arXiv subjects
Publications and source records attributed to Riccardo Fantoni.
We propose a new Brownian bridge construction for our newly devised Coherent States Path Integral Monte Carlo algorithm. We apply it to the numerically exact calculation of the thermodynamic properties of the Helium fluid on a plane at low non zero temperature. We find very good agreement with the conventional plane waves path integral Monte Carlo results.
We performed numerical (restricted) path integral Monte Carlo experiments on metallic Hydrogen from first principles. We study a quantum two component plasma where one component is made of pointwise particles of negative unitary charge and the other is made of charged hard spheres of positive unitary charge. We study both the additive mixture and a nonadditive mixture where we only keep a hard core between unlike species. We specialize to the case of the electron-proton plasma with a 1:1 ratios between the molar fraction of the two species. We measured thermodynamic and structural properties of the plasma. From an analysis of the structure we see a transition from a metallic Hydrogen phase, to a molecular Hydrogen phase as the temperature is lowered. As expected at high density the correlations are diminished.
We propose a new quantum simulation method for a many body quantum liquid of identical particles at finite (non-zero) temperature. The new scheme expands the high temperature density matrix on the overcomplete set of single particles coherent states of John Rider Klauder instead of the usual plane waves as in conventional path integral methods. One is free to tune the elastic constant and/or the mass of the harmonic oscillator subtending the coherent states so as to maximize the computational efficiency of the algorithm. We prove that in the limit of an extremely stiff harmonic oscillator the results for the internal energy tends towards the correct expected values. Moreover we suggest that a stiff harmonic oscillator could allow the use of larger (imaginary) timesteps. This additional degree of freedom is the characteristic feature of our new algorithm and is not available in more conventional path integral methods.
We review the physics of many bodies in the context of general relativity. Starting from the stress energy tensor for one body, for a swarm of bodies, for a perfect fluid, we review relativistic hydrodynamics, kinetic theory, and statistical physics of $N$ identical bodies. We conclude our excursion with a thermal equivalence principle in physics.
We solve numerically exactly a simple toy model to quantum general relativity or more properly to path integral on a curved space. We consider the thermal equilibrium of a quantum many body problem on the sphere, the surface of constant positive curvature. We use path integral Monte Carlo to measure the kinetic energy, the internal energy and the static structure of a bosons, fermions and anyons fluid at low temperatures on the sphere. For bosons we also measure the superfluid fraction and compare its behavior at the critical temperature with the universal jump predicted by Nelson and Kosterlitz in flat space in the thermodynamic limit at the superfluid phase transition. For fermions and anyons it is necessary to use the restricted path integral recipe in order to overcome the sign problem. Even if this recipe is exact for the non interacting fluid it reduces to just an approximation for an interacting system. And we make the example of the electron gas at low temperature. Snapshots of the many body path configuration during the evolution of the computer experiment show that the ``speed'' of the single particle path near the poles slows down as a consequence of the ``hairy ball theorem'' of Poincar\'e. The influence of curvature on the thermodynamic and structural properties of the many body fluid is also studied.
We study a fluid of quantum hard-spheres treated with affine-quantization. Assuming that the fluid obeys to Bose-Einstein statistics we solve for its thermodynamic properties using the path integral Monte Carlo method.
We study the localization problem in quantum stochastic mechanics. We start from the Edwards model for a particle in a bath of scattering centers and prove static localization of the ground state wavefunction of the particle in a one dimensional square well coupled to Dirac delta like scattering centers in arbitrary but fixed positions. We see how the localization increases for increasing coupling $g$ and increasing number of scattering centers at constant density. Then we choose the scattering centers positions as pseudo random numbers with a uniform probability distribution and observe an increase in the localization of the average of the ground state over the many positions realizations. We discuss how this averaging procedure is consistent with a picture of a particle in a Bose-Einstein condensate of of non interacting boson scattering centers interacting with the particle with Dirac delta functions pair potential. We then study the dynamics of the ground state wave function. We conclude with a discussion of the affine quantization version of the Lax model which reduces to a system of contiguous square wells with walls in arbitrary positions independently of the coupling constant $g$.
In a recent trilogy we proposed a Statistical Theory of General Relativity spacetime. Here we apply our new theory to determine the (energy) ``density'' and (virial) ``temperature'' dependence of the structure of the spacetime quantum vacuum working on the simple case of a real massless scalar field in a local Lorentz frame.
We compare two kinds of affine localizations in physics: the localization in a short range polaron and the one in a Wick rotated Anderson stochastic model. The conditions on the interaction potential necessary to see the transnational symmetry breaking localization phase transition is identical in the two problems. We therefore suggest that they should belong to the same universality class of the renormalization group for the localization phase transition.
While the quantum realm seems hidden, it can also reach examples of infinite energy, especially when a part of space is roughly removed until it disappears, possibly forever. Since it follows that Nothing can enter a region where the space is missing, the quantum realm, as seen now in affine quantization, will automatically come to help everything else by creating colossal `quantum walls' that will ensure that everything stays out of all black holes. In this article, we show that the expanded quantum realm allows Nothing to ever fall into a black hole.
We review the linear response theory in the horizontal quantum liquids framework spanning from Coulomb liquids to Atomic gases. There are several well known references about this subject, like the onset of the Kramers-Kronig relations and the fluctuation-dissipation theorem. For the Coulomb systems we show the connection between the linear response function and the dielectric function which settles a parallelism between statistical mechanics and electrostatic properties. For (very degenerate, dilute, trapped, two dimensional) Atomic (Bose) gases we will prove, in full generality, how the response properties of the gas depend from the frequency of the harmonic trap.
We discuss the foundations of the statistical gravity theory we proposed in a recent publication [Riccardo Fantoni, Quantum Reports, 6, 706 (2024)].
We revisit the problem of relaxation in scalar gravitational field theory proposing a novel numerical solution to the problem.
The ensemble inequivalence in a (unscreened) Coulomb liquid has been known since the years 1960s. The structure described by the canonical ensemble and the grand canonical ensemble are not equivalent. We show that this fact also affects many long range fluid.
I propose a possible way to introduce the effect of temperature (defined through the virial theorem) into Einstein's theory of general relativity. This requires the computation of a path integral on a 10-dimensional flat space in a four dimensional spacetime lattice. Standard path integral Monte Carlo methods can be used to compute it.
We present a self contained derivation of the Friedel oscillations in a degenerate ideal electron plasma using a not commonly known theorem on the asymptotic behavior of the Fourier transform of a generalized function presenting some singularities.
We show that for the ground state of a one dimensional free electron gas on a circle the analytic expression for the canonical ensemble partition function can be easily derived from the density matrix by assuming that the thermodynamic limit coincides with the limit of the eigenfunction expansion of the kinetic energy. This approximation fails to give the finite temperature partition function because those two limits cannot be chosen as coincident.
We prove through path integral Monte Carlo computer experiments that the affine quantization of the $φ_4^4$ scaled Euclidean covariant relativistic scalar field theory is a valid quantum field theory with a well defined continuum limit of the one- and two-point-function. Affine quantization leads to a completely satisfactory quantization of field theories using situations that involve scaled behavior leading to an unexpected, $\hbar^2/φ^2$ which arises only in the quantum aspects.