Related papers: Continuity Equation in Presence of a Non-local pot…
We introduce a new formalism to study nonequilibrium steady-state currents in stochastic field theories. We show that generalizing the exterior derivative to functional spaces allows identifying the subspaces in which the system undergoes…
Electron density and electron momentum density, while independently tractable experimentally, bear no direct connection without going through the many-electron wave function. However, invoking a variant of the constrained-search formulation…
Interaction of linearized gravitational waves with a otherwise free particle has been studied quantum mechanically in a noncommutative phase-space to examine whether the particle's response to the gravitational wave gets modified due to…
We have studied nonequilibrium dynamics of the one-dimensional Hubbard model using the generalized hydrodynamic theory. We mainly investigated the spatio-temporal profile of charge density, energy density and their currents using the…
The applicability of the local hardness as defined by the derivative of the chemical potential with respect to the electron density is undermined by an essential ambiguity arising from this definition. Further, the local quantity defined in…
We analyze the equilibrium statistical mechanics of canonical, non-canonical and non-Hamiltonian equations of motion by throwing light into the peculiar geometric structure of phase space. Some fundamental issues regarding time translation…
In this paper, we study the existence and concentration phenomena of solutions for the following non-local regional Schr\"odinger equation $$ \left\{ \begin{array}{l} \epsilon^{2\alpha}(-\Delta)_\rho^{\alpha} u + Q(x)u =…
We study the equation of motion for the Noether current in an electron gas within the framework of the Schwinger-Keldysh Closed-Time-Path formalism. The equation is shown to be highly non-linear and irreversible even for a non-interacting,…
The model of dynamical noncommutativity is proposed. The system consists of two interrelated parts. The first of them describes the physical degrees of freedom with coordinates q^1, q^2, the second one corresponds to the noncommutativity r…
We study the stability of excitonic Mott phases in the presence of a periodic potential and a non-local exciton-exciton interaction. The non-local interaction is treated in a mean-field approximation, while the local repulsion of the…
We prove local boundedness and H\"older continuity for weak solutions to nonlocal double phase problems concerning the following fractional energy functional \[ \int_{\mathbb{R}^n}\int_{\mathbb{R}^n} \frac{|v(x)-v(y)|^p}{|x-y|^{n+sp}} +…
Non-local continuity equation describes an infinite system of identical particles, which interact with each other through the common field. Solution of this equation is a probability measure that stands for spatial distribution of…
The electron and current density distributions in the close proximity of quantum point contacts (QPCs) are investigated. A three dimensional Poisson equation is solved self-consistently to obtain the electron density and potential profile…
We consider a class of nonconvex energy functionals that lies in the framework of the peridynamics model of continuum mechanics. The energy densities are functions of a nonlocal strain that describes deformation based on pairwise…
We consider the spatially inhomogeneous non-cutoff Boltzmann equation with hard potentials in the non-perturbative setting. For initial data with polynomial decay in the velocity variable, we establish the local-in-time existence and…
We propose a new approach to understand hierarchy problem for cosmological constant in terms of considering noncommutative nature of space-time. We calculate that vacuum energy density of the noncommutative quantum field theories in…
In this paper, we consider the local well-posedness of the Prandtl boundary layer equations that describe the behavior of boundary layer in the small viscosity limit of the compressible isentropic Navier-Stokes equations with non-slip…
We investigate the merging process in N-body self-gravitating system from the viewpoints of the local virial relation which is the relation between the local kinetic energy and the local potential. We compare both the density profile and…
Physical systems with non-reciprocal or dissipative forces evolve according to a generalization of Liouville's equation that accounts for the expansion and contraction of phase space volume. Here, we connect geometric descriptions of these…
The cubic nonlinear Schr\"odinger equation with repulsive nonlinearity and an elliptic function potential models a quasi-one-dimensional repulsive dilute gas Bose-Einstein condensate trapped in a standing light wave. New families of…