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A recently developed non-linear fluctuating hydrodynamics theory has been quite successful in describing various features of anomalous energy transport. However the diffusion and the noise terms present in this theory are not derived from…
Polymers with active segments constitute prospective future materials and are used as a model for some biological systems such as chromatin. The directions of the active forces are typically introduced with temporal or spatial correlations…
We consider a general class of nonlinear diffusive models with bulk dissipation and boundary driving, and derive its hydrodynamic description in the large size limit. Both the average macroscopic behavior and the fluctuating properties of…
In this work a theory is developed for unifying large classes of nonlinear discrete-time dynamical systems obeying a superposition of a weighted maximum or minimum type. The state vectors and input-output signals evolve on nonlinear spaces…
This work addresses the imposition of outflow boundary conditions for one-dimensional conservation laws. While a highly accurate numerical solution can be obtained in the interior of the domain, boundary discretization can lead to…
This study derives geometric, variational discretizations of continuum theories arising in fluid dynamics, magnetohydrodynamics (MHD), and the dynamics of complex fluids. A central role in these discretizations is played by the geometric…
Large-scale electrical and thermal currents in ordinary metals are well approximated by effective medium theory: global transport properties are governed by the solution to homogenized coupled diffusion equations. In some metals, including…
We study charged hydrodynamics in a periodic lattice background. Fluctuations are Bloch waves rather than single momentum Fourier modes. At boundaries of the unit cell where hydrodynamic fluctuations are formally degenerate with their…
We investigate an explicit example of how spatial decoherence can lead to hydrodynamic behavior in the late-time, long-wavelength regime of open quantum systems. We focus on the case of a single non-relativistic quantum particle linearly…
This thesis develops advanced Tensor Network (TN) methods to address Hamiltonian Lattice Gauge Theories (LGTs), overcoming limitations in real-time dynamics and finite-density regimes. A novel dressed-site formalism is introduced, enabling…
In a one dimensional lattice thermal fluctuations destroy the long-range order making particles of the lattice move on a scale much larger than the lattice spacing. We discuss the assumption that this motion may be responsible for the…
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…
Several systems display an equilibrium condensation transition, where a finite fraction of a conserved quantity is spatially localized. The presence of two conservation laws may induce the emergence of such transition in an…
In systems removed from equilibrium, intrinsic microscopic fluctuations become correlated over distances comparable to the characteristic macroscopic length over which the external constraint is exerted. In order to investigate this…
The last decade has witnessed an impressive progress in the theoretical understanding of transport properties of clean, one-dimensional quantum lattice systems. Many physically relevant models in one dimension are Bethe-ansatz integrable,…
It has been conjectured that transport in integrable one-dimensional (1D) systems is necessarily ballistic. The large diffusive response seen experimentally in nearly ideal realizations of the S=1/2 1D Heisenberg model is therefore puzzling…
We discuss the relaxation kinetics of a one-dimensional dimer adsorption model as recently proposed for the binding of biological dimers like kinesin on microtubules. The non-equilibrium dynamics shows several regimes: irreversible…
Understanding the timescales associated with relaxation to equilibrium in closed quantum many-body systems is one of the central focuses in the study of their non-equilibrium dynamics. At late times, these relaxation processes exhibit…
In this paper, we consider an autonomous semi-dynamical system driven by semilinear time-nonlocal evolution equations, these type equations are used to describe the Rayleigh-Stokes problem for a non-Newtonain fluid to a generalized second…
We develop an effective field theory for dissipative fluids which governs the dynamics of long-lived gapless modes associated with conserved quantities. The resulting theory gives a path integral formulation of fluctuating hydrodynamics…