Relativistic dynamics compels a thermalized Fermi gas to a unique intrinsic parity eigenstate

Abstract

Dirac equation describes the dynamics of a relativistic spin-1/2 particle regarding its spatial motion and intrinsic degrees of freedom. Here we adopt the point of view that the spinors describe the state of a massive particle carrying two qubits of information: helicity and intrinsic parity. We show that the density matrix for a gas of free fermions, in thermal equilibrium, correlates helicity and intrinsic parity. Our results introduce the basic elements for discussing the spin-parity correlation for a Fermi gas: (1) at the ultra-relativistic domains, when the temperature is quite high, $T>10^{10}K$, the fermions have no definite intrinsic parity (50% : 50%), which is maximally correlated with the helicity; (2) at very low temperature, $T\approx 3K$, a unique parity dominates (conventionally chosen positive), by $10^{20}$ to $1$, while the helicity goes into a mixed state for spin up and down, and the quantum correlation decoheres. For the anti-fermions we get the opposite behavior. In the framework of quantum information, our result could be considered as a plausible explanation of why we do accept, as a fact (consistent with the experimental observation), that fermions (and anti-fermions), in our present epoch of a cool universe, have a unique intrinsic parity. The framework for constructing spin-parity entangled states is established.

14 pages, 2 figures

References in corpus (3)

• From qubits and actions to the Pauli-Schroedinger equation
• Degenerate Fermi gas perturbations at standard background cosmology
• Reproducing neutrino effects on the matter power spectrum through a degenerate Fermi gas approach

Cited by in corpus (12)

• Lattice-layer entanglement in Bernal-stacked bilayer graphene
• Global Dirac bispinor entanglement under Lorentz boosts
• Entanglement of Dirac bi-spinor states driven by Poincaré classes of $\mbox{SU}(2) \otimes \mbox{SU}(2)$ coupling potentials
• Quantum transitions and quantum entanglement from Dirac-like dynamics simulated by trapped ions
• $SU(2)\otimes SU(2)$ bi-spinor structure entanglement induced by a step potential barrier scattering in two-dimensions
• Graphene lattice-layer entanglement under non-Markovian phase noise
• Effects of Lorentz boosts on Dirac bispinor entanglement
• Schrödinger cat and Werner state disentanglement simulated by trapped ion systems
• Phase-space elementary information content of confined Dirac spinors
• Lorentz Invariant Quantum Concurrence for SU(2) x SU(2) spin-parity states
• CP symmetry and thermal effects on Dirac bi-spinor spin-parity local correlations
• Dirac bi-spinor entanglement under local noise and its simulation by Jaynes-Cummings interactions