In this article we study the quench dynamics of Galilean and scale invariant many-body systems which can be prepared using interacting atomic gases. The far-away from equilibrium dynamics are investigated by employing m-body density matrices, which are most conveniently defined in terms of a special basis -the conformal tower states. We explicitly illustrate that, although during the initial stage of the dynamics all symmetries can be broken and absent in the unitary evolution because of the initialization of the state, there is always an emergent conformal symmetry in the long time limit. The emergence of this dynamic conformal symmetry is robust, and always occurs -even when scale and other symmetries (such as rotational symmetry) are still fully broken in the many-body states; it uniquely defines the characteristics of the asymptotic dynamics near a scale invariant strong coupling fixed point. As an immediate application of the asymptotic dynamics of the microscopic density matrices, we have focused on the effects of this emergent conformal symmetry on two observables: the moment of inertia tensor, Iij(t), i, j = x, y, z, and the entropy density field, S(r, t), in the hydrodynamic flow of strongly interacting particles. We show that the long time behaviour of these observables is completely set by conformal symmetry, while the leading long time corrections depend on interference effects between different conformal tower states. The emergent conformal symmetry naturally leads to entropy conservation, and conformal cooling, an energy conserving cooling of a strongly interacting gas during free expansion. When the interaction Hamiltonian breaks the scale symmetry, we further demonstrate that there is a direct cause-effect relation between conformal symmetry breaking in the long time limit, and a non-vanishing entropy production. This suggests that the entropy production rate is a natural parameter for categorizing the breaking of conformal symmetry. arXiv:1904.11549v1 [cond-mat.quant-gas]

In this work we develop a general formalism that categorizes the action of broken scale invariance on the non-equilibrium dynamics of non-relativistic quantum systems. This approach is equally applicable to both strongly and weakly interacting systems. We show that any small deviation from the strongly interacting fixed point, in three spatial dimensions, leads to non-pertubative effects in the long time dynamics, dramatically altering the dynamics observed at the scale invariant fixed point. As a concrete example, we apply this approach to the non-equilibrium dynamics for the interacting two-body problem, and for a non-interacting quantum gas in the presence of an impurity, both in three spatial dimensions. Slightly away from the resonantly-interacting scale invariant fixed point, we show that the dynamics are altered by a non-perturbative log-periodic beat. The presence of the beat depends only on deviating from the resonant fixed point, while the frequency depends on the microscopic parameters of the system.

Quantum simulations based on near-resonance Bose gases are limited by their short lifetimes due to severe atom losses. In addition to this, the recently predicted thermodynamical instability adds another constraint on accessing the resonant Bose gases. In this Letter, we offer a potential solution by proposing long-lived resonant Bose gases in both two and three dimensions, where the conventional few-body losses are strongly suppressed. We show that the thermodynamical properties as well as the lifetimes of these strongly interacting systems are universal, and independent of shortrange physics.

In this article, we illustrate the scaling properties of a family of solutions for A attractive bosonic atoms in the limit of large A. These solutions represent the quantized dynamics of solitonic degrees of freedom in atomic droplets. In dimensions lower than two, or d = 2 -e, we demonstrate that the number of isotropic droplet states scales as A 3/2/ e 1/2, and for e = 0, or d = 2, scales as N 2. The ground-state energies scale as A 2/e+1 in d -2 -e, and when d = 2, scale as an exponential function of A. We obtain the universal energy spectra and the generalized Tjon relation; their scaling properties are uniquely determined by the asymptotic freedom of quantum bosonic fields at short distances, a distinct feature in low dimensions. We also investigate the effect of quantum loop corrections that arise from various virtual processes and show that the resultant lifetime for a wide range of excited states scales as N e/2E '~e/2.

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In this paper we explore the transport properties of three-component Fermi gases confined to one spatial dimension, interacting via a three-body interaction, in the high temperature limit. At the classical level, the three-body interaction is scale invariant in one dimension. However, upon quantization, an anomaly appears which breaks the scale invariance. This is very similar to the physics of two-component fermions in two spatial dimensions, where the two-body interaction is also anomalous. Previous studies have already hinted that the physics of these two systems are intimately related. Here we expand upon those studies by examining the thermodynamic properties of this anomalous one dimensional system in the high temperature limit. We show there is an exact mapping between the traditional two-body anomalous interaction in two dimensions, to that of three-body interaction in one dimension. This result is valid in the high temperature limit, where the thermodynamics can be understood in terms of few-body correlations.

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