Metastable Phases and Perturbation Expansions

Yaroslav V. Kartashov, Boris A. Malomed, Lluís Torner

We show that metastable ring-shaped clusters can be constructed from two-dimensional quantum droplets in systems described by the Gross-Pitaevskii equations augmented with Lee-Huang-Yang quantum corrections. The clusters exhibit dynamical behavior ranging from contraction to rotation with simultaneous periodic pulsations, or expansion, depending on the initial radius of the necklace pattern and phase shift between adjacent quantum droplets. We show that, using an energy-minimization analysis, one can predict equilibrium values of the cluster radius that correspond to rotation without radial pulsations. In such a regime, the clusters evolve as metastable states, withstanding abrupt variations in the underlying scattering lengths and keeping their azimuthal symmetry in the course of evolution, even in the presence of considerable perturbations.

Jean Bricmont, Joseph Slawny

James G. Glimm, Arthur Jaffe

Shankar Balasubramanian, Margarita Davydova, Ting-Chun Lin +1 more

We show that the 2D classical spin model constructed in arXiv:2605.10943 hosts many metastable states at non-zero temperature which are stable to arbitrary Hamiltonian perturbations, providing the first such example. Our proof relies on a recursive application of the cluster expansion.

Tomasz Wasak, Jan Chwedeńczuk, Paweł Zin +1 more

Using the perturbative approach, it is demonstrated that the widths of the density and second-order correlation function of atoms scattered from a quasicondensate in a Raman process are sensitive to the phase fluctuations induced by the nonzero temperature of the mother cloud. It is also shown how these widths evolve during expansion of the halo of scattered atoms. It is also argued that if the Raman scattering is preceded by expansion of the mother cloud, the density of atoms widens substantially, while the second-order correlation function remains practically unchanged. These results are useful for planning future Raman scattering experiments and indicate the degree of spatial resolution of atom-position measurements necessary to detect the temperature dependence of the quasicondensate. All the calculations are performed using experimental parameters of a metastable ${}^{4}$He${}^{*}$ quasicondensate of the Palaiseau group.

Da-Wu Xiao, Chong Chen

The dissipative quantum Rabi model exhibits rich non-equilibrium physics, including a dissipative phase transition from the normal phase to the superradiant phase. In this work, we investigate the stability of the superradiant phase in the presence of a weak spin relaxation. We find that even a weak spin relaxation can render the superradiant phase a superradiant metastable phase, in which symmetry-breaking states are stable only for a finite time. This arises because each spin jump induced by relaxation applies as a strong perturbation to the system, potentially driving the system from a symmetry-breaking state to the symmetry-preserving saddle point with finite probability, before it eventually relaxes back to a symmetry-breaking state. Such dynamical processes lead to a finite lifetime of the symmetry-breaking states and restore the symmetry in the steady state. To substantiate these results, we combine mean-field and cumulant expansion analyses with exact numerical simulations. The lifetimes of the symmetry-breaking states are analyzed in finite-size systems and the conclusions are extrapolated to the thermodynamic limit via finite-size scaling. Our findings establish the metastable nature of the symmetry-breaking states in the dissipative quantum Rabi model and reveal the complexity of the dissipative phase transition beyond their equilibrium counterpart. The mechanisms uncovered here can be generalized to a broad class of open quantum systems, highlighting fundamental distinctions between equilibrium phase transitions and steady-state phase transitions.