Search results for "Bethe"
showing 10 items of 82 documents
Classical thermodynamics of the Heisenberg chain in a field by generalized Bethe ansatz method
1990
Abstract Using the classical action-angle variables for the continuous model, we study the thermodynamics of the classical Heisenberg chain in an applied field by a generalized Bethe ansatz approach. The crucial point consists in the derivation of a phase-shifted density of states for the excitations of the model, obtained by imposing periodic boundary conditions. In the thermodynamic limit, the free energy can be expressed in terms of the solution of a non-linear integral equation, showing the universal dependece of the variable x=(JH) 1 2 /T .
Schwinger mechanism in linear covariant gauges
2016
In this work we explore the applicability of a special gluon mass generating mechanism in the context of the linear covariant gauges. In particular, the implementation of the Schwinger mechanism in pure Yang-Mills theories hinges crucially on the inclusion of massless bound-state excitations in the fundamental nonperturbative vertices of the theory. The dynamical formation of such excitations is controlled by a homogeneous linear Bethe-Salpeter equation, whose nontrivial solutions have been studied only in the Landau gauge. Here, the form of this integral equation is derived for general values of the gauge-fixing parameter, under a number of simplifying assumptions that reduce the degree of…
Study of theZb(10610) andZb(10650) states through $B\bar{B}^*$ and $B^*\bar{B}^*$ interactions using local hidden gauge approach
2016
We have studied the $B\bar{B}^*$ and $B^*\bar{B}^*$ interactions for isospin I = 1 using the Local Hidden gauge approach. Since both interactions via one light meson exchange are not allowed by Okubo-Zweig-Iizuka (OZI) rule, we investigated the contributions for those interactions coming from two pions, interacting and noninteracting among themselves, and also due to the heavy vector meson exchange, in which the OZI rule no longer holds. From the amplitudes calculated by these mechanism, we determine an effective potential which is used as a kernel of the Bethe-Salpeter equation. Our goal is look for poles in the T-matrix in attemp to relate them with the charged Zb (10610) and Zb (10650) s…
Green functions for nearest- and next-nearest-neighbor hopping on the Bethe lattice
2005
We calculate the local Green function for a quantum-mechanical particle with hopping between nearest and next-nearest neighbors on the Bethe lattice, where the on-site energies may alternate on sublattices. For infinite connectivity the renormalized perturbation expansion is carried out by counting all non-self-intersecting paths, leading to an implicit equation for the local Green function. By integrating out branches of the Bethe lattice the same equation is obtained from a path integral approach for the partition function. This also provides the local Green function for finite connectivity. Finally, a recently developed topological approach is extended to derive an operator identity whic…
Aharonov–Bohm/Casher effect in a Kondo ring
2000
The in#uence of a magnetic impurity or ultrasmall quantum dot on the spin and charge persistent currents of a mesoscopic ring is investigated. The system consists of electrons in a one-dimensional ring threaded by spin-dependent Aharonov}Bohm/Casher #uxes, and coupled via an antiferromagnetic exchange interaction to a localized electron. The problem is mapped onto a Kondo model for the even-parity channel plus free electrons in the odd-parity channel. The twisted boundary conditions representing the #uxes couple states of opposite parity unless the twist angles / a satisfy / a "f a p, where f a are integers, with spin index a"C, B. For these special values of / a , the model is solvable by …
Statistical Mechanics of the Sine-Gordon Equation
1986
We give two fundamental methods for evaluation of classical free energies of all the integrable models admitting soliton solutions; the sine-Gordon equation is one example. Periodic boundary conditions impose integral equations for allowed phonon and soliton momenta. From these, generalized Bethe-Ansatz and functional-integration methods using action-angle variables follow. Results for free energies coincide, and coincide with those that we find by transfer-integral methods. Extension to the quantum case, and quantum Bethe Ansatz, on the lines to be reported elsewhere for the sinh-Gordon equation, is indicated.
Improving the ultraviolet behavior in baryon chiral perturbation theory
2004
We introduce a new formulation of baryon chiral perturbation theory which improves the ultraviolet behavior of propagators and can be interpreted as a smooth cutoff regularization scheme. It is equivalent to the standard approach, preserves all symmetries and therefore satisfies the Ward identities. Our formulation is equally well defined in the vacuum, one- and few-nucleon sectors of the theory. The equations (Bethe-Salpeter, Lippmann-Schwinger, etc.) for the scattering amplitudes of the few-nucleon sector are free of divergences in the new approach. Unlike the usual cutoff regularization, our 'cutoffs' are parameters of the Lagrangian and do not have to be removed.
Linear confinement in momentum space: singularity-free bound-state equations
2014
Relativistic equations of Bethe-Salpeter type for hadron structure are most conveniently formulated in momentum space. The presence of confining interactions causes complications because the corresponding kernels are singular. This occurs not only in the relativistic case but also in the nonrelativistic Schr\"odinger equation where this problem can be studied more easily. For the linear confining interaction the singularity reduces to one of Cauchy principal value form. Although this singularity is integrable, it still makes accurate numerical solutions difficult. We show that this principal value singularity can be eliminated by means of a subtraction method. The resulting equation is much…
On the chiral covariant approach to ρρ scattering
2017
We examine in detail a recent work (D.~G\"ulmez, U.-G.~Mei\ss ner and J.~A.~Oller, Eur. Phys. J. C 77:460 (2017)), where improvements to make $\rho\rho$ scattering relativistically covariant are made. The paper has the remarkable conclusion that the $J=2$ state disappears with a potential which is much more attractive than for $J=0$, where a bound state is found. We trace this abnormal conclusion to the fact that an "on-shell" factorization of the potential is done in a region where this potential is singular and develops a large discontinuous and unphysical imaginary part. A method is developed, evaluating the loops with full $\rho$ propagators, and we show that they do not develop singula…
Study ofBB¯*andB*B¯*interactions inI=1and relationship to theZb(10610),Zb(10650)states
2015
We use the local hidden gauge approach in order to study the $B{\overline{B}}^{*}$ and ${B}^{*}{\overline{B}}^{*}$ interactions for isospin $I=1$. We show that both interactions via one light meson exchange are not allowed by the Okubo-Zweig-Iizuka rule and, for that reason, we calculate the contributions due to the exchange of two pions, interacting and noninteracting among themselves, and also due to the heavy vector mesons. Then, to compare all these contributions, we use the potential related to the heavy vector exchange as an effective potential corrected by a factor which takes into account the contribution of the other light meson exchanges. In order to look for poles, this effective…