Spontaneous U(1) Symmetry Breaking and Phase Transitions in Rotating Interacting Bose Gases

We investigate spontaneous U(1) symmetry breaking and the associated phase transitions in rotating interacting Bose gases. Using a theoretical framework that combines mean-field analysis with rotational dynamics, we analyze how rigid rotation modifies the condensate structure and critical behavior. The study identifies the emergence of Goldstone modes and clarifies their role in the low-energy excitation spectrum. The results provide insight into the interplay between symmetry, rotation, and many-body interactions, contributing to a deeper theoretical understanding of phase structures in Bose systems.We investigate spontaneous U(1) symmetry breaking and the associated phase transitions in rotating interacting Bose gases. Using a theoretical framework that combines mean-field analysis with rotational dynamics, we analyze how rigid rotation modifies the condensate structure, critical behavior, and low-energy excitation spectrum. We identify the emergence of Goldstone modes (massless rotons and massive phonons) in the symmetry-broken phase and clarify their role in mediating low-energy excitations—findings that remain robust at low momentum regardless of rotation. A key result is the angular velocity (Ω) dependence of the critical temperature (Tc) for U(1) phase transition, where Tc scales as Ω^(1/3), distinct from the Ω^(2/5) (nonrelativistic) and Ω^(1/4) (ultrarelativistic) scaling observed in noninteracting rotating Bose gases. Rotation also alters the temperature dependence of the thermodynamic potential minima, changing the characteristic factor from (1 - t) (t = T/Tc for nonrotating systems) to (1 - t³) for rotating gases. We further demonstrate that rotation preserves the second-order nature of the phase transition, while modifying the critical exponents and reducing the discontinuity in heat capacity with increasing Ω. Additionally, we define a σ meson dissociation temperature (Tdiss) characterized by mσ(Tdiss) = 2mπ(Tdiss), showing that Tdiss is always lower than Tc. Thermal mass corrections are shown to ensure the validity of Goldstone’s theorem in the rotating frame, even in the chiral limit. These results deepen our understanding of the interplay between symmetry, rotation, and many-body interactions, with implications for interpreting extreme conditions in heavy-ion collisions and compact astrophysical objects, while advancing the theoretical framework for phase structures in rotating Bose systems.