Related papers: Lighthill equation for quantum liquids
In the present article, we construct a 2D formulation of quantum gravity in the framework of a deterministic theory. In this context, a Quantum stationary Hamilton-Jacobi equation is derived from the Klein- Gordon equation written in the…
Liouville's theorem -- the preservation of phase-space volume -- is often presented as a corollary of Hamilton's canonical equations. Here we adopt an ensemble-first viewpoint in which the starting point is local probability conservation on…
The relativistic scattering of a spin-1/2 particle from an infinitely long solenoid is considered in the framework of covariant perturbation theory. The first order term agrees with the corresponding term in the series expansion of the…
In this paper hyperbolic partial differential equations with random coefficients are discussed. Such random partial differential equations appear for instance in traffic flow problems as well as in many physical processes in random media.…
The conserved probability densities (attributed to the conserved currents derived from relativistic wave equations) should be non-negative and the integral of them over an entire hypersurface should be equal to one. To satisfy these…
We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational…
A new form of governing equations is derived from Hamilton's principle of least action for a constrained Lagrangian, depending on conserved quantities and their derivatives with respect to the time-space. This form yields conservation laws…
An equation describing the irreversible evolution of the local density of a continuous medium without involving any statistical hypotheses and assumptions is derived. The derivation is based on the smoothing of the microscopic dynamic…
We provide an estimation of the dissipation of the Wasserstein 2 distance between the law of some interacting $N$-particle system, and the $N$ times tensorized product of solution to the corresponding limit nonlinear conservation law. It…
A density-functional theory is established for inhomogeneous superfluids at finite temperature, subject to time-dependent external fields in isothermal conditions. After outlining parallelisms between a neutral superfluid and a charged…
The second derivative of the luminosity distance with respect to the redshift is written in terms of the deceleration parameter $q_0$. We point out that the third derivative contains the information regarding the sound speed of cosmic…
We consider a one-dimensional aggregation-diffusion equation, which is the gradient flow in the Wasserstein space of a functional with competing attractive-repulsive interactions. We prove that the fully deterministic particle…
The relativistic hydrodynamical equations are being examined with the aim of extracting the quantum-mechanical equations (the relativistic Klein-Gordon equation and the Schr\"odinger equation in the non-relativistic limit). In both cases it…
Everettian Quantum Mechanics, or the Many Worlds Interpretation, lacks an explanation for quantum probabilities. We show that the values given by the Born rule equal projection factors, describing the contraction of Lebesgue measures in…
We investigate the validity of the generalized second law of thermodynamics in a universe governed by Horava-Lifshitz gravity. Under the equilibrium assumption, that is in the late-time cosmological regime, we calculate separately the…
We consider the Landau-Khalatnikov two-fluid hydrodynamics of superfluid liquid as an effective theory, which provides a self-consistent analog of Einstein equations for gravity and matter.
We investigate superfluidity, and the mechanism for creation of quantized vortices, in the relativistic regime. The general framework is a nonlinear Klein-Gordon equation in curved spacetime for a complex scalar field, whose phase dynamics…
We use two different approaches to derive multipartite Leggett-type inequalities, which are generalizations of the two-qubit Leggett-type inequality obtained in [Nature Phys. \textbf{4}, 681 (2008)]. The first approach is based on the…
We investigate the cosmological applications of fluids having an equation of state which is the analog to the one related to the isotropic deformation of crystalline solids, that is containing logarithmic terms of the energy density,…
We explore whether quantum field theory can be understood as the statistical mechanics of a time-reversal-invariant stochastic generalization of Hamiltonian dynamics. The motivation for this project, started with this paper, is to assign…