Universal amplitudes ratios for critical aging via functional renormalization group

Vodret M., Chiocchetta A., We discuss how to calculate non-equilibrium universal amplitude ratios in the functional renormalization group approach, extending its applicability. In particular, we focus on the critical relaxation of the Ising model with non-conserved dynamics (model A) and calculate the universal amplitude ratio associated with the fluctuation-dissipation ratio of the order parameter, considering a critical quench from a high-temperature initial condition. Our predictions turn out to be in good agreement with previous perturbative renormalization-group calculations and Monte Carlo simulations.

Nonequilibrium relaxation of a trapped particle in a near-critical Gaussian field

Venturelli D., Ferraro F., We study the nonequilibrium relaxational dynamics of a probe particle linearly coupled to a thermally fluctuating scalar field and subject to a harmonic potential, which provides a cartoon for an optically trapped colloid immersed in a fluid close to its bulk critical point. The average position of the particle initially displaced from the position of mechanical equilibrium is shown to feature long-time algebraic tails as the critical point of the field is approached, the universal exponents of which are determined in arbitrary spatial dimensions. As expected, this behavior cannot be captured by adiabatic approaches which assumes fast field relaxation. The predictions of the analytic, perturbative approach are qualitatively confirmed by numerical simulations.

Stochastic dynamics of chemotactic colonies with logistic growth

Ben Alì Zinati R., Duclut C., Mahdisoltani S., The interplay between cellular growth and cell-cell signaling is essential for the aggregation and proliferation of bacterial colonies, as well as for the self-organization of cell tissues. To investigate this interplay, we focus here on the collective properties of dividing chemotactic cell colonies by studying their long-time and large-scale dynamics through a renormalization group (RG) approach. The RG analysis reveals that a relevant but unconventional chemotactic interaction - corresponding to a polarity-induced mechanism - is generated by fluctuations at macroscopic scales, even when an underlying mechanism is absent at the microscopic level. This emerges from the interplay of the well-known Keller-Segel (KS) chemotactic nonlinearity and cell birth and death processes. At one-loop order, we find no stable fixed point of the RG flow equations. We discuss a connection between the dynamics investigated here and the celebrated Kardar-Parisi-Zhang (KPZ) equation with long-range correlated noise, which points at the existence of a strong-coupling, nonperturbative fixed point. ©

Non-equilibrium dynamics of the open quantum O(n)-model with non-Markovian noise: Exact results

Wald S., Henkel M., The collective and purely relaxational dynamics of quantum many-body systems after a quench at temperature T = 0, from a disordered state to various phases is studied through the exact solution of the quantum Langevin equation of the spherical and the O(n)-model in the limit n → ∞. The stationary state of the quantum dynamics is shown to be a non-equilibrium state. The quantum spherical and the quantum O(n)-model for n → ∞ are in the same dynamical universality class. The long-time behaviour of single-time and two-time correlation and response functions is analysed and the universal exponents which characterise quantum coarsening and quantum ageing are derived. The importance of the non-Markovian long-time memory of the quantum noise is elucidated by comparing it with an effective Markovian noise having the same scaling behaviour and with the case of non-equilibrium classical dynamics.

Critical properties of the prethermal Floquet time crystal

Natsheh M., The critical properties characterizing the formation of the Floquet time crystal in the prethermal phase are investigated analytically in the periodically driven O(N) model. In particular, we focus on the critical line separating the trivial phase with period synchronized dynamics and the absence of long-range spatial order from the nontrivial phase where long-range spatial order is accompanied by period-doubling dynamics. In the vicinity of the critical line, with a combination of dimensional expansion and exact solution for N→∞, we determine the exponent ν that characterizes the divergence of the spatial correlation length of the equal-time correlation functions, the exponent β characterizing the growth of the amplitude of the order parameter, as well as the initial-slip exponent θ of the aging dynamics when a quench is performed from deep in the trivial phase to the critical line. The exponents ν,β,θ are found to be identical to those in the absence of the drive. In addition, the functional form of the aging is found to depend on whether the system is probed at times that are small or large compared to the drive period. The spatial structure of the two-point correlation functions, obtained as a linear response to a perturbing potential in the vicinity of the critical line, is found to show algebraic decays that are longer ranged than in the absence of a drive, and besides being period doubled are also found to oscillate in space at the wave vector ω/(2v), v being the velocity of the quasiparticles, and ω being the drive frequency.

Fluctuations of the critical Casimir force

Gross M., The critical Casimir force (CCF) arises from confining fluctuations in a critical fluid and thus it is a fluctuating quantity itself. While the mean CCF is universal, its (static) variance has previously been found to depend on the microscopic details of the system which effectively set a large-momentum cutoff in the underlying field theory, rendering it potentially large. This raises the question how the properties of the force variance are reflected in experimentally observable quantities, such as the thickness of a wetting film or the position of a suspended colloidal particle. Here, based on a rigorous definition of the instantaneous force, we analyze static and dynamic correlations of the CCF for a conserved fluid in film geometry for various boundary conditions within the Gaussian approximation. We find that the dynamic correlation function of the CCF is independent of the momentum cutoff and decays algebraically in time. Within the Gaussian approximation, the associated exponent depends only on the dynamic universality class but not on the boundary conditions. We furthermore consider a fluid film, the thickness of which can fluctuate under the influence of the time-dependent CCF. The latter gives rise to an effective non-Markovian noise in the equation of motion of the film boundary and induces a distinct contribution to the position variance. Within the approximations used here, at short times, this contribution grows algebraically in time whereas, at long times, it saturates and contributes to the steady-state variance of the film thickness.

Optical trapping and critical Casimir forces

Callegari A., Magazzù A., Critical Casimir forces emerge between objects, such as colloidal particles, whenever their surfaces spatially confine the fluctuations of the order parameter of a critical liquid used as a solvent. These forces act at short but microscopically large distances between these objects, reaching often hundreds of nanometers. Keeping colloids at such distances is a major experimental challenge, which can be addressed by the means of optical tweezers. Here, we review how optical tweezers have been successfully used to quantitatively study critical Casimir forces acting on particles in suspensions. As we will see, the use of optical tweezers to experimentally study critical Casimir forces can play a crucial role in developing nano-technologies, representing an innovative way to realize self-assembled devices at the nano- and microscale.

Nonequilibrium polarity-induced chemotaxis: Emergent Galilean symmetry and exact scaling exponents

Mahdisoltani S., Zinati R.B.A., Duclut C., A generically observed mechanism that drives the self-organization of living systems is interaction via chemical signals among the individual elements - which may represent cells, bacteria, or even enzymes. Here we propose an unconventional mechanism for such interactions, in the context of chemotaxis, which originates from the polarity of the particles and which generalizes the well-known Keller-Segel interaction term. We study the resulting large-scale dynamical properties of a system of such chemotactic particles using the exact stochastic formulation of Dean and Kawasaki along with dynamical renormalization group analysis of the critical state of the system. At this critical point, an emergent "Galilean"symmetry is identified, which allows us to obtain the dynamical scaling exponents exactly. These exponents reveal superdiffusive density fluctuations and non-Poissonian number fluctuations. We expect our results to shed light on how molecular regulation of chemotactic circuits can determine large-scale behavior of cell colonies and tissues.

Critical properties of the Floquet time crystal within the Gaussian approximation

Natsheh M., The periodically driven O(N) model is studied near the critical line separating a disordered paramagnetic phase from a period doubled phase, the latter being an example of a Floquet time crystal. The time evolution of one-point and two-point correlation functions are obtained within the Gaussian approximation and perturbatively in the drive amplitude. The correlations are found to show not only period doubling, but also power-law decays at large spatial distances. These features are compared with the undriven O(N) model, within the Gaussian approximation, in the vicinity of the paramagnetic-ferromagnetic critical point. The algebraic decays in space are found to be qualitatively different in the driven and the undriven cases. In particular, the spatiotemporal order of the Floquet time crystal leads to position-momentum and momentum-momentum correlation functions which are more long-ranged in the driven than in the undriven model. The light-cone dynamics associated with the correlation functions is also qualitatively different as the critical line of the Floquet time crystal shows a light cone with two distinct velocities, with the ratio of these two velocities scaling as the square-root of the dimensionless drive amplitude. The Floquet unitary, which describes the time evolution due to a complete cycle of the drive, is constructed for modes with small momenta compared to the drive frequency, but having a generic relationship with the square-root of the drive amplitude. At intermediate momenta, which are large compared to the square-root of the drive amplitude, the Floquet unitary is found to simply rotate the modes. On the other hand, at momenta which are small compared to the square-root of the drive amplitude, the Floquet unitary is found to primarily squeeze the modes, to an extent which increases upon increasing the wavelength of the modes, with a power-law dependence on it.

Controlling particle currents with evaporation and resetting from an interval

Tucci G., We investigate the Brownian diffusion of particles in one spatial dimension and in the presence of finite regions within which particles can either evaporate or be reset to a given location. For open boundary conditions, we highlight the appearance of a Brownian yet non-Gaussian diffusion: At long times, the particle distribution is non-Gaussian but its variance grows linearly in time. Moreover, we show that the effective diffusion coefficient of the particles in such systems is bounded from below by 1-2/π times their bare diffusion coefficient. For periodic boundary conditions, i.e., for diffusion on a ring with resetting, we demonstrate a "gauge invariance"of the spatial particle distribution for different choices of the resetting probability currents, in both stationary and nonstationary regimes. Finally, we apply our findings to a stochastic biophysical model for the motion of RNA polymerases during transcriptional pauses, deriving analytically the distribution of the length of cleaved RNA transcripts and the efficiency of RNA cleavage in backtrack recovery.

Dynamics of large deviations in the hydrodynamic limit: Noninteracting systems

Perfetto G., We study the dynamics of the statistics of the energy transferred across a point along a quantum chain which is prepared in the inhomogeneous initial state obtained by joining two identical semi-infinite parts thermalized at two different temperatures. In particular, we consider the transverse field Ising and harmonic chains as prototypical models of noninteracting fermionic and bosonic excitations, respectively. Within the so-called hydrodynamic limit of large space-time scales we first discuss the mean values of the energy density and current, and then, aiming at the statistics of fluctuations, we calculate exactly the scaled cumulant generating function of the transferred energy. From the latter, the evolution of the associated large deviation function is obtained. A natural interpretation of our results is provided in terms of a semiclassical picture of quasiparticles moving ballistically along classical trajectories. Similarities and differences between the transferred energy scaled cumulant and the large deviation functions in the cases of noninteracting fermions and bosons are discussed.

Quasilocalized dynamics from confinement of quantum excitations

Lerose A., Surace F.M., Mazza P.P., Perfetto G., Collura M., Confinement of excitations induces quasilocalized dynamics in disorder-free isolated quantum many-body systems in one spatial dimension. This occurrence is signaled by severe suppression of quantum correlation spreading and of entanglement growth, long-time persistence of spatial inhomogeneities, and long-lived coherent oscillations of local observables. In this work, we present a unified understanding of these dramatic effects. The slow dynamical behavior is shown to be related to the Schwinger effect in quantum electrodynamics. We demonstrate that it is quantitatively captured for long-time scales by effective Hamiltonians exhibiting Stark localization of excitations and weak growth of the entanglement entropy for arbitrary coupling strength. This analysis explains the phenomenology of real-time string dynamics investigated in a number of lattice gauge theories, as well as the anomalous dynamics observed in quantum Ising chains after quenches. Our findings establish confinement as a robust mechanism for hindering the approach to equilibrium in translationally invariant quantum statistical systems with local interactions.

Erratum: Controlling the dynamics of colloidal particles by critical Casimir forces (Soft Matter (2019) 15 (2152-2162) DOI: 10.1039/C8SM01376D)

Magazzù A., Callegari A., Staforelli J.P., The authors regret an error in the grant number for one of the authors in the Acknowledgements section. The Acknowledgements section should read as follows: This work was partially supported by the ERC Starting Grant ComplexSwimmers (grant no. 677511) and by Vetenskapsrådet (grant no. 2016-03523). A. C. acknowledges partial financial support from TUBITAK (grant no. 116F111). J. P. S. acknowledges partial financial support from FONDECYT (grant no. 1171013). The Royal Society of Chemistry apologises for these errors and any consequent inconvenience to authors and reade

Lattice Gauge Theories and String Dynamics in Rydberg Atom Quantum Simulators

Surace F.M., Mazza P.P., Giudici G., Lerose A., Gauge theories are the cornerstone of our understanding of fundamental interactions among elementary particles. Their properties are often probed in dynamical experiments, such as those performed at ion colliders and high-intensity laser facilities. Describing the evolution of these strongly coupled systems is a formidable challenge for classical computers and represents one of the key open quests for quantum simulation approaches to particle physics phenomena. In this work, we show how recent experiments done on Rydberg atom chains naturally realize the real-time dynamics of a lattice gauge theory at system sizes at the boundary of classical computational methods. We prove that the constrained Hamiltonian dynamics induced by strong Rydberg interactions maps exactly onto the one of a U(1) lattice gauge theory. Building on this correspondence, we show that the recently observed anomalously slow dynamics corresponds to a string-inversion mechanism, reminiscent of the string breaking typically observed in gauge theories. This underlies the generality of this slow dynamics, which we illustrate in the context of one-dimensional quantum electrodynamics on the lattice. Within the same platform, we propose a set of experiments that generically show long-lived oscillations, including the evolution of particle-antiparticle pairs, and discuss how a tunable topological angle can be realized, further affecting the dynamics following a quench. Our work shows that the state of the art for quantum simulation of lattice gauge theories is at 51 qubits and connects the recently observed slow dynamics in atomic systems to archetypal phenomena in particle physics.

Dynamics of uctuations in the Gaussian model with dissipative Langevin Dynamics

Corberi F., Mazzarisi O., We study the dynamics of the fluctuations of the variance s of the order parameter of the Gaussian model, following a temperature quench of the thermal bath. At each time t, there is a critical value s c(t) of s such that fluctuations with s > sc (t) are realized by condensed configurations of the systems, i.e., a single degree of freedom contributes macroscopically to s. This phenomenon, which is closely related to the usual condensation occurring on average quantities, is usually referred to as condensation of fluctuations. We show that the probability of fluctuations with s < inft[sc (t)], associated to configurations that never condense, after the quench converges rapidly and in an adiabatic way towards the new equilibrium value. The probability of fluctuations with s > inft[sc (t)], instead, displays a slow and more complex behavior, because the macroscopic population of the condensing degree of freedom is involved.

Universal late-time dynamics in isolated one-dimensional statistical systems with topological excitations

Bastianello A., Chiocchetta A., Cugliandolo L.F., We investigate the nonequilibrium dynamics of a class of isolated one-dimensional systems possessing two degenerate ground states, initialized in a low-energy symmetric phase. We report the emergence of a timescale separation between fast (radiation) and slow (kink or domain wall) degrees of freedom. We find a universal long-time dynamics, largely independent of the microscopic details of the system, in which the kinks control the relaxation of relevant observables and correlations. The resulting late-time dynamics can be described by a set of phenomenological equations, which yield results in excellent agreement with the numerical tests.

Dynamics of fluctuations in the Gaussian model with conserved dynamics

Corberi F., Mazzarisi O., We study the fluctuations of the Gaussian model, with conservation of the order parameter, evolving in contact with a thermal bath quenched from an initial inverse temperatureto a final one. At every time there exists a critical value of the variance s of the order parameter per degree of freedom such that the fluctuations with are characterized by a macroscopic contribution of the zero wavevector mode, similarly to what occurs in an ordinary condensation transition. We show that the probability of fluctuations with>, for which condensation never occurs, rapidly converges towards a stationary behavior. By contrast, the process of populating the zero wavevector mode of the variance, which takes place for , induces a slow non-equilibrium dynamics resembling that of systems quenched across a phase transition.

Prethermal quantum many-body Kapitza phases of periodically driven spin systems

Lerose A., Marino J., As realized by Kapitza long ago, a rigid pendulum can be stabilized upside down by periodically driving its suspension point with tuned amplitude and frequency. While this dynamical stabilization is feasible in a variety of systems with few degrees of freedom, it is natural to search for generalizations to multiparticle systems. In particular, a fundamental question is whether, by periodically driving a single parameter in a many-body system, one can stabilize an otherwise unstable phase of matter against all possible fluctuations of its microscopic degrees of freedom. In this paper, we show that such stabilization occurs in experimentally realizable quantum many-body systems: A periodic modulation of a transverse magnetic field can make ferromagnetic spin systems with long-range interactions stably trapped around unstable paramagnetic configurations as well as in other unconventional dynamical phases with no equilibrium counterparts. We demonstrate that these quantum Kapitza phases have a long lifetime and can be observed in current experiments with trapped ions.

Quench action and large deviations: Work statistics in the one-dimensional Bose gas

Perfetto G., Piroli L., We study the statistics of large deviations of the intensive work done in an interaction quench of a one-dimensional Bose gas with a large number N of particles, system size L, and fixed density. We consider the case in which the system is initially prepared in the noninteracting ground state and a repulsive interaction is suddenly turned on. For large deviations of the work below its mean value, we show that the large-deviation principle holds by means of the quench action approach. Using the latter, we compute exactly the so-called rate function and study its properties analytically. In particular, we find that fluctuations close to the mean value of the work exhibit a marked non-Gaussian behavior, even though their probability is always exponentially suppressed below it as L increases. Deviations larger than the mean value exhibit an algebraic decay whose exponent cannot be determined directly by large-deviation theory. Exploiting the exact Bethe ansatz representation of the eigenstates of the Hamiltonian, we calculate this exponent for vanishing particle density. Our approach can be straightforwardly generalized to quantum quenches in other interacting integrable systems.

Suppression of transport in nondisordered quantum spin chains due to confined excitations

Mazza P.P., Perfetto G., Lerose A., Collura M., The laws of thermodynamics require any initial macroscopic inhomogeneity in extended many-body systems to be smoothed out by the time evolution through the activation of transport processes. In generic quantum systems, transport is expected to be governed by a diffusion law, whereas a sufficiently strong quenched disorder can suppress it completely due to many-body localization of quantum excitations. Here, we show that the confinement of quasiparticles can also suppress transport even if the dynamics are generated by nondisordered Hamiltonians. We demonstrate this in the quantum Ising chain with transverse and longitudinal magnetic fields, prepared in a paradigmatic state with a domain wall and thus with a spatially varying energy density. We perform extensive numerical simulations of the dynamics which turn out to be in excellent agreement with an effective analytical description valid within both weak and strong confinement regimes. Our results show that the energy flow from "hot" to "cold" regions of the chain is suppressed for all accessible times. We argue that this phenomenon is general, as it relies solely on the emergence of confinement of excitations.