Damping of collective modes in DIC: Quantal versus statistical fluctuations

A model is developed to describe the transformation of relative kinetic energy into intrinsic excitation energy in DIC. Energy dissipation is viewed as an indirect process, in which collective vibrational modes are first excited coherently and then damped due to the coupling to the remaining non-collective degrees of freedom. Both collective and intrinsic degrees of freedom are included explicitly, and the coupling between them is treated in a random-matrix model. Under certain assumptions it is shown that, in the weak-coupling limit, the collective probability distribution in phase space obeys a Fokker-Planek equation. This transport equation is used to derive equations of motion for the expectation values of some “macroscopic” quantities characterizing the process. Some numerical results are presented and a qualitative comparison with the Copenhagen model is attached.     

General semi-classical method for collective motion and its connection with the Rowe-Basserman and marumori theories,and adiabatic limits

In recent work, we have shown that in the adiabatic limit (large amplitude, small momentum), time-dependent Hartree-Fock theory (TDHF) yields a well-defined theory of large-amplitude collective motion which provides an essentially unique construction for a collective hamiltonian. An alternative theory, put forward by Rowe and Basserman and by Marumori is, apparently, not restricted to small momenta. We describe a general framework for the study of collective motion in the semi-classical limit without limitation on the size of coordinates or momenta, which includes all previous methods as limiting cases. We find it convenient, as in the past, to consider two general systems: first, a system with n degrees of freedom and no special permutation symmetry, and, second, a system of fermions described in TDHF. For both systems the problem can be formulated as a search for a hamiltonian flow confined to a finite-dimensional hypersurface in a phase space, which itself may be finite- or infinite-dimensional. Though, in general, there are no exact solutions to this problem, we can formulate consistent approximation schemes corresponding to both the adiabatic and Rowe-Basserman, and Marumori limits. We also show how to extend the momentum expansion, which underlies the adiabatic approximation, to higher orders in the momentum. We thereby confirm the structure of the theory found in our previous work.     

Application of the dyson boson mapping to the analysis of the phase transition at N = 88–90

The Dyson boson mapping theory is applied to the analysis of the phase transition from vibrational to rotational spectra in the Sm isotopes. The original quasiparticle space consisting of multi-quadrupole collective-phonon states on the spherical shell-model bases is transformed into a boson space by the Dyson mapping. In this boson space, numerical analysis is carried out for ^146–154Sm. In addition, the boson space is extended to contain non-collective phonon degrees of freedom and in this extended space the coupling effect between collective and non-collective phonons is precisely estimated. The numerical results show that the contribution from the noncollective phonon degrees of freedom cannot be neglected in the transitional region.     

Non-classical configurations in Euclidean field theory as minima of constrained systems

We study a systematic method of applying the semiclassical approximation to Euclidean field theory. First, we extract generalized collective coordinates which are not in general zero modes. We then apply the semiclassical approximation to the other degrees of freedom by minimizing the action with constraints. Hence we are using configurations which are not classical solutions of the original system. After Gaussian integration we are left with a truncated system, involving only the collective coordinates, with non-trivial dynamics. In particular, this is a clear-cut way to introduce multi-instanton or meron-type configurations. The collective coordinates should be chosen such that their dynamics are a good approximation to the original system for the physical phenomenon considered; a familiar concept in other branches of physics with many degrees of freedom. The formalism leads naturally to the introduction of dynamics in an extra time evolution; in particular cases, we show that this is a very powerful tool. In this paper, we only discuss general ideas and formalisms. Specific applications are postponed to to later publications.     

Importance of the internal shape mode in magnetic vortex dynamics

We investigate the motion of a nonplanar vortex in a circular easy-plane magnet with a rotating in-plane magnetic field. Our numerical simulations of the Landau-Lifshitz equations show that the vortex tends to a circular limit trajectory, with an orbit frequency which is lower than the driving field frequency. To describe this we develop a new collective variable theory by introducing additional variables which account for the internal degrees of freedom of the vortex core, strongly coupled to the translational motion. We derive the evolution equations for these collective variables and find limit-cycle solutions whose characteristics are in qualitative agreement with the simulations of the many-spin system.     

Precise implementation of cluster transfer matrix method in the single electron box

The partition function of the single electron box (SEB), a small metallic island connected by a tunnel junction to the source lead and by a gate capacitor to the gate, can be expressed in path-integral form, which contains the effective action of the collective variable, phase, after integrating out the background electron degrees of freedom. The cluster transfer matrix method (CTM) is applied to the SEB. By using an improved numerical algorithm and more intensive calculations with larger cluster size, we obtained a highly accurate result for the effective charging energy of SEB up to a large barrier conductance. With a clear converging tendency and the fact that we do not use any approximation in calculation of the partition function, our CTM calculation is systematic and exact. The result is in excellent agreement with the real time renormalization group method of König and Schoeller.     

DESCRIPTIONS OF THE EQUILIBRATION PROCESS OF THE INTRINSIC DEGREES OF FREEDOM AND DISSIPATIVE PROCESS OF THE NUCLEAR COLLECTIVE MOTION

In this paper the Hamiltonian model is used for studying the nuclear dynamics by taking both the one-body and two-body interaction mechanisms into account. On the basis of the Von Neuman equation the coupling between the collective motion and the single particle degrees of freedom is discussed. Thus, the equations obtained are physically transparent and easy for numerical computations. They may be useful for describing the dissipative process of the nuclear collective motion as well as the equilibration process of the intrinsic degrees of freedom.     

Interaction Dynamics of the External and Internal Degrees of Freedom of an Atom in the Resonant Field of a Standing Light Wave

The theory of the dynamic interaction of the external (translational) and internal (electronic) degrees of freedom of a twolevel atom in the field of a standing light wave in a perfect cavity of the Fabry–Perot type was developed. The theory describes the energy exchange between three subsystems, namely, translational, electronic, and field subsystems, as opposed to the theories of the parametric interaction (in the approximations of Raman–Nath and/or large resonance detuning) and of the atomic motion in free space. In the semiclassical approximation, the corresponding Heisenberg equations of motion were shown to form a closed Hamiltonian dynamic system with two degrees of freedom, namely, translational and collective electron–field degrees of freedom. This system is integrated in terms of the elliptic Jacobian functions in the resonance limit. The solutions obtained describe the effects of trapping of an atom in the periodic potential of the standing light wave, and its cooling and heating, as well as the effect of the dynamic Rabi oscillations. The latter is caused by the interaction of the internal and external atomic degrees of freedom through the radiation field.     

Faddeev random phase approximation applied to molecules

The Faddeev Random Phase Approximation (FRPA) is a Green’s function method which couples collective degrees of freedom to the single particle motion by resumming an infinite number of Feynman diagrams. The Faddeev technique is applied to describe the two-particle-one-hole (2p1h) and two-hole-one-particle (2h1p) Green’s function in terms of non-interacting propagators and kernels for the particle-particle (pp) and particle-hole (ph) interactions. This results in an equal treatment of the intermediary pp and ph channels. In FRPA both the pp and ph phonons are calculated on the random phase approximation (RPA) level. In this work the equations that lead to the FRPA eigenvalue problem are derived. The method is then applied to atoms, small molecules and the Hubbard model, for which the ground state energy and the ionization energies are calculated. Special attention is directed to the RPA instability in the dissociation limit of diatomic molecules and in the Hubbard model. Several solutions are proposed to overcome this problem.     

How adiabatic is quantum tunneling?

We consider the coupling between collective and intrinsic degrees of freedom of a many-dimensional quantum system. We give a criterion for the validity of the adiabatic approximation in tunneling processes and derive an equation for the “lag” of the intrinsic wave function with respect to the adiabatic groundstate. Solutions for several simple cases are presented.     

Coherent regimes of globally coupled dynamical systems

This Letter presents a method by which the mean field dynamics of a population of dynamical systems with parameter diversity and global coupling can be described in terms of a few macroscopic degrees of freedom. The method applies to populations of any size and functional form in the region of coherence. It requires linear variation or a narrow distribution for the dispersed parameter. Although an approximation, the method allows us to quantitatively study the transitions among the collective regimes as bifurcations of the effective macroscopic degrees of freedom. To illustrate, the phenomenon of oscillator death and the route to full locking are examined for chaotic oscillators with time scale mismatch.     

Shape mixing dynamics in the low-lying states of proton-rich Kr isotopes

We study the oblate–prolate shape mixing in the low-lying states of proton-rich Kr isotopes using the five-dimensional quadrupole collective Hamiltonian. The collective Hamiltonian is derived microscopically by means of the CHFB (constrained Hartree–Fock–Bogoliubov) + Local QRPA (quasiparticle random phase approximation) method, which we have developed recently on the basis of the adiabatic self-consistent collective coordinate method. The results of the numerical calculation show the importance of large-amplitude collective vibrations in the triaxial shape degree of freedom and rotational effects on the oblate–prolate shape mixing dynamics in the low-lying states of these isotopes.     

A microscopic boson model for collective transition nuclei: Schwinger representation of the SO(8) shell model algebra

An equivalent representation of the SO(8) fermion pair algebra is given in terms of s- and d-bosons. The s-boson is a quasispin vector-boson in our formalism. Boson quasispin is the clue to treating the pairing degrees of freedom on the same footing as the particle-hole degrees of freedom. As a consequence, we obtain the pairing rotation as a collective mode, in addition to the spatial rotations described by the IBM. We compare results of the exact numerical solution of the secular equation with those calculated in the HFB mean field approximation which attains the form of boson coherent states in our method. Goldstone bosons can be introduced which represent collective soft modes. Two components of the quasispin vector-boson can be associated with the removal and addition modes of the pairing vibration. The third component is the IBM s-boson.     

压缩真空中梯形三能级原子的辐射压力

研究了压缩真空中梯形三能级原子在单色行波场中的辐射压力。从系统的哈密顿量出发,利用玻因-马尔可夫近似,推导出了原子的光学布洛赫方程。此时用数值方法求得布洛赫方程的稳态解,然后用图示法考察了原子的辐射压力随双光子失谐、拉比频率、自发发射率等参量的依赖关系。结果表明：单光子跃迁和双光子跃迁可导致辐射压力出现各自的多普勒位移共振峰;辐射压力表现出较宽的失谐范围且强烈依赖于压缩参量以及压缩真空和相干光之间的相位关系。当相位满足匹配条件时,辐射压力减小。     

Free-energy transition in a gas of noninteracting nonlinear wave particles

We investigate the dynamics of a gas of noninteracting particlelike soliton waves, demonstrating that phase transitions originate from their collective behavior. This is predicted by solving exactly the nonlinear equations and by employing methods of the statistical mechanics of chaos. In particular, we show that a suitable free energy undergoes a metamorphosis as the input excitation is increased, thereby developing a first-order phase transition whose measurable manifestation is the formation of shock waves. This demonstrates that even the simplest phase-space dynamics, involving independent (uncoupled) degrees of freedom, can sustain critical phenomena.     

Model analysis of the world data on the pion transition form factor

The evolution of neck for the asymmetric system ⁵⁸Fe + ²⁴⁴Pu at E _c.m. = 260 MeV has been studied with the coupled Langevin equations in two-dimensional collective space and the results compared to those obtained with a one-dimensional approach under the frozen assumption. It is found that the coupling between the radial and neck degrees of freedom reduces the drift velocity of neck growth and delays the transition from dinucleus to mononucleus. Besides, the coupling brings the system into a somehow elongated shape when the injection into the asymmetric fission valley takes place, hence, the fusion probability and the relevant evaporation residue (ER) cross-sections decrease. For the system ⁵⁸Fe + ²⁴⁴Pu , the ER cross-sections decrease by about 30% as compared to those obtained under the frozen approximation. Therefore, we may arrive at the conclusion that for the heavy asymmetric systems such as ⁵⁸Fe + ²⁴⁴Pu the coupling between different degrees of freedom has important effects on the evolution from dinucleus to mononucleus and the frozen approximation is basically not satisfied as far as the neck dynamics is concerned. However, as compared to the symmetric reactions, the influence of the neck dynamics on the fusion hindrance factor of heavy systems is much weaker for the asymmetric reactions.     

Dynamics of a single ion in a perturbed Penning trap: octupolar perturbation

Imperfections in the design or implementation of Penning traps may give rise to electrostatic perturbations that introduce nonlinearities in the dynamics. In this paper we investigate, from the point of view of classical mechanics, the dynamics of a single ion trapped in a Penning trap perturbed by an octupolar perturbation. Because of the axial symmetry of the problem, the system has two degrees of freedom. Hence, this model is ideal to be managed by numerical techniques like continuation of families of periodic orbits and Poincaré surfaces of section. We find that, through the variation of the two parameters controlling the dynamics, several periodic orbits emanate from two fundamental periodic orbits. This process produces important changes (bifurcations) in the phase space structure leading to chaotic behavior.     

Dual boson approach to collective excitations in correlated fermionic systems

We develop a general theory of a boson decomposition for both local and non-local interactions in lattice fermion models which allows us to describe fermionic degrees of freedom and collective charge and spin excitations on equal footing. An efficient perturbation theory in the interaction of the fermionic and the bosonic degrees of freedom is constructed in the so-called dual variables in the path-integral formalism. This theory takes into account all local correlations of fermions and collective bosonic modes and interpolates between itinerant and localized regimes of electrons in solids. The zero-order approximation of this theory corresponds to an extended dynamical mean-field theory (EDMFT), a regular way to calculate nonlocal corrections to EDMFT is provided. It is shown that dual ladder summation gives a conserving approximation beyond EDMFT. The method is especially suitable for consideration of collective magnetic and charge excitations and allows to calculate their renormalization with respect to “bare” RPA-like characteristics. General expression for the plasmonic dispersion in correlated media is obtained. As an illustration it is shown that effective superexchange interactions in the half-filled Hubbard model can be derived within the dual-ladder approximation.