The non-equilibrium dynamics of an isolated quantum system after a sudden quench to a dynamical critical point is expected to be characterized by scaling and universal exponents due to the absence of time scales. We explore these features for a quench of the parameters of a Hamiltonian with O(N ) symmetry, starting from a ground state in the disordered phase. In the limit of infinite N , the exponents and scaling forms of the relevant two-time correlation functions can be calculated exactly. Our analytical predictions are confirmed by the numerical solution of the corresponding equations. Moreover, we find that the same scaling functions, yet with different exponents, also describe the coarsening dynamics for quenches below the dynamical critical point.
Non-thermal dynamical critical behavior can arise in isolated quantum systems brought out of equilibirum by a change in time of their parameters. While this phenomenon has been studied in a variety of systems in the case of a sudden quench, here we consider its sensitivity to a change of protocol by considering the experimentally relevant case of a linear ramp in time. Focusing on the O(N ) model in the large N limit, we show that a dynamical phase transition is always present for all ramp durations and discuss the resulting crossover between the sudden quench transition and one dominated by the equilibrium quantum critical point. We show that the critical behavior of the statistics of the excitations, signaling the non-thermal nature of the transition are robust against changing protocol. An intriguing crossover in the equal time correlation function, related to an anomalous coarsening is also discussed.
We discuss the emergence of nonadiabatic behavior in the dynamics of the order parameter in a low-dimensional quantum many-body system subject to a linear ramp of one of its parameters. While performing a ramp within a gapped phase seems to be the most favorable situation for adiabaticity, we show that such a change leads eventually to the disruption of the order, no matter how slowly the ramp is performed. We show this in detail by studying the dynamics of the onedimensional quantum Ising model subject to linear variation of the transverse magnetic field within the ferromagnetic phase, and then propose a general argument applicable to other systems. PACS numbers:The nonequilibrium dynamics of isolated quantum many-body systems is one of the most active and interdisciplinary fields that emerged recently 1-3 . Indeed, while interest in this area has been spurred by the opportunity to directly access the nonequilibrium dynamics in cold atom gases loaded in optical lattices 4 , many of the questions addressed in that context turn out to be of importance in others, such as high energy physics 5 and cosmology 6,7 . In all intriguing issues addressed in the recent literature, such as the meaning and occurrence of thermalization in isolated quantum systems, or the quest for "universal" behavior out of equilibrium, a recurring theme has been the characterization of the response of a many-body system to the variation of the Hamiltonian parameters. In particular, the main focus has been on the two extremes of instantaneous changes (quenches) and slow ones (known under the oxymoron "slow quenches"). The latter has been mostly studied for systems driven across a quantum critical point, where a generalization of the classical Kibble-Zurek theory led to the prediction of a universal scaling of the excitation density with the speed at which the critical point is crossed 8,9 , successively extended also to quenches within gapless phases 10,11 , where even full violation of adiabaticity may occur 12 . Specifically, universality is expected whenever the scaling dimension of the fidelity susceptibility 13 (or its generalization for non linear protocols) is negative, and extends to other quantities besides the excitation density, such as the excess energy. We also mention that spontaneous generation of defects in the nonequilibrium dynamics has been observed experimentally in spinor condensates 14 .Intuitive quantum mechanical arguments, rooted ultimately on the adiabatic theorem, suggest that the case of quenches within a gapped phase is much less interesting. Indeed, in this case the scaling dimension of the fidelity susceptibility is always positive, implying that the density of excitations and the excess energy always tends to zero with the square of the switching rate for linear ramps (generalization to generic power-law ramps is straightforward). This also suggests that other thermodynamics quantities share the same property 10 , i.e., corrections with respect to their equilibrium value are quadratic in the rate 1 . However, ...
We study a weak interaction quench in a three-dimensional Fermi gas. We first show that, under some general assumptions on time-dependent perturbation theory, the perturbative expansion of the long-wavelength structure factor S(q) is not compatible with the hypothesis that steady-state averages correspond to thermal ones. In particular, S(q) does develop an analytical component ∼ const.+O(q 2 ) at q → 0, as implied by thermalization, but, in contrast, it maintains a non-analytic part ∼ |q| characteristic of a Fermi-liquid at zero-temperature. In real space, this non-analyticity corresponds to persisting power-law decaying density-density correlations, whereas thermalization would predict only an exponential decay. We next consider the case of a dilute gas, where one can obtain non-perturbative results in the interaction strength but at lowest order in the density. We find that in the steady-state the momentum distribution jump at the Fermi surface remains finite, though smaller than in equilibrium, up to second order in kF f0, where f0 is the scattering length of two particles in the vacuum. Both results question the emergence of a finite length scale in the quench-dynamics as expected by thermalization.
Abstract:We show that a linear term coupling the atoms of an ultracold binary mixture provides a simple method to induce an effective and tunable population imbalance between them. This term is easily realized by Rabi coupling between different hyperfine levels of the same atomic species. The resulting effective imbalance holds for one-particle states dressed by the Rabi coupling and obtained by diagonalizing the mixing matrix of the Rabi term. This way of controlling the chemical potentials applies to both bosonic and fermionic atoms and it also allows for spatially-and temporally-dependent imbalances. As a first application, we show that, in the case of two attractive fermionic hyperfine levels with equal chemical potentials coupled by the Rabi pulse, the same superfluid properties of an imbalanced binary mixture are recovered. We finally discuss the properties of m-species mixtures in the presence of SU(m)-invariant interactions.
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