In the present study, we investigate the properties of an ensemble of free Dirac fermions, at finite inverse temperature β and finite chemical potential μ , undergoing rigid rotation with an imaginary angular velocity Ω = i Ω I . Our purpose is to establish the analytical structure of such states, as well as the prospects (and dangers) of extrapolating results obtained under imaginary rotation to the case of real rotation. We show that in the thermodynamic limit, the state of the system is akin to a stationary system with modified inverse temperature β q = q β and the same chemical potential, where q is the denominator of the irreducible fraction ν = β Ω I / 2 π = p / q . The temperature of the system becomes a fractal function of the rotation parameter, as in the case of the scalar field. The chemical potential breaks the fractalization of fermions. We also compute the thermodynamic potential Φ and associated thermodynamic functions, showing that they also exhibit fractal behavior. Finally, we evaluate the axial and helical fluxes through the transverse plane, generated through the vortical effects, and show that they diverge in the thermodynamic limit, in the case when ν = 1 / q and q → ∞ .
In the present study, we investigate the properties of an ensemble of free Dirac fermions, at finite inverse temperature β and finite chemical potential μ , undergoing rigid rotation with an imaginary angular velocity Ω = i Ω I . Our purpose is to establish the analytical structure of such states, as well as the prospects (and dangers) of extrapolating results obtained under imaginary rotation to the case of real rotation. We show that in the thermodynamic limit, the state of the system is akin to a stationary system with modified inverse temperature β q = q β and the same chemical potential, where q is the denominator of the irreducible fraction ν = β Ω I / 2 π = p / q . The temperature of the system becomes a fractal function of the rotation parameter, as in the case of the scalar field. The chemical potential breaks the fractalization of fermions. We also compute the thermodynamic potential Φ and associated thermodynamic functions, showing that they also exhibit fractal behavior. Finally, we evaluate the axial and helical fluxes through the transverse plane, generated through the vortical effects, and show that they diverge in the thermodynamic limit, in the case when ν = 1 / q and q → ∞ .
We suggest the existence of systems in which the statistics of a particle changes with the quantum level it occupies. The occupation numbers in thermal equilibrium depend on a continuous statistical parameter that interpolates between bosonic or fermionic and ghost-like statistical distributions. We call such particle states ``ninions'': they are different from anyons and can exist in 3+1 dimensions. We suggest that ninions can be associated with coherent angular momentum states. In the Euclidean imaginary-time formalism, the ninionic statistics can be implemented via the rotwisted boundary conditions, which are associated with the rigid global rotation of the system with an imaginary angular frequency. The imaginary rotation is characterized by a PT-symmetric non-Hermitian Hamiltonian and possesses a well-defined thermodynamic limit. The physics of ninions in thermal equilibrium is accessible for numerical simulations on Euclidean lattices. We provide a no-go theorem on the absence of analytical continuation between real and imaginary rotations in the thermodynamic limit. The ground state of ninions shares similarity with the θ-vacuum in QCD. The ninions can produce negative pressure and energy, similar to the Casimir effect and the cosmological dark energy. In the thermodynamic limit, the dependence of thermal energy of free ninions on the statistical parameter is a fractal.
By combining methods from thermal field theory and statistical mechanics, we reexamine the spin polarization caused by the relativistic Barnett effect in a rigidly rotating Fermi gas. We determine the pressure of this medium and show that it depends on an effective chemical potential, which includes contributions from orbital angular momentum-rotation and spin-rotation coupling. We introduce a specific regularization scheme to sum over the angular momentum quantum numbers. As a result, the thermal pressure and all thermodynamic quantities are separated into two parts that differ only in the spin fugacities of spin-up and spin-down fermions. We calculate the Fermi energy for both components and show that the Fermi energy of the spin-down fermions is lower than that of the spin-up ones. This difference arises from the spin-rotation coupling and leads to a spin polarization consistent with the Barnett effect. In particular, we introduce the spin-chemicorotational ratio η≡Ω(0)/2μ(0), which adjusts the spin polarization of the Fermi gas. Here, Ω(0) and μ(0) represent the angular velocity and chemical potential at zero temperature, respectively. The factor 1/2 accounts for the fermion's spin. We explore the temperature dependence of μ and Ω, while assuming that the number of spin-up and spin-down fermions remains temperature independent. Our findings indicate that the spin-down component of the rotating Fermi gas dilutes at lower temperatures compared to the spin-up component. Additionally, we calculate the magnetic susceptibility arising from the Barnett magnetization and demonstrate that it is proportional to the moment of inertia I of the rotating Fermi gas. Finally, we prove that I exhibits a 1/T behavior in the high-temperature limit, similar to the Curie law of paramagnetism.
We establish scaling relations governing the equilibrium thermodynamics of real-spectrum non-Hermitian Dirac fermions in a magnetic field. Assuming thermalization with respect to the quasi-Hermitian Hamiltonian, a similarity transformation maps the system at the same applied field onto a Hermitian Dirac model with reduced velocity, while the Landau-level spectrum also admits a representation in terms of a reduced effective magnetic field. This structure yields scaling relations for the chemical potential, entropy, heat capacities, and orbital magnetic response in different thermodynamic ensembles. At fixed projected filling factor (PFF), the self-consistent chemical potential follows the compressed ladder of Landau levels, and the canonical thermodynamic functions are rescaled Hermitian responses. At fixed chemical potential, Landau-level crossings generate oscillatory caloric and magnetic responses governed by the same spectral compression. Quasistatic non-Hermitian deformation at fixed PFF further yields adiabatic temperature scaling. More broadly, these results establish a thermodynamic framework for real-spectrum non-Hermitian quantum matter and provide a starting point for incorporating the effects of interactions and disorder within the same formalism.
We study the thermodynamic properties of a rigidly rotating relativistic Bose gas. First, we derive the solution of the equation of motion corresponding to a rotating complex Klein-Gordon field and determine the free propagator of this model utilizing the Fock-Schwinger proper-time method. Using this propagator, we then obtain the thermodynamic potential of this model in the zeroth and first perturbative level. In addition, we compute the nonperturbative ring contribution to this potential. Our focus is on the dependence of these expressions on the angular velocity, which effectively acts as a chemical potential. Using this thermodynamic potential, we calculate several quantities, including the pressure, angular momentum and entropy densities, heat capacity, speed of sound, and moment of inertia of this rigidly rotating Bose gas as functions of temperature ( T ), angular velocity ( Ω ), and the coupling constant ( α ). We show that certain thermodynamic instabilities appear at high temperatures and large couplings. They are manifested as zero and negative values of the above quantities, particularly the moment of inertia and heat capacity. Zero moment of inertia leads to the phenomenon of supervorticity at certain T or α . Supervortical temperatures (couplings) decrease with increasing coupling (temperature). We also observe superluminal sound velocities at high T and for large α . Published by the American Physical Society 2024
A formal thermodynamic mapping is established between the attractive Fermi–Hubbard model and the repulsive Bose–Hubbard model at finite temperature and at imaginary chemical potential μ=iθ. By utilizing a large N-expansion, it is shown that the partition functions of the two models are related by a plain shift θ→θ+π. This condition maps the BCS–BEC crossover of attractive fermions to a Bose–Fermi crossover (fermion-like occupation) of repulsive bosons. A central feature of this correspondence is the thermal kernel g(βE,ϕ) (with β the inverse absolute temperature, E the energy scale, and ϕ the phase angle), whose analytic continuation gB(βE,ϕ)=gF(βE,ϕ+π) governs the bosonic (B) and fermionic (F) sectors. Interestingly, the particular angles ϕ=2π/3 and 4π/3 for fermions correspond to ϕ=π/3 and 5π/3 for bosons, marking the boundaries of an universal thermal window. It is further argued that the present mechanism shows how an emergent, fermionization-like phenomenon can occur at finite interaction strength through a thermodynamic effect induced by the imaginary chemical potential. It is emphasized that this does not imply a transmutation of quantum statistics at the operator level, but rather a thermodynamic exclusion-like behavior driven by the imaginary chemical potential, unlike the Tonks–Girardeau limit, where fermionization arises from an infinite repulsive interaction and anyonic or Floquet-engineered systems where transmutation emerges from modified statistics or dynamics. Effectively, the phase ϕ is a statistical parameter; by twisting the thermal phase, it generates fermion-like behavior without hard-core constraints or infinite repulsion through purely thermodynamic mechanisms. The gap equation and number equation for the bosonic model are derived, highlighting the role of the imaginary chemical potential as a statistical regulator. The results obtained here provide a unified framework for understanding crossovers in interacting lattice systems.
We present a nonperturbative computation of the equation of state of polarized, attractively interacting, nonrelativistic fermions in one spatial dimension at finite temperature. We show results for the density, spin magnetization, magnetic susceptibility, and Tan's contact. We compare with the second-order virial expansion, a next-to-leading-order lattice perturbation theory calculation, and interpret our results in terms of pairing correlations. Our lattice Monte Carlo calculations implement an imaginary chemical potential difference to avoid the sign problem. The thermodynamic results on the imaginary side are analytically continued to obtain results on the real axis. We focus on an intermediate- to strong-coupling regime, and cover a wide range of temperatures and spin imbalances.