15 research outputs found
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 , the heat
conductivity , and the three viscosities
(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 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