Uniqueness of the collective submanifold in the adiabatic theory of large amplitude collective motion

It is emphasized that the conditions for the existence of a collective submanifold which follow from adiabatic time-dependent Hartree-Fock theory are precisely the conditions for the existence of a manifold of solutions of Hamilton's equations confined to a surface of reduced dimensionality. A constructive procedure, valid in any number of dimensions and involving the concept of the multidimensional valley, is developed to determine whether a given system admits such a manifold. It is extended to include the idea of the approximate manifold, and an application to a generalized landscape model is described.     

A study of collective paths in the time-dependent hartree-fock approach to large amplitude collective nuclear motion

In a simple two-dimensional landscape model the collective paths of Rowe-Bassermann and Marumori, of Villars, of Goeke-Reinhard, and of Baranger-Veneroni are determined and compared. The uniqueness of the solutions and the practicability of the methods regarding numerical applications are discussed.     

Application of a self-consistent theory of large amplitude collective motion to the generalized meshkov-glick-lipkin model

A recent formulation of the theory of large amplitude collective motion in the adiabatic limit is applied to a generalized monopole shell model. Numerical calculations are carried out for the three-level model, approximately equivalent to a classical system with two degrees of freedom. Our results go somewhat beyond previous treatments of this system and provide substantiation for the validity of the method, in suitable parameter ranges, as a way of recognizing and decoupling the collective and the non-collective degrees of freedom.     

A unification scheme for the Einstein and Maxwell theories

A unification scheme for the Einstein and Maxwell theories is developed within a Riemann-Cartan geometry. The electromagnetic field is introduced at the level of the connection and it is, in fact, coded in the torsion. Within our framework, the unification of the massless spin-one and spin-two fields requires the inclusion of a massless spin-zero field, whose introduction may give rise to a non-constant gravitational coupling. However, for the case of dust-filled homogeneous and isotropic universe the result is essentially the same as the one supplied by general relativity.     

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.     

Framework for possible unification of quantum and relativity theories

We put forward a framework, inspired by recent axiomatic and operational approaches to generalized quantum theories, wherein we investigate the possibility of unifying quantum and relativity theories. The framework concentrates on a detailed analysis of a general construction of reality that can be used in both quantum and relativity theories. By means of this construction of reality we clarify some well-known conceptual problems that stand in the way of a conceptual unification of quantum and relativity theories on a more profound physical level than the purely mathematical algebraic level on which unification attempts are generally investigated. More specifically we concentrate on the problem of what is physical reality in quantum and relativity theories.     

Excitation of lattice motion by interaction with large amplitude electron plasma oscillations

Fast heavy-ion bombardment on solids in which a “free-electron”-limit for high excitations exists, generates plasma oscillations with very large amplitudes, as found in no other process. This should uniquely enable the observation of their coupling with other degrees of freedom such as phonons. The frequency spectrum of phonons excited by second-order coupling with plasmons and the respective energy loss to the lattice are calculated, using a simple two-fluid-model and the Lagrangian formalism as appropriate for high coherent excitations.     

Relation between the local harmonic formulation and the generalized valley formulation of the exact decoupling conditions in the adiabatic theory of large amplitude collective motion

In recent work, partially recapitulated, we have shown how the conditions for the existence of exactly decoupled classical motion in the adiabatic limit can be transformed into a constructive procedure, designated the generalized valley method, for the determination of the submanifold on which the motion occurs. We prove, for any number of decoupled coordinates, that where the conditions for exact decoupling in the adiabatic limit are satisfied, this formulation is equivalent to the local harmonic one which is widely discussed in the literature. The two formulations are however equivalent, in the general case where the decoupling is not exact, only for the one-dimensional submanifold. An alternative form of the local harmonic formulation, which does not utilize the metric properties associated with the mass tensor, and can therefore be extended to a general hamiltonian, is also discussed briefly.     

Exact canonically conjugate momentum to the quadrupole tensor and a microscopic derivation of the nuclear collective hamiltonian

Two momenta conjugate to the mass quadrupole tensor are given. The first is a canonical momentum only in a subspace of the shell model space. A microscopic collective kinetic energy in terms of this momentum and the quadrupole tensor is then obtained and compared with that of Bohr's hamiltonian. The second momentum is, on the other hand, canonically conjugate to the quadrupole tensor in the entire state space.     

The moment map and collective motion

Given a Hamiltonian action of a Lie group G on a symplectic manifold M there is an induced map Φ: $\text{M → g}{}^1$ where $\text{g}{}^1$ is the dual space to the Lie algebra, g, of G. The map Φ is called the moment map. Any function P on $\text{g}{}^1$ then gives rise to a function F = P ° Φ on M which is a “collective Hamiltonian” associated to the group action G. We show how the rigid rotor, liquid drop, and other collective models of the nucleus fit into this framework. We describe the steps involved in integrating collective equations of motion and indicate some principles involved in the choice of collective Hamiltonians, i.e., the functions P. We discuss these constructions in some detail for the case that G is a semidirect product.     

Large amplitude collective motion in nuclei and metallic clusters — Applicability of adiabatic theory for a pairing model

A model Hamiltonian describing a two-level system with a crossing plus a pairing force is investigated using the technique of large-amplitude collective motion. The collective path, which is determined by the decoupling conditions, is found to be almost identical to the one in the Born-Oppenheimer approximation for the case of a strong pairing force. For the weak pairing case, the obtained path describes a diabatic dynamics of the system. Presented by T. Nakatsukasa at the International Conference on “Atomic Nuclei and Metallic Clusters”, Prague, September 1–5, 1997. This work is supported by EPSRC (UK).     

Phenomenology of superstring theories with SO(10) unification

The phenomenology of superstring theories in which the gauge symmetry after compactification is SO(10) × E′₈, instead of E₆ × E′₈, is discussed. In particular, the generation of an intermediate scale, the radiative breaking of electroweak symmetry, and the supersymmetric particle spectrum are investigated.     

On the unification of the law of motion

Following a heuristic modification of the principle of inertia and the principle of equivalence, a higher-dimensional metric theory is constructed on the manifold of the SO(3, 2) De Sitter group which allows us to treat structureless and spinning particles on the same footing. A dimensional analysis of the physical magnitudes is performed.     

Algebraic structures and eigenstates for integrable collective field theories

Conditions for the construction of polynomial eigen-operators for the Hamiltonian of collective string field theories are explored. Such eigen-operators arise for only one monomial potentialv(x)=x ² in the collective field theory. They form aw -algebra isomorphic to the algebra of vertex operators in 2d gravity. Polynomial potentials of orders only strictly larger or smaller than 2 have no non-zero-energy polynomial eigen-operators. This analysis leads us to consider a particular potentialv(x)=x ²+g/x ². A Lie algebra of polynomial eigen-operators is then constructed for this potential. It is a symmetric 2-index Lie algebra, also represented as a subalgebra ofU(sl(2)).Work supported in part by the Department of Energy under contract DE-AC02-76ER03130-Task AWork supported by Brown University Exchange Program P.I. 135     

Illustration of the semiclassical theory of large amplitude collective excitations and fission by means of a schematic model

The recently developed semiclassical theory of large amplitude collective excitations and fission is applied to the so-called Suzuki model, which is exactly soluble within this theory. In particular we study the leading order quantum corrections to the time-dependent mean-field approximation in the fission problem.     

Particle motion in guide potentials and the collective nuclear motion

The motion of a particle which is constrained by a guide potential to move on a curve is studied in the framework of the Generator Coordinate Method (GCM). In the limit of narrow guide potentials a differential equation for the wave function of the constrained motion is obtained which differs from the corresponding Schrödinger equation by an additional potential. This additional potential is due to the embedding of the curve in the space and depends on the form of the guide potential and on the curvature of the curve. Nonadiabatic transitions in the constrained motion are possible for finite widths of the guide potential. The coupling terms are given explicitly and it is shown that an adiabatic limit exists. Since the GCM can equally well describe the collective motion of nuclei, some insight into the more complicated problem of collective motion is obtained from its analogies to the studied problem of constrained particle motion: The collective motion of a nucleus can be considered as the motion of a particle with variable mass along a curve in a guide potential which is given by the interaction potential between the nucleons. It is shown that Schrödinger's quantized kinetic energy is correctly used in the cranking model and that the additional potential terms mentioned above are included there by the definition of the collective potential energy. Approximations to the idealized GCM used here are discussed and the connection with the method of Born, Oppenheimer and Villars is indicated.     

Determination of the parameters of molecular motion from the amplitude spectrum of a spin-echo signal

The amplitude spectrum of the harmonics of a spin-echo signal is determined. The possibilities of obtaining information about the parameters of molecular motion of nuclear spin systems from the spectrum are discussed.Translated from Izvestiya Vyssikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 13–16, December, 1984.