arXiv subjects

Kay Brandner

Publications and source records attributed to Kay Brandner.

At least 19 recordsLinked to original sources

arXiv2025

Weak-Memory Dynamics in Discrete Time

Discrete dynamics arise naturally in systems with broken temporal translation symmetry and are typically described by first-order recurrence relations representing classical or quantum Markov chains. When memory effects induced by hidden degrees of freedom are relevant, however, higher-order discrete evolution equations are generally required. Focusing on linear dynamics, we identify a well-delineated weak-memory regime where such equations can, on an intermediate time scale, be systematically reduced to a unique first-order counterpart acting on the same state space. We formulate our results as a mathematical theorem and work out two examples showing how they can be applied to stochastic Floquet dynamics under coarse-grained and quantum collisional models.

cond-mat.stat-mech↗

arXiv2025

Thermodynamic bound on current fluctuations in coherent conductors

We derive a universal bound on the large-deviation functions of particle currents in coherent conductors. This bound depends only on the mean value of the relevant current and the total rate of entropy production required to maintain a non-equilibrium steady state, thus showing that both typical and rare current fluctuations are ultimately constrained by dissipation. Our analysis relies on the scattering approach to quantum transport and applies to any multi-terminal setup with arbitrary chemical potential and temperature gradients, provided the transmission coefficients between reservoirs are symmetric. This condition is satisfied for any two-terminal system and, more generally, when the dynamics of particles within the conductor are symmetric under time-reversal. For typical current fluctuations, we recover a recently derived thermodynamic uncertainty relation for coherent transport. To illustrate our theory, we analyze a specific model comprising two reservoirs connected by a chain of quantum dots, which shows that our bound can be saturated asymptotically.

cond-mat.stat-mech↗

arXiv2025

Thermodynamic Uncertainty Relations for Coherent Transport

We derive a universal thermodynamic uncertainty relation for Fermionic coherent transport, which bounds the total rate of entropy production in terms of the mean and fluctuations of a single particle current. This bound holds for any multi-terminal geometry and arbitrary chemical and thermal biases, as long as no external magnetic fields are applied. It can further be saturated in two-terminal settings with boxcar-shaped transmission functions and reduces to its classical counterpart in linear response. Upon insertion of a numerical factor, our bound also extends to systems with broken time-reversal symmetry. As an application, we derive trade-off relations between the figures of merit of coherent thermoelectric heat engines and refrigerators, which show that such devices can attain ideal efficiency only at vanishing mean power or diverging power fluctuations. To illustrate our results, we work out a model of a coherent conductor consisting of a chain of quantum dots.

cond-mat.stat-mech↗

arXiv2024

Dynamics of micro and nanoscale systems in the weak-memory regime: A mathematical framework beyond the Markov approximation

The visible dynamics of small-scale systems are strongly affected by unobservable degrees of freedom, which can belong either to external environments or internal subsystems and almost inevitably induce memory effects. Formally, such inaccessible degrees of freedom can be systematically eliminated from essentially any microscopic model through projection operator techniques, which result in non-local time evolution equations. This article investigates how and under what conditions locality in time can be rigorously restored beyond the standard Markov approximation, which generally requires the characteristic time scales of accessible and inaccessible degrees of freedom to be sharply separated. Specifically, we consider non-local time evolution equations that are autonomous and linear in the variables of interest. For this class of models, we prove a mathematical theorem that establishes a well-defined weak-memory regime, where faithful local approximations exists, even if the relevant time scales are of comparable order of magnitude. The generators of these local approximations, which become exact in the long-time limit, are time independent and can be determined to arbitrary accuracy through a convergent perturbation theory in the memory strength, where the Markov generator is recovered in first order. For illustration, we work out three simple, yet instructive, examples covering coarse grained Markov jump networks, semi-Markov jump processes and generalized Langevin equations.

cond-mat.stat-mech↗

arXiv2024

Dynamics of Micro and Nanoscale Systems in the Weak-Memory Regime

Memory effects are ubiquitous in small-scale systems. They emerge from interactions between accessible and inaccessible degrees of freedom and give rise to evolution equations that are non-local in time. If the characteristic time scales of accessible and inaccessible degrees of freedom are sharply separated, locality can be restored through the standard Markov approximation. Here, we show that this approach can be rigorously extended to a well-defined weak-memory regime, where the relevant time scales can be of comparable order of magnitude. We derive explicit bounds on the error of the local approximation and a convergent perturbation scheme for its construction. Being applicable to any non-local time evolution equation that is autonomous and linear in the variables of interest, our theory provides a unifying framework for the systematic description of memory effects.

cond-mat.stat-mech↗

arXiv2024

Quasiperiodic Floquet-Gibbs states in Rydberg atomic systems

Open systems that are weakly coupled to a thermal environment and driven by fast, periodically oscillating fields are commonly assumed to approach an equilibrium-like steady state with respect to a truncated Floquet-Magnus Hamiltonian. Using a general argument based on Fermi's golden rule, we show that such Floquet-Gibbs states emerge naturally in periodically modulated Rydberg atomic systems, whose lab-frame Hamiltonian is a quasiperiodic function of time. Our approach applies as long as the inherent Bohr frequencies of the system, the modulation frequency and the frequency of the driving laser, which is necessary to uphold high-lying Rydberg excitations, are well separated. To corroborate our analytical results, we analyze a realistic model of up to five interacting Rydberg atoms with periodically changing detuning. We demonstrate numerically that the second-order Floquet-Gibbs state of this system is essentially indistinguishable from the steady state of the corresponding Redfield equation if the modulation and driving frequencies are sufficiently large.

cond-mat.stat-mech↗

arXiv2024

Stochastic Thermodynamics at the Quantum-Classical Boundary: A Self-Consistent Framework Based on Adiabatic-Response Theory

Microscopic thermal machines promise to play an important role in future quantum technologies. Making such devices widely applicable will require effective strategies to channel their output into easily accessible storage systems like classical degrees of freedom. Here, we develop a self-consistent theoretical framework that makes it possible to model such quantum-classical hybrid devices in a thermodynamically consistent manner. Our approach is based on the assumption that the quantum part of the device is subject to strong decoherence and dissipation induced by a thermal reservoir. Due to the ensuing separation of time scales between slowly evolving classical and fast relaxing quantum degrees of freedom, the dynamics of the hybrid system can be described by means of adiabatic-response theory. We show that, upon including fluctuations in a minimally consistent way, the resulting equations of motion can be equipped with a first and second law, both on the ensemble level and on the level of individual trajectories of the classical part of the system, where thermodynamic quantities like heat and work become stochastic variables. As an application of our theory, we work out a physically transparent model of a quantum-classical hybrid engine, whose working system consists of a chain of Rydberg atoms, which is confined in an optical cavity and driven by periodic temperature variations. We demonstrate through numerical simulations that the engine can sustain periodic oscillations of a movable mirror, which acts as a classical load, against external friction and extract the full distributions of input heat and output work. By making the statistics of thermodynamic processes in quantum-classical hybrid systems accessible without the need to further specify a measurement protocol, our work contributes to bridging the long-standing gap between classical and quantum stochastic thermodynamics.

cond-mat.stat-mech↗

arXiv2023

Rydberg ion flywheel for quantum work storage

Trapped ions provide a platform for quantum technologies that offers long coherence times and high degrees of scalability and controllability. Here, we use this platform to develop a realistic model of a thermal device consisting of two laser-driven, strongly coupled Rydberg ions in a harmonic trap. We show that the translational degrees of freedom of this system can be utilized as a flywheel storing the work output that is generated by a cyclic thermodynamic process applied to its electronic degrees of freedom. Mimicking such a process through periodic variations of external control parameters, we use a mean-field approach underpinned by numerical and analytical calculations to identify relevant physical processes and to determine the charging rate of the flywheel. Our work paves the way for the design of microscopic thermal machines based on Rydberg ions that can be equipped with both many-body working media and universal work storages.

cond-mat.stat-mech↗

arXiv2023

Lee-Yang theory of Bose-Einstein condensation

Bose-Einstein condensation happens as a gas of bosons is cooled below its transition temperature, and the ground state becomes macroscopically occupied. The phase transition occurs in the thermodynamic limit of many particles. However, recent experimental progress has made it possible to assemble quantum many-body systems from the bottom up, for example, by adding single atoms to an optical lattice one at a time. Here, we show how one can predict the condensation temperature of a Bose gas from the energy fluctuations of a small number of bosons. To this end, we make use of recent advances in Lee-Yang theories of phase transitions, which allow us to determine the zeros and the poles of the partition function in the complex plane of the inverse temperature from the high cumulants of the energy fluctuations. By increasing the number of bosons in the trapping potential, we can predict the convergence point of the partition function zeros in the thermodynamic limit, where they reach the inverse critical temperature on the real axis. Using less than 100 bosons, we can estimate the condensation temperature for a Bose gas in a harmonic potential in two and three dimensions, and we also find that there is no phase transition in one dimension as one would expect.

cond-mat.quant-gas↗

arXiv2022

Thermodynamic geometry of ideal quantum gases: a general framework and a geometric picture of BEC-enhanced heat engines

Thermodynamic geometry provides a physically transparent framework to describe thermodynamic processes in meso- and micro-scale systems that are driven by slow variations of external control parameters. Focusing on periodic driving for thermal machines, we extend this framework to ideal quantum gases. To this end, we show that the standard approach of equilibrium physics, where a grand-canonical ensemble is used to model a canonical one by fixing the mean particle number through the chemical potential, can be extended to the slow driving regime in a thermodynamically consistent way. As a key application of our theory, we use a Lindblad-type quantum master equation to work out a dynamical model of a quantum many-body engine using a harmonically trapped Bose gas. Our results provide a geometric picture of the BEC-induced power enhancement that was previously predicted for this type of engine on the basis of an endoreversible model [New J. Phys. 24, 025001 (2022)]. Using an earlier derived universal trade-off relation between power and efficiency as a benchmark, we further show that the Bose-gas engine can deliver significantly more power at given efficiency than an equally large collection of single-body engines. Our work paves the way for a more general thermodynamic framework that makes it possible to systematically assess the impact of quantum many-body effects on the performance of thermal machines.

cond-mat.quant-gas↗

arXiv2022

Reservoir-induced stabilisation of a periodically driven many-body system

Exploiting the rich phenomenology of periodically-driven many-body systems is notoriously hindered by persistent heating in both the classical and quantum realm. Here, we investigate to what extent coupling to a large thermal reservoir makes stabilisation of a non-trivial steady state possible. To this end, we model both the system and the reservoir as classical spin chains where driving is applied through a rotating magnetic field, and simulate the Hamiltonian dynamics of this setup. We find that the intuitive limits of infinite and vanishing frequency, where the system dynamics is governed by the average and the instantaneous Hamiltonian, respectively, can be smoothly extended into entire regimes separated only by a small crossover region. At high frequencies, the driven system stroboscopically attains a Floquet-type Gibbs state at the reservoir temperature. At low frequencies, a synchronised Gibbs state emerges, whose temperature may depart significantly from that of the reservoir. Although our analysis in some parts relies on the specific properties our setup, we argue that much of its phenomenology should be generic for a large class of systems.

cond-mat.stat-mech↗

arXiv2022

Reservoir-induced stabilisation of a periodically driven classical spin chain: local vs. global relaxation

Floquet theory is an indispensable tool for analysing periodically-driven quantum many-body systems. Although it does not universally extend to classical systems, some of its methodologies can be adopted in the presence of well-separated timescales. Here we use these tools to investigate the stroboscopic behaviours of a classical spin chain that is driven by a periodic magnetic field and coupled to a thermal reservoir. We detail and expand our previous work: we investigate the significance of higher-order corrections to the classical Floquet-Magnus expansion in both the high- and low-frequency regimes; explicitly probe the evolution the dynamics of the reservoir; and further explore how the driven system synchronises with the applied field at low frequencies. In line with our earlier results, we find that the high-frequency regime is characterised by a local Floquet-Gibbs ensemble with the reservoir acting as a nearly-reversible heatsink. At low frequencies, the driven system rapidly enters a synchronised state, which can only be fully described in a global picture accounting for the concurrent relaxation of the reservoir in a fictitious magnetic field arising from the drive. We highlight how the evolving nature of the reservoir may still be incorporated in a local picture by introducing an effective temperature. Finally, we argue that dissipative equations of motion for periodically-driven many-body systems, at least at intermediate frequencies, must generically be non-Markovian.

cond-mat.stat-mech↗

arXiv2022

Thermodynamics of Permutation-Invariant Quantum Many-Body Systems: A Group-Theoretical Framework

Quantum systems of indistinguishable particles are commonly described using the formalism of second quantisation, which relies on the assumption that any admissible quantum state must be either symmetric or anti-symmetric under particle permutations. Coherence-induced many-body effects such as superradiance, however, can arise even in systems whose constituents are not fundamentally indistinguishable as long as all relevant dynamical observables are permutation-invariant. Such systems are not confined to symmetric or anti-symmetric states and therefore require a different theoretical approach. Focusing on non-interacting systems, here we combine tools from representation theory and thermodynamically consistent master equations to develop such a framework. We characterise the structure and properties of the steady states emerging in permutation-invariant ensembles of arbitrary multi-level systems that are collectively weakly coupled to a thermal environment. As an application of our general theory, we further explore how these states can in principle be used to enhance the performance of quantum thermal machines. Our group-theoretical framework thereby makes it possible to analyse various limiting cases that would not be accessible otherwise. In addition, it allows us to show that the properties of multi-level ensembles differ qualitatively from those of spin ensembles, which have been investigated earlier using the standard Clebsch-Gordan theory. Our results have a large scope for future generalisations and pave the way for systematic investigations of collective effects arising from permutation-invariance in quantum thermodynamics.

quant-ph↗

arXiv2022

Many-body radiative decay in strongly interacting Rydberg ensembles

When atoms are excited to high-lying Rydberg states they interact strongly with dipolar forces. The resulting state-dependent level shifts allow to study many-body systems displaying intriguing nonequilibrium phenomena, such as constrained spin systems, and are at the heart of numerous technological applications, e.g., in quantum simulation and computation platforms. Here, we show that these interactions have also a significant impact on dissipative effects caused by the inevitable coupling of Rydberg atoms to the surrounding electromagnetic field. We demonstrate that their presence modifies the frequency of the photons emitted from the Rydberg atoms, making it dependent on the local neighborhood of the emitting atom. Interactions among Rydberg atoms thus turn spontaneous emission into a many-body process which manifests, in a thermodynamically consistent Markovian setting, in the emergence of collective jump operators in the quantum master equation governing the dynamics. We discuss how this collective dissipation - stemming from a mechanism different from the much studied super- and sub-radiance - accelerates decoherence and affects dissipative phase transitions in Rydberg ensembles.

quant-ph↗

arXiv2022

Geometric Bounds on the Power of Adiabatic Thermal Machines

We analyze the performance of slowly driven meso- and micro-scale refrigerators and heat engines that operate between two thermal baths with small temperature difference. Using a general scaling argument, we show that such devices can work arbitrarily close to their Carnot limit only if heat-leaks between the baths are fully suppressed. Their power output is then subject to a universal geometric bound that decays quadratically to zero at the Carnot limit. This bound can be asymptotically saturated in the quasi-static limit if the driving protocols are suitably optimized and the temperature difference between the baths goes to zero with the driving frequency. These results hold under generic conditions for any thermodynamically consistent dynamics admitting a well-defined adiabatic-response regime and a generalized Onsager symmetry. For illustration, we work out models of a qubit-refrigerator and a coherent charge pump operating as a cooling device.

cond-mat.stat-mech↗

arXiv2021

Thermodynamic uncertainty relations for coherently driven open quantum systems

In classical Markov jump processes, current fluctuations can only be reduced at the cost of increased dissipation. To explore how quantum effects influence this trade-off, we analyze the uncertainty of steady-state currents in Markovian open quantum systems. We first consider three instructive examples and then systematically minimize the product of uncertainty and entropy production for small open quantum systems. As our main result, we find that the thermodynamic cost of reducing fluctuations can be lowered below the classical bound by coherence. We conjecture that this cost can be made arbitrarily small in quantum systems with sufficiently many degrees of freedom. Our results thereby provide a general guideline for the design of thermal machines in the quantum regime that operate with high thermodynamic precision, meaning low dissipation and small fluctuations around average values.

cond-mat.stat-mech↗

arXiv2020

Nonequilibrium many-body quantum engine driven by time-translation symmetry breaking

Quantum many-body systems out of equilibrium can host intriguing phenomena such as transitions to exotic dynamical states. Although this emergent behaviour can be observed in experiments, its potential for technological applications is largely unexplored. Here, we investigate the impact of collective effects on quantum engines that extract mechanical work from a many-body system. Using an opto-mechanical cavity setup with an interacting atomic gas as a working fluid, we demonstrate theoretically that such engines produce work under periodic driving. The stationary cycle of the working fluid features nonequilibrium phase transitions, resulting in abrupt changes of the work output. Remarkably, we find that our many-body quantum engine operates even without periodic driving. This phenomenon occurs when its working fluid enters a phase that breaks continuous time-translation symmetry: the emergent time-crystalline phase can sustain the motion of a load generating mechanical work. Our findings pave the way for designing novel nonequilibrium quantum machines.

cond-mat.stat-mech↗

arXiv2020

Quantum jump approach to microscopic heat engines

Modern technologies could soon make it possible to investigate the operation cycles of quantum heat engines by counting the photons that are emitted and absorbed by their working systems. Using the quantum jump approach to open-system dynamics, we show that such experiments would give access to a set of observables that determine the trade-off between power and efficiency in finite-time engine cycles. By analyzing the single-jump statistics of thermodynamic fluxes such as heat and entropy production, we obtain a family of general bounds on the power of microscopic heat engines. Our new bounds unify two earlier results and admit a transparent physical interpretation in terms of single-photon measurements. In addition, these bounds confirm that driving-induced coherence leads to an increase in dissipation that suppresses the efficiency of slowly driven quantum engines in the weak-coupling regime. A nanoscale heat engine based on a superconducting qubit serves as an experimentally relevant example and a guiding paradigm for the development of our theory.

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