We propose a novel mechanism for a nonequilibrium phase transition in a U (1)-broken phase of an electron-hole-photon system, from a Bose-Einstein condensate of polaritons to a photon laser, induced by the non-Hermitian nature of the condensate. We show that a (uniform) steady state of the condensate can always be classified into two types, namely, arising either from lower or upperbranch polaritons. We prove (for a general model) and demonstrate (for a particular model of polaritons) that an exceptional point where the two types coalesce marks the endpoint of a firstorder-like phase boundary between the two types, similar to a critical point in a liquid-gas phase transition. Since the phase transition found in this paper is not in general triggered by population inversion, our result implies that the second threshold observed in experiments is not necessarily a strong-to-weak-coupling transition, contrary to the widely-believed understanding. Although our calculation mainly aims to clarify polariton physics, our discussion is applicable to general drivendissipative condensates composed of two complex fields.

Objectives To describe the frictional forces (FF) that constrain wire sliding in the initial alignment phase of treatment using a new term, the “constraining force” (CF), and to hypothesize that CF is dependent on two factors: the hyperelastic behavior of archwires and the specific type of tooth geometric malalignment present. Materials and Methods A laboratory device that simulates the four distinct malalignment types (in-out, rotation, tipping, and vertical step) was used to couple with an Instron testing apparatus. Incremental CF data for the four types of malalignment were recorded. Each type had five trials per increment of severity, from which the CF was averaged using 0.016-inch copper-nickel-titanium (CuNiTi) archwires. Results Two types of friction curves were obtained: a traditional step function response and a power regression response. For all malalignment types, increasing degrees of irregularity increased power regression responses and CF. A severity turning point, displayed as a sudden increase in CF, occurred for each malalignment. The rotation type of malalignment yielded the lowest CF, while the vertical step type resulted in the highest CF. Conclusions The data infer a hypothesis that malrotation type having weak CF might act as a limiting factor in the alignment phase to unravel the neighboring teeth. Future investigations to compare clinical and bench data can help explain more fully the constraints impeding alignment resolution and the factors governing the ability to bring malaligned teeth into alignment.

We describe a Monte Carlo renormalization group approach to the calculation of critical behavior for percolation models. This approach can be utilized to determine the renormalized bond probabilities and the values of the critical exponents. We illustrate the method for two-dimensional bond percolation, but the method is also applicable to other percolation models and other dimensions.

The Higgs amplitude mode is a collective excitation studied and observed in a broad class of matter, including superconductors, charge density waves, antiferromagnets, 3 He p-wave superfluid, and ultracold atomic condensates. In all the observations reported thus far, the amplitude mode was excited by perturbing the condensate out of equilibrium. Studying an exciton-polariton condensate, here we report the first observation of this mode purely driven by intrinsic quantum fluctuations without such perturbations. By using an ultrahigh quality microcavity and a Raman spectrometer to maximally reject photoluminescence from the condensate, we observe weak but distinct photoluminescence at energies below the condensate emission. We identify this as the so-called ghost branches of the amplitude mode arising from quantum depletion of the condensate into this mode.These energies, as well as the overall structure of the photoluminescence spectra, are in good agreement with our theoretical analysis. I. INTRODUCTIONSpontaneous breaking of a continuous symmetry occurs in various branches of modern physics, such as cosmology [1,2], particle physics [3-5], and a variety of condensed matter systems [6][7][8]. In this broken phase, in addition to the phase (Goldstone) mode [9,10], a collective amplitude (Higgs) excitation [11,12] emerges ubiquitously in various condensates. Such a Higgs amplitude mode has been observed in many condensed matter systems: superconductors [13,14], charge density waves [15], antiferromagnets [16], p-wave superfluids of 3 He [17], ultracold Fermi superfluid in the Bardeen-Cooper-Schrieffer-Bose Einstein Condensate (BCS-BEC) crossover region [18], bosons loaded in an optical lattice [19], and a supersolid realized in two crossed optical cavities [20]. In all the above observations, it was essential to drive the condensate out of equilibrium to excite and detect this mode.However, these collective modes are intrinsically driven by quantum fluctuations without such external perturbations, even in the ground state where no thermal fluctuations exist. Being in a state of definite phase, interactions in the condensate enable processes that do not conserve the number of condensed particles. As a result, quantum fluctuations coherently expel the particles out of the condensate. This phenomenon, known as quantum depletion, was formulated by Bogoliubov [21] and was recently confirmed in an atomic BEC [22] and an exciton-polariton BEC experiment [23].The expelled particles occupy the collective modes of the condensate. The spectral signature of this fascinating property is a set of "ghost branches" (GB), the time-reversed partners of the normal collective modes (normal branch or NB) which appear at energies below the ground state. Since the quantum mechanical Bose statistics are crucial in occupying the GB, the observation of these branches provides an unambiguous signature of quantum depletion. Although