Related papers: Dirac Theory in Hydrodynamic Form
On their roller coaster ride through turbulence, tracer particles sample the fluctuations of the underlying fields in space and time. Quantitatively relating particle and field statistics remains a fundamental challenge in a large variety…
The success of relativistic hydrodynamics as an essential part of the phenomenological description of heavy-ion collisions at RHIC and the LHC has motivated a significant body of theoretical work concerning its fundamental aspects. Our…
Exact solutions of the Dirac equation, a system of four partial differential equations, are rare. The vast majority of them are for highly symmetric stationary systems. Moreover, only a handful of solutions for time dependent dynamics…
Quantum fluid (or hydrodynamic) models provide an attractive alternative for the modeling and simulation of the electron dynamics in nano-scale objects. Compared to more standard approaches, such as density functional theory or phase-space…
We propose a generalization of equations of quantum mechanics in the hydrodynamic form by introducing the terms taking into account the diffusion velocity at zero and finite temperatures and the density energy of diffusion pressure of the…
The first-order textbook formulations of relativistic viscous hydrodynamics are unstable and acausal. These shortcomings may be rectified by using effective theories which maintain stability and causality. In this dissertation, which is…
The hydrodynamic formulation of the Dirac equation has historically been hindered by the inability to close the system of physical variables without resorting to infinite moment hierarchies. We resolve this longstanding issue by developing…
We describe main ideas of method of many-particle quantum hydrodynamics allows to derive equations for description of quantum plasma evolution. We also present definitions of collective quantum variables suitable for quantum plasmas. We…
The Dirac equation provides a description of spin 1/2 particles, consistent with both the principles of quantum mechanics and of special relativity. Often its presentation to students is based on mathematical propositions that may hide the…
In the pilot-wave theory of quantum mechanics particles have definite positions and velocities and the system evolves deterministically. The velocity of a particle is determined by the wave function of the system (the guidance equation) and…
Hydrodynamics is nowadays understood as an effective field theory that describes the dynamics of the long-wavelength and slow-time fluctuations of an underlying microscopic theory. In this work we extend the relativistic hydrodynamics to…
We present the theory of Dirac spinors in the formulation given by Bohm on the idea of de Broglie: the quantum relativistic matter field is equivalently re-written as a special type of classical fluid and in this formulation it is shown how…
We present the explicit expressions of different pseudo-gauge transformations for Dirac and Proca fields considering a general interaction term. The particular case of the interaction of Dirac and Proca fields with a background…
We establish covariant semiclassical transport equations of massive spin-1/2 particles which are generated by the quantum kinetic equation modified by enthalpy current dependent terms. The purpose of modification is to take into account the…
We consider hydrodynamics with non conserved number of particles and show that it can be modeled with effective fluid Lagrangians which explicitly depend on the velocity potentials. For such theories, the {}``shift symetry''…
We revisit the canonical formulation of spin hydrodynamics for Dirac fermions with a general thermal vorticity. The orders of the general thermal vorticity and the corresponding spin variables are considered independently from those of the…
Second-order relativistic hydrodynamics is surprisingly predictive, even in the presence of large gradients. The hydrodynamic expansion from the method of moments does not require a gradient expansion, but it is intrinsically bound to the…
In this work, a connection has been indicated between the different existing formulations of relativistic hydrodynamic theories, which, in order to be causal and stable, (i) either requires `non-fluid' variables apart from velocity and…
We review the calculation of polarization in a relativistic fluid within the framework of statistical quantum field theory. We derive the expressions of the spin density matrix and the mean spin vector both for a single quantum relativistic…
The Hamiltonian formulation of the motion of a spinning relativistic particle in an external electromagnetic field is considered. The approach is based on the introduction of new coordinates and their conjugated momenta to describe the spin…