The behaviour of energy during rapid changes in quantum systems presents a fundamental challenge in physics, and Donny Dwiputra, Mir Faizal, Francesco Marino, and Freddy P. Zen investigate this phenomenon by exploring the statistics of work performed during ‘quenches’ in gapless systems. Their research reveals that the scaling of work fluctuations follows predictable patterns, mirroring the well-established Kibble-Zurek mechanism which describes defect formation during phase transitions. By analysing a specific example, the nonequilibrium dynamics of a quenched Heisenberg XXZ chain, the team demonstrates that these scaling laws hold true across both fast and slow changes, confirmed by comparison with precise numerical calculations. This work provides valuable insight into the thermodynamics of adiabatic processes and expands our understanding of how energy behaves in rapidly evolving quantum environments.
Quench Dynamics and Excitation Distributions in Luttinger Liquids
This research investigates how one-dimensional quantum systems respond to sudden changes, known as quenches, in their properties. The study focuses on understanding the distribution of energy created by the quench and how this distribution evolves over time, particularly in systems known as Luttinger liquids, which model interacting electrons in one dimension. Researchers utilize statistical measures called cumulants to characterize this distribution, comparing the behavior of systems starting from both their lowest energy state and a state with a finite temperature. The results demonstrate that the first cumulant scales logarithmically with time, indicating a slow relaxation process, while higher-order cumulants decay more rapidly. When the system starts at a finite temperature, all cumulants scale inversely with both temperature and a characteristic time related to the quench, reflecting the influence of thermal fluctuations and the tendency of collective excitations to bunch together. Comparisons with other systems highlight the importance of particle statistics, with the Luttinger liquid exhibiting different scaling behavior due to its bosonic excitations.
Work Statistics in Gapless Quantum Systems
Scientists have explored the statistics of work performed on quantum systems during rapid or slow changes, known as quenches, in systems lacking an energy gap. They employed a two-time measurement scheme to define work, tracking energy changes resulting from a time-dependent force. This approach allows for the calculation of the probability distribution of work, revealing the stochastic nature of energy differences. The team focused on the Heisenberg XXZ chain, a model system in quantum physics, and mapped its behavior onto a Tomonaga-Luttinger liquid, a theoretical framework describing interacting electrons in one dimension, using a mathematical technique called Abelian bosonization.
Researchers then derived the cumulant generating function, a mathematical tool that encodes information about the system’s thermodynamics and fluctuations. The study demonstrates that this function exhibits distinct scaling behavior depending on the speed of the quench and reveals oscillatory patterns in finite-sized systems. Analytical results were validated through exact numerical calculations on a finite XXZ chain, confirming the shared characteristics of fast and slow quench regimes. This combined theoretical and numerical approach provides a robust understanding of work statistics in gapless systems and expands the application of the Kibble-Zurek mechanism to a broader range of physical scenarios.
Work Statistics Universal Across Rapid Changes
Researchers have demonstrated the universality of work statistics during rapid changes, or quenches, in gapless physical systems, confirming a connection to the Kibble-Zurek mechanism. The research confirms that statistical measures of work, called cumulants, scale predictably depending on the speed of the change, mirroring behavior observed in traditional phase transitions. Analysis of a quenched Heisenberg XXZ chain supports these findings, showing that cumulants exhibit a power-law scaling analogous to that predicted by the Kibble-Zurek mechanism. Experiments revealed that the first three cumulants of the XXZ chain consistently followed a specific scaling behavior for fast quenches.
For slower quenches, the cumulants saturated to plateaus, exhibiting finite size oscillations that decreased with larger system sizes, a phenomenon accurately predicted by the theoretical model. Detailed measurements of the first and second cumulants demonstrated that higher-order cumulants also saturate, indicating that the distribution of work performed during the quench is non-Gaussian. Furthermore, the scaling of these cumulants is influenced by the system’s temperature, with thermal quenches exhibiting a specific scaling due to the bosonic nature of the excitations within the Luttinger liquid, contrasting with systems of fermions.
Work Fluctuation Scaling in Gapless Quenches
This research demonstrates a universal scaling behaviour in the statistics of work performed during rapid changes, or quenches, in physical systems lacking an energy gap. The team established that the fluctuations in work scale predictably with the duration of the quench, mirroring the well-known Kibble-Zurek mechanism. Specifically, the researchers found that higher-order statistical moments, known as cumulants, exhibit a power-law relationship with the quench duration, a result confirmed through analysis of the Heisenberg XXZ chain. The study extends this understanding to quenches initiated at finite temperatures and provides a theoretical framework directly testable in current experimental platforms, including quantum annealers and simulators of gapless quantum systems. This achievement offers valuable insight into non-equilibrium dynamics and provides a foundation for exploring the thermodynamics of rapid, adiabatic processes.