Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAdiabatic approach to large-amplitude collective motion with the higher-order collective-coordinate operator
74
0
0.0
(
0
)
Authors
Koichi Sato
Ask ChatGPT about the research
No Arabic abstract
We propose a new set of equations to determine the collective Hamiltonian including the second-order collective-coordinate operator on the basis of the adiabatic self-consistent collective-coordinate (ASCC) theory. We illustrate, with the two-level Lipkin model, that the collective operators including the second-order one are self-consistently determined. We compare the results of the calculations with and without the second-order operator and show that, without the second-order operator, the agreement with the exact solution becomes worse as the excitation energy increases, but that, with the second-order operator included, the exact solution is well reproduced even for highly excited states. We also reconsider which equations one should adopt as the basic equations in the case where only the first-order operator is taken into account, and suggest an alternative set of fundamental equations instead of the conventional ASCC equations. Moreover, we briefly discuss the gauge symmetry of the new basic equations we propose in this paper.
rate research
Read More
We investigate the relation of $a^dagger a$ terms in the collective operator to the higher-order terms in the adiabatic self-consistent collective coordinate (ASCC) method. In the ASCC method, a state vector is written as $e^{ihat G(q,p,n)}|phi(q)rangle$ with $hat G(q,p,n)$ which is a function of collective coordinate $q$, its conjugate momentum $p$ and the particle number $n$. According to the generalized Thouless theorem, $hat G$ can be written as a linear combination of two-quasiparticle creation and annihilation operators $a^dagger_mu a^dagger_ u$ and $a_ u a_mu$. We show that, if $a^dagger a$ terms are included in $hat G(q,p,n)$, it corresponds to the higher-order terms in the adiabatic expansion of $hat G$. This relation serves as a prescription to determine the higher-order collective operators from the $a^dagger a$ part of the collective operator, once it is given without solving the higher-order equations of motion.
The adiabatic self-consistent collective coordinate (ASCC) method is a practical method for the description of large-amplitude collective motion in atomic nuclei with superfluidity and an advanced version of the adiabatic time-dependent Hartree-Fock-Bogoliubov theory. We investigate the gauge symmetry in the ASCC method on the basis of the theory of constrained systems. The gauge symmetry in the ASCC method is originated from the constraint on the particle number in the collective Hamiltonian, and it is partially broken by the adiabatic expansion. The validity of the adiabatic expansion under the general gauge transformation is also discussed.
We study gauge symmetry breaking by adiabatic approximation in the adiabatic self-consistent collective coordinate (ASCC) method. In the previous study, we found that the gauge symmetry of the equation of collective submanifold is (partially) broken by its decomposition into the three moving-frame equations depending on the order of $p$. In this study, we discuss the gauge symmetry breaking by the truncation of the adiabatic expansion. A particular emphasis is placed on the symmetry under the gauge transformations which are not point transformations. We also discuss a possible version of the ASCC method including the higher-order operators which can keep the gauge symmetry.
Finite-dimensional Lie algebras of vector fields determine geometrical collective models in quantum and classical physics. Every set of vector fields on Euclidean space that generates the Lie algebra sl(3, R) and contains the angular momentum algebra so(3) is determined. The subset of divergence-free sl(3, R) vector fields is proven to be indexed by a real number $Lambda$. The $Lambda=0$ solution is the linear representation that corresponds to the Riemann ellipsoidal model. The nonlinear group action on Euclidean space transforms a certain family of deformed droplets among themselves. For positive $Lambda$, the droplets have a neck that becomes more pronounced as $Lambda$ increases; for negative $Lambda$, the droplets contain a spherical bubble of radius $|Lambda|^{{1/3}}$. The nonlinear vector field algebra is extended to the nonlinear general collective motion algebra gcm(3) which includes the inertia tensor. The quantum algebraic models of nonlinear nuclear collective motion are given by irreducible unitary representations of the nonlinear gcm(3) Lie algebra. These representations model fissioning isotopes ($Lambda>0$) and bubble and two-fluid nuclei ($Lambda<0$).
The general problem of dissipation in macroscopic large-amplitude collective motion and its relation to energy diffusion of intrinsic degrees of freedom of a nucleus is studied. By applying the cranking approach to the nuclear many-body system, a set of coupled dynamical equations for the collective classical variable and the quantum mechanical occupancies of the intrinsic nuclear states is derived. Different dynamical regimes of the intrinsic nuclear motion and its consequences on time properties of collective dissipation are discussed.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
