Littérature scientifique sur le sujet « Semirelativistico »

AbstractPlasmas with moderate flow velocity and sound speed, but large Alfvén speed have been described by the semirelativistic magnetohydrodynamics (MHD) equations. While these are correct when restricted to their range of validity, they may have the undesirable effect of predicting unphysical accelerations, much faster than the ones of classical MHD. We present a family of planar models on which the Lorentz force acts more forcefully in the semirelativistic approach, yielding a flow velocity which rapidly exceeds the limits within which the equations are valid.

We calculate the [Formula: see text] mass spectrum, the splitting values and some other properties in the framework of the semirelativistic equation by applying the shifted large-N expansion technique. We use seven different central potentials together with an improved QCD-motivated interquark potentials calculated to two loops in the modified minimal-subtraction [Formula: see text] scheme. The parameters of these potentials are fitted to generate the semirelativistic bound states of [Formula: see text] quarkonium system in close conformity with the experimental and the present available calculated center-of-gravity (c.o.g.) data. Calculations of the energy bound states are carried out up to third order. Our results are in excellent fit with the results of the other works.

We review various attempts to localize the discrete spectra of semirelativistic Hamiltonians of the form [Formula: see text] (defined, without loss of generality but for definiteness, in three spatial dimensions) as entering, for instance, in the spinless Salpeter equation; every Hamiltonian in this class of operators consists of the relativistic kinetic energy [Formula: see text], where β > 0 allows for the possibility of more than one particles of mass m, and a spherically symmetric attractive potential V(r), r ≡ |x|. In general, accurate eigenvalues of a nonlocal Hamiltonian operator can only be found by the use of a numerical approximation procedure. Our main emphasis, however, is on the derivation of rigorous semianalytical expressions for both upper and lower bounds to the energy levels of such operators. We compare the bounds obtained within different approaches and present relationships existing between the bounds.

This review discusses several aspects of the semirelativistic description of bound states by the spinless Salpeter equation (which represents the simplest equation of motion incorporating relativistic effects) and, in particular, presents or recalls some very simple and elementary methods which allow us to derive rigorous statements on the corresponding solutions, that is, on energy levels as well as wave functions.

We investigate the structure of the SU(3) octet and decuplet baryons employing a constituent chiral quark model. We study the ground, s-wave and p-wave excited states of the three-quark system with many range gaussian bases. The method, which we employ here, is shown to work quite well in describing the structure of the SU(3) s-wave and p-wave baryons. It is found that the mass differences between positive and negative parity states are well reproduced. It is also found that the pseudoscalar (ps) meson exchange potential plays a very important role in describing the mass of the nucleon resonance N*(1440) (roper). We also discuss how the semirelativistic approach works in the chiral quark model, and how to treat the potential terms in the semirelativistic approach.

We study the bound state problem for semirelativistic N attractive Dirac δ-potentials in one dimension. We give a sufficient condition for the Hamiltonian to have N bound states and give an explicit criterion for it.

It is shown that the ground-state eigenvalue of a semirelativistic Hamiltonian of the form [Formula: see text] is bounded below by the Schrödinger operator m + β p2 + V, for suitable β>0. An example is discussed.

Abstract The electron cyclotron maser (ECM) instability is a very important nonthermal radiation mechanism. It has been developed by proposing various electron distribution functions as well as the relativistic resonance condition, called the semirelativistic correction. Taking account of the relativistic effects of both the velocity distribution of energetic electrons and the resonance condition, called the fully relativistic correction, the present paper investigates the ECM instability driven by a power-law electron distribution with a low-energy cutoff. The results show that (1) both in the semirelativistic and fully relativistic cases, the growth rate and relative frequency bandwidth of ordinary (O) and extraordinary (X) modes show a positive correlation with cutoff energy E c , i.e., the peak frequency decreases with increasing E c ; (2) the peak frequency ratio (H peak/F peak) of the harmonic and fundamental waves is always ∼2; (3) compared with the semirelativistic case, the fully relativistic case has a larger growth rate (for both the O and X mode) and a smaller peak frequency (only for the O mode) for energy > 50 keV, and there is almost no difference at lower energy for the two cases; (4) the peak frequency of the X1 mode can be higher than its cutoff frequency in a strongly magnetized plasma, implying that the X1 mode emission may escape more easily for a higher E c and stronger magnetic field. These results can be helpful for us to understand better the physics of radio bursts from the Sun and other objects.

Scopo di questa tesi è mostrare i risultati ottenuti per tre equazioni differenziali alle derivate parziali ellittiche di tipo Schrödinger. Queste equazioni, sebbene condividano la particolarità di essere definite in tutto lo spazio, sono state affrontate con diversi metodi, e per ognuna è stato fornito un risultato di esistenza di soluzioni. Rimarchiamo che l'ultima equazione ha un forte legame con le equazioni di Maxwell. Problema 1) Consideriamo un'equazione di tipo Schrödinger, con potenziale di tipo convolutivo ed una nonlinearità perturbata e pesata derivante dalla fisica quantistica con gravitazione Newtoniana. Se consideriamo questa equazione definita in tutto lo spazio R2, otterremo un potenziale di tipo logaritmico, che rende l'analisi più delicata, in quanto il funzionale associato non è ben definito. Va dunque introdotto un opportuno setting variazionale per dimostrare la buona positura del problema. Successivamente, per gestire la perturbazione utilizziamo la tecnica perturbativa della teoria dei punti critici. Assumendo opportune ipotesi sulla funzione peso, si dimostra l'esistenza di soluzioni locali e globali. Problema 2) La seconda equazione è un'equazione di tipo Choquard governata da un operatore semirelativistico di Schrödinger, dove il potenziale ha una parte singolare ed è presente una nonlinearità generale, definita in tutto lo spazio RN. Grazie alla rappresentazione mediante trasformata di Fourier dell'operatore semirelativistico, si può dimostrare che la norma generata dalla forma quadratica associata al problema è equivalente alla norma standard. Grazie ad un risultato astratto, si prova prima l'esistenza di una successione di Cerami e successivamente la sua limitatezza. Adattando un argomento di decomposizione per successioni di Palais-Smale, si dimostra poi la convergenza di questa successione ad un punto critico non banale. Infine, viene fornita una quasi-caratterizzazione per l'esistenza di soluzioni di tipo ground-state (i.e. soluzioni corrispondenti al livello di energia minima del sistema). Per queste soluzioni, è fornito anche un risultato di compattezza rispetto al termine singolare. Problema 3) Viene fornito un Teorema astratto di tipo linking infinito-dimensionale che permette lo studio di problemi fortemente indefiniti (cioè il punto origine appartiene ad un gap spettrale dell'operatore) e con nonlinearità generali di segno variabile. Come applicazione, questo Teorema viene applicato ad un'equazione di tipo Schrödinger fortemente indefinita con potenziale singolare e nonlinearità a segno variabile, definita in tutto lo spazio RN. Per questa equazione viene dimostrata l'esistenza di una soluzione non banale. Sfruttando un risultato di equivalenza, viene fornita l'esistenza di una soluzione nonbanale anche per un'equazione di tipo curl-curl: questo tipo di equazioni sono strettamente legate alle equazioni di Maxwell.
The purpose of this thesis is to show the results obtained for three Schrödinger type elliptic partial differential equations. These equations, although sharing the feature of being entire, i.e. defined in the whole the space, have been approached with different methods, and for each a result of the existence of solutions has been provided. We emphasize that the last equation has a strong connection with Maxwell's equations. Problem 1) Let us consider a Schrödinger type equation, with convolutive potential and a perturbed and weighted nonlinearity copuling from quantum physics with Newtonian gravitation. If we consider this equation defined in all the space R2, we will obtain a logarithmic type potential, which makes the analysis more delicate, since the associated functional is not well defined. Therefore, a suitable variational setting must be introduced to show the well-posedness of the problem. Next, to manage the perturbation we use the perturbation technique of the critical point theory. Assuming suitable hypotheses on the weight function, the existence of local and global solutions is proved. Problem 2) The second equation is a Choquard type equation driven by a semirelativistic Schrödinger operator, defined in the whole space RN, where the potential has a singular part and a general nonlinearity is considered. Using the Fourier transform representation of the semirelativistic operator, it can be shown that the norm generated by the quadratic form associated with the problem is equivalent to the standard one. Thanks to an abstract result, we first prove the existence of a Cerami-sequence and then its boundedness. By adapting a Palais-Smale-sequence decomposition argument, the strong convergence of this sequence to a non-trivial critical point is then showed. Finally, an almost-characterization criterion is provided for the existence of ground-state solutions (i.e. solutions corresponding to the minimum energy level of the system). For these solutions, a compactness result is also given with respect to the singular term. Problem 3) An abstract infinite-dimensional linking-type Theorem is provided, which allows the study of strongly indefinite problems (i.e. the origin belongs to a spectral gap of the operator) and with general sign-changing nonlinearities. As an application, this Theorem is applied to a strongly indefinite Schrödinger equation with singular potential and sign-changing nonlinearity, defined in the whole space RN. For this equation the existence of a non-trivial solution is proved. By exploiting an equivalence result, the existence of a non-trivial solution is also provided for a curl-curl equation: this type of equations are closely related to Maxwell's equations.