Related papers: Ergodicity and hydrodynamics: from quantum to clas…
Ergodic theory provides a rigorous mathematical description of chaos in classical dynamical systems, including a formal definition of the ergodic hierarchy. How ergodic dynamics is reflected in the energy levels and eigenstates of a quantum…
After briefly touching on relativistic hydrodynamics, we provide a detailed description of recent developments in spin hydrodynamics. We discuss the theory of perfect spin hydrodynamics within two different approaches, which lead to…
We give a formulation of quantum ergodicity for Pauli Hamiltonians with arbitrary spin in terms of a Wigner-Weyl calculus. The corresponding classical phase space is the direct product of the phase space of the translational degrees of…
The thermalizing dynamics of many-body systems is often described through the lens of the Eigenstate Thermalization Hypothesis (ETH). ETH postulates that the statistical properties of observables, when expressed in the energy eigenbasis,…
Identifying universal properties of non-equilibrium quantum states is a major challenge in modern physics. A fascinating prediction is that classical hydrodynamics emerges universally in the evolution of any interacting quantum system.…
In their seminal work, Fermi, Pasta, Ulam and Tsingou explored the connection between statistical mechanics and dynamical properties, such as chaos and ergodicity. Even today, seventy years later, the topic is not fully understood: while…
In ergodic quantum systems, physical observables have a non-relaxing component if they "overlap" with a conserved quantity. In interacting microscopic models, how to isolate the non-relaxing component is unclear. We compute exact dynamical…
Classical secular theory can be a powerful tool to describe the qualitative character of multi-planet systems and offer insight into their histories. The eigenmodes of the secular behavior, rather than current orbital elements, can help…
In a first part the scope of classical thermodynamics and statistical mechanics is discussed in the broader context of formal dynamical systems, including computer programmes. In this context classical thermodynamics appears as a particular…
The specific heat and susceptibilities for the two- and one-dimensional spin--orbital models are calculated in the framework of a spherically symmetric self-consistent approach at different temperatures and relations between the parameters…
Spin polarization and spin transport are common phenomena in many quantum systems. Relativistic spin hydrodynamics provides an effective low-energy framework to describe these processes in quantum many-body systems. The fundamental symmetry…
Equilibrium properties of many-body systems with a large number of degrees of freedom are generally expected to be described by statistical mechanics. Such expectations are closely tied to the observation of thermalization, as manifested…
A classical particle system coupled with a thermostat driven by an external constant force reaches its steady state when the ensemble-averaged drift velocity does not vary with time. The statistical mechanics of such a system is derived…
Hydrodynamics of gases in the classical domain are examined from the perspective that the gas has a well-defined wavefunction description at all times. Specifically, the internal energy and volume exclusion of decorrelated vortex structures…
The emergence of hydrodynamics is one of the deepest phenomena in many-body systems. Arguably, the hydrodynamic equations are also the most important tools for predicting large-scale behaviour. Understanding how such equations emerge from…
We derive a formulation of relativistic spin hydrodynamics with totally antisymmetric spin tensors that satisfy the Frenkel-Mathisson-Pirani condition. In our proposed spin hydrodynamics, the second law of thermodynamics is fulfilled by the…
We investigate the statistical equilibrium properties of a system of classical particles interacting via Newtonian gravity, enclosed in a three-dimensional spherical volume. Within a mean-field approximation, we derive an equation for the…
The literature on dynamical systems has, for the most part, considered self-oscillators (i.e., systems capable of generating and maintaining a periodic motion at the expense of an external energy source with no corresponding periodicity)…
Statistical mechanics is founded on the assumption that all accessible configurations of a system are equally likely. This requires dynamics that explore all states over time, known as ergodic dynamics. In isolated quantum systems, however,…
We revisit the canonical formulation of spin hydrodynamics for Dirac fermions with a general thermal vorticity. The orders of the general thermal vorticity and the corresponding spin variables are considered independently from those of the…