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Paolo Muratore-Ginanneschi

Publications and source records attributed to Paolo Muratore-Ginanneschi.

At least 19 recordsLinked to original sources
arXiv2026

Decay of the survival probability of a local excitation in multi-qubit platforms

We present a theoretical study of the survival probability of a state initially prepared in the one-particle sector of a multi-qubit system. The motivation for our work is the ongoing laboratory development of multi-qubit platforms based on superconducting circuits. Using elementary concepts of random matrix theory, we obtain analytic expressions for the survival probability in mathematical models of platforms which, albeit stylized, have been previously shown to provide relevant benchmarks for experimental data. In particular, we show that the decay properties are sensitive to the property of the Hamilton operator to have extended states. The survival probability does not appear instead to depend on whether the interaction between qubits is described by a Gaussian orthogonal ensemble (often interpreted as a model of ''chaotic'' dynamics) or is modeled by an analytically solvable chain. We interpret this phenomenon as a manifestation of a general mechanism for the emergence of equilibration in purely unitary dynamics. Finally, under the same hypothesis of an initial preparation with projection on a large fraction of the extended eigenstates of the Hamilton operator, we show how to extend the classical Kac-Mazur-Montroll estimate of the return time to the quantum survival probability.

quant-ph↗
arXiv2026

Universal bound on the Lyapunov spectrum of quantum master equations

The spectral properties of positive maps are pivotal for understanding the dynamics of quantum systems interacting with their environment. Furthermore, central problems in quantum information such as the characterization of entanglement can be reformulated in terms of spectral properties of positive maps. The present work aims to contribute to a better understanding of the spectrum of positive maps. Specifically, our main result is a new proof of a universal bound on the $d^{2}-1$ generically non vanishing decay rates $Γ_{i}$ of time-autonomous quantum master equations on a $d$-dimensional Hilbert space: $$Γ_{\mathrm{max}}\,\leq\,\varkappa_{d}\,\sum_{i=1}^{d^{2}-1}Γ_{i}$$ The prefactor $\varkappa_{d}$ %, which we explicitly determine, depends only on the dimension $d$ and varies depending on the sub-class of positive maps to which the semigroup solution of the master equation belongs. We provide a brief but self-consistent survey of these concepts. We obtain our main result by resorting to the theory of Lyapunov exponents, a central concept in the study of dynamical systems, control theory, and out-of-equilibrium statistical mechanics. We thus show that progress in understanding positive maps in quantum mechanics may require ideas at the crossroads between different disciplines. For this reason, we adopt a notation and presentation style aimed at reaching readers with diverse backgrounds.

quant-ph↗
arXiv2026

Thermalization in high-dimensional systems: the (weak) role of chaos

In their seminal work, Fermi, Pasta, Ulam and Tsingou explored the connection between statistical mechanics and dynamical properties, such as chaos and ergodicity. Even today, seventy years later, the topic is not fully understood: while most results of statistical mechanics require the ergodic hypothesis to be rigorously proved, there are many indications that these predictions, both in and out of equilibrium, hold even in the absence of a rigorous form of ergodicity. Motivated by the above considerations, in this work we reconsider the point of view that the relevant ingredients for the validity of statistical mechanics are the large number of degrees of freedom and the choice of extensive observables, while the details of the dynamics do not play an essential role. This is the idea behind Khinchin's famous proof of the typicality of macroscopic observables at equilibrium. We extend this perspective to the context of non equilibrium, by investigating the thermalization properties of both harmonic (integrable) and nonharmonic (chaotic) oscillator chains initially prepared in out-of-equilibrium conditions. In integrable systems, thermalization occurs, or not, depending on the observable. In the chaotic regime, instead, thermalization is reached by any observable, although the relaxation timescale might be larger than the observation time.

cond-mat.stat-mech↗
arXiv2026

What is a minimum work transition in stochastic thermodynamics?

We reassess the concept of transition at minimum work in classical stochastic finite-time thermodynamics, when the system dynamics is modelled by a diffusion process. We show that a well-posed formulation of the optimal control problem corresponding to the minimization of the mean work done on the system during a finite-time transition necessarily requires taking into account speed limits on control protocols. This fact has major qualitative consequences. First, it permits to discriminate between optimal swift engineered equilibration and transitions at minimum work. Second, it shows that in the limit when speed limits are removed, only transitions specified by generalized Schrödinger bridges admit a consistent physical interpretation. To illustrate these points, we focus on the simplest model problem: a levitating particle in a Gaussian moving trap.

cond-mat.stat-mech↗
arXiv2026

Heat flow through the quantum heat valve coupled to ohmic baths via a master equation approach

We provide a theoretical model for the non-equilibrium steady state heat flow through a quantum heat valve. The model is based on a master equation approach, where the partial secular approximation has been carefully performed in order to obtain accurate results. Our study assumes an ohmic spectral density for the two thermal baths of the model. This is in contrast with previous treatments of the quantum heat valve, where the baths have been assumed as being structured with a peaked spectral density near the resonance frequency of the resonator. These studies have also taken the resonator to be a part of the open quantum system of interest, which results in double counting of the resonator, as the latter appears both in the spectral density of the bath and as a part of the open system. Although this model accounts for the observations in a satisfactory way, it raises issues regarding its physical interpretation. Our method solves this conceptual problem. We apply it to describe an experiment on a quantum heat valve, showing that it successfully captures the experimental results and improves upon the previous theoretical model, which suffered from the resonator double-counting issue. Our findings confirm that the careful application of the master equation approach, in particular when it comes to the secular approximation, is a useful tool for explaining realistic experimental setups.

quant-ph↗
arXiv2025

Classical uncertainty relations and entropy production in non-equilibrium statistical mechanics

We analyze Fürth's 1933 classical uncertainty relations in the modern language of stochastic differential equations. Our interest is motivated by applications to non-equilibrium classical statistical mechanics. We show that Fürth's uncertainty relations are a property enjoyed by martingales under the measure of a diffusion process. This result implies a lower bound on fluctuations in current velocities of entropic quantifiers of transitions in stochastic thermodynamics. In cases of particular interest, we recover an inequality well known in optimal mass transport relating the mean kinetic energy of the current velocity and the squared quadratic Wasserstein distance between the probability distributions of the entropy. In performing our analysis, we also avail us of an unpublished argument due to Krzysztof Gawȩdzki to derive a lower bound to the entropy production by transition described by Langevin-Kramers process in terms of the squared quadratic Wasserstein distance between the initial and final states of the transition. Finally, we illustrate how Fürth's relations admit a straightforward extension to piecewise deterministic processes. We thus show that the results in the paper concern properties enjoyed by general Markov processes.

cond-mat.stat-mech↗
arXiv2025

Optimal Control of Engineered Swift Equilibration of Nanomechanical Oscillators

We propose a reformulation of the problem of optimally controlled transitions in stochastic thermodynamics. We impose that any terminal cost specified by a thermodynamic functional should depend only on state variables and not on control protocols, according to the canonical Bolza form. In this way, we can unambiguously discriminate between transitions at minimum dissipation between genuine equilibrium states, and transitions at minimum work driving a system from a genuine equilibrium to a non-equilibrium state. For underdamped dynamics subject to a mechanical force, genuine equilibrium means a Maxwell-Boltzmann probability distribution defining a vanishing current velocity. Transitions at minimum dissipation between equilibria are a model of optimal swift engineered equilibration. Remarkably, we show that transitions at minimum work do not directly imply explicit boundary conditions on terminal values of parameters of the mechanical force and on control protocols. Thus, the problem often discussed in the literature, that optimal protocols need terminal jumps to satisfy boundary conditions, completely disappears. The quantitative properties of optimal controls are entirely determined by the form of the penalty modelling an experimental setup. More generally, we use centre manifold theory to analytically account for the tendency of optimal controls to exhibit a turnpike property: optimal protocols in the bulk of the control horizon tend to converge to a universal centre manifold determined only by the running cost. Exponential deviations from the centre manifold occur at the ends of the control horizon in order to satisfy the boundary conditions. Our findings are supported numerically.

cond-mat.stat-mech↗
arXiv2025

A universal constraint for relaxation rates for quantum Markov generators: complete positivity and beyond

Relaxation rates are key characteristics of quantum processes, as they determine how quickly a quantum system thermalizes, equilibrates, decoheres, and dissipates. While they play a crucial role in theoretical analyses, relaxation rates are also often directly accessible through experimental measurements. Recently, it was shown that for quantum processes governed by Markovian semigroups, the relaxation rates satisfy a universal constraint: the maximal rate is upper-bounded by the sum of all rates divided by the dimension of the Hilbert space. This bound, initially conjectured a few years ago, was only recently proven using classical Lyapunov theory. In this work, we present a new, purely algebraic proof of this constraint. Remarkably, our approach is not only more direct but also allows for a natural generalization beyond completely positive semigroups. We show that complete positivity can be relaxed to 2-positivity without affecting the validity of the constraint. This reveals that the bound is more subtle than previously understood: 2-positivity is necessary, but even when further relaxed to Schwarz maps, a slightly weaker -- yet still non-trivial -- universal constraint still holds. Finally, we explore the connection between these bounds and the number of steady states in quantum processes, uncovering a deeper structure underlying their behavior.

quant-ph↗
arXiv2025

Quantum and classical Shapiro steps in small Josephson junctions

We propose a model describing the formation of both dual (quantum) and classical Shapiro steps in small Josephson junctions. According to this model, the dual Shapiro steps are formed at relatively low frequency of the microwave signal and low microwave power, while the classical steps are formed in the opposite limit of high frequency and power. The crossover between the two regimes is controlled by a single parameter - the effective relaxation time of the environment. The model accounts for the effect of a large inductor in the bias circuit, which has been used in recent experiments to protect the junction from the high frequency noise of the environment. We predict the possibility of observing both types of steps in the same sample. Our model describes the I-V curves observed in the experiments with reasonable accuracy, thus opening up an opportunity for quantitative fitting of the data.

cond-mat.supr-con↗
arXiv2025

Thermalization is typical in large classical and quantum harmonic systems

We establish an analytical criterion for dynamical thermalization within harmonic systems, applicable to both classical and quantum models. Specifically, we prove that thermalization of various observables, such as particle energies in physically relevant random quadratic Hamiltonians, is typical for large systems ($N \gg 1$) with initial conditions drawn from the microcanonical distribution. Moreover, we show that thermalization can also arise from non-typical initial conditions, where only a finite fraction of the normal modes is excited. A different choice of initial conditions, such as all the initial energy localized in a single particle, instead leads to energy equipartition without thermalization. Since the models we consider are integrable, our findings provide a general dynamical basis for an approach to thermalization that bypasses chaos and ergodicity, focusing instead on the physical requirement that thermodynamic observables depend on a large number of normal modes, and build a bridge between the classical and quantum theories of thermalization.

cond-mat.stat-mech↗
arXiv2025

Universal Bound on the Eigenvalues of 2-Positive Trace-Preserving Maps

We prove an upper bound on the trace of any 2-positive, trace-preserving map in terms of its smallest eigenvalue. We show that this spectral bound is tight, and that 2-positivity is necessary for this inequality to hold in general. Moreover, we use this to infer a similar bound for generators of one-parameter semigroups of 2-positive trace-preserving maps. With this approach we generalize known results for completely positive trace-preserving dynamics while providing a significantly simpler proof that is entirely algebraic.

math.RA↗
arXiv2025

Analytical solution of the open dispersive Jaynes-Cummings model and perturbative analytical solution of the open quantum Rabi model

The Jaynes-Cummings and quantum Rabi models are fundamental to cavity and circuit quantum electrodynamics, as they describe the simplest form of light-matter interaction, where a single qubit is coupled to a single bosonic mode. A scenario that is commonly encountered in the experimental practice arises when the bosonic mode interacts with an external dissipative thermal bath, making the qubit-boson system open. In this work, we present new analytical solution of the Lindblad master equations for the open dispersive Jaynes-Cummings model and a perturbative analytical solution of the open quantum Rabi model in the limit of weak qubit-boson coupling $g$, using the holomorphic formalism in Bargmann space. Specifically, we derive the most general solution of the local Lindblad master equation for the open dispersive Jaynes-Cummings model coupled to a thermal bath, with the only assumptions that the initial state of the qubit-boson system is separable. Additionally, we obtain a perturbative analytical solution for the open quantum Rabi model up to second order in $g$. Notably, our findings include a new formula for the qubit's steady state at zeroth order, showing that the stationary populations depend on both qubit and boson frequencies in the quantum Rabi model, but not in the Jaynes-Cummings model, regardless of the value of $g$. Our results are of general interest to the study of open quantum systems in the context of light-matter interaction.

quant-ph↗
arXiv2025

Minimal work protocols for inertial particles in non-harmonic traps

Progress in miniaturized technology allows us to control physical systems at nanoscale with remarkable precision. Experimental advancements have sparked interest in control problems in stochastic thermodynamics, typically concerning a time-dependent potential applied to a nanoparticle to reach a target stationary state in a given time with minimal energy cost. We study this problem for a particle subject to thermal fluctuations in a regime that takes into account the effects of inertia, and, building on the results of a previous work, provide a numerical method to find optimal controls even for non-Gaussian initial and final conditions, corresponding to non-harmonic confinements. The control protocol and the time-dependent position distribution are qualitatively different from the corresponding overdamped limit: in particular, a symmetry of the boundary conditions, which is preserved in the absence of inertia, turns out to be broken in the underdamped regime. We also show that the momentum mean tends to a constant value along the trajectory, except close to the boundary, while the evolution of the position mean and of the second moments is highly non-trivial. Our results also support that the lower bound on the optimal entropy production computed from the overdamped case is tight in the adiabatic limit.

cond-mat.stat-mech↗
arXiv2025

On the numerical integration of the Fokker-Planck equation driven by a mechanical force and the Bismut-Elworthy-Li formula

Optimal control theory aims to find an optimal protocol to steer a system between assigned boundary conditions while minimizing a given cost functional in finite time. Equations arising from these types of problems are often non-linear and difficult to solve numerically. In this note, we describe numerical methods of integration for two partial differential equations that commonly arise in optimal control theory: the Fokker-Planck equation driven by a mechanical potential for which we use Girsanov theorem; and the Hamilton-Jacobi-Bellman, or dynamic programming, equation for which we find the gradient of its solution using the Bismut-Elworthy-Li formula. The computation of the gradient is necessary to specify the optimal protocol. Finally, we give an example application of the numerical techniques to solving an optimal control problem without spacial discretization using machine learning.

math.OC↗
arXiv2024

Universal bound on the relaxation rates for quantum Markovian dynamics

Relaxation rates provide important characteristics both for classical and quantum processes. Essentially they control how fast the system thermalizes, equilibrates, {decoheres, and/or dissipates}. Moreover, very often they are directly accessible to be measured in the laboratory and hence they define key physical properties of the system. Experimentally measured relaxation rates can be used to test validity of a particular theoretical model. Here we analyze a fundamental question: {\em does quantum mechanics provide any nontrivial constraint for relaxation rates?} We prove the conjecture formulated a few years ago that any quantum channel implies that a maximal rate is bounded from above by the sum of all the relaxation rates divided by the dimension of the Hilbert space. It should be stressed that this constraint is universal (it is valid for all quantum systems with finite number of energy levels) and it is tight (cannot be improved). In addition, the constraint plays an analogous role to the seminal Bell inequalities and the well known Leggett-Garg inequalities (sometimes called temporal Bell inequalities). Violations of Bell inequalities rule out local hidden variable models, and violations of Leggett-Garg inequalities rule out macrorealism. Similarly, violations of the bound rule out completely positive-divisible evolution.

quant-ph↗
arXiv2024

Optimal Control of Underdamped Systems: An Analytic Approach

Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an open and challenging research frontier, with a spectrum of applications ranging from stochastic thermodynamics to biophysics and data science. Among these, the design of nanoscale electronic components motivates the study of underdamped dynamics. In this work, we develop analytic techniques to determine protocols steering finite time transitions at a minimum thermodynamic cost for stochastic underdamped dynamics. As cost functions, we consider two paradigmatic thermodynamic indicators. The first is the Kullback-Leibler divergence between the probability measure of the controlled process and that of a reference process. The corresponding optimization problem is the underdamped version of the Schrödinger diffusion problem that has been widely studied in the overdamped regime. The second is the mean entropy production during the transition, corresponding to the second law of modern stochastic thermodynamics. For transitions between Gaussian states, we show that optimal protocols satisfy a Lyapunov equation, a central tool in stability analysis of dynamical systems. For transitions between states described by general Maxwell-Boltzmann distributions, we introduce an infinite-dimensional version of the Poincaré-Linstedt multiscale perturbation theory around the overdamped limit. This technique fundamentally improves the standard multiscale expansion. Indeed, it enables the explicit computation of momentum cumulants, whose variation in time is a distinctive trait of underdamped dynamics and is directly accessible to experimental observation.

cond-mat.stat-mech↗
arXiv2023

On the unraveling of open quantum dynamics

It is well known that the state operator of an open quantum system can be generically represented as the solution of a time-local equation -- a quantum master equation. Unraveling in quantum trajectories offers a picture of open system dynamics dual to solving master equations. In the unraveling picture, physical indicators are computed as Monte-Carlo averages over a stochastic process valued in the Hilbert space of the system. This approach is particularly adapted to simulate systems in large Hilbert spaces. We show that the dynamics of an open quantum system generically admits an unraveling in the Hilbert space of the system described by a Markov process generated by ordinary stochastic differential equations for which rigorous concentration estimates are available. The unraveling can be equivalently formulated in terms of norm-preserving state vectors or in terms of linear ``ostensible" processes trace preserving only on average. We illustrate the results in the case of a two level system in a simple boson environment. Next, we derive the state-of-the-art form of the Diosi-Gisin-Strunz Gaussian random ostensible state equation in the context of a model problem. This equation provides an exact unraveling of open systems in Gaussian environments. We compare and contrast the two unravelings and their potential for applications to quantum error mitigation.

quant-ph↗