Critical Langevin dynamics of the O(<i>N</i>) Ginzburg–Landau model with correlated noise

Bonart, Julius; Cugliandolo, Leticia F.; Gambassi, Andrea

doi:10.1088/1742-5468/2012/01/p01014

Cited by 15 publications

(18 citation statements)

References 53 publications

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“…This is known to occur for quenches in * These authors contributed equally. classical systems in the presence of a thermal bath [49][50][51][52] and, more recently, for quantum impurities [53,54] or open quantum systems [55,56]. A quench introduces a "temporal boundary" by breaking the time-translational invariance (TTI) that characterizes equilibrium dynamics, causing the emergence of short-time universal scaling, analogous to universal short-distance scaling in the presence of spatial boundaries in equilibrium [57][58][59].…”

Section: Introductionmentioning

confidence: 99%

Short-time universal scaling in an isolated quantum system after a quench

et al. 2015

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Renormalization-group methods provide a viable approach for investigating the emergent collective behavior of classical and quantum statistical systems in both equilibrium and nonequilibrium conditions. Within this approach we investigate here the dynamics of an isolated quantum system represented by a scalar φ 4 theory after a global quench of the potential close to a dynamical critical point. We demonstrate that, within a pre-thermal regime, the time dependence of the relevant correlations is characterized by a short-time universal exponent, which we calculate at the lowest order in a dimensional expansion.

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Section: Introductionmentioning

confidence: 99%

Short-time universal scaling in an isolated quantum system after a quench

et al. 2015

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“…As this field is attracting increasing interest, it is of some value to connect the SPGPE model to related recent work. We note that non-Markovian additive noise was shown to generate modified dynamical exponents in a G-L model [40]. Interestingly, quantum quenches may leave important signatures behind in higher order operator moments [41]; such information is almost certainly absent from the classical field theory used in this work.…”

Section: Discussionmentioning

confidence: 80%

Reservoir interactions during Bose-Einstein condensation: Modified critical scaling in the Kibble-Zurek mechanism of defect formation

McDonald

Bradley

2015

Phys. Rev. A

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As a test of the Kibble-Zurek mechanism (KZM) of defect formation, we simulate the Bose-Einstein condensation transition in a toroidally confined Bose gas using the stochastic projected Gross-Pitaevskii equation (SPGPE), with and without the energy-damping reservoir interaction. Energy-damping alters the scaling of the winding number distribution with the quench time -a departure from the universal KZM theory that relies on equilibrium critical exponents. Numerical values are obtained for the correlation-length critical exponent ν and the dynamical critical exponent z for each variant of reservoir interaction theory. The energy-damping reservoir interactions cause significant modification of the dynamical critical exponent of the phase transition, whilst preserving the essential KZM critical scaling behavior. Comparison of numerical and analytical two-point correlation functions further illustrates the effect of energy damping on the correlation length during freeze out.

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“…We need to evaluate the short time behavior of the non-interacting Keldysh function g K (t, t ), for which it is useful to introduce a double Laplace-transformation (see Ref. 81)…”

Section: Quench From the Disordered Phasementioning

confidence: 99%

“…The analysis of the classical case was extended to colored noise in Ref. 81. Previously, we have reported results on the dissipative quantum ϕ 4 -model using a renormalizationgroup (RG) approach in non-equilibrium and calculated the new exponent θ in an expansion in = 4 − d − z close to the upper critical dimension 82 .…”

Section: Introductionmentioning

confidence: 99%

Universal postquench coarsening and aging at a quantum critical point

2015

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The non-equilibrium dynamics of a system that is located in the vicinity of a quantum critical point is affected by the critical slowing down of order-parameter correlations with the potential for novel out-of-equilibrium universality. After a quantum quench, i.e. a sudden change of a parameter in the Hamiltonian such a system is expected to almost instantly fall out of equilibrium and undergo aging dynamics, i.e. dynamics that depends on the time passed since the quench. Investigating the quantum dynamics of a N -component ϕ 4 -model coupled to an external bath, we determine this universal aging and demonstrate that the system undergoes a coarsening, governed by a critical exponent that is unrelated to the equilibrium exponents of the system. We analyze this behavior in the large-N limit, which is complementary to our earlier renormalization group analysis, allowing in particular the direct investigation of the order-parameter dynamics in the symmetry broken phase and at the upper critical dimension. By connecting the long time limit of fluctuations and response, we introduce a distribution function that shows that the system remains non-thermal and exhibits quantum coherence even on long timescales.

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Critical Langevin dynamics of the O(N) Ginzburg–Landau model with correlated noise

Cited by 15 publications

References 53 publications

Short-time universal scaling in an isolated quantum system after a quench

Short-time universal scaling in an isolated quantum system after a quench

Reservoir interactions during Bose-Einstein condensation: Modified critical scaling in the Kibble-Zurek mechanism of defect formation

Universal postquench coarsening and aging at a quantum critical point

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