Search

We analyze the dynamics of a gravitational bounded cloud of generic bosons or a boson star in the non-relativistic regime, assuming from the very beginning that the boson star is in a Bose-Einstein condensed state. Also, we have taken into account multi-particle interactions within the boson star, which are described through the so-called logarithmic potential. Assuming energy conservation conditions at any time, we are able to describe the boson star as a some kind of gravitational quantum liquid, or more specifically, as a macroscopic gravitational quantum droplet. The assumption of logarithmic interactions, lead us to establish several scenarios in which the system is able to oscillates around the equilibrium radius. The approach analyzed in the present report shows that the interpretation of a boson star as a macroscopic gravitational quantum droplet can be applied to the dynamics analysis of a large number of systems on different size scales., Comment: 15 pages, 10 figures

The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an arbitrary active motion pattern modelled by a scattering function that defines the dynamics of the change of the self-propulsion direction. The exact probability density of the particle positions at a given time is obtained. From it, the time dependence of the moments, i.e., the mean square displacement and the kurtosis for an arbitrary scattering function, are derived and analysed. Anomalous diffusion is found with a crossover of the scaling exponent from $2\alpha$ in the short-time regime to $\alpha$ in the long-time one, $0<\alpha<1$ being the order of the fractional derivative considered. It is shown that the exact solution found satisfies a fractional diffusion equation that accounts for the non-local and retarded effects of the Laplacian of the probability density function through a coupled temporal and spatial memory function. Such a memory function holds the complete information of the active motion pattern. In the long-time regime, space and time are decoupled in the memory function, and the time fractional telegrapher's equation is recovered. Our results are widely applicable in systems ranging from biological microorganisms to artificially designed self-propelled micrometer particles.

In this paper, we show the relation between $sp(4,\mathbb{R})$, the Lie algebra of the symplectic group, and the elements of $Sp(4,\mathbb{R})$. We use this result to obtain some special cases of symplectic matrices relevant to the study of squeezed states. In this regard, we provide some applications in quantum mechanics and analyze the squeezed polymer states obtained from the polymer representation of the symplectic group. Remarkably, the polymer's dispersions are the same as those obtained for the squeezed states in the usual representation., Comment: 31 pages, 2 figures

In the present work, we analyze the structural configuration of a collection of generic non-relativistic bosons forming a gravitational bound Bose-Einstein condensate that we interpreted as a non-relativistic boson star. We prove that the system's behavior can be obtained by analyzing its fundamental constituent's properties, i.e., the single particle properties. Additionally, we show that by expressing the corresponding Newtonian gravitational potential, under certain circumstances, as a harmonic oscillator potential ones, we can describe the conditions in which the non-relativistic boson star can form equilibrium configurations. In order to analyze the structural configuration related to the boson star, we employ four different \textit{ans\"atze} commonly used in the literature. The use of these \textit{ans\"atze} allows to compare the structural properties of the bosonic cloud or the boson star that leads to obtain several equilibrium configurations from compact objets matching to the size of typical stars to very gigantic systems comparable to the size of galaxy cluster dark matter halos. Finally, we show that these \textit{ans\"atze} predict, qualitatively speaking, the same structural and gravitational equilibrium configurations for different values of the parameters involved., Comment: 9 pages, 5 figures

We analyze the problem of one dimensional quantum particle falling in a constant gravitational field, also known as the {\it bouncing ball}, employing a semiclassical approach known as momentous effective quantum mechanics. In this formalism the quantum evolution is described through a dynamical system of infinite dimension for the position, the momentum and all dispersions. Usually the system is truncated to have a finite dimensional one, however, in this case equations of motion decouple and the system can be solved. For a specific set of initial conditions we find that the time dependent dispersion in position is always around the classical trajectory., Comment: 1 figure

In the present report we analyze the eventual modifications caused by the polymer quantization upon the ground state of a homogeneous one-dimensional Bose-Einstein condensate. We obtain the ground state energy of the corresponding N-body system and, consequently, the corresponding speed of sound, allowing us to explore the sensitivity of the system to corrections caused by the polymer quantization. The corrections arising from the polymer quantization can be improved for dense systems together with small values of the corresponding one-dimensional scattering length. However, these corrections remain constrained due to finite size effects of the system. The contributions of the polymer length scale to the properties of the ground state energy of the system allow us to explore, as a first approximation and when the Bogoliubov's formalism is valid, the sensitivity of this many-body system to traces caused by the discreteness of space suggested by the polymer quantization., Comment: 6 pages. arXiv admin note: text overlap with arXiv:1604.01730

In this work we study a completely degenerated fermion gas at zero temperature within a semiclassical approximation for the Hamiltonian arising in polymer quantum mechanics. Polymer quantum systems are quantum mechanical models quantized in a similar way as in loop quantum gravity that allow the study of the discreteness of space and other features of the loop quantization in a simplified way. We obtain the polymer modified thermodynamical properties noticing that the corresponding Fermi energy is exactly the same as if one directly polymerizes the momentum $p_F$. We also obtain the corresponding expansion of thermodynamical variables for small values of the polymer length scale $\lambda$. With this results we study a simple model of a compact object where the gravitational collapse is supported by electron degeneracy pressure. We find polymer corrections to the mass of the star. When compared with typical measurements of the mass of white dwarfs we obtain a bound on the polymer length of $\lambda^2\lesssim 10^{-26}m^2$.

We report fully relativistic molecular-dynamics simulations that verify the appearance of thermal equilibrium of a classical gas inside a uniformly accelerated container. The numerical experiments confirm that the local momentum distribution in this system is very well approximated by the J\"uttner function -- originally derived for a flat spacetime -- via the Tolman-Ehrenfest effect. Moreover, it is shown that when the acceleration or the container size is large enough, the global momentum distribution can be described by the so-called modified J\"uttner function, which was initially proposed as an alternative to the J\"uttner function.

We study the Hydrogen atom as a quantum mechanical system with a Coulomb like potential, with a semiclassical approach based on an effective description of quantum mechanics. This treatment allows us to describe the quantum state of the system as a system of infinite many classical equations for expectation values of configuration variables, their moments and quantum dispersions. It also provides a semiclassical description of the orbits and the evolution of observables and spreadings and their back-reaction on the evolution., Comment: 22 pages, 28 Figures, PACS numbers: 03.65.-w, 03.65.Sq The full document was restructured and rewritten, some subsections were removed and 12 figures were added

Polymer quantum systems are mechanical models quantized similarly as loop quantum gravity. It is actually in quantizing gravity that the polymer term holds proper as the quantum geometry excitations yield a reminiscent of a polymer material. In such an approach both non-singular cosmological models and a microscopic basis for the entropy of some black holes have arisen. Also important physical questions for these systems involve thermodynamics. With this motivation, in this work, we study the statistical thermodynamics of two one dimensional {\em polymer} quantum systems: an ensemble of oscillators that describe a solid and a bunch of non-interacting particles in a box, which thus form an ideal gas. We first study the spectra of these polymer systems. It turns out useful for the analysis to consider the length scale required by the quantization and which we shall refer to as polymer length. The dynamics of the polymer oscillator can be given the form of that for the standard quantum pendulum. Depending on the dominance of the polymer length we can distinguish two regimes: vibrational and rotational. The first occur for small polymer length and here the standard oscillator in Schr\"odinger quantization is recovered at leading order. The second one, for large polymer length, features dominant polymer effects. In the case of the polymer particles in the box, a bounded and oscillating spectrum that presents a band structure and a Brillouin zone is found. The thermodynamical quantities calculated with these spectra have corrections with respect to standard ones and they depend on the polymer length. For generic polymer length, thermodynamics of both systems present an anomalous peak in their heat capacity $C_V$.

The relativistic equilibrium velocity distribution plays a key role in describing several high-energy and astrophysical effects. Recently, computer simulations favored Juttner's as the relativistic generalization of Maxwell's distribution for d=1,2,3 spatial dimensions and pointed to an invariant temperature. In this work we argue an invariant temperature naturally follows from manifest covariance. We present a new derivation of the manifestly covariant Juttner's distribution and Equipartition Theorem. The standard procedure to get the equilibrium distribution as a solution of the relativistic Boltzmann's equation is here adopted. However, contrary to previous analysis, we use cartesian coordinates in d+1 momentum space, with d spatial components. The use of the multiplication theorem of Bessel functions turns crucial to regain the known invariant form of Juttner's distribution. Since equilibrium kinetic theory results should agree with thermodynamics in the comoving frame to the gas the covariant pseudo-norm of a vector entering the distribution can be identified with the reciprocal of temperature in such comoving frame. Then by combining the covariant statistical moments of Juttner's distribution a novel form of the Equipartition Theorem is advanced which also accommodates the invariant comoving temperature and it contains, as a particular case, a previous not manifestly covariant form., Comment: 21 pages, 1 figure

A covariant Fokker-Planck type equation for a simple gas and an equation for the Brownian motion are derived from a relativistic kinetic theory based on the Boltzmann equation. For the simple gas the dynamic friction four-vector and the diffusion tensor are identified and written in terms of integrals which take into account the collision processes. In the case of Brownian motion, the Brownian particles are considered as non-relativistic whereas the background gas behaves as a relativistic gas. A general expression for the semi-relativistic viscous friction coefficient is obtained and the particular case of constant differential cross-section is analyzed for which the non-relativistic and ultra relativistic limiting cases are calculated., Comment: To appear in PRE