Quantum heat waves in a one-dimensional condensate

Abstract

We study the dynamics of phase relaxation between a pair of one-dimensional condensates created by a bi-directional, supersonic 'unzipping' of a finite single condensate. We find that the system fractures into different extensive chunks of space-time, within which correlations appear thermal but correspond to different effective temperatures. Coherences between different eigen-modes are crucial for understanding the development of such thermal correlations; at no point in time can our system be described by a generalized Gibbs' ensemble despite nearly always appearing locally thermal. We rationalize a picture of propagating fronts of hot and cold sound waves, populated at effective, relativistically red-and blue-shifted temperatures to intuitively explain our findings. The disparity between these hot and cold temperatures vanishes for the case of instantaneous splitting but diverges in the limit where the splitting velocity approaches the speed of sound; in this limit, a sonic boom occurs wherein the system is excited only along an infinitely narrow, and infinitely hot beam. We expect our findings to apply generally to the study of superluminal perturbations in systems with emergent Lorentz symmetry.

Potential and spin-exchange interaction between Anderson impurities in graphene

“…We then investigate the effective spin-spin exchange coupling J eff (R) between two Anderson impurities in graphene and compare it with our recent results for substitutional potential impurities 16 . We limit our analysis to the lowest (second) order in the coupling J between the localized spins and conduction electrons but explore a broad range of the parameters ǫ o and γ.…”

“…Green's function at coinciding points G iω (0, 0) is given by Eq. (16). To simplify calculations further let us introduce dimensionless distance ρ = ǫ o R/vα 0 as (here, α o = γ 2 A o /πv 2 , defined earlier in Eq.…”

“…We then explore how J eff (R) behaves in the strong coupling limit. In our recent work 16 , we have shown that the effective spin exchange coupling between substitutional magnetic impurities can become resonantly enhanced at a specific distance where an impurity level crosses the Dirac point. We find similar enhancement for Anderson impurities for sufficiently large couplings γ 2 /ǫ o .…”

“…It is instructive to begin our analysis of the Andersontype impurities with a discussion of potential impurities. Recent studies of impurity-impurity interaction in the case of substitution impurities with an onsite potential U have obtained an analytical expression exact in U 15,16,33 . In particular, in the large U limit, interaction between impurities on the same sublattice is long range, ∝ 1/R (up to logarithmic factors), and is repulsive, in contrast to the weak U limit where it decays as 1/R 3 and is attractive.…”

Quantum dynamics of few dipolar bosons in a double-well potential

“…To study effects of quantum fluctuations and collapse-revival, one may resort to quantum two-mode models [21][22][23][24][25][26][27][28]. Beyond mean-field effects are very important for coupled onedimensional systems [29][30][31][32][33][34].…”