arXiv subjects

Alberto Imparato

Publications and source records attributed to Alberto Imparato.

At least 19 recordsLinked to original sources

arXiv2026

First passage time for an underdamped harmonic oscillator and application to the power of an information engine

The distribution of the first passage time $t_{fp}$ for the position $x$ to overcome a threshold $x_B$ is calculated in an underdamped harmonic oscillator. The proof combines several approaches based on the determination of the eigenvalues of the Kramers differential operator for the intermediate and long time regimes and on a Hamiltonian approximation for the short times. The theoretical predictions are in excellent agreement with the results of an experiment on an underdamped micro-cantilever. The knowledge of the $t_{fp}$ distribution opens the way to several applications, among them the precise estimation of the power of information engines, which we have also experimentally checked.

cond-mat.stat-mech↗

arXiv2026

First passage time distribution in underdamped harmonic oscillators

We derive the distribution of the first passage time $t_{fp}$ for the position $x$ of an underdamped harmonic oscillator to overcome a threshold $x_B$. As the $t_{fp}$ distribution depends on the oscillator quality factor $Q$ different approaches are used. At very large quality factor ($Q\gg 100$) and intermediate and long $t_{fp}$ the proof is based on an energy diffusion model, whereas at medium quality factor ($Q\sim 10$) the proof is based on the study of the eigenvalues of the Kramers linear differential operator with absorbing boundary conditions. For all $Q$ and short $t_{fp}$ we use a Hamiltonian approximation. The theoretical predictions are in excellent agreement with direct numerical simulations of underdamped oscillator dynamics. Finally we show that the mean of the trajectories ending at $t_{fp}$ presents a particular shape driven by a specific noise pattern.

cond-mat.stat-mech↗

arXiv2025

Broken Detailed Balance and Entropy Production in CPTP Quantum Brownian Motion

We rigorously analyze the non-equilibrium thermodynamic behavior of various formulations of quantum Brownian motion (QBM) using the framework of stochastic thermodynamics. While the widely used Caldeira-Leggett master equation exhibits desirable thermodynamic features, such as the fulfilment of a detailed balance, it fails to ensure complete positivity. In contrast, several completely positive and trace-preserving (CPTP) extensions turn out to be thermodynamically controversial. We show that such extensions introduce anomalous phase-space structures that violate detailed balance at the steady state, leading to non-vanishing entropy production and effective non-equilibrium current of unclear physical origins. Our results highlight a fundamental tension between quantum consistency and thermodynamic equilibration in open quantum systems.

quant-ph↗

arXiv2024

Information engine fueled by first-passage times

Using a mechanical cantilever submitted to electrostatic feedback control, we investigate the thermodynamic properties of an information engine that extracts work from thermal fluctuations. The cantilever position is rapidly sampled and the feedback is triggered by the first passage of the system across a fixed threshold. The information $\Delta I$ associated with the feedback is based on the first-passage-time distribution. In this setting, we derive and experimentally verify two distinct fluctuation theorems that involve $\Delta I$ and give a tight bound on the work produced by the engine. Our results extend beyond the specific application to our experiment: we develop a general framework for obtaining fluctuation theorems and work bounds, formulated in terms of probability distributions of protocols rather than underlying measurement outcomes.

cond-mat.stat-mech↗

arXiv2023

Destructive effect of fluctuations on the performance of a Brownian gyrator

The Brownian gyrator (BG) is often called a minimal model of a nano-engine performing a rotational motion, judging solely upon the fact that in non-equilibrium conditions its torque, angular momentum ${\cal L}$ and angular velocity $\cal W$ have non-zero mean values. For a time-discretized model, which is most adapted for the analysis of an essentially discrete-time data garnered in experiments or numerical simulations, we calculate the previously unknown probability density functions (PDFs) of ${\cal L}$ and $\cal W$. For finite time-step $\delta t$, the PDF of ${\cal L}$ has exponential tails and all moments are therefore well-defined, but the noise-to-signal ratio can attain big values for small $\delta t$. Conversely, the PDF of ${\cal W}$ exhibits heavy power-law tails and its mean ${\cal W}$ is the only existing moment. The BG is therefore not an engine in the common sense: it does not exhibit regular rotations on each run and its fluctuations are not only a minor nuisance -- on contrary, their effect is completely destructive for the performance. Our theoretical predictions are confirmed by numerical simulations and experimental data. We discuss some plausible improvements

cond-mat.stat-mech↗

arXiv2023

Interaction-induced transition in quantum many-body detection probability

With the advent of digital and analog quantum simulation experiments, it is now possible to experimentally simulate dynamics of quantum many-body lattice systems and make site-resolved measurements. These experiments make it pertinent to consider the probability of getting any specific measurement outcome, which we call the `signal', on placing multiple detectors at various sites while simulating dynamics of a quantum many-body lattice system. In this work, we formulate and investigate this problem, introducing the concept of quantum many-body detection probability (QMBDP), which refers to the probability of detecting a chosen signal at least once in a given time. We show that, on tuning some Hamiltonian parameters, there can be sharp transition from a regime where QMBDP $\approx 1$, to a regime, where QMBDP $\approx 0$. Most notably, the effects of such a transition can be observed at a single trajectory level. This is not a measurement-induced transition, but rather a non-equilibrium transition reflecting opening of a specific type of gap in the many-body spectrum. We demonstrate this in a single-impurity non-integrable model, where changing the many-body interaction strength brings about such a transition. Our findings suggest that instead of measuring expectation values, single-shot stroboscopic measurements could be used to observe non-equilibrium transitions.

quant-ph↗

arXiv2023

A thermodynamic approach to optimization in complex quantum systems

We consider the problem of finding the energy minimum of a complex quantum Hamiltonian by employing a non-Markovian bath prepared in a low energy state. The energy minimization problem is thus turned into a thermodynamic cooling protocol in which we repeatedly put the system of interest in contact with a colder auxiliary system. By tuning the internal parameters of the bath, we show that the optimal cooling is obtained in a regime where the bath exhibits a quantum phase transition in the thermodynamic limit. This result highlights the importance of collective effects in thermodynamic devices. We furthermore introduce a two-step protocol that combines the interaction with the bath with a measure of its energy. While this protocol does not destroy coherence in the system of interest, we show that it can further enhance the cooling effect.

quant-ph↗

arXiv2023

Out-of-equilibrium dynamics of two interacting optically-trapped particles

We present a theoretical analysis of a non-equilibrium dynamics in a model system consisting of two particles which move randomly on a plane. The two particles interact via a harmonic potential, experience their own (independent from each other) noises characterized by two different temperatures $T_1$ and $T_2$, and each particle is being held by its own optical tweezer. Such a system with two particle coupled by hydrodynamic interactions was previously realised experimentally in Bérut et al. [EPL {\bf 107}, 60004 (2014)], and the difference between two temperatures has been achieved by exerting an additional noise on either of the tweezers. Framing the dynamics in terms of two coupled over-damped Langevin equations, we show that the system reaches a non-equilibrium steady-state with non-zero (for $T_1 \neq T_2$) probability currents that possess non-zero curls. As a consequence, in this system the particles are continuously spinning around their centers of mass in a completely synchronised way - the curls of currents at the instantaneous positions of two particles have the same magnitude and sign. Moreover, we demonstrate that the components of currents of two particles are strongly correlated and undergo a rotational motion along closed elliptic orbits.

cond-mat.stat-mech↗

arXiv2022

Cooperative dynamics in two-component out-of-equilibrium systems: Molecular "spinning tops"

We study the two-dimensional Langevin dynamics of a two-component system, whose components are in contact with heat baths kept at different temperatures. Dynamics is constrained by an optical trap and the \text{dissimilar} species interact via a quadratic potential. We realize that the system evolves towards a peculiar non-equilibrium steady-state with a non-zero probability current possessing a non-zero curl, such that the randomly moving particles are spinning around themselves, like "spinning top" toys. Our analysis shows that the spinning motion is correlated and also reveals an emerging cooperative behavior of the spatial components of the probability currents of dissimilar species.

cond-mat.stat-mech↗

arXiv2022

A quantum fluctuation theorem for any Lindblad master equation

We present a general quantum fluctuation theorem for the entropy production of an open quantum system coupled to multiple environments, not necessarily at equilibrium. Such a general theorem, when restricted to the weak-coupling and Markovian regime, holds for both local and global master equations, corroborating the thermodynamic consistency of local quantum master equations. The theorem is genuinely quantum, as it can be expressed in terms of conservation of a Hermitian operator, describing the dynamics of the system state operator and of the entropy change in the baths. The integral fluctuation theorem follows from the properties of such an operator. Furthermore, it is also valid when the system is described by a time-dependent Hamiltonian. As such, the quantum Jarzynski equality is a particular case of the general result presented here. Moreover, our result can be extended to nonthermal baths, as long as microreversibility is preserved. We present some numerical examples to showcase the exact results previously obtained. We finally generalize the fluctuation theorem to the case where the interaction between the system and the bath is explicitly taken into account. We show that the fluctuation theorem amounts to a relation between time-reversed dynamics of the global density matrix and a two-time correlation function along the forward dynamics involving the baths' entropy alone.

quant-ph↗

arXiv2021

Quantum batteries at the verge of a phase transition

Starting from the observation that the reduced state of a system strongly coupled to a bath is, in general, an athermal state, we introduce and study a cyclic battery-charger quantum device that is in thermal equilibrium, or in a ground state, during the charge storing stage. The cycle has four stages: the equilibrium storage stage is interrupted by disconnecting the battery from the charger, then work is extracted from the battery, and then the battery is reconnected with the charger; finally, the system is brought back to equilibrium. At no point during the cycle are the battery-charger correlations artificially erased. We study the case where the battery and charger together comprise a spin-1/2 Ising chain, and show that the main figures of merit - the extracted energy and the thermodynamic efficiency - can be enhanced by operating the cycle close to the quantum phase transition point. When the battery is just a single spin, we find that the output work and efficiency show a scaling behavior at criticality and derive the corresponding critical exponents. Due to always present correlations between the battery and the charger, operations that are equivalent from the perspective of the battery can entail different energetic costs for switching the battery-charger coupling. This happens only when the coupling term does not commute with the battery's bare Hamiltonian, and we use this purely quantum leverage to further optimize the performance of the device.

quant-ph↗

arXiv2021

Open Quantum Rotors: Connecting Correlations and Physical Currents

We consider a finite one-dimensional chain of quantum rotors interacting with a set of thermal baths at different temperatures. When the interaction between the rotors is made chiral, such a system behaves as an autonomous thermal motor, converting heat currents into non-vanishing rotational ones. Such a dynamical response is strongly pronounced in the range of the Hamiltonian parameters for which the ground state of the system in the thermodynamic limit exhibits a quantum phase transition. Such working points are associated with large quantum coherence and multipartite quantum correlations within the state of the system. This suggests that the optimal operating regime of such quantum autonomous motor is one of maximal quantumness.

quant-ph↗

arXiv2021

Energy conservation and fluctuation theorem are incompatible for quantum work

Characterizing fluctuations of work in coherent quantum systems is notoriously problematic. Here we reveal the ultimate source of the problem by proving that ($\mathfrak{A}$) energy conservation and ($\mathfrak{B}$) the Jarzynski fluctuation theorem cannot be observed at the same time. Condition $\mathfrak{A}$ stipulates that, for any initial state of the system, the measured average work must be equal to the difference of initial and final average energies, and that untouched systems must exchange deterministically zero work. Condition $\mathfrak{B}$ is only for thermal initial states and encapsulates the second law of thermodynamics. We prove that $\mathfrak{A}$ and $\mathfrak{B}$ are incompatible for work measurement schemes that are differentiable functions of the state and satisfy two mild structural constraints. This covers all existing schemes and leaves the theoretical possibility of jointly observing $\mathfrak{A}$ and $\mathfrak{B}$ open only for a narrow class of exotic schemes. For the special but important case of state-independent schemes, the situation is much more rigid: we prove that, essentially, only the two-point measurement scheme is compatible with $\mathfrak{B}$.

quant-ph↗

arXiv2021

Quantum thermodynamically consistent local master equations

Local master equations are a widespread tool to model open quantum systems, especially in the context of many-body systems. These equations, however, are believed to lead to thermodynamic anomalies and violation of the laws of thermodynamics. In contrast, here we rigorously prove that local master equations are consistent with thermodynamics and its laws without resorting to a microscopic model, as done in previous works. In particular, we consider a quantum system in contact with multiple baths and identify the relevant contributions to the total energy, heat currents and entropy production rate. We show that the second law of thermodynamics holds when one considers the proper expression we derive for the heat currents. We confirm the results for the quantum heat currents by using a heuristic argument that connects the quantum probability currents with the energy currents, using an analogous approach as in classical stochastic thermodynamics. We finally use our results to investigate the thermodynamic properties of a set of quantum rotors operating as thermal devices and show that a suitable design of three rotors can work as an absorption refrigerator or a thermal rectifier. For the machines considered here, we also perform an optimisation of the system parameters using an algorithm of reinforcement learning.

quant-ph↗

arXiv2020

Charging assisted by thermalization

A system in thermal equilibrium with a bath will generally be in an athermal state, if the system-bath coupling is strong. In some cases, it will be possible to extract work from that athermal state, after disconnecting the system from the bath. We use this observation to devise a battery charging and storing unit, simply consisting of a system, acting as the battery, and a bath. The charging cycle---connect, let thermalize, disconnect, extract work---requires very little external control and the charged state of the battery, being a part of global thermal equilibrium, can be maintained indefinitely and for free. The efficiency, defined as the ratio of the extractable work stored in the battery and the total work spent on connecting and disconnecting, is always $\leq 1$, which is a manifestation of the second law of thermodynamics. Moreover, coupling, being a resource for the device, is also a source of dissipation: the entropy production per charging cycle is always significant, strongly limiting the efficiency in all coupling strength regimes. We show that our general results also hold for generic microcanonical baths. We illustrate our theory on the Caldeira-Leggett model with a harmonic oscillator (the battery) coupled to a harmonic bath, for which we derive general asymptotic formulas in both weak and ultrastrong coupling regimes, for arbitrary Ohmic spectral densities. We show that the efficiency can be increased by connecting several copies of the battery to the bath. Finally, as a side result, we derive a general formula for Gaussian ergotropy, that is, the maximal work extractable by Gaussian unitary operations from Gaussian states of multipartite continuous-variable systems.

quant-ph↗

arXiv2019

Quantum duets working as autonomous thermal motors

We study the dynamic properties of a thermal autonomous machine made up of two quantum Brownian particles, each of which is in contact with an environment at different temperature and moves on a periodic sinusoidal track. When such tracks are shifted, the center of mass of the system exhibits a non-vanishing velocity, for which we provide an exact expression in the limit of small track undulations. We discuss the role of the broken spatial symmetry in the emergence of directed motion in thermal machines. We then consider the case in which external deterministic forces are applied to the system, and characterize its steady state velocity. If the applied external force opposes the system motion, work can be extracted from such a steady state thermal machine, without any external cyclic protocol. When the two particles are not interacting, our results reduce to those of refs. [1,2] for a single particle moving in a periodic tilted potential. We finally use our results for the motor velocity to check the validity of the quantum molecular dynamics algorithm in the non--linear, non--equilibrium regime.

quant-ph↗

arXiv2019

Out-of-equilibrium clock model at the verge of criticality

We consider an out-of-equilibrium lattice model consisting of 2D discrete rotators, in contact with heat reservoirs at different temperatures. The equilibrium counterpart of such model, the clock-model, exhibits three phases; a low-temperature ordered phase, a quasi-liquid phase, and a high-temperature disordered phase, with two corresponding phase transitions. In the out-of-equilibrium model the simultaneous breaking of spatial symmetry and thermal equilibrium give rise to directed rotation of the spin variables. In this regime the system behaves as a thermal machine converting heat currents into motion. In order to quantify the susceptibility of the machine to the thermodynamic force driving it out-of-equilibrium, we introduce and study a dynamical response function. We show that the optimal operational regime for such a thermal machine occurs when the out-of-equilibrium disturbance is applied around the critical temperature at the boundary between the first two phases, namely where the system is mostly susceptible to external thermodynamic forces and exhibits a sharper transition. We thus argue that critical fluctuations in a system of interacting motors can be exploited to enhance the machine overall dynamic and thermodynamic performances.

cond-mat.stat-mech↗

arXiv2019

Quantum current in dissipative systems

Describing current in open quantum systems can be problematic due to the subtle interplay of quantum coherence and environmental noise. Probing the noise-induced current can be detrimental to the tunneling-induced current and vice versa. We derive a general theory for the probability current in quantum systems arbitrarily interacting with their environment that overcomes this difficulty. We show that the current can be experimentally measured by performing a sequence of weak and standard quantum measurements. We exemplify our theory by analyzing a simple Smoluchowski-Feynman-type ratchet consisting of two particles, operating deep in the quantum regime. Fully incorporating both thermal and quantum effects, the current generated in the model can be used to detect the onset of "genuine quantumness" in the form of quantum contextuality. The model can also be used to generate steady-state entanglement in the presence of arbitrarily hot environment.

quant-ph↗