Search results for "equation"
showing 10 items of 4219 documents
Motion of the wave-function zeros in spin-boson systems.
1995
In the analytic Bargmann representation associated with the harmonic oscillator and spin coherent states, the wave functions considered as consisting of entire complex functions can be factorized in terms of their zeros in a unique way. The Schr\"odinger equation of motion for the wave function is turned to a system of equations for the zeros of the wave function. The motion of these zeros as a nonlinear flow of points is studied and interpreted for linear and nonlinear bosonic and spin Hamiltonians. Attention is given to the study of the zeros of the Jaynes-Cummings model and to its finite analog. Numerical solutions are derived and dicussed.
Observation of instabilities in a Paul trap with higher-order anharmonicities
1995
Systematic measurements of the relative ion number stored in a Paul trap within the stability diagram given by the solution of the equation of motion reveal many lines, where only few or no ions can be confined. The observations can be explained by the presence of perturbations from higher-order components in the trapping potential, which is a quadrupole potential in the ideal case. The resonances follow the equation (nr/2)βr + (nr/2)βz = 1,nr +nz =N, where 2N is the order of the perturbation,nr,nz are integer andβr,βz are stability parameters of the trap. The experiments were performed on H+ and H2+ ions, which are detected after a storage time of 0.3 s by ejection from the trap.
Exact Solution of Quantum Optical Models by Algebraic Bethe Ansatz Methods
1996
From long standing interests in solitons and integrable systems, e.g. SIT (1968– 74)1,2, “optical solitons” CQ04 (1977)3, we solve exactly, by algebraic Bettie ansatz (= quantum inverse) methods4, models of importance to quantum optics including the quantum Maxwell-Bloch envelope equations for plane-wave quantum self-induced transparency (SIT) in one space variable (x) and one time (t)2; and in the one tinte (t)5 a family of models surrounding and extending the Tavis-Cummings model6 of N 2-level atoms coupled to one cavity mode for ideal cavity (Q = ∞) QED. Additional Kerr type nonlinearities or Stark shifted levels can he incorporated into the Hamiltonian H of one of the most general model…
Quantum Criticality in a Bosonic Josephson Junction
2011
In this paper we consider a bosonic Josephson junction described by a two-mode Bose-Hubbard model, and we thoroughly analyze a quantum phase transition occurring in the system in the limit of infinite bosonic population. We discuss the relation between this quantum phase transition and the dynamical bifurcation occurring in the spectrum of the Discrete Self Trapping equations describing the system at the semiclassical level. In particular, we identify five regimes depending on the strength of the effective interaction among bosons, and study the finite-size effects arising from the finiteness of the bosonic population. We devote a special attention to the critical regime which reduces to th…
A non-relativistic model for the $[cc][\bar{c}\bar{c}]$ tetraquark
2017
We use a non-relativistic model to study the spectroscopy of a tetraquark composed of $[cc][\bar{c}\bar{c}]$ in a diquark-antidiquark configuration. By numerically solving the Schr\"{o}dinger equation with a Cornell-inspired potential, we separate the four-body problem into three two-body problems. Spin-dependent terms (spin-spin, spin-orbit and tensor) are used to describe the splitting structure of the $c\bar{c}$ spectrum and are also extended to the interaction between diquarks. Recent experimental data on charmonium states are used to fix the parameters of the model and a satisfactory description of the spectrum is obtained. We find that the spin-dependent interaction is sizable in the …
Color glass condensate at next-to-leading order meets HERA data
2020
We perform the first dipole picture fit to HERA inclusive cross section data using the full next-to-leading order (NLO) impact factor combined with an improved Balitsky-Kovchegov evolution including the dominant effects beyond leading logarithmic accuracy at low $x$. We find that three different formulations of the evolution equation that have been proposed in the recent literature result in a very similar description of HERA data, and robust predictions for future deep inelastic scattering experiments. We find evidence pointing towards a significant nonperturbative contribution to the structure function for light quarks, which stresses the need to extend the NLO impact factor calculation t…
Ultrarelativistic quark-nucleus scattering in a light-front Hamiltonian approach
2020
We investigate the scattering of a quark on a heavy nucleus at high energies using the time-dependent basis light-front quantization (tBLFQ) formalism, which is the first application of the tBLFQ formalism in QCD. We present the real-time evolution of the quark wave function in a strong classical color field of the relativistic nucleus, described as the color glass condensate. The quark and the nucleus color field are simulated in the QCD SU(3) color space. We calculate the total and the differential cross sections, and the quark distribution in coordinate and color spaces using the tBLFQ approach. We recover the eikonal cross sections in the eikonal limit. We find that the differential cro…
Bridging a gap between continuum-QCD and ab initio predictions of hadron observables
2015
Within contemporary hadron physics there are two common methods for determining the momentum-dependence of the interaction between quarks: the top-down approach, which works toward an ab initio computation of the interaction via direct analysis of the gauge-sector gap equations; and the bottom-up scheme, which aims to infer the interaction by fitting data within a well-defined truncation of those equations in the matter sector that are relevant to bound-state properties. We unite these two approaches by demonstrating that the renormalisation-group-invariant running-interaction predicted by contemporary analyses of QCD's gauge sector coincides with that required in order to describe ground-s…
Single inclusive forward hadron production at next-to-leading order
2016
We discuss single inclusive hadron production from a high energy quark scattering off a strong target color field in the Color Glass Condensate formalism. Recent calculations of this process at the next-to-leading order accuracy have led to negative cross sections at large transverse momenta. We identify the origin of this problem as an oversubtraction of the rapidity divergence into the Balitsky-Kovchegov evolution equation for the target. We propose a new way to implement the kinematical restriction on the emitted gluons to overcome this difficulty.
Nucleon Form Factors at high q2 within constituent quark models
2000
The nucleon form factors are calculated using a non-relativistic description in terms of constituent quarks. The emphasis is put on the reliability of present numerical methods used to solve the three-body problem in order to correctly reproduce the expected asymptotic behavior of form factors. Nucleon wave functions obtained in the hyperspherical formalism or employing Faddeev equations have been considered. While a q**(-8) behavior is expected at high q for a quark-quark force behaving like 1/r at short distances, it is found that the hypercentral approximation in the hyperspherical formalism (K=0) leads to a q**(-7) behavior. An infinite set of waves is required to get the correct behavi…