Relativistic interaction of ultra-intense laser pulses with cluster targets is of particular interest for high-energy-density physics, compact X-ray source development, and laboratory astrophysics. Understanding the dynamics of such plasmas requires precise control of their parameters, in particular temperature, on subpicosecond timescales. In this study, X-ray spectral methods were used to diagnose the laser plasma of krypton cluster targets, created at laser pulse intensities of the order of 1020–1021 W/cm2. The use of a time-dependent detailed radiation-collisional kinetic model made it possible to describe the results of the observed X-ray spectra in the femtosecond laser plasma of a cluster target. We present a method for diagnosing the non-stationary plasma of high-atomic-number (krypton) clusters using resonance spectral lines 1s22s22p53s 1P1–1s22s22p6 1S0 and 1s22s22p53s 3P1–1s22s22p6 1S0 of the Ne-like Kr XXVII ion, allowing one to determine the plasma temperature at the moment of “plasma channel” formation. In the experiment, this temperature was shown to be 55 ± 5 eV. The same spectroscopic approach can be extended to other cluster species (for example, Ar, Xe) for non-stationary plasma diagnostics in the relativistic regime.
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.
