A mobile impurity coupled to a weakly-interacting Bose gas, a Bose polaron, displays several interesting effects. While a single attractive quasiparticle is known to exist at zero temperature, we show here that the spectrum splits into two quasiparticles at finite temperatures for sufficiently strong impurity-boson interaction. The ground state quasiparticle has minimum energy at Tc, the critical temperature for Bose-Einstein condensation, and it becomes overdamped when T Tc. The quasiparticle with higher energy instead exists only below Tc, since it is a strong mixture of the impurity with thermally excited collective Bogoliubov modes. This phenomenology is not restricted to ultracold gases, but should occur whenever a mobile impurity is coupled to a medium featuring a gapless bosonic mode with a large population for finite temperature.Mobile impurities in a quantum bath play a fundamental role in a wide range of systems including metals and dielectric materials [1] [19,20]. Bose polarons have been investigated using a variety of theoretical techniques [21][22][23][24][25][26][27][28][29][30][31][32], and they have also been considered in one dimension [33][34][35][36][37].A qualitatively new feature of the Bose polaron with respect to polarons in a Fermi gas or in solid state systems is that the environment undergoes a phase transition to a BEC at T c . This changes drastically the low-energy density-of-states of the environment, and should therefore affect significantly the polaron. Temperature effects on Bose polarons have been examined so far only theoretically, either in the mean-field regime [38], at high temperature [39], or for immobile Rydberg atoms [30].Here, we develop a strong coupling diagrammatic scheme designed to include scattering processes important for finite temperature. Using this, we show that the polaron splits into two quasiparticle states for 0 < T < T c for strong attractive coupling. The energy of the lower polaron depends non-monotonically on temperature with a minimum at T c , whereas the energy of the upper polaron increases until its quasiparticle residue vanishes at T c . The generic mechanism causing these effects is the coupling between the impurity and low energy Bogoliubov modes with an infrared divergent population for finite T . Consequently, similar effects should occur whenever a mobile impurity is coupled to a gapless bosonic mode, as for example in Helium liquids or quantum mag-Feynman diagrams yielding the self-energy Σ within the "extended" ladder approximation. Thin blue lines represent the bare impurity propagator, solid red lines are Bogoliubov propagators, dashed red lines are condensate bosons, and wavy lines represent the vacuum scattering matrix Tv. The ladder self-energy is indicated by ΣL, and the double blue line is an impurity dressed by the condensate only.nets. Indeed, an analogous splitting has been predicted for quasiparticle modes in hot electron and quark-gluon plasmas [40][41][42][43], providing an interesting link between low and high energy quantum...

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Superfluid vortex dynamics on an infinite cylinder differs significantly from that on a plane. The requirement that a condensate wave function be single valued upon once encircling the cylinder means that such a single vortex cannot remain stationary. Instead, it acquires one of a series of quantized translational velocities around the circumference, the simplest being ± /(2M R), with M the mass of the superfluid particles and R the radius of the cylinder. A generalization to a finite cylinder automatically includes these quantum-mechanical effects through the pairing of the single vortex and its image in either the top or bottom end of the surface. The dynamics of a single vortex on this surface provides a hydrodynamic analog of Laughlin pumping. The interaction energy for two vortices on an infinite cylinder is proportional to the classical stream function χ(r12), and it crosses over from logarithmic to linear when the intervortex separation r12 becomes larger than the cylinder radius. An Appendix summarizes the connection to an earlier study of Ho and Huang for one or more vortices on an infinite cylinder. A second Appendix reviews the topologically equivalent planar annulus, where such quantized vortex motion has no offset, but Laughlin pumping may be more accessible to experimental observation.

The superfluid flow velocity is proportional to the gradient of the phase of the superfluid order parameter, leading to the quantization of circulation around a vortex core. In this work, we study the dynamics of a superfluid film on the surface of a torus. Such a compact surface allows only configurations of vortices with zero net vorticity. We derive analytic expressions for the flow field, the total energy, and the time-dependent dynamics of the vortex cores. The local curvature of the torus and the presence of non-contractable loops on this multiply connected surface alter both the superfluid flow and the vortex dynamics. Finally we consider more general surfaces of revolution, called toroids.

Circular coloring is a constraints satisfaction problem where colors are assigned to nodes in a graph in such a way that every pair of connected nodes has two consecutive colors (the first color being consecutive to the last). We study circular coloring of random graphs using the cavity method. We identify two very interesting properties of this problem. For sufficiently many color and sufficiently low temperature there is a spontaneous breaking of the circular symmetry between colors and a phase transition forwards a ferromagnet-like phase. Our second main result concerns 5-circular coloring of random 3-regular graphs. While this case is found colorable, we conclude that the description via one-step replica symmetry breaking is not sufficient. We observe that simulated annealing is very efficient to find proper colorings for this case. The 5-circular coloring of 3-regular random graphs thus provides a first known example of a problem where the ground state energy is known to be exactly zero yet the space of solutions probably requires a full-step replica symmetry breaking treatment.