Monday, 17 January 2022

The hyperbolic Calogero-Moser model are classical particles moving on the real line and interacting pairwise through the repulsive 1/sinh^2(x) potential. The model is integrable. Of great interest is its generalized free energy, since with this input one can write the Euler type hydrodynamic equations. We will explain a novel method for computing the generalized free energy by using scattering coordinates (action-angle variables for the open system) obtained by Ruijsenaars in 1995.

An interesting class of open quantum systems is defined by the so-called repeated interaction scheme, where the system interacts sequentially with small and fresh subsystems or units coming from the reservoir. The interaction is unitary and relatively easy to analyze. However, it must be switched on and off, and this action introduces or extracts energy in many cases of interest, performing work and preventing thermalization. As a consequence, the repeated interaction scheme cannot be used to model thermostats in quantum thermodynamics.

We overcome this problem by considering collisional reservoirs where the units are particles that collide with the system. The whole setup is autonomous and, if the units are in thermal equilibrium, the work to switch on and off the interaction becomes heat, and thermalization is recovered in most cases. However, to induce well-defined collisions, one needs to bombard the system with wave packets of finite width, and, surprisingly, this finite width can keep and even generate coherences in the system in some situations. These results prompt a fundamental question for quantum thermodynamics: what comes out by effusion from a container with a quantum gas in thermal equilibrium: waves or particles?

Tuesday, 18 January 2022

The theory of fluctuating hydrodynamics has been an important tool for analyzing macroscopic behavior of transport. However, despite its practical success, its microscopic derivation is still incomplete. We provide the microscopic derivation of fluctuating hydrodynamics, using the coarse-graining and projection technique; the equivalence of ensembles turns out to be critical. The Green-Kubo-like formula for the bare transport coefficients are presented in a numerically computable form. Our numerical simulations show that the bare transport coefficients exist for a sufficiently large but finite coarse-graining length in the infinite lattice within the framework of the GK-like formula. This demonstrates that the bare transport coefficients uniquely exist for each physical system. In addition, we provide thermodynamics of the hydrodynamics from the viewpoint of stochastic thermodynamics.

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

Wednesday, 19 January 2022

Nondiffusive thermal conduction suggests that thermal conductivity of a material would increase linearly (ballistic) or sublinearly (anomalous) with its length. Although various nondiffusive thermal conduction has been found in bulk or in nanowires, controversies remain regarding their data interpretations or their origins. Similar inconsistencies also exist when people employ molecular dynamics simulations (MD) to study thermal conductivities of carbon nanotubes. In this talk, I will review the current status of nondiffusive thermal conduction and our efforts in understanding it. An overlooked effect of contact resistance has led to misinterpretations of data in experiments as well as in MD simulations. When the sample is nondiffusive, I will show that the simple concept of two-probe thermal conduction cannot be naïvely extended to three or more probes. Two kinds of unusual nonlocal effects are found. Their implications in new applications will be discussed.

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.

Thursday, 20 January 2022

Run-and-tumble particles, frequently considered today for modeling bacterial locomotion, naturally appear outside a biological context as well. Here, we consider them in a quantum mechanical context, using a wave function to drive their propulsion and tumbling. Such quantum-active motion realizes a jittery motion of Dirac electrons (as in the famous Zitterbewegung): the Dirac electron is a run-and-tumble particle, where the tumbling is between chiralities. We visualize the electron trajectories in single and double slit experiments and discuss their dependence on the spin-direction. In particular, that yields the time-of-arrival statistics of the electrons at the screen. Finally, we observe that away from pure quantum guidance, run-and-tumble particles with suitable spacetime-dependent parameters produce an interference pattern as well.

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.

Friday, 21 January 2022

In the quantum world, measuring a quantum system irreversibly perturbs its state. A measurement channel can thus provide energy and entropy, in the same way a thermal bath does. Building on this analogy, it is possible to design engines fueled by quantum measurement. In this talk I will present an overview of this exciting research line, focusing on the last theoretical proposals. I will provide snapshots on current experimental efforts to build such engines, and comment on how this topics relates to interpretations of quantum mechanics.

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).

Monday, 24 January 2022

Classically the first time a particle reaches a target, either via a diffusive mechanism or deterministically, controls many processes in science. In the absence of a well defined path the first arrival time to a target state of a quantum particle can be treated in several ways. Such problems arise in the excitation transfer to a reaction centre in light harvesting systems, and more recently in the context of quantum search algorithms. We will review the challenges of search, starting with the quantum renewal equation, dark states and their relation to symmetry, and topological aspects of the first return problem. This is done for a protocol with unitary dynamics pierces by repeated strong measurements aimed to detect a quantum walker on a node of a graph. We will then show how to construct tight binding Hamiltonians that speed up state-transfer both in the presence and the absence of repeated measurements. These are related to a mass-less Dirac quasi particle and a large degenracy of the eigenvalues of the underlying non-Hermitian survival operator.

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

Tuesday, 25 January 2022

The study of out-of-equilibrium thermodynamics of quantum systems has received increasing attention in recent years thanks to tremendous theoretical and experimental progress. While most of the studies in quantum thermodynamics bear a close resemblance to their classical counterparts, especially close to equilibrium, there are only a few examples of genuine quantum features, e.g. coherence, squeezing and entanglement, that provide an advantage over classical thermodynamic devices. In this contribution, I will show how thermal equilibrium reservoirs equipped with an infinitesimal amount of quantum coherence exhibit such an advantage. In fact, reservoir quantum coherence allows the design of engine and refrigerators with efficiencies that exceed the corresponding Carnot's efficiency of a classical machine operating with the same temperatures. Such thermal machines provide efficiencies at maximum power that exceed the classical Curzon-Ahlborn value. Moreover, the injected coherence allows for a hybrid refrigerators which extracts heat from the coldest bath and simultaneously produces work.

References:

[1] K. Hammam, H. Leitch, Y. Hassouni and G. De Chiara (in preparation)

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.

Wednesday, 26 January 2022

We study the response of an infinite system of point particles on the line initially at rest to the instantaneous release of energy in a localized region. The blast generates shock waves, and we make a detailed comparison of the density, velocity, and temperature in the growing region between the shock waves predicted by Euler equations for the ideal non-dissipative compressible gas and the results of direct microscopic simulations. At long times, the scaling functions obtained from the microscopic dynamics show a remarkable agreement with the Taylor–von Neumann–Sedov (TvNS) predictions, except at the blast core where a different scaling form is observed. We show that this is due to heat conduction becoming important in the core.

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.

Thursday, 27 January 2022

In equilibrium thermodynamics, the Boltzmann entropy serves as a complete thermodynamic potential that characterizes state convertibility in a necessary and sufficient manner. In this talk, I will present our result [1,2] that a complete thermodynamic potential emerges for a broad class of quantum many-body systems under physically reasonable assumptions, even in out-of-equilibrium and fully quantum situations. Our proof is based on the resource-theoretic formalism of thermodynamics [3] and the quantum ergodic theorem. The complete thermodynamic potential is in general given by a quantity called the spectral divergence rate, while under some assumptions it reduces to the Kullback-Leibler (KL) divergence rate. Moreover, I will discuss the case where an auxiliary system called a catalyst is introduced, and show that the KL divergence again serves as a complete thermodynamic potential if a small amount of correlation is allowed between the system and the catalyst [4].

References:

[1] P. Faist, T. Sagawa, K. Kato, H. Nagaoka, F. Brandao, Phys. Rev. Lett. 123, 250601 (2019).

[2] T. Sagawa, P. Faist, K. Kato, K. Matsumoto, H. Nagaoka, F. Brandao, J. Phys. A: Math. Theor. 54, 495303 (2021).

[3] T. Sagawa, "Entropy, Divergence, and Majorization in Classical and Quantum Thermodynamics" (SpringerBriefs in Mathematical Physics, 2022); arXiv:2007.09974.

[4] N. Shiraishi, T. Sagawa, Phys. Rev. Lett. 126, 150502 (2021).

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.

Friday, 28 January 2022

I will discuss some of our recent experiments to probe and tune Berry curvature hotspots in a moiré flat band system. In particular, we use a small-angle twisted double bilayer graphene [1] (TDBG) device (AB bilayer + AB bilayer (θ)) and study the Hall effect without explicitly breaking time-reversal symmetry. Despite reduced Fermi velocity in a flat band, we observe large nonlocal voltage several micrometers away. We use a perpendicular electric field to gain further control on these Berry curvature hotspots—specifically we are able to control the spreading of Berry curvature in k-space. TDBG provides new opportunities for realizing valley current via its tunable bandgaps and bandwidth.

We gratefully acknowledge funding from Department of Science and technology, India, and Department of Atomic Energy, India.

[1] Pratap Chandra Adak*, Subhajit Sinha*, Tunable bandwidths and gaps in twisted double bilayer graphene system on the verge of correlations, Phys. Rev. B 101, 125428 (2020).

[2] S. Sinha*, P. C. Adak*, Bulk valley transport and Berry curvature spreading at the edge of flat bands, Nat. Commun. 11, 5548 (2020).

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.