ICTS

The state of a quantum system can be classified according to the possibility of extracting energy with a unitary process. One calls the state active if this is possible and passive if not.

The equilibrium Gibbs state of a system weakly coupled to a thermal bath is passive, but the reduced state of a system strongly coupled to a bath is, in general, different from the Gibbs state, and therefore, they can be active. Equilibrium states are easy to achieve and require little effort to sustain. Therefore, studying systems with active equilibrium states is an exciting way towards developing quantum energy storing devices, a.k.a. quantum batteries.

This talk will introduce and study a battery--charger quantum device storing energy in thermal equilibrium or a ground state [1,2]. The device operates in a cycle with 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. We found [3] equivalent operations from the perspective of the battery, with different energetic costs for the cycle, and we use this purely quantum leverage to optimize the device's performance.

We study the case where the battery and charger together comprise a spin-1/2 Ising chain [3]. We show that the thermodynamic efficiency and the extracted energy 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.

[1] Dissipative charging of a quantum battery
F Barra
Physical review letters 122 (21), 210601

[2] Charging assisted by thermalization
KV Hovhannisyan, F Barra, A Imparato
Physical Review Research 2 (3), 033413

[3] Quantum batteries at the verge of a phase transition
Felipe Barra, Karen V. Hovhannisyan, Alberto Imparato
arXiv:2110.10600

In this talk I will review some recent results concerning the nonequilibrium properties of the boundary driven exclusion process and the  boundary driven zero-range process with long jumps when the variance of the jumps probability is infinite. The hydrodynamics are then described by fractional diffusions with various boundary conditions.

I will discuss heat transport by thermal microwave photons. This is an important mechanism which makes it possible to devise quantum heat valves, rectifiers and refrigerators. I will conclude the talk by discussing observation of microwave photons by calorimetry.

Open quantum systems have a natural connection to non-Hermitian physics. Their time evolution, captured by the Liouvillian, usually accounts for a free Hamiltonian evolution (i.e., Hermitian contribution) and for dissipation due to coupling to the reservoirs, this one being clearly non- Hermitian. A hallmark of non-Hermitian physics is the possibility for the system to reach exceptional points (EPs); dissipative open quantum systems can therefore exhibit Liouvillian EPs (to be contrasted to Hamiltonian EPs that can appear in a closed quantum system described by a non-Hermitian Hamiltonian). By definition, EPs are specific points in parameter space at which two or more eigenvalues of a non-Hermitian matrix and their corresponding eigenvectors coalesce. Recently, Hamiltonian EPs have attracted lots of interest in the context of quantum sensing and have been demonstrated experimentally on photonics and superconducting platforms by engineering non-Hermitian Hamiltonians.

In contrast, Liouvillian EPs have only been discussed for simple systems, such as a single dissipative spin or in the absence of quantum jumps, i.e., considering a semiclassical approach to the dynamics. Open questions concern the search for Hamiltonian and Liouvillian EPs in state-of-the-art physical platforms and their signatures, especially in the quantum regime. In this talk, I will present recent results considering a minimal model for an open quantum system made of two Interacting quantum systems. We solve analytically the dynamics of this non- Hermitian quantum system. We demonstrate the existence of Liouvillian EPs for an experimentally accessible range of parameters. We uncover a signature of EPs in the long-time dynamics, in the form of critical decay towards the steady state, in analogy to critical damping in a classical harmonic oscillator. These results broaden the class of systems exhibiting EPs and opens new routes for controlling the quantum dynamics of out-of-equilibrium nanoscale devices.

Reference:
S. Khandelwal, N. Brunner, G. Haack, PRX Quantum 2, 040346 (2021).

Starting from the seminal works of Aharonov and Bohm and Berry, geometric effects have pervaded many areas of physics. In quantum transport, distinct contributions of geometric origin affect charge and energy currents. In the absence of an additional dc bias, the pumped charge in a periodically driven system was shown to be of geometric origin, and can thus be expressed in terms of a closed-path integral in parameter space, akin to the Berry phase.  Geometric concepts like a thermodynamic metric and a thermodynamic length were recently introduced as promising tools to characterize the dissipated energy and to design optimal driving protocols. Similar ideas are behind the description of the adiabatic time-evolution of many-body ground states of closed systems in terms of a geometric tensor. 

This large body of work linking geometry to transport naturally hints at similar connections for thermal machines. In this seminar, I will discuss how, under quite general assumptions, the operation of quantum thermal machines and the underlying heat-work conversion is fundamentally tied to such geometric effects. We recently formulated a unified description in terms of a geometric tensor for all the relevant energy fluxes, which we refer to as thermal geometric tensor [1]. Within this description, pumping and dissipation are, respectively, associated with the antisymmetric and symmetric components of this tensor. Furthermore, we show that the problem of optimizing the power generation of a heat engine and the efficiency of both the heat engine and refrigerator operational modes is reduced to an isoperimetric problem with non-trivial underlying metrics and curvature. This corresponds to the maximization of the ratio between the area enclosed by a closed curve and its corresponding length [2]. A simple example of this operation is a slowly driven qubit asymmetrically coupled to two reservoirs kept at different temperatures. 

[1]Geometric properties of adiabatic quantum thermal machines (https://journals.aps.org/prb/abstract/10.1103/PhysRevB.102.155407, arXiv:2002.02225)
Bibek Bhandari, Pablo Terrén Alonso, Fabio Taddei, Felix von Oppen, Rosario Fazio, Liliana Arrachea

[2]Geometric optimization of non-equilibrium adiabatic thermal machines and implementation in a qubit system

PT Alonso, P Abiuso, M Perarnau-Llobet, L Arrachea - arXiv preprint arXiv:2109.12648, 2021

Nonequilibrium and thermal transport properties of classical integrable 1D systems like the Toda chain or the hard point gas, subject to additional (nonintegrable) terms are considered. For energy and momentum-conserving weak perturbations, heat transport is mostly supplied by quasiparticles with a very large mean free path l. Upon increasing the system size L, three different regimes can be observed: a ballistic one, an intermediate diffusive range, and, eventually, the crossover to the anomalous (hydrodynamic) regime. We discuss the case of the perturbed harmonic chain, which exhibits a yet different scenario.

The presence of uphill diffusion in particle or spin models is a remarkable problem of statistical mechanics, that was first envisaged by Darken in his pioneering work dating back to 1949. Uphill diffusion appears when the current flows along the gradient, in contrast with the Fick’s law, which states that the current is proportional to minus the gradient. Such phenomenon is typically observed in presence of multi-component systems as a result of the interaction between different species. Remarkably, some numerical and theoretical evidence supports the conclusion that uphill diffusion may also occur in single-component systems undergoing a phase transition. We shall discuss some deterministic and stochastic models which give rise to non-equilibrium steady states characterized by a phase transition sustaining the uphill motion of the particles.

Unlike their macroscopic classical analogues, nanoscale quantum devices can utilize quantum effects as a resource for their operation. On the downside, fluctuations become more prominent at the small scale, obscuring function. In my talk I will discuss the following two questions - based on examples: What is the role of quantum coherences in the operation of quantum thermal machines? What useful information is conveyed in the current noise?
I will begin by describing a kinetic model for quantum absorption refrigerators (QARs), considering "standard" measures such as the cooling current and efficiency. I will then present a quantum refrigerator in which coherences lead to the suppression of the cooling power. As for fluctuations, we recently derived upper and lower bounds on ratios of fluctuations of output to input currents, valid in the linear response regime, which I will describe and exemplify with QARs. As time allows, I will turn to other aspects of nanoscale thermal machines, probing the impact of strong system-bath coupling on their performance.

The energy equipartition hypothesis is one of the dynamic foundations of statistical mechanics. In my talk, I will first review recent progress on the proof of this hypothesis in one-dimensional (1D) lattices. Then I will show that for typical 1D lattices in the thermodynamic limit, either with uniform or disordered distribution of masses, thermalization can be approached by arbitrarily small nonlinear perturbations following a universal law of , where is the equipartition time and is the perturbation strength . To observe such a law, the integrable part of the Hamiltonian should be chosen properly, i.e., for symmetric interatomic interactions one can adopt the Hamiltonian of the harmonic oscillators while for asymmetric interatomic interactions one should take the Hamiltonian of the Toda lattice to be the integrable Hamiltonian, respectively. In this part, the studies for finite-size systems, as well as the studies for extending the thermalization law to systems with strong nonlinear interactions will be briefly introduced. I will then report our recent studies on high-dimensional lattices. In the framework of the perturbation approach and the generalized Gibbs ensemble ansatz, we obtain the relaxation equation of actions. We show that the interconnect condition of normal modes required by the wave turbulence approach can be easily satisfied for high-dimensional lattices. As a consequence, typical high-dimensional lattices also obey the universal law of thermalization. Indeed, with multi-branches of phonons high- dimensional systems may be thermalized more easily than 1D lattices. These predictions are verified by numerical simulations. I finally discuss whether four-phonon processes can dominate the thermalization of certain high- dimensional lattices, how to correlate the thermalization behavior to heat conduction, and whether the thermalization of classical and quantum systems can be integrated in the same framework.