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I investigate the problem of finding a statistical description of a complex many-body system whose invariant measure cannot be constructed stemming from classical thermodynamics ensembles. By taking solitons as a reference system and by…

We consider translation invariant quantum systems in thermodynamic limit. We argue that their energy-momentum spectra should have shapes consistent with effective models involving quasiparticles. Our main example is second quantized…

Given a spatially dependent mass distribution we obtain potential functions for exactly solvable nonrelativistic problems. The energy spectrum of the bound states and their wavefunctions are written down explicitly. This is accomplished by…

We describe the physical hypothesis in which an approximate model of water waves is obtained. For an irrotational unidirectional shallow water flow, we derive the Camassa-Holm equation by a variational approach in the Lagrangian formalism.

Various classification schemes exist for homogeneous and isotropic (CP) world models, which include pressureless matter (so-called dust) and Einstein's cosmological constant Lambda. We here classify the solutions of more general world…

A formalism is presented that allows cosmological experiments to be tested for consistency, and allows a simple frequentist interpretation of the resulting significance levels. As an example of an application, this formalism is used to…

The signature of superfluidity in bosonic systems is a sound wave-like spectrum of the single particle excitations which in the case of strong interactions is roughly temperature independent. In fermionic systems, where fermion pairing…

For the one-dimensional repulsive Bose gas (Lieb-Liniger model), we study a special class of highly-excited states obtained by giving a finite momentum to subgroups of particles. These states, which correspond to `splitting' the ground…

We consider the problem of calculating the excitation spectrum of a gas of nonrelativistic anyons. When the anyons have statistics close to fermionic and the statistical angle has the form $\theta=\pi (1-\frac{1}{k})$ where $k$ is a large…

The thermodynamic properties of dark energy fluids described by an equation of state parameter $\omega=p/\rho$ are rediscussed in the context of FRW type geometries. Contrarily to previous claims, it is argued here that the phantom regime…

This paper examines the inhomogeneous Einstein equation for a static spherically symmetric metric with a source term corresponding to a perfect fluid with p=-rho. By a careful treatment of the equation near the origin we find an analytic…

We discuss the density fluctuations of a fluid due to zero point motion. These can be regarded as density fluctuations in the phonon vacuum state. We assume a linear dispersion relation with a fixed speed of sound and calculate the density…

We analyze the properties of a generic cosmological fluid described by the van der Waals equation of state. Exact solutions for the energy density evolution are found as implicit functions of the scale factor for a flat…

A simple derivation of the static Gross-Pitaevskii (GP) equation is given from an energy variational principle. The result is then generalized heuristically to the time-dependent GP form. With this as background, a number of different…

We consider the one-dimensional Lieb-Liniger model (bosons interacting via 2-body delta potentials) in the infinite coupling constant limit (the so-called Tonks-Girardeau model). This model might be relevant as a description of atomic Bose…

A supersymmetric extension of the two-phase fluid flow system is formulated. A superalgebra of Lie symmetries of the supersymmetric extension of this system is computed. The classification of the one-dimensional subalgebras of this…

We consider a microscopic model of spherical particles with inertia in a Stokes flow. As the particle number grows to infinity and their size goes to zero we derive the monokinetic Vlasov-Stokes equations as mean-field limit. We do this…

We present a technique that allows to obtain certain results in the compressible fluid theory: in particular, it is a nonexistence result for the highly decreasing at infinity solutions to the Navier-Stokes equations, the construction of…

Consider the open symmetric exclusion process on a connected graph with vertexes in $[N-1]:=\{1,\ldots, N-1\}$ where points $1$ and $N-1$ are connected, respectively, to a left reservoir and a right reservoir with densities…

A universal description of correlation functions of one-dimensional anyonic gapless systems in the low-momentum regime is presented. We point out a number of interesting features, including universal oscillating terms with frequency…