When energy is added to a system, for example by stirring, the ensuing equilibration dynamics usually leads to more disorder. However, in a bounded two-dimensional fluid containing quantized vortices, Onsager found a surprising result: continuing to add energy leads to highly-ordered, persistent vortex clusters. Here, for the first time, we realize these high-energy vortex clusters in a planar superfluid and demonstrate that they persist for long times, despite being far from equilibrium with the surrounding fluid. Our experiments explore a new regime of vortex matter at negative absolute temperature, diametrically opposed to the Kosterlitz-Thouless transition at positive temperature. Such vortex cluster states are directly relevant to studies of two-dimensional turbulence, and are potentially realizable in helium films, exciton-polariton superfluids, nonlinear optical materials, and fermion superfluids. arXiv:1801.06951v2 [cond-mat.quant-gas]
Flatband networks are characterized by the coexistence of dispersive and flatbands. Flatbands (FBs) are generated by compact localized eigenstates (CLSs) with local network symmetries, based on destructive interference. Correlated disorder and quasiperiodic potentials hybridize CLSs without additional renormalization, yet with surprising consequences: (i) states are expelled from the FB energy E_{FB}, (ii) the localization length of eigenstates vanishes as ξ∼1/ln(E-E_{FB}), (iii) the density of states diverges logarithmically (particle-hole symmetry) and algebraically (no particle-hole symmetry), and (iv) mobility edge curves show algebraic singularities at E_{FB}. Our analytical results are based on perturbative expansions of the CLSs and supported by numerical data in one and two lattice dimensions.
We study the interplay of superfluidity and glassy ordering of hard core bosons with random, frustrating interactions. This is motivated by bosonic systems such as amorphous supersolid, disordered superconductors with preformed pairs, and helium in porous media. We analyze the fully connected mean field version of this problem, which exhibits three low-temperature phases, separated by two continuous phase transitions: an insulating, glassy phase with an amorphous frozen density pattern, a nonglassy superfluid phase, and an intermediate phase, in which both types of order coexist. We elucidate the nature of the phase transitions, highlighting in particular the role of glassy correlations across the superfluid-insulator transition. The latter suppress superfluidity down to T=0, due to the depletion of the low-energy density of states, unlike in the standard BCS scenario. Further, we investigate the properties of the coexistence (superglass) phase. We find anticorrelations between the local order parameters and a nonmonotonous superfluid order parameter as a function of T. The latter arises due to the weakening of the glassy correlation gap with increasing temperature. Implications of the mean field phenomenology for finite dimensional bosonic glasses with frustrating Coulomb interactions are discussed.Comment: 14 pages, 3 figures, comparison with Monte Carlo data adde
Clustering of like-sign vortices in a planar bounded domain is known to occur at negative temperature, a phenomenon that Onsager demonstrated to be a consequence of bounded phase space. In a confined superfluid, quantized vortices can support such an ordered phase, provided they evolve as an almost isolated subsystem containing sufficient energy. A detailed theoretical understanding of the statistical mechanics of such states thus requires a microcanonical approach. Here we develop an analytical theory of the vortex clustering transition in a neutral system of quantum vortices confined to a two-dimensional disk geometry, within the microcanonical ensemble. The choice of ensemble is essential for identifying the correct thermodynamic limit of the system, enabling a rigorous description of clustering in the language of critical phenomena. As the system energy increases above a critical value, the system develops global order via the emergence of a macroscopic dipole structure from the homogeneous phase of vortices, spontaneously breaking the Z 2 symmetry associated with invariance under vortex circulation exchange, and the rotational SO(2) symmetry due to the disk geometry. The dipole structure emerges characterized by the continuous growth of the macroscopic dipole moment which serves as a global order parameter, resembling a continuous phase transition. The critical temperature of the transition, and the critical exponent associated with the dipole moment, are obtained exactly within mean-field theory. The clustering transition is shown to be distinct from the final state reached at high energy, known as supercondensation. The dipole moment develops via two macroscopic vortex clusters and the cluster locations are found analytically, both near the clustering transition and in the supercondensation limit. The microcanonical theory shows excellent agreement with Monte Carlo simulations, and signatures of the transition are apparent even for a modest system of 100 vortices, accessible in current Bose-Einstein condensate experiments.
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