Related papers: A mathematical formulation of the random phase app…
We show that nonlinear continuum elasticity can be effective in modeling plastic flows in crystals if it is viewed as Landau theory with an infinite number of equivalent energy wells whose configuration is dictated by the symmetry group…
Maxwell-Stefan systems describing the dynamics of the molar concentrations of a gas mixture with an arbitrary number of components are analyzed in a bounded domain under isobaric, isothermal conditions. The systems consist of mass balance…
We test the performance of a recently proposed fundamental measure density functional of aligned hard cylinders by calculating the phase diagram of a monodisperse fluid of these particles. We consider all possible liquid crystalline…
We consider the dynamics of bodies with "active" microstructure described by vector-valued phase fields. For waves with time-varying amplitude, the associated evolution equation involves a matrix that can be non-normal, depending on the…
Many materials such as martensitic or ferromagnetic crystals are observed to be in metastable states exhibiting a fine-scale, structured spatial oscillation called microstructure; and hysteresis is observed as the temperature, boundary…
We propose a simple phenomenological model describing composite crystals, constructed from two parallel sets of periodic inter-penetrating chains. In the harmonic approximation and neglecting thermal fluctuations we find the eigenmodes of…
Deriving macroscopic phenomenological laws of irreversible thermodynamics from simple microscopic models is one of the tasks of non-equilibrium statistical mechanics. We consider stationary energy transport in crystals with reference to…
Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is…
We develop continuum theory of self-assembly and pattern formation in metallic microparticles immersed in a poorly conducting liquid in DC electric field. The theory is formulated in terms of two conservation laws for the densities of…
The paper continues a series of papers devoted to treatment of the crystalline state on the basis of the approach in equilibrium statistical mechanics proposed earlier by the author. This paper is concerned with elaboration of a…
Discrete time crystals (DTC) exhibit a special non-equilibrium phase of matter in periodically driven many-body systems with spontaneous breaking of time translational symmetry. The presence of decoherence generally enhances thermalization…
We study numerically the phase diagram and the response under a driving force of the phase field crystal model for pinned lattice systems introduced recently for both one and two dimensional systems. The model describes the lattice system…
The Harper equation arising out of a tight-binding model of electrons on a honeycomb lattice subject to a uniform magnetic field perpendicular to the plane is studied. Contrasting and complementary approaches involving von Neumann entropy,…
We present a detailed study of the time-dependent Gutzwiller approximation for the Hubbard model. The formalism, labelled GA+RPA, allows us to compute random-phase approximation-like (RPA) fluctuations on top of the Gutzwiller approximation…
Disordered mechanical systems with high connectivity represent a limit opposite to the more familiar case of disordered crystals. Individual ions in a crystal are subjected essentially to nearest-neighbor interactions. In contrast, the…
The problem of plane-wave diffraction on semi-infinite orthorhombic electromagnetic (photonic) crystals of general kind is considered. Boundary conditions are obtained in the form of infinite system of equations relating amplitudes of…
In this article, we revisit the question of the validity of Hartree-Fock and random-phase approximations. We show that there is a connection between the two and while the RPA as it is known in much of the physics literature is of limited…
In this short paper, we consider discrete-time Markov chains on lattices as approximations to continuous-time diffusion processes. The approximations can be interpreted as finite difference schemes for the generator of the process. We…
Isotropic but otherwise largely arbitrary Heisenberg models in the presence of a homogeneous magnetic field are considered, including various integrable, non-integrable, as well as disordered examples, and not necessarily restricted to one…
We study level-set percolation for the harmonic crystal on $\mathbb{Z}^d$, $d \geq 3$, with uniformly elliptic random conductances. We prove that this model undergoes a non-trivial phase transition at a critical level that is almost surely…