arXiv subjects

Giuseppe Del Vecchio Del Vecchio

Publications and source records attributed to Giuseppe Del Vecchio Del Vecchio.

15 recordsLinked to original sources

arXiv2026

Partial Localization and Multifractality in Heterogeneous Population Growth with Resetting

We study a model of heterogeneous multiplicative growth with mean-field redistribution and independent local stochastic resetting. The model describes populations or wealth distributed over sites with quenched growth-rate heterogeneity, while resets represent random local extinction or bankruptcy events. At large redistribution or resetting rate, we find a delocalized phase and we compute the growth rate as well as the stationary distribution of the population of a given site. We show that reset-free growth episodes generate power-law stationary tails with site-dependent exponents. For weak resetting and redistribution, favorable sites can undergo long reset-free episodes and localize. This produces a partially localized phase, in which a finite fraction of the total population is carried by a small set of sites whose identity changes on an $O(1)$ time scale within a subextensive pool of $N^{u^\star}$ favorable candidates, with $0<u^\star<1$. We derive the corresponding growth rate from a saddle point analysis, and show that the averaged stationary fractions display multifractal behavior.

cond-mat.stat-mech↗

arXiv2026

On the relaxation problem in statistical mechanics

We reformulate the relaxation problem in statistical mechanics by making explicit what are the \emph{operational} objects subject to relaxation: the local time statistics of the recorded signal $Z(t)$. These local time statistics are simply the estimated histograms of observations $\{Z(t_i)\}_{i=1}^M$ performed at uniformly random times $\{t_i\}_{i=1}^M$ by a clockless observer. The subject of prediction is a belief about a future fresh out-of-sample reading of a measurement outcome whose distribution is inferred from the mathematical model believed to be true. For finite bounded systems of $N\ge 1$ degrees of freedom global irreversible relaxation of predictions can occur but special initial conditions exist. The form of the predictions depends on certain loss functions whose choice is up to the particular observer. Finally, entropy is given a learning interpretation as mutual information between the observer and the unknown past of the system under consideration and, in complete generality, its stationary value depends on the information available.

cond-mat.stat-mech↗

arXiv2026

A transition in the hole probability at finite temperature for free fermions in $d$ dimensions

In a free Fermi gas at temperature $T$ much higher than the Fermi temperature one expects that the fluctuations of the number of particles in a given region has Poissonian/classical statistics. On the other hand at low temperature the Pauli exclusion principle leads to non trivial counting statistics. It is of great interest from a theoretical and experimental point of view to characterize the crossover between these two limits. Here we focus on the hole probability $P(R,T)$, i.e. the probability that a region of size $R$ is devoid of particles, in dimension $d$, and on the case of a spherical region of large radius $R$. We show that at low temperature it takes the scaling form $P(R,T)\sim \exp\big[-(k_F R)^{d+1}Φ_d(u=2R\,T/k_F)\big],$ where $k_F$ is the Fermi momentum. By mapping the problem to an effective Coulomb gas, we compute exactly the scaling function $Φ_d(u)$ in any dimension. Remarkably, it exhibits a transition of order $\tfrac{3}{2}(d+1)$ at the universal critical value $u_c=2/π$, signaling a sharp change in the mechanism of rare fluctuations, associated with the emergence of a macroscopic gap in the optimal density of the associated Coulomb gas. Our analytical predictions are supported by precise numerical evaluations of the corresponding Fredholm determinants.

cond-mat.stat-mech↗

arXiv2026

Sluggish quantum mechanics of noninteracting fermions with spatially varying effective mass

We analyze a class of one-dimensional quantum systems characterized by a position-dependent kinetic term arising as the continuum limit of an inhomogeneous tight-binding model with spatially varying hopping amplitudes. In this limit, the Schrodinger equation takes the so-called BenDaniel-Duke form with an effective mass, scaling as $m_{eff}(x) = m_{eff}|x|^α$ with $α> 0$, leading to a framework we term sluggish quantum mechanics, where particle motion is progressively suppressed at larger distances. Both without any external potential and with $V_{ext}(x)=\frac{1}{2}m_{eff}ω^2 |x|^{α+2}$, we obtain the eigenfunctions and the quantum propagators exactly. We then investigate the problem of $N$ noninteracting spinless fermions in the trap, determining the many-body ground-state wavefunction and the joint probability density function of the positions of the $N$ fermions. We show that the many-body quantum probability density in the ground state forms a determinantal point process whose correlation kernel can be computed for any $N$, giving access to the average density as well as higher order correlation functions for any finite $N$. Moreover, we analyze the scaling form of this kernel in the large $N$ limit in the bulk, near the edge, and close to the origin. Our results show that the scaled average density profile for large $N$ has a finite support symmetric with respect to the origin, but has a non-monotonic shape with a vanishing minimum at the origin for any $α>0$. One of the key findings of our work is that the scaled kernel near the origin $x=0$ for $α>0$ is neither the Bessel nor the Airy kernel (that are standard for trapped fermions), but is new, and is given by a sum of two Bessel kernels with different indices. Our results thus provide a framework relevant to engineered optical lattices with position-dependent tunneling.

cond-mat.stat-mech↗

arXiv2026

Proxitaxis: an adaptive search strategy based on proximity and stochastic resetting

We introduce \emph{proxitaxis}, a simple search strategy where the searcher has only information about the distance from the target but not the direction. The strategy consists of three crucial components: (i) local adaptive moves with distance-dependent hopping rate, (ii) intermittent long range returns via stochastic resetting to a certain location $\vec{R}_0$, and (iii) an inspection move where the searcher dynamically updates the resetting position $\vec{R}_0$. We compute analytically the capture probability of the target within this strategy and show that it can be maximized by an optimal choice of the control parameters of this strategy. Moreover, the optimal strategy undergoes multiple phase transitions as a function of the control parameters. These phase transitions are generic and occur in all dimensions.

cond-mat.stat-mech↗

arXiv2026

Observing quantum phase transitions at non-zero temperature: non-analytic behavior of order-parameter correlation times

Phase transitions occur when a macroscopic number of local degrees of freedom coherently change their behavior. In ground states of quantum many-body systems, phase transitions due to quantum fluctuations are observed as non-analytic behaviors of order parameters, such as magnetization, as functions of a conjugate parameter, such as the magnetic field. However, as soon as thermal fluctuations are present, these effects are believed to disappear for local observables. We show that this is not necessarily the case: order parameters may still show non-analytic behaviors within their dynamics. With the example of the Ising model and using methods based on hydrodynamic fluctuations, we evaluate the exact order-parameter correlation time, in space-time directions of all velocities, in equilibrium states at nonzero temperature. We reveal non-analytic behaviors of spin correlation times as functions of the magnetic field, velocity, and temperature. As a function of the magnetic field, they occur at values that continuously approach that of the zero-temperature equilibrium transition point as the velocity is decreased and reach it within the light cone, where we obtain a new, temperature-independent logarithmic divergence characterizing the collective dynamics. Thus, collective effects induced by quantum fluctuations persist within the dynamics of local observables.

cond-mat.stat-mech↗

arXiv2025

Universal Random Matrix Behavior of a Fermionic Quantum Gas

The pursuit of universal governing principles is a foundational endeavor in physics, driving breakthroughs from thermodynamics to general relativity and quantum mechanics. In 1951, Wigner introduced the concept of a statistical description of energy levels of heavy atoms, which led to the rise of Random Matrix Theory (RMT) in physics. The theory successfully captured spectral properties across a wide range of atomic systems, circumventing the complexities of quantum many-body interactions. Rooted in the fundamental principles of stochasticity and symmetry, RMT has since found applications and revealed universal laws in diverse physical contexts, from quantum field theory to disordered systems and wireless communications. A particularly compelling application arises in describing the mathematical structure of the many-body wavefunction of non-interacting Fermi gases, which underpins a complex spatial organization driven by Pauli's exclusion principle. However, experimental validation of the counting statistics predicted in such systems has remained elusive. Here, we probe at the single-atom level ultracold atomic Fermi gases made of two interacting spin states, obtaining direct access to their counting statistics in situ. Our measurements show that, while the system is strongly attractive, each spin-component is extremely well described by RMT predictions based on Fredholm determinants. Our results constitutes the first experimental validation of the Fermi-sphere point process through the lens of RMT, and establishes its relevance for strongly-interacting systems.

cond-mat.quant-gas↗

arXiv2025

Optimal detection of quantum states via projective measurements

We consider the quantum dynamical evolution of a fully-connected quantum system subjected to random projective measurements and study the first detection time of an extended subspace of the Hilbert space. Exact analytical expressions are obtained for the mean first detection time and the full first detection probability distribution as functionals of the initial state $\ket{ψ_0}$ and the measurement rate $r$. Exact enumeration agrees perfectly with our analytical predictions.

quant-ph↗

arXiv2024

Generalized arcsine laws for a sluggish random walker with subdiffusive growth

We study a simple one dimensional sluggish random walk model with subdiffusive growth. In the continuum hydrodynamic limit, the model corresponds to a particle diffusing on a line with a space dependent diffusion constant D(x)= |x|^{-α} and a drift potential U(x)=|x|^{-α}, where α\geq 0 parametrizes the model. For α=0 it reduces to the standard diffusion, while for α>0 it leads to a slow subdiffusive dynamics with the distance scaling as x\sim t^μ at late times with μ= 1/(α+2)\leq 1/2. In this paper, we compute exactly, for all α\ge 0, the full probability distributions of three observables for a sluggish walker of duration T starting at the origin: (i) the occupation time t_+ denoting the time spent on the positive side of the origin, (ii) the last passage time t_{\rm l} through the origin before T, and (iii) the time t_M at which the walker is maximally displaced on the positive side of the origin. We show that while for α=0 all three distributions are identical and exhibit the celebrated arcsine laws of Lévy, they become different from each other for any α>0 and have nontrivial shapes dependent on α. This generalizes the Lévy's three arcsine laws for normal diffusion (α=0) to the subdiffusive sluggish walker model with a general α\geq 0. Numerical simulations are in excellent agreement with our analytical predictions.

cond-mat.stat-mech↗

arXiv2024

Quantum fluctuating theory for one-dimensional shock waves

We study the formation and the subsequent dynamics of shock waves in repulsive one-dimensional Bose gases during the free expansion of a density hump. By building coherent Fermi states for interacting Bethe fermions, we define a quantum fluctuating initial state expressed in terms of universal quantities, namely the density and the Luttinger parameter. In the integrable case, this fluctuating state is then evolved by generalized hydrodynamics (GHD) and, differently from non-fluctuating initial states, it develops density ripples on top of the hydrodynamic mean value. Our analysis gives a general theory of quantum ripples and wave breaking in integrable and quasi-integrable one-dimensional liquids and clarifies the role of the interaction strength. In particular, for strongly/intermediately interacting bosons, we find quantum ripples originating from low-energy modes at the Fermi surface interfering when transported by GHD. In the low coupling limit, near the quasicondensate regime, we find instead that density ripples have a semi-classical nature, and their description requires information on the curvature of the Fermi surface.

cond-mat.stat-mech↗

arXiv2024

Exact large-scale fluctuations of the phase field in the sine-Gordon model

We present the first exact theory and analytical formulas for the large-scale phase fluctuations in the sine-Gordon model, valid in all regimes of the field theory, for arbitrary temperatures and interaction strengths. Our result is based on the Ballistic Fluctuation Theory combined with Generalized Hydrodynamics, and can be seen as an exact ``dressing" of the phenomenological soliton-gas picture first introduced by Sachdev and Young [S. Sachdev and A. P. Young, PRL 78, 2220 (1997)], to the modes of Generalised Hydrodynamics. The resulting physics of phase fluctuations in the sine-Gordon model is qualitatively different, as the stable quasi-particles of integrability give coherent ballistic propagation instead of diffusive spreading. We provide extensive numerical checks of our analytical predictions within the classical regime of the field theory by using Monte Carlo methods. We discuss how our results are of ready applicability to experiments on tunnel-coupled quasicondensates.

cond-mat.stat-mech↗

arXiv2023

Entanglement Rényi Entropies from Ballistic Fluctuation Theory: the free fermionic case

The large-scale behaviour of entanglement entropy in finite-density states, in and out of equilibrium, can be understood using the physical picture of particle pairs. However, the full theoretical origin of this picture is not fully established yet. In this work, we clarify this picture by investigating entanglement entropy using its connection with the large-deviation theory for thermodynamic and hydrodynamic fluctuations. We apply the universal framework of Ballistic Fluctuation Theory (BFT), based the Euler hydrodynamics of the model, to correlation functions of \emph{branch-point twist fields}, the starting point for computing Rényi entanglement entropies within the replica approach. Focusing on free fermionic systems in order to illustrate the ideas, we show that both the equilibrium behavior and the dynamics of Rényi entanglement entropies can be fully derived from the BFT. In particular, we emphasise that long-range correlations develop after quantum quenches, and accounting for these explain the structure of the entanglement growth. We further show that this growth is related to fluctuations of charge transport, generalising to quantum quenches the relation between charge fluctuations and entanglement observed earlier. The general ideas we introduce suggest that the large-scale behaviour of entanglement has its origin within hydrodynamic fluctuations.

quant-ph↗

arXiv2022

The hydrodynamic theory of dynamical correlation functions in the XX chain

By the hydrodynamic linear response theory, dynamical correlation functions decay as power laws along certain velocities, determined by the flux Jacobian. Such correlations are obtained by hydrodynamic projections, and physically, they are due to propagating "sound waves" or generalisation thereof, transporting conserved quantities between the observables. However, some observables do not emit sound waves, such as order parameters associated to symmetry breaking. In these cases correlation functions decay exponentially everywhere, a behaviour not captured by the hydrodynamic linear response theory. Focussing on spin-spin correlation functions in the XX quantum chain, we first review how hydrodynamic linear response works, emphasising that the necessary fluid cell averaging washes out oscillatory effects. We then show how, beyond linear response, Euler hydrodynamics can still predict the exponential decay of correlation functions of order parameters. This is done by accounting for the large-scale fluctuations of domain walls, via the recently developed ballistic fluctuation theory. We use the framework of generalised hydrodynamics, which is particularly simple in this model due to its free fermion description. In particular, this reproduces, by elementary calculations, the exponential decay in the celebrated formulae by A.R. Its, A.G. Izergin, V.E. Korepin, N.A. Slavnov (1993) and by X. Jie (1998), which were originally obtained by intricate Fredholm determinant analysis; and gives a new formula in a parameter domain where no result was obtained before. We confirm the results by numerical simulations.

math-ph↗

arXiv2021

Transport through interacting defects and lack of thermalisation

We consider 1D integrable systems supporting ballistic propagation of excitations, perturbed by a localised defect that breaks most conservation laws and induces chaotic dynamics. Focusing on classical systems, we study an out-of-equilibrium protocol engineered activating the defect in an initially homogeneous and far from the equilibrium state. We find that large enough defects induce full thermalisation at their center, but nonetheless the outgoing flow of carriers emerging from the defect is non-thermal due to a generalization of the celebrated Boundary Thermal Resistance effect, occurring at the edges of the chaotic region. Our results are obtained combining ab-initio numerical simulations for relatively small-sized defects, with the solution of the Boltzmann equation, which becomes exact in the scaling limit of large, but weak defects.

cond-mat.stat-mech↗

arXiv2020

Exact out-of-equilibrium steady states in the semiclassical limit of the interacting Bose gas

We study the out-of-equilibrium properties of a classical integrable non-relativistic theory, with a time evolution initially prepared with a finite energy density in the thermodynamic limit. The theory considered here is the Non-Linear Schrodinger equation which describes the dynamics of the one-dimensional interacting Bose gas in the regime of high occupation numbers. The main emphasis is on the determination of the late-time Generalised Gibbs Ensemble (GGE), which can be efficiently semi-numerically computed on arbitrary initial states, completely solving the famous quench problem in the classical regime. We take advantage of known results in the quantum model and the semiclassical limit to achieve new exact results for the momenta of the density operator on arbitrary GGEs, which we successfully compare with ab-initio numerical simulations. Furthermore, we determine the whole probability distribution of the density operator (full counting statistics), whose exact expression is still out of reach in the quantum model.

cond-mat.stat-mech↗