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Register a new userTemperature inversion in long-range interacting systems
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Temperature inversion due to velocity filtration, a mechanism originally proposed to explain the heating of the solar corona, is demonstrated to occur also in a simple paradigmatic model with long-range interactions, the Hamiltonian mean-field model. Using molecular dynamics simulations, we show that when the system settles into an inhomogeneous quasi-stationary state in which the velocity distribution has suprathermal tails, the temperature and density profiles are anticorrelated: denser parts of the system are colder than dilute ones. We argue that this may be a generic property of long-range interacting systems.
Completely open systems can exchange heat, work, and matter with the environment. While energy, volume, and number of particles fluctuate under completely open conditions, the equilibrium states of the system, if they exist, can be specified using the temperature, pressure, and chemical potential as control parameters. The unconstrained ensemble is the statistical ensemble describing completely open systems and the replica energy is the appropriate free energy for these control parameters from which the thermodynamics must be derived. It turns out that macroscopic systems with short-range interactions cannot attain equilibrium configurations in the unconstrained ensemble, since temperature, pressure, and chemical potential cannot be taken as a set of independent variables in this case. In contrast, we show that systems with long-range interactions can reach states of thermodynamic equilibrium in the unconstrained ensemble. To illustrate this fact, we consider a modification of the Thirring model and compare the unconstrained ensemble with the canonical and grand canonical ones: the more the ensemble is constrained by fixing the volume or number of particles, the larger the space of parameters defining the equilibrium configurations.
Systems with long-range interactions display a short-time relaxation towards Quasi Stationary States (QSSs) whose lifetime increases with system size. The application of Lynden-Bells theory of violent relaxation to the Hamiltonian Mean Field model leads to the prediction of out-of-equilibrium first and second order phase transitions between homogeneous (zero magnetization) and inhomogeneous (non-zero magnetization) QSSs, as well as an interesting phenomenon of phase re-entrances. We compare these theoretical predictions with direct $N$-body numerical simulations. We confirm the existence of phase re-entrance in the typical parameter range predicted from Lynden-Bells theory, but also show that the picture is more complicated than initially thought. In particular, we exhibit the existence of secondary re-entrant phases: we find un-magnetized states in the theoretically magnetized region as well as persisting magnetized states in the theoretically unmagnetized region.
The presence of non-local and long-range interactions in quantum systems induces several peculiar features in their equilibrium and out-of-equilibrium behavior. In current experimental platforms control parameters such as interaction range, temperature, density and dimension can be changed. The existence of universal scaling regimes, where diverse physical systems and observables display quantitative agreement, generates a common framework, where the efforts of different research communities can be -- in some cases rigorously -- connected. Still, the application of this general framework to particular experimental realisations requires the identification of the regimes where the universality phenomenon is expected to appear. In the present review we summarise the recent investigations of many-body quantum systems with long-range interactions, which are currently realised in Rydberg atom arrays, dipolar systems, trapped ion setups and cold atoms in cavity experiments. Our main aim is to present and identify the common and (mostly) universal features induced by long-range interactions in the behaviour of quantum many-body systems. We will discuss both the case of very strong non-local couplings, i.e. the non-additive regime, and the one in which energy is extensive, but nevertheless low-energy, long wavelength properties are altered with respect to the short-range limit. Cases of competition with other local effects in the above mentioned setups are also reviewed.
We study two dimensional stripe forming systems with competing repulsive interactions decaying as $r^{-alpha}$. We derive an effective Hamiltonian with a short range part and a generalized dipolar interaction which depends on the exponent $alpha$. An approximate map of this model to a known XY model with dipolar interactions allows us to conclude that, for $alpha <2$ long range orientational order of stripes can exist in two dimensions, and establish the universality class of the models. When $alpha geq 2$ no long-range order is possible, but a phase transition in the KT universality class is still present. These two different critical scenarios should be observed in experimentally relevant two dimensional systems like electronic liquids ($alpha=1$) and dipolar magnetic films ($alpha=3$). Results from Langevin simulations of Coulomb and dipolar systems give support to the theoretical results.
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