Equilibration and coarsening in the quantum<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mi>N</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>model at infinite<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>

Chandran, Anushya; Nanduri, Arun; Gubser, Steven S.; Sondhi, S. L.

doi:10.1103/physrevb.88.024306

Cited by 84 publications

(126 citation statements)

References 39 publications

(57 reference statements)

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“…Many years ago, Kibble [1], and subsequently Zurek [2], argued that observables like defect density indeed show scaling behavior. These arguments -which were first developed for thermal quench and recently generalized to quantum quench 1 [7] -imply that for a driving involving a single relevant operator, the time dependence of the one point function of an operator O with conformal dimension x is of the form [4] O(t, v) ∼ v where v is the rate of change of the coupling, ν is the correlation length exponent and z is the dynamical critical exponent. The arguments which lead to (1.1) involve (i) an assumption that once adiabaticity breaks the system evolve in a diabatic fashion and (ii) in the critical region the instantaneous correlation length is the only length scale in the problem.…”

Section: Introductionmentioning

confidence: 99%

Kibble-Zurek scaling in holographic quantum quench: backreaction

Das

Morita

2015

J. High Energ. Phys.

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Abstract:We study gauge and gravity backreaction in a holographic model of quantum quench across a superfluid critical transition. The model involves a complex scalar field coupled to a gauge and gravity field in the bulk. In earlier work (arXiv:1211.7076) the scalar field had a strong self-coupling, in which case the backreaction on both the metric and the gauge field can be ignored. In this approximation, it was shown that when a time dependent source for the order parameter drives the system across the critical point at a rate slow compared to the initial gap, the dynamics in the critical region is dominated by a zero mode of the bulk scalar, leading to a Kibble-Zurek type scaling function. We show that this mechanism for emergence of scaling behavior continues to hold without any selfcoupling in the presence of backreaction of gauge field and gravity. Even though there are no zero modes for the metric and the gauge field, the scalar dynamics induces adiabaticity breakdown leading to scaling. This yields scaling behavior for the time dependence of the charge density and energy momentum tensor.

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Section: Introductionmentioning

confidence: 99%

Kibble-Zurek scaling in holographic quantum quench: backreaction

Das

Morita

2015

J. High Energ. Phys.

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“…A characterization in terms of traditional critical exponents would suggest that the dynamical transition of the O(N ) model is of the same universality as the corresponding thermal phase transition 22 . In contrast, the full statistics of defects clearly differs from the thermal case and characterizes the dynamical criticality: while the number fluctuations of defects saturate in time for quenches above the dynamical critical point (i.e., quenches to the dynamically disordered phase), they grow indefinitely for quenches to or below the dynamical critical point (i.e., to the dynamically ordered phase), see Fig.…”

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confidence: 99%

Exploring dynamical phase transitions and prethermalization with quantum noise of excitations

et al. 2015

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Dynamical phase transitions can occur in isolated quantum systems that are brought out of equilibrium by sudden parameter changes. We discuss the characterization of such dynamical phase transitions based on the statistics of produced excitations. We consider both the O(N) model in the large N limit and a spin model with long range interactions and show that the dynamical criticality of their prethermal steady-states manifests most dramatically not in the average number of excitations but in their higher moments. We argue that the growth of defect fluctuations carries unique signatures of the dynamical criticality, irrespective of the precise details of the model. Our theoretical results should be relevant to quantum quench experiments with ultracold bosonic atoms in optical lattices.

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“…It would be interesting to investigate this issue for QFTs in light of our findings. Finally, quasi-local charges may also be of importance for understanding the equilibration of QFTs in large-N limits [86]. This work was supported by the EPSRC under grants EP/I032487/1 and EP/J014885/1.…”

Section: Nonlinear Schrödinger Model (Nls) the Hamiltonian Density Omentioning

confidence: 99%

Generalized Gibbs ensembles for quantum field theories

2015

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We consider the non-equilibrium dynamics in quantum field theories (QFTs). After being prepared in a density matrix that is not an eigenstate of the Hamiltonian, such systems are expected to relax locally to a stationary state. In presence of local conservation laws, these stationary states are believed to be described by appropriate generalized Gibbs ensembles. Here we demonstrate that in order to obtain a correct description of the stationary state, it is necessary to take into account conservation laws that are not (ultra-)local in the usual sense of QFT, but fulfil a significantly weaker form of locality. We discuss implications of our results for integrable QFTs in one spatial dimension. PACS numbers:Introduction. The last decade has witnessed dramatic progress in realizing and analyzing isolated many-particle quantum systems out of equilibrium [1][2][3][4][5][6]. Key questions that emerged from these experiments is why and how observables relax towards time independent values, and what principles underlie a possible statistical description of the latter . It was demonstrated early on that non-equilibrium dynamics is strongly affected by dimensionality, and that conservation laws play an important role. In particular, the experiments of [2] on trapped 87 Rb atoms established that three-dimensional condensates rapidly relax to a stationary state characterized by an effective temperature, whereas constraining the motion of atoms to one dimension greatly reduces the relaxation rate and dramatically changes the nature of the stationary state. The suggestion that this unusual steady state is a consequence of (approximate) conservation laws motivated a host of theoretical studies investigation the role played by conservation laws. We may summarize the results of these works as follows: given an initial state |Ψ and a translationally invariant system with Hamiltonian H ≡ I 0 and conservation laws I n such that [I n , I m ] = 0, the stationary behaviour of n-point functions of local operators O a (x) in the thermodynamic limit is described by a generalized Gibbs ensemble, as proposed by Rigol et al in a seminal paper [9]

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Equilibration and coarsening in the quantumO(N)model at infiniteN

Cited by 84 publications

References 39 publications

Kibble-Zurek scaling in holographic quantum quench: backreaction

Kibble-Zurek scaling in holographic quantum quench: backreaction

Exploring dynamical phase transitions and prethermalization with quantum noise of excitations

Generalized Gibbs ensembles for quantum field theories

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