Related papers: Hot Fluids and Nonlinear Quantum Mechanics
By a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations, including systems with…
It is is explained why physical consistency requires substituting linear observables by nonlinear ones for quantum systems with nonlinear time evolution of pure states. The exact meaning and the concrete physical interpretation are…
This work is concerned with our recently developed formalism of non-equilibrium thermodynamics. This formalism extends the classical irreversible thermodynamics which leads to classical thermodynamics and can not describe physical phenomena…
The original idea of quantum optical spring arises from the requirement of quantization of the frequency of oscillations in the Hamiltonian of harmonic oscillator. This purpose is achieved by considering a spring whose constant (and so its…
We introduce a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics problem. We…
Existence, uniqueness and stability of solutions is studied for a set of nonlinear fixed point equations which define self-consistent hydrostatic equilibria of a classical continuum fluid that is confined inside a container and in contact…
A perfect fluid is quantized by the canonical method. The constraints are found and this allows the Dirac brackets to be calculated. Replacing the Dirac brackets with quantum commutators formally quantizes the system. There is a momentum…
A formula to calculate the quantum fluctuations of energy in small subsystems of a hot and relativistic gas is derived. We find an increase in fluctuations for subsystems of small sizes, but we agrees with the energy fluctuations in the…
In [arXiv:1004.2488], Baumann et al. present a new formalism for studying cosmological systems where the characteristic scale of non-linearities is much smaller than the Hubble scale. By integrating out the short-wavelength modes, it is…
The relativistic fluid is a highly successful model used to describe the dynamics of many-particle systems moving at high velocities and/or in strong gravity. It takes as input physics from microscopic scales and yields as output…
Thermal gradients lead to macroscopic fluid motion if a confining surface is present along the gradient. This fundamental nonequilibrium effect, known as thermo-osmosis, is held responsible for particle thermophoresis in colloidal…
The first-order general relativistic theory of a generic dissipative (heat-conducting, viscous, particle-creating) fluid is rediscussed from a unified covariant frame-independent point of view. By generalizing some previous works in the…
A general class of discrete unitary models are described whose behavior in the continuum limit corresponds to a many-body Schrodinger equation. On a quantum computer, these models could be used to simulate quantum many-body systems with an…
We have developed a theoretical formalism to introduce temperature as a parameter into the framework of non-relativistic quantum mechanics using the laws of classical thermodynamics and the canonical ensemble scheme of statistical…
The Schroedinger equation with the nonlinear term is derived by the natural generalization of the hydrodynamical model of quantum mechanics. The nonlinear term appears to be logically necessary because it enables explanation of the…
Classical and quantum mechanics laws are rebuilt in the frame of new thermodynamics. Heat is the sum of kinetic energy, system work, and system potential of a system, while force is the heat gradients over distance. Hence, collision,…
For many years, the Luttinger liquid theory has served as a useful paradigm for the description of one-dimensional (1D) quantum fluids in the limit of low energies. This theory is based on a linearization of the dispersion relation of the…
Quantum computing holds great promise to accelerate scientific computations in fluid dynamics and other classical physical systems. While various quantum algorithms have been proposed for linear flows, developing quantum algorithms for…
We analyze the possible concentration behavior of heat flows related to the Moser-Trudinger energy and derive quantization results completely analogous to the quantization results for solutions of the corresponding elliptic equation. As an…
In this note we demonstrate that vortices in a non-relativistic Chern-Simons theory form a quantum Hall fluid. We show that the vortex dynamics is controlled by the matrix mechanics previously proposed by Polychronakos as a description of…