arXiv subjects

Andrea Gambassi

Publications and source records attributed to Andrea Gambassi.

At least 37 records · Page 2Linked to original sources

arXiv2023

Critical Casimir forces in soft matter

We review recent advances in the theoretical, numerical, and experimental studies of critical Casimir forces in soft matter, with particular emphasis on their relevance for the structures of colloidal suspensions and on their dynamics. Distinct from other interactions which act in soft matter, such as electrostatic and van der Waals forces, critical Casimir forces are effective interactions characterised by the possibility to control reversibly their strength via minute temperature changes, while their attractive or repulsive character is conveniently determined via surface treatments or by structuring the involved surfaces. These features make critical Casimir forces excellent candidates for controlling the equilibrium and dynamical properties of individual colloids or colloidal dispersions as well as for possible applications in micro-mechanical systems. In the past 25 years a number of theoretical and experimental studies have been devoted to investigate these forces primarily under thermal equilibrium conditions, while their dynamical and non-equilibrium behaviour is a largely unexplored subject open for future investigations.

cond-mat.soft↗

arXiv2023

Large Deviations Beyond the Kibble-Zurek Mechanism

The Kibble-Zurek mechanism (KZM) predicts that the average number of topological defects generated upon crossing a continuous or quantum phase transition obeys a universal scaling law with the quench time. Fluctuations in the defect number near equilibrium are approximately of Gaussian form, in agreement with the central limit theorem. Using large deviations theory, we characterize the universality of fluctuations beyond the KZM and report the exact form of the rate function in the transverse-field quantum Ising model. In addition, we characterize the scaling of large deviations in an arbitrary continuous phase transition, building on recent evidence establishing the universality of the defect number distribution.

quant-ph↗

arXiv2023

Memory-induced oscillations of a driven particle in a dissipative correlated medium

The overdamped dynamics of a particle is in general affected by its interaction with the surrounding medium, especially out of equilibrium, and when the latter develops spatial and temporal correlations. Here we consider the case in which the medium is modeled by a scalar Gaussian field with relaxational dynamics, and the particle is dragged at constant velocity through the medium by a moving harmonic trap. This mimics the setting of an active microrheology experiment conducted in a near-critical medium. When the particle is displaced from its average position in the nonequilibrium steady state, its subsequent relaxation is shown to feature damped oscillations. This is similar to what has been recently predicted and observed in viscoelastic fluids, but differs from what happens in the absence of driving or for an overdamped Markovian dynamics, in which cases oscillations cannot occur. We characterize these oscillating modes in terms of the parameters of the underlying mesoscopic model for the particle and the medium, confirming our analytical predictions via numerical simulations.

cond-mat.stat-mech↗

arXiv2023

Non-Gaussian fluctuations of a probe coupled to a Gaussian field

The motion of a colloidal probe in a complex fluid, such as a micellar solution, is usually described by the generalized Langevin equation, which is linear. However, recent numerical simulations and experiments have shown that this linear model fails when the probe is confined, and that the intrinsic dynamics of the probe is actually non-linear. Noting that the kurtosis of the displacement of the probe may reveal the non-linearity of its dynamics also in the absence confinement, we compute it for a probe coupled to a Gaussian field and possibly trapped by a harmonic potential. We show that the excess kurtosis increases from zero at short times, reaches a maximum, and then decays algebraically at long times, with an exponent which depends on the spatial dimensionality and on the features and correlations of the dynamics of the field. Our analytical predictions are confirmed by numerical simulations of the stochastic dynamics of the probe and the field where the latter is represented by a finite number of modes.

cond-mat.stat-mech↗

arXiv2023

A hydrodynamic approach to Stark localization

When a free Fermi gas on a lattice is subject to the action of a linear potential it does not drift away, as one would naively expect, but it remains spatially localized. Here we revisit this phenomenon, known as Stark localization, within the recently proposed framework of generalized hydrodynamics. In particular, we consider the dynamics of an initial state in the form of a domain wall and we recover known results for the particle density and the particle current, while we derive analytical predictions for relevant observables such as the entanglement entropy and the full counting statistics. Then, we extend the analysis to generic potentials, highlighting the relationship between the occurrence of localization and the presence of peculiar closed orbits in phase space, arising from the lattice dispersion relation. We also compare our analytical predictions with numerical calculations and with the available results, finding perfect agreement. This approach paves the way for an exact treatment of the interacting case known as Stark many-body localization.

cond-mat.stat-mech↗

arXiv2023

Taxis of cargo-carrying microswimmers in traveling activity waves

Many fascinating properties of biological active matter crucially depend on the capacity of constituting entities to perform directed motion, e.g., molecular motors transporting vesicles inside cells or bacteria searching for food. While much effort has been devoted to mimicking biological functions in synthetic systems, such as transporting a cargo to a targeted zone, theoretical studies have primarily focused on single active particles subject to various spatial and temporal stimuli. Here we study the behavior of a self-propelled particle carrying a passive cargo in a travelling activity wave and show that this active-passive dimer displays a rich, emergent tactic behavior. For cargoes with low mobility, the dimer always drifts in the direction of the wave propagation. For highly-mobile cargoes, instead, the dimer can also drift against the traveling wave. The transition between these two tactic behaviors is controlled by the ratio between the frictions of the cargo and the microswimmer. In slow activity waves the dimer can perform an active surfing of the wave maxima, with an average drift velocity equal to the wave speed. These analytical predictions, which we confirm by numerical simulations, might be useful for the future efficient design of bio-hybrid microswimmers.

cond-mat.stat-mech↗

arXiv2023

Interface dynamics in the two-dimensional quantum Ising model

In a recent paper [Phys. Rev. Lett. 129, 120601] we have shown that the dynamics of interfaces, in the symmetry-broken phase of the two-dimensional ferromagnetic quantum Ising model, displays a robust form of ergodicity breaking. In this paper, we elaborate more on the issue. First, we discuss two classes of initial states on the square lattice, the dynamics of which is driven by complementary terms in the effective Hamiltonian and may be solved exactly: (a) strips of consecutive neighbouring spins aligned in the opposite direction of the surrounding spins, and (b) a large class of initial states, characterized by the presence of a well-defined "smooth" interface separating two infinitely extended regions with oppositely aligned spins. The evolution of the latter states can be mapped onto that of an effective one-dimensional fermionic chain, which is integrable in the infinite-coupling limit. In this case, deep connections with noteworthy results in mathematics emerge, as well as with similar problems in classical statistical physics. We present a detailed analysis of the evolution of these interfaces both on the lattice and in a suitable continuum limit, including the interface fluctuations and the dynamics of entanglement entropy. Second, we provide analytical and numerical evidence supporting the conclusion that the observed non-ergodicity -- arising from Stark localization of the effective fermionic excitations -- persists away from the infinite-Ising-coupling limit, and we highlight the presence of a timescale $T\sim e^{c L\ln L}$ for the decay of a region of large linear size $L$. The implications of our work for the classic problem of the decay of a false vacuum are also discussed.

cond-mat.stat-mech↗

arXiv2022

Stochastic Representation of the Quantum Quartic Oscillator

Recent experimental advances have inspired the development of theoretical tools to describe the non-equilibrium dynamics of quantum systems. Among them an exact representation of quantum spin systems in terms of classical stochastic processes has been proposed. Here we provide first steps towards the extension of this stochastic approach to bosonic systems by considering the one-dimensional quantum quartic oscillator. We show how to exactly parameterize the time evolution of this prototypical model via the dynamics of a set of classical variables. We interpret these variables as stochastic processes, which allows us to propose a novel way to numerically simulate the time evolution of the system. We benchmark our findings by considering analytically solvable limits and providing alternative derivations of known results.

quant-ph↗

arXiv2022

Inducing oscillations of trapped particles in a near-critical Gaussian field

We study the nonequilibrium dynamics of two particles confined in two spatially separated harmonic potentials and linearly coupled to the same thermally fluctuating scalar field, a cartoon for optically trapped colloids in contact with a medium close to a continuous phase transition. When an external periodic driving is applied to one of these particles, a nonequilibrium periodic state is eventually reached in which their motion synchronizes thanks to the field-mediated effective interaction, a phenomenon already observed in experiments. We fully characterize the nonlinear response of the second particle as a function of the driving frequency, and in particular far from the adiabatic regime in which the field can be assumed to relax instantaneously. We compare the perturbative, analytic solution to its adiabatic approximation, thus determining the limits of validity of the latter, and we qualitatively test our predictions against numerical simulations.

cond-mat.stat-mech↗

arXiv2022

Localization and melting of interfaces in the two-dimensional quantum Ising model

We study the non-equilibrium evolution of coexisting ferromagnetic domains in the two-dimensional quantum Ising model -- a setup relevant in several contexts, from quantum nucleation dynamics and false-vacuum decay scenarios to recent experiments with Rydberg-atom arrays. We demonstrate that the quantum-fluctuating interface delimiting a large bubble can be studied as an effective one-dimensional system through a "holographic" mapping. For the considered model, the emergent interface excitations map to an integrable chain of fermionic particles. We discuss how this integrability is broken by geometric features of the bubbles and by corrections in inverse powers of the ferromagnetic coupling, and provide a lower bound to the timescale after which the bubble is ultimately expected to melt. Remarkably, we demonstrate that a symmetry-breaking longitudinal field gives rise to a robust ergodicity breaking in two dimensions, a phenomenon underpinned by Stark many-body localization of the emergent fermionic excitations of the interface.

cond-mat.stat-mech↗

arXiv2022

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

We study the non-equilibrium 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 assume fast field relaxation. The predictions of the analytic, perturbative approach are qualitatively confirmed by numerical simulations.

cond-mat.stat-mech↗

arXiv2022

First-passage time of run-and-tumble particles with non-instantaneous resetting

We study the statistics of the first-passage time of a single run and tumble particle (RTP) in one spatial dimension, with or without resetting, to a fixed target located at $L>0$. First, we compute the first-passage time distribution of a free RTP, without resetting nor in a confining potential, but averaged over the initial position drawn from an arbitrary distribution $p(x)$. Recent experiments used a non-instantaneous resetting protocol that motivated us to study in particular the case where $p(x)$ corresponds to the stationary non-Boltzmann distribution of an RTP in the presence of a harmonic trap. This distribution $p(x)$ is characterized by a parameter $ν>0$, which depends on the microscopic parameters of the RTP dynamics. We show that the first-passage time distribution of the free RTP, drawn from this initial distribution, develops interesting singular behaviours, depending on the parameter $ν$. We then switch on resetting, mimicked by thermal relaxation of the RTP in the presence of a harmonic trap. Resetting leads to a finite mean first-passage time (MFPT) and we study this as a function of the resetting rate for different values of the parameters $ν$ and $b = L/c$ where $c$ is the right edge of the initial distribution $p(x)$. In the diffusive limit of the RTP dynamics, we find a rich phase diagram in the $(b,ν)$ plane, with an interesting re-entrance phase transition. Away from the diffusive limit, qualitatively similar rich behaviours emerge for the full RTP dynamics.

cond-mat.stat-mech↗

arXiv2022

Tunable critical Casimir forces counteract Casimir-Lifshitz attraction

Casimir forces in quantum electrodynamics emerge between microscopic metallic objects because of the confinement of the vacuum electromagnetic fluctuations occurring even at zero temperature. Their generalization at finite temperature and in material media are referred to as Casimir--Lifshitz forces. These forces are typically attractive, leading to the widespread problem of stiction between the metallic parts of micro- and nanodevices. Recently, repulsive Casimir forces have been experimentally realized but their reliance on specialized materials prevents their dynamic control and thus limits their further applicability. Here, we experimentally demonstrate that repulsive critical Casimir forces, which emerge in a critical binary liquid mixture upon approaching the critical temperature, can be used to actively control microscopic and nanoscopic objects with nanometer precision. We demonstrate this by using critical Casimir forces to prevent the stiction caused by the Casimir--Lifshitz forces. We study a microscopic gold flake above a flat gold-coated substrate immersed in a critical mixture. Far from the critical temperature, stiction occurs because of dominant Casimir--Lifshitz forces. Upon approaching the critical temperature, however, we observe the emergence of repulsive critical Casimir forces that are sufficiently strong to counteract stiction. This experimental demonstration can accelerate the development of micro- and nanodevices by preventing stiction as well as providing active control and precise tunability of the forces acting between their constituent parts.

cond-mat.soft↗

arXiv2022

Modelling Active Non-Markovian Oscillations

Modelling noisy oscillations of active systems is one of the current challenges in physics and biology. Because the physical mechanisms of such processes are often difficult to identify, we propose a linear stochastic model driven by a non-Markovian bistable noise that is capable of generating self-sustained periodic oscillation. We derive analytical predictions for most relevant dynamical and thermodynamic properties of the model. This minimal model turns out to describe accurately bistable-like oscillatory motion of hair bundles in bullfrog sacculus, extracted from experimental data. Based on and in agreement with these data, we estimate the power required to sustain such active oscillations to be of the order of one hundred $k_B T$ per oscillation cycle.

cond-mat.stat-mech↗

arXiv2021

Universal amplitudes ratios for critical aging via functional renormalization group

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.

cond-mat.stat-mech↗

arXiv2021

Stochastic dynamics of chemotactic colonies with logistic growth

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.

cond-mat.stat-mech↗

arXiv2021

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

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 $n\to\infty$. 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 $n\to\infty$ 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.

cond-mat.stat-mech↗

arXiv2021

Critical properties of the prethermal Floquet Time Crystal

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 absence of long-range spatial order from the non-trivial 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 $N\to\infty$, 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 $ω/(2 v)$, $v$ being the velocity of the quasiparticles, and $ω$ being the drive frequency.

cond-mat.stat-mech↗