arXiv subjects

Gabriele de Mauro

Publications and source records attributed to Gabriele de Mauro.

4 recordsLinked to original sources

arXiv2026

Tuning the strength of emergent correlations in a Brownian gas via batch resetting

We study a gas of $N$ diffusing particles on the line subject to batch resetting: at rate $r$, a uniformly random subset of $m$ particles is reset to the origin. Despite the absence of interactions, the dynamics generates a nonequilibrium stationary state (NESS) with long-range correlations. Since standard renewal methods fail for $m<N$, we introduce a new general Fokker--Planck framework with an exact recursive closure of marginal densities. We obtain exact results, both for the NESS and for the time dependence of the correlations, which are valid for arbitrary $m$ and $N$. By varying $m$, the system interpolates between an uncorrelated regime ($m=1$) and the fully synchronous resetting case ($m=N$). For all $1<m<N$, correlations exhibit a non-monotonic time dependence due to the emergence of an intrinsic decorrelation mechanism. In the stationary state, the correlation strength can be tuned by varying $m$, and it displays a transition at a critical value $N_c=6$. Our predictions extend to any spatial dimension $d$, where the critical value $N_c=6$ remains unchanged, and they are experimentally testable in existing optical-trap setups.

cond-mat.stat-mech↗

arXiv2026

Quantum resetting with memory

We introduce a quantum stochastic resetting protocol with uniform memory, in which each resetting event returns the system to a state visited at a time chosen uniformly from its entire history. The resulting dynamics is nonunitary, non-Markovian and a direct quantum generalization of the classical preferential relocation model. Working in the energy eigenbasis, we derive the exact evolution of every density-matrix element for an arbitrary time-independent Hamiltonian and show that the Hamiltonian enters the dynamics only through the corresponding Bohr frequencies. This leads to a natural distinction between two classes of quantum systems: gapped and gapless. In \emph{gapped systems} (systems with a discrete energy spectrum), while the diagonal elements remain unchanged, the off-diagonal elements of the density matrix in the energy eigenbasis decay algebraically with a continuously varying exponent and with an amplitude that oscillates periodically in $\log t$. The system therefore approaches a stationary state that is independent of the resetting rate and retains a strong memory of the initial state. In \emph{gapless systems} (systems with a continuous energy spectrum), arbitrarily small Bohr frequencies prevent stationarity. Instead, the position distribution spreads on the universal (ultra-slow) scale $\log(rt)/r$, independently of the initial state and of the details of the Hamiltonian. We illustrate these results with a two-level system, a harmonic oscillator, and a free quantum particle, and contrast them with their classical counterparts.

cond-mat.stat-mech↗

arXiv2026

Effects of confinement in a Brownian gas with simultaneous stochastic resetting and dynamically emergent correlations

We study $N$ non-interacting Brownian particles in an external potential under simultaneous stochastic resetting to the origin. Although they do not interact directly, common resets generate strong dynamically emergent correlations (DEC). We analyze how confinement modifies these correlations and the nonequilibrium stationary state for $V(x)=κ|x|^α$, $α\geq0$, focusing mainly on two analytically tractable cases: harmonic confinement (HC), $α=2$, and box confinement (BC), $α\to\infty$. In both cases the stationary state is controlled by the competition between confinement and resetting lengths. We derive exact results for the stationary joint distribution, density, correlations, extreme value statistics (EVS), and gap statistics. While the density behaves similarly in HC and BC, the normalized correlation coefficient differs sharply. In BC it is non-monotonic and overshoots the unconfined value, as hard walls suppress decorrelating trajectories. In HC it instead increases monotonically toward the unconfined limit. For general $α$, the behavior is monotonic for $0<α<α_c=1+\sqrt{5}$ and non-monotonic for $α>α_c$. The difference between HC and BC is also visible in edge observables. In HC, the maximum scales as $M_1=O(\sqrt{\ln N})$ and has a limiting distribution with bounded support and a shape transition controlled by the ratio of the two length scales. In BC, the maximum is at distance $O(1/N)$ from the boundary, as in equilibrium, but its fluctuations have a broad power-law tail with logarithmic corrections. The first gap shows a similar contrast: BC gives a smaller typical gap but stronger anomalous fluctuations than HC. Finally, we extend the EVS analysis to general $α$ and identify, via simulations and scaling arguments, three universality classes: $0\leqα\leq1$, $1<α<\infty$, and the singular limit $α\to\infty$.

cond-mat.stat-mech↗

arXiv2026

Dynamically emergent correlations in Brownian particles subject to simultaneous non-Poissonian resetting protocols

We consider a one-dimensional gas of $N$ independent Brownian particles subject to simultaneous stochastic resetting, with inter-reset times drawn from a general waiting-time distribution $ψ(τ)$. This includes the well-known Poissonian case, where $ψ(τ)=re^{-rτ}$, and extends to more general classes of resetting, such as heavy-tailed and bounded distributions. We show that the simultaneous resetting generates correlations between particles dynamically. These correlations grow with time and eventually drive the system into a strongly correlated non-equilibrium stationary state (NESS). Exploiting the renewal structure of the resetting dynamics, we derive explicit analytical expressions for the joint distribution of the positions of the particles in the NESS. We show that the NESS has a conditionally independent and identically distributed (CIID) structure that enables us to compute various physical observables exactly for arbitrary $ψ(τ)$. These observables include the average density, extreme value and order statistics, the spacing distribution between consecutive particles and the full counting statistics, i.e., the distribution of the number of particles in a given interval centered at the origin. We discuss the universal features of the large $N$ scaling behaviors of these observables for different choices of the resetting protocol $ψ(τ)$. Our results provide an interesting example of a stochastic control whereby, by tuning the inter-reset distribution $ψ(τ)$, one can generate a class of tunable, and yet solvable, strongly correlated NESS in a many-body system.

cond-mat.stat-mech↗