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>1010 K, the fermions have no definite intrinsic parity (50% : 50%), which is maximally correlated with the helicity; (2) at very low temperature,
T≈3 K, a unique parity dominates (conventionally chosen positive), by
1020 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.
Abstract We study a many-body system of interacting fermionic atoms of two species that are in thermodynamic equilibrium with their condensed heteronuclear bound states (molecules). In order to describe such an equilibrium state, we use a microscopic approach that involves the Bogoliubov model for a weakly interacting Bose gas and approximate formulation of the second quantization method in the presence of bound states of particles elaborated earlier by the authors. This microscopic approach is valid at low temperatures, when the average kinetic energy of all the components in the system is small in comparison with the bound state energy. The coupled equations, which relate the chemical potentials of fermionic components and molecular condensate density, are obtained within the proposed theory. At zero temperature, these equations are analyzed both analytically and numerically, attracting the relevant experimental data. We find the conditions at which a condensate of heteronuclear molecules coexists in equilibrium with degenerate components of a Fermi gas. The ground state energy and single-particle excitation spectrum are found. The boundaries of the applicability of the developed microscopic approach are analyzed.
We apply the thermal (imaginary time) perturbative expansion to the relevant effective field theory to compute characteristics of the phase transition to the ordered state which can occur at low temperatures in the gas of (nonrelativistic) spin 1/2 fermions interacting through a short-range spin independent repulsive binary interaction potential. We show how to obtain a systematic expansion of the system's free energy depending on the densities
n+ and
n− of spin-up and spin-down fermions. In this paper we truncate this expansion at the second order and determine, by numerically minimizing the free energy, the equilibrium proportions of
n+ and
n− (that is, the system's polarization) as functions of the temperature, the system's overall density
n=n++n− and the strength of the interaction.