposed Pmmm chiral condensate lattice. A one-dimensional DTQW simulation with a non-Hermitian quantum coin generates coherent evolution of one wave packet component, providing promising support for the proposed framework. We further assume that in the vicinity of black hole horizons the chiral condensate lattice melts, thereby enabling a reaction of three Pionic tetraquarks that produce deuteron and anti-deuteron pairs, which further react with Pionic tetraquarks to produce protons, electrons, and anti-neutrons that fall beneath the black hole horizon while matter particles escape.