Universal scaling of unequal-time correlation functions in ultracold Bose gases far from equilibrium

Schachner, Andreas; Orioli, Asier Piñeiro; Berges, Jürgen

doi:10.1103/physreva.95.053605

Cited by 23 publications

(22 citation statements)

References 31 publications

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“…Evaluating, furthermore, our low-energy effective description for the case of a single Bose gas, N = 1, we obtain the same spatio-temporal scaling exponent β = 1/2, despite the fact that the dynamical exponent is z = 1 in this case. This analytical result corroborates earlier numerical findings presented in [48,59,81].…”

Section: Discussionsupporting

confidence: 91%

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Low-energy effective theory of nonthermal fixed points in a multicomponent Bose gas

2019

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Non-thermal fixed points in the evolution of a quantum many-body system quenched far out of equilibrium manifest themselves in a scaling evolution of correlations in space and time. We develop a low-energy effective theory of non-thermal fixed points in a bosonic quantum many-body system by integrating out long-wavelength density fluctuations. The system consists of N distinguishable spatially uniform Bose gases with U(N)symmetric interactions. The effective theory describes interacting Goldstone modes of the total and relativephase excitations. It is similar in character to the non-linear Luttinger-liquid description of low-energy phonons in a single dilute Bose gas, with the markable difference of a universal non-local coupling function depending, in the large-N limit, only on momentum, single-particle mass, and density of the gas. Our theory provides a perturbative description of the non-thermal fixed point, technically easy to apply to experimentally relevant cases with a small number of fields N. Numerical results for N = 3 allow us to characterize the analytical form of the scaling function and confirm the analytically predicted scaling exponents. The fixed point which is dominated by the relative phases is found to be Gaussian, while a non-Gaussian fixed point is anticipated to require scaling evolution with a distinctly lower power of time.

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Section: Discussionsupporting

confidence: 91%

“…A. We find analytically that the dynamical exponent z, in the large-N limit, is z = 2, corresponding to the Goldstone dispersion (8) and confirming the numerical results of, e.g., [59,81].…”

Section: Concluding Remarks On the Scaling Dynamicssupporting

confidence: 83%

Low-energy effective theory of nonthermal fixed points in a multicomponent Bose gas

2019

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“…The index 'g' refers to near-Gaussian, in contrast to the strongly anomalous scaling ('a') found in the previous section. We emphasize that our findings are compatible with a small but non-zero anomalous scaling [83]. When we refer to the fixed point as the 'Gaussian' one in the following, it is meant in relation to the much larger value (14) at the anomalous fixed point, not in an absolute sense.…”

Section: (Near-)gaussian Fixed Pointsupporting

confidence: 80%

“…see also [83]. The dynamical exponent z d is associated with the particular dynamic universality class which the near-critical evolution of the effective, defect-bearing order-parameter field falls into.…”

Section: Relation To Scaling Behavior In Driven Stationary Systemsmentioning

confidence: 99%

Strongly anomalous non-thermal fixed point in a quenched two-dimensional Bose gas

2017

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Universal scaling behavior in the relaxation dynamics of an isolated two-dimensional Bose gas is studied by means of semi-classical stochastic simulations of the Gross-Pitaevskii model. The system is quenched far out of equilibrium by imprinting vortex defects into an otherwise phase-coherent condensate. A strongly anomalous non-thermal fixed point is identified, associated with a slowed decay of the defects in the case that the dissipative coupling to the thermal background noise is suppressed. At this fixed point, a large anomalous exponent h - 3 and, related to this, a large dynamical exponent  z 5 are identified. The corresponding power-law decay is found to be consistent with three-vortex-collision induced loss. The article discusses these aspects of non-thermal fixed points in the context of phaseordering kinetics and coarsening dynamics, thus relating phenomenological and analytical approaches to classifying far-from-equilibrium scaling dynamics with each other. In particular, a close connection between the anomalous scaling exponent η, introduced in a quantum-field theoretic approach, and conservation-law induced scaling in classical phase-ordering kinetics is revealed. Moreover, the relation to superfluid turbulence as well as to driven stationary systems is discussed. analysis as well as a comprehensive classification scheme of far-from-equilibrium universal dynamics are lacking so far.Here we consider possible universal scaling behavior of a time-evolving isolated two-dimensional (2D) quantum-degenerate Bose gas quenched far out of equilibrium. We discuss the numerically found scaling in time and in the spatial degrees of freedom in the framework of non-thermal fixed points [34][35][36][37][38]. This approach builds on a scaling analysis of non-perturbative dynamic equations for field correlation functions in the spirit of a renormalization-group approach to far-from-equilibrium dynamics [35,[39][40][41][42][43][44]. Close to a non-thermal fixed point, correlation functions show a time evolution which takes the form of a rescaling in space and time [38]. In consequence, the relaxation is critically slowed down, while correlations evolve as a power law rather than exponentially in time.We prepare far-from-equilibrium states by imprinting phase defects, i.e., quantum vortex excitations, into an otherwise strongly phase-coherent condensate. Different kinds of initial states are realized by varying the number of defects, their arrangement, and their winding numbers. Independently of the microscopic details of the initial state, such as the statistics of fluctuations, the system is attracted to one or more non-thermal fixed points where the information about these details gets lost. Close to such a fixed point the correlations exhibit and evolve according to universal power laws [45][46][47][48][49][50].More than one attractor can exist for the dynamical evolution of the system, as we will demonstrate being the case for the 2D Bose gas studied here. Consequently, different types of universal evolution wit...

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“…This is based on the observation that there is an effective loss of details about the initial conditions and model parameters as time proceeds. In recent years this culminated in the discovery of new universality classes far from equilibrium [7], which characterize a significant part of the systems' dynamical evolution in terms of scaling exponents and scaling functions that are the same for a wide range of different relativistic models [7,[14][15][16][17][18][19] as well as non-relativistic systems of ultracold quantum gases [17,[19][20][21][22][23][24].…”

Section: Two-component Bose Gasmentioning

confidence: 99%

Inflationary preheating dynamics with two-species condensates

2017

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We discuss the amplification of loop corrections in quantum many-body systems through dynamical instabilities. As an example, we investigate both analytically and numerically a two-component ultracold atom system in one spatial dimension. The model features a tachyonic instability, which incorporates characteristic aspects of the mechanisms for particle production in early-universe inflaton models. We establish a direct correspondence between measureable macroscopic growth rates for occupation numbers of the ultracold Bose gas and the underlying microscopic processes in terms of Feynman loop diagrams. We analyze several existing ultracold atom setups featuring dynamical instabilities and propose optimized protocols for their experimental realization. We demonstrate that relevant dynamical processes can be enhanced using a seeding procedure for unstable modes and clarify the role of initial quantum fluctuations and the generation of a non-linear secondary stage for the amplification of modes.

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Universal scaling of unequal-time correlation functions in ultracold Bose gases far from equilibrium

Cited by 23 publications

References 31 publications

Low-energy effective theory of nonthermal fixed points in a multicomponent Bose gas

Low-energy effective theory of nonthermal fixed points in a multicomponent Bose gas

Strongly anomalous non-thermal fixed point in a quenched two-dimensional Bose gas

Inflationary preheating dynamics with two-species condensates

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