Time-dependent Harmonic Oscillator Dynamics Reveal Particle Creation across Non-Quasi-Static Regions

The behaviour of quantum systems driven by time-varying forces remains a fundamental challenge in physics, and recent work by Salvador J. Robles-Perez and Salvador Castillo-Rivera, both from Universidad Carlos III de Madrid, sheds new light on this area. Their investigation focuses on the dynamics of a time-dependent harmonic oscillator, revealing a surprising connection between particle creation, the system’s ability to evolve slowly, and the emergence of irreversible processes. The researchers present analytical results that track the oscillator’s behaviour across all stages of its evolution, including previously unexplored regions, and demonstrate how the system undergoes a reversible thermalisation process, generating a concept of temperature solely from its internal dynamics. This achievement challenges conventional understandings of classical thermodynamics and offers potential implications for the design of future thermal machines, while also establishing a link between particle creation and entropy within the quantum system.

Quantum Thermodynamics, Decoherence, and Open Systems

This document represents a comprehensive compilation of research concerning quantum thermodynamics, decoherence, and related fields, encompassing core themes such as the application of thermodynamics to quantum systems, the process of decoherence, and the study of open quantum systems. The collection also delves into non-equilibrium quantum systems, concepts from quantum information and computation, and surprising connections between quantum field theory, cosmology, and gravity. The document consists of a vast list of publications, papers, books, and articles, covering a wide range of topics within these core themes, interspersed with mathematical formulas and equations. This compilation serves as a valuable resource for experts deeply involved in research within these complex fields, representing a long-term accumulation of knowledge gathered during an ongoing research project.

Time-Dependent Oscillator Dynamics and Irreversibility

Scientists have developed a rigorous methodology to explore the dynamics and thermodynamics of a time-dependent harmonic oscillator, focusing on the relationship between particle creation, adiabaticity, and irreversibility. This research pioneers an exact description of the oscillator’s evolution, valid for both quasi-static and non-quasi-static processes, allowing researchers to monitor its behaviour across all stages of frequency change. This approach enables tracking thermodynamic properties throughout the oscillator’s evolution, unlike previous work focused on asymptotic regions. The team calculated analytic solutions applicable throughout the oscillator’s entire evolution, providing a comprehensive understanding of its thermodynamics at any given time.

Researchers analysed the system using three distinct representations, initial, diagonal, and invariant, each modelling different particle measurement realizations. Crucially, the invariant representation received particular attention for its potential in novel experimental setups. Scientists demonstrated that the number of particles, and consequently the quantum analogs of heat and work, depend on the chosen representation, mirroring the classical observation that heat and work are path-dependent. This representation dependence is particularly relevant for the design of quantum thermal machines, where selecting an appropriate representation could significantly impact efficiency. The study employed precise calculations to determine particle occupation numbers and total particle counts in each representation, providing a detailed thermodynamic profile of the time-dependent harmonic oscillator.

Time-Dependent Harmonic Oscillator Dynamics and Thermodynamics

Scientists have achieved an exact description of the dynamics and thermodynamics of a time-dependent harmonic oscillator, providing a comprehensive framework applicable to both quasi-static and non-quasi-static processes. This work investigates the interconnectedness of particle creation, adiabaticity, and irreversibility, utilizing three distinct representations, initial, diagonal, and invariant, to monitor thermodynamic magnitudes. The research delivers analytical results valid for any functional value of the frequency and throughout the entire evolution of the oscillator. Experiments reveal that the largest modes within certain representations can undergo a reversible process resembling thermalization, where a concept of temperature emerges naturally from the unitary evolution of the oscillator, independent of any external temperature source.

This unexpected behaviour allows scientists to monitor a classical-to-quantum transition, potentially violating the third principle of classical thermodynamics. The team adapted customary definitions of quantum heat and work to account for particle creation, demonstrating that these quantities depend on the chosen representation. Measurements confirm a relationship between particle creation and diagonal entropy, suggesting a mode temperature that corresponds to thermal temperature under specific conditions. This research establishes a foundation for understanding quantum thermodynamics, potentially optimizing thermodynamic processes, and challenges conventional assumptions about thermalization, demonstrating that it can occur through unitary evolution without dissipative interactions.

Adiabaticity, Irreversibility, and Emergent Temperature in Oscillators

This research presents a detailed examination of the dynamics of a time-dependent harmonic oscillator, focusing on how particle creation relates to concepts of adiabaticity and irreversibility. By analysing the oscillator’s behaviour in different mathematical representations, initial, diagonal, and invariant, the team achieved analytical results applicable across the entire evolution of the system. These results demonstrate that the largest modes within certain representations can undergo a reversible process resembling thermalization, where a concept of temperature emerges naturally from the system’s unitary evolution, independent of any external temperature source. The study adapted conventional definitions of heat and work to account for particle creation, revealing that these quantities depend on the chosen representation. Importantly, the research establishes a connection between particle creation and diagonal entropy, suggesting a mode temperature that corresponds to thermal temperature under specific conditions. The team’s findings offer a new perspective on the interplay between quantum dynamics, thermodynamics, and the emergence of temperature in non-equilibrium systems, providing valuable insights into the fundamental principles governing quantum systems and opening avenues for developing novel technologies based on quantum thermodynamics.