Microscopic approach to the macrodynamics of matter with broken symmetries

A unified set of hydrodynamic equations describing condensed phases of matter with broken continuous symmetries is derived using a generalization of the statistical-mechanical approach based on the local equilibrium distribution. The dissipativeless and dissipative parts of the current densities and the entropy production are systematically deduced in this approach by expanding in powers of the gradients of the macrofields. Green-Kubo formulas are obtained for all the transport coefficients. The results apply to both crystalline solids and liquid crystals. The consequences of microreversibility and spatial symmetries are investigated, leading to the prediction of cross effects resulting from Onsager-Casimir reciprocal relations

An Hamilton-Jacobi formulation of anisotropic inflation

Classifying inflationary scenarios according to their scaling properties is a powerful way to connect theory with observations. A useful tool to make such a classification is the beta-function formalism. By describing inflation in terms of renormalization group equations, within this framework, it is possible to define universality classes, which can be considered as sets of theories that share a common scale invariant limit. In this paper we apply the formalism to define such classes of universality for models of inflation where the inflaton is coupled to gauge fields. We show that the formalism may consistently be extended to capture the peculiar features of these models such as statistical anisotropy. We also obtain some consistency conditions which serve as useful guidelines for model building.Comment: 29 pages, 1 figure, 2 appendice

Elastic and transport coefficients of the perfect hard-sphere crystal from the poles of the hydrodynamic spectral functions

The elastic and transport coefficients of a perfect face-centered cubic crystal of hard spheres are computed from the poles of the dynamic structure factor and of the spectral functions of transverse momentum density fluctuations. For such crystals, the relevant coefficients are the three isothermal elastic constants $(C_{11}^T,C_{12}^T,C_{44}^T)$, the heat conductivity $\kappa$, and the three viscosities $(\eta_{11},\eta_{12},\eta_{44})$ (in Voigt's notations), which are directly computed using molecular dynamics simulations. The elastic and transport coefficients are then compared to the values of the same coefficients obtained with the method of Helfand moments, showing good agreement and providing strong support for the microscopic hydrodynamic theory of perfect crystals based on the local-equilibrium approach.Comment: 21 pages, 11 figures, 11 table

Identifying Universality in Warm Inflation

Ideas borrowed from renormalization group are applied to warm inflation to characterize the inflationary epoch in terms of flows away from the de Sitter regime. In this framework different models of inflation fall into universality classes. Furthermore, for warm inflation this approach also helps to characterise when inflation can smoothly end into the radiation dominated regime. Warm inflation has a second functional dependence compared to cold inflation due to dissipation, yet despite this feature, it is shown that the universality classes defined for cold inflation can be consistently extended to warm inflation.Comment: 20 pages, 5 figures, 1 appendi

Spatial Current Patterns, Dephasing and Current Imaging in Graphene Nanoribbons

Using the non-equilibrium Keldysh Green's function formalism, we investigate the local, non-equilibrium charge transport in graphene nanoribbons (GNRs). In particular, we demonstrate that the spatial current patterns associated with discrete transmission resonances sensitively depend on the GNRs' geometry, size, and aspect ratio, the location and number of leads, and the presence of dephasing. We identify a relation between the spatial form of the current patterns, and the number of degenerate energy states participating in the charge transport. Furthermore, we demonstrate a principle of superposition for the conductance and spatial current patterns in multiple-lead configurations. We demonstrate that scanning tunneling microscopy (STM) can be employed to image spatial current paths in GNR with atomic resolution, providing important insight into the form of local charge transport. Finally, we investigate the effects of dephasing on the spatial current patterns, and show that with decreasing dephasing time, the current patterns evolve smoothly from those of a ballistic quantum network to those of classical resistor network.Comment: 25 pages, 12 figure

Stability of the pion string in a thermal and dense medium

We investigate the stability of the pion string in a thermal bath and a dense medium. We find that stability is dependent on the order of the chiral transition. String core stability within the experimentally allowed regime is found only if the chiral transition is second order, and even there the stable region is small, i.e., the temperature below which the core is unstable is close to the critical temperature of the phase transition. We also find that the presence of a dense medium, in addition to the thermal bath, enhances the experimentally accessible region with stable strings. We also argue that once the string core decays, the "effective winding" of the string persists at large distances from the string core. Our analysis is done both in the chiral limit, which is mainly what has been explored in the literature up to now, and for the physical $h \ne 0$ case, where a conceptual framework is set up for addressing this regime and some simple estimates are done.Comment: 16 pages, 6 figures. Replaced with version matching the published on

Erratum: Microscopic approach to the macrodynamics of matter with broken symmetries (J. Stat. Mech. (2020) (103203) DOI: 10.1088/1742-5468/abb0e0)

Equation (4.20) should read (equation presented) with commas separating the three formulas. Equation (6.9) should be (equation presented).SCOPUS: er.jinfo:eu-repo/semantics/publishe

Erratum: Nonequilibrium statistical mechanics of crystals (J. Stat. Mech. (2021) (063207) DOI: 10.1088/1742-5468/ac02c9)

Equation (3.29) should be (equation presented) where the extra term comes from equation (B.4) with va = 0 and φab = 0 in our previous paper [1]. The rest of the paper is unaffected.SCOPUS: er.jinfo:eu-repo/semantics/publishe

Poles of hydrodynamic spectral functions and Einstein-Helfand formulas for transport coefficients

The local-equilibrium approach to transport processes is related to the approach based on time-dependent correlation functions and their associated spectral functions characterizing the equilibrium fluctuations of particle, momentum and other densities. On the one hand, the transport coefficients are calculated with the Einstein-Helfand formulas derived in the local-equilibrium approach. On the other hand, the poles of the spectral functions at complex frequencies give the damping rates of the hydrodynamic modes. Since these rates also depend on the transport coefficients, their values can be compared to the predictions of the local-equilibrium approach. This comparison is systematically carried out for the hard-sphere fluid by computing numerically the transport coefficients, the spectral functions, and their poles as a function of the wave number in the hydrodynamic limit. The study shows the consistency between the two approaches for the determination of the transport properties

Nonequilibrium statistical mechanics of crystals

The local equilibrium approach previously developed by the authors (J Mabillard and P Gaspard 2020 J. Stat. Mech. 103203) for matter with broken symmetries is applied to crystalline solids. The macroscopic hydrodynamics of crystals and their local thermodynamic and transport properties are deduced from the microscopic Hamiltonian dynamics. In particular, the Green-Kubo formulas are obtained for all the transport coefficients. The eight hydrodynamic modes and their dispersion relation are studied for general and cubic crystals. In the same twenty crystallographic classes as those compatible with piezoelectricity, cross effects coupling transport between linear momentum and heat or crystalline order are shown to split the degeneracy of damping rates for modes propagating in opposite generic directions.SCOPUS: ar.jinfo:eu-repo/semantics/publishe