Search results for "Exact solution"
showing 10 items of 77 documents
Exact solution of the 1D Hubbard model in the atomic limit with inter-site magnetic coupling
2012
In this paper we present for the first time the exact solution in the narrow-band limit of the 1D extended Hubbard model with nearest-neighbour spin-spin interactions described by an exchange constant J. An external magnetic field h is also taken into account. This result has been obtained in the framework of the Green's functions formalism, using the Composite Operator Method. By means of this theoretical background, we have studied some relevant features such as double occupancy, magnetization, spin-spin and charge-charge correlation functions and derived a phase diagram for both ferro (J>0) and anti-ferro (J<0) coupling in the limit of zero temperature. We also report a study on de…
Grid-based Methods in Relativistic Hydrodynamics and Magnetohydrodynamics
2015
An overview of grid-based numerical methods used in relativistic hydrodynamics (RHD) and magnetohydrodynamics (RMHD) is presented. Special emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods. Results of a set of demanding test bench simulations obtained with different numerical methods are compared in an attempt to assess the present capabilities and limits of the various numerical strategies. Applications to three astrophysical phenomena are briefly discussed to motivate the need for and to demonstrate the success of RHD and RMHD simulations in their understanding. The review further provides FORTRAN programs to compute the exact solution…
Switching synchronization in one-dimensional memristive networks: An exact solution.
2017
We study a switching synchronization phenomenon taking place in one-dimensional memristive networks when the memristors switch from the high- to low-resistance state. It is assumed that the distributions of threshold voltages and switching rates of memristors are arbitrary. Using the Laplace transform, a set of nonlinear equations describing the memristors dynamics is solved exactly, without any approximations. The time dependencies of memristances are found, and it is shown that the voltage falls across memristors are proportional to their threshold voltages. A compact expression for the network switching time is derived.
High-momentum tails as magnetic-structure probes for strongly correlatedSU(κ)fermionic mixtures in one-dimensional traps
2016
A universal ${k}^{\ensuremath{-}4}$ decay of the large-momentum tails of the momentum distribution, fixed by Tan's contact coefficients, constitutes a direct signature of strong correlations in a short-range interacting quantum gas. Here we consider a repulsive multicomponent Fermi gas under harmonic confinement, as in the experiment of G. Pagano et al. [Nat. Phys. 10, 198 (2014)], realizing a gas with tunable $\text{SU}(\ensuremath{\kappa})$ symmetry. We exploit an exact solution at infinite repulsion to show a direct correspondence between the value of the Tan's contact for each of the $\ensuremath{\kappa}$ components of the gas and the Young tableaux for the ${S}_{N}$ permutation symmetr…
Correlation functions for a strongly coupled boson system and plane partitions.
2011
A quantum phase model is introduced as a limit for very strong interactions of a strongly correlated q -boson hopping model. The exact solution of the phase model is reviewed, and solutions are also provided for two correlation functions of the model. Explicit expressions, including both amplitude and scaling exponent, are derived for these correlation functions in the low temperature limit. The amplitudes were found to be related to the number of plane partitions contained in boxes of finite size.
New approach to describe two coupled spins in a variable magnetic field
2021
We propose a method to describe the evolution of two spins coupled by hyperfine i nteraction in an external time- dependent magnetic field. We apply the approach to the case of hyperfine interaction with axial symmetry, which can be solved exactly in a constant, appropriately oriented magnetic field. In order to t reat t he n onstationary d ynamical p roblem, we modify the time-dependent Schrödinger equation through a change of representation that, by exploiting an instantaneous (adiabatic) basis makes the time-dependent Hamiltonian diagonal at any time instant. The solution of the transformed time-dependent Schrödinger FRVBUJPO in the form of chronologically ordered exponents with transpar…
Evolution of the $B$-Meson Light-Cone Distribution Amplitude in Laplace Space
2020
The $B$-meson light-cone distribution amplitude is a central quantity governing non-perturbative hadronic dynamics in exclusive $B$ decays. We show that the information needed to describe such processes at leading power in $\Lambda_{\rm QCD}/m_b$ is most directly contained in its Laplace transform $\tilde\phi_+(\eta)$. We derive the renormalization-group (RG) equation satisfied by this function and present its exact solution. We express the RG-improved QCD factorization theorem for the decay $B^-\to\gamma\ell^-\bar\nu$ in terms of $\tilde\phi_+(\eta)$ and show that it is explicitly independent of the factorization scale. We propose an unbiased parameterization of $\tilde\phi_+(\eta)$ in ter…
On the existence of exotic and non-exotic multiquark meson states
2007
To obtain an exact solution of a four-body system containing two quarks and two antiquarks interacting through two-body terms is a cumbersome task that has been tackled with more or less success during the last decades. We present an exact method for the study of four-quark systems based on the hyperspherical harmonics formalism that allows us to solve it without resorting to further approximations, like for instance the existence of diquark components. We apply it to systems containing two heavy and two light quarks using different quark-quark potentials. While $QQ\bar n \bar n$ states may be stable in nature, the stability of $Q\bar Qn \bar n$ states would imply the existence of quark cor…
On a radiating fluid in a general relativistic context
2006
A model for the radiation hydrodynamics in general relativity is analyzed, describing the gravitational collapse and supernovae explosion. As these physical phenomena can be assumed spherically symmetric, the equations of motion for a unique fluid, representing the interaction between matter and radiation, are written in a spherical symmetric space-time with respect to a comoving frame. The system is completed by using the Eddington closure, assuming a local thermodynamical equilibrium for the radiation field. The resulting system is analyzed by the Lie symmetry approach and a reduction to an ODEs system is obtained. Numerical simulations of the solutions are performed, showing a realistic …
Estimating radiant fields in flat heterogeneous photoreactors by the six-flux model
2006
Heterogeneous photoreactor modeling is a task complicated by the integro-differential nature of the Radiation Transfer Equation (RTE) when scattering phenomena are important. In the present work, a novel “Six Flux Model” (SFM) is proposed, which may be regarded as a step forward with respect to the previously proposed “Two Flux Model” (TFM). In order to validate the newly proposed model, Monte Carlo simulations of an indefinite plane-slab photoreactor have been performed. As no simplifying assumptions are involved in this case, the information obtained may be regarded as “pseudo-experimental,” and therefore compared with the predictions of both TFM and SFM models. Results show that the nove…