Universal Energy Fluctuations in Inelastic Scattering Processes.

Quantum scattering is used ubiquitously in both experimental and theoretical physics across a wide range of disciplines, from high-energy physics to mesoscopic physics. In this Letter, we uncover universal relations for the energy fluctuations of a quantum system scattering inelastically with a particle at arbitrary kinetic energies. In particular, we prove a fluctuation relation describing an asymmetry between energy absorbing and releasing processes which relies on the nonunital nature of the underlying quantum map.

Thermalization and Dephasing in Collisional Reservoirs.

We introduce a wide class of quantum maps that arise in collisional reservoirs and are able to thermalize a system if they operate in conjunction with an additional dephasing mechanism. These maps describe the effect of collisions and induce transitions between populations that obey detailed balance, but also create coherences that prevent the system from thermalizing. We combine these maps with a unitary evolution acting during random Poissonian times between collisions and causing dephasing.

A firebreak placement model for optimizing biodiversity protection at landscape scale.

A solution approach is proposed to optimize the selection of landscape cells for inclusion in firebreaks. It involves linking spatially explicit information on a landscape's ecological values, historical ignition patterns and fire spread behavior. A firebreak placement optimization model is formulated that captures the tradeoff between the direct loss of biodiversity due to the elimination of vegetation in areas designated for placement of firebreaks and the protection provided by the firebreaks from losses due to future forest fires.

Collective enhancement in dissipative quantum batteries.

We study a quantum battery made out of N nonmutually interacting qubits coupled to a dissipative single electromagnetic field mode in a resonator. We quantify the charging energy, ergotropy, transfer rate, and power of the system, showing that collective enhancements are still present despite losses, and can even increase with dissipation. Moreover, we observe that a performance deterioration due to dissipation can be reduced by scaling up the battery size.

Efficiency Fluctuations in a Quantum Battery Charged by a Repeated Interaction Process.

A repeated interaction process assisted by auxiliary thermal systems charges a quantum battery. The charging energy is supplied by switching on and off the interaction between the battery and the thermal systems. The charged state is an equilibrium state for the repeated interaction process, and the ergotropy characterizes its charge.

The mediating/moderating role of cultural context factors on self-care practices among those living with diabetes in rural Appalachia.

Background: The aim of this study was to examine whether cultural factors, such as religiosity and social support, mediate/moderate the relationship between personal/psychosocial factors and T2DM self-care in a rural Appalachian community.

Methods: Regression models were utilized to assess for mediation and moderation. Multilevel linear mixed effects models and GEE-type logistic regression models were fit for continuous (social support, self-care) and binary (religiosity) outcomes, respectively.

Dissipative Charging of a Quantum Battery.

We show that a cyclic unitary process can extract work from the thermodynamic equilibrium state of an engineered quantum dissipative process. Systems in the equilibrium states of these processes serve as batteries, storing energy. The dissipative process that brings the battery to the active equilibrium state is driven by an agent that couples the battery to thermal systems.

Landau-Zener Lindblad equation and work extraction from coherences.

We show that the dynamics of a driven quantum system weakly coupled to a finite reservoir can be approximated by a sequence of Landau-Zener transitions if the level spacing of the reservoir is large enough. This approximation can be formulated as a repeated interaction dynamics and leads to a quantum master equation for the driven system which is of Lindblad form. The approach is validated by comparison with the numerically exact full system dynamics.

Stochastic thermodynamics of quantum maps with and without equilibrium.

We study stochastic thermodynamics for a quantum system of interest whose dynamics is described by a completely positive trace-preserving (CPTP) map as a result of its interaction with a thermal bath. We define CPTP maps with equilibrium as CPTP maps with an invariant state such that the entropy production due to the action of the map on the invariant state vanishes. Thermal maps are a subgroup of CPTP maps with equilibrium.

Kinetics and thermodynamics of a driven open quantum system.

Redfield theory provides a closed kinetic description of a quantum system in weak contact with a very dense reservoir. Landau-Zener theory does the same for a time-dependent driven system in contact with a sparse reservoir. Using a simple model, we analyze the validity of these two theories by comparing their predictions with exact numerical results.

Dissipation in small systems: Landau-Zener approach.

We establish a stochastic thermodynamics for a Fermionic level driven by a time-dependent force and interacting with initially thermalized levels playing the role of a reservoir. The driving induces consecutive avoided crossings between system and reservoir levels described within Landau-Zener theory. We derive the resulting system dynamics and thermodynamics and identify energy, work, heat, entropy, and dissipation.

The thermodynamic cost of driving quantum systems by their boundaries.

The laws of thermodynamics put limits to the efficiencies of thermal machines. Analogues of these laws are now established for quantum engines weakly and passively coupled to the environment providing a framework to find improvements to their performance. Systems whose interaction with the environment is actively controlled do not fall in that framework.

Diffusive transport of waves in a periodic waveguide.

We study the propagation of waves in quasi-one-dimensional finite periodic systems whose classical (ray) dynamics is diffusive. By considering a random matrix model for a chain of L identical chaotic cavities, we show that its average conductance as a function of L displays an ohmic behavior even though the system has no disorder. This behavior, with an average conductance decay N/L, where N is the number of propagating modes in the leads that connect the cavities, holds for 1≪L≲√N.

Number of propagating modes of a diffusive periodic waveguide in the semiclassical limit.

We study the number of propagating Bloch modes N(B) of an infinite periodic billiard chain. The asymptotic semiclassical behavior of this quantity depends on the phase-space dynamics of the unit cell, growing linearly with the wave number k in systems with a non-null measure of ballistic trajectories and going like ∼square root of k in diffusive systems. We have calculated numerically N(B) for a waveguide with cosine-shaped walls exhibiting strongly diffusive dynamics.

Surface acoustic waves in interaction with a dislocation.

A surface acoustic wave can interact with dislocations that are close to the surface. We characterize this interaction and its manifestations as scattered surface acoustic waves for different orientations with respect to the surface of an edge dislocation. For dislocations that are parallel or perpendicular to the free surface, we present an analytical result for short dislocations with respect to the wave-length that reproduce qualitatively the main features observed for dislocations of various sizes.

Fractality of the nonequilibrium stationary states of open volume-preserving systems. II. Galton boards.

Galton boards are models of deterministic diffusion in a uniform external field, akin to driven periodic Lorentz gases, here considered in the absence of dissipation mechanism. Assuming a cylindrical geometry with axis along the direction of the external field, the two-dimensional board becomes a model for one-dimensional mass transport along the direction of the external field. This is a purely diffusive process which admits fractal nonequilibrium stationary states under flux boundary conditions.

Fractality of the nonequilibrium stationary states of open volume-preserving systems. I. Tagged particle diffusion.

Deterministic diffusive systems, such as the periodic Lorentz gas, multibaker map, as well as spatially periodic systems of interacting particles, have nonequilibrium stationary states with fractal properties when put in contact with particle reservoirs at their boundaries. We study the macroscopic limits of these systems and establish a correspondence between the thermodynamics of the macroscopic diffusion process and the fractality of the stationary states that characterize the phase-space statistics. In particular the entropy production rate is recovered from first principles using a formalism due to Gaspard [J.

Multiple scattering from assemblies of dislocation walls in three dimensions. Application to propagation in polycrystals.

The attenuation of ultrasound in polycrystalline materials is modeled with grain boundaries considered as arrays of dislocation segments, a model valid for low angle mismatches. The polycrystal is thus studied as a continuous medium containing many dislocation "walls" of finite size randomly placed and oriented. Wave attenuation is blamed on the scattering by such objects, an effect that is studied using a multiple scattering formalism.

Steady-state conduction in self-similar billiards.

The self-similar Lorentz billiard channel is a spatially extended deterministic dynamical system which consists of an infinite one-dimensional sequence of cells whose sizes increase monotonically according to their indices. This special geometry induces a nonequilibrium stationary state with particles flowing steadily from the small to the large scales. The corresponding invariant measure has fractal properties reflected by the phase-space contraction rate of the dynamics restricted to a single cell with appropriate boundary conditions.

Drift of particles in self-similar systems and its Liouvillian interpretation.

We study the dynamics of classical particles in different classes of spatially extended self-similar systems, consisting of (i) a self-similar Lorentz billiard channel, (ii) a self-similar graph, and (iii) a master equation. In all three systems, the particles typically drift at constant velocity and spread ballistically. These transport properties are analyzed in terms of the spectral properties of the operator evolving the probability densities.

Quasistatic brittle fracture in inhomogeneous media and iterated conformal maps: modes I, II, and III.

The method of iterated conformal maps is developed for quasistatic fracture of brittle materials, for all modes of fracture. Previous theory, that was relevant for mode III only, is extended here to modes I and II. The latter require the solution of the bi-Laplace rather than the Laplace equation.

Iterated conformal dynamics and Laplacian growth.

The method of iterated conformal maps for the study of diffusion limited aggregates (DLA) is generalized to the study of Laplacian growth patterns and related processes. We emphasize the fundamental difference between these processes: DLA is grown serially with constant size particles, while Laplacian patterns are grown by advancing each boundary point in parallel, proportional to the gradient of the Laplacian field. We introduce a two-parameter family of growth patterns that interpolates between DLA and a discrete version of Laplacian growth.

Quasistatic fractures in brittle media and iterated conformal maps.

We study the geometrical characteristic of quasistatic fractures in brittle media, using iterated conformal maps to determine the evolution of the fracture pattern. This method allows an efficient and accurate solution of the Lamé equations without resorting to lattice models. Typical fracture patterns exhibit increased ramification due to the increase of the stress at the tips.