Transition probabilities and static moments of excited states in even-even nuclei

A new approach is made to calculate the generalized single-particle density matrixp ^μv in even-even nuclei. It is shown that this quantity is included in the three particle response function, for which we derived a renormalized equation. Taking into account in a consequent way the effective particle-hole interaction we received a formula for the static moment of excited states and the transition probability between such states which is essentially different from the usual RPA theory.     

Green's function approach to the quantum many-body theory of the solid state

TheGreen's function approach is used to develop a quantum many-body theory of the solid state which should work at low temperatures as well as in the neighbourhood of phase transition points. The theory is applicable also in those cases where the traditional expansion of the potential in powers of the atomic displacements is entirely inadequate (crystalline helium). The starting point of our approach is the concept of broken symmetry since the invariance of the equilibrium ensemble under the continuous group of infinitesimal translations is reduced in a crystalline solid to the invariance under finite translations through a lattice vector. A homogeneous integral equation is derived which has nontrivial solutions in the crystalline state. By this equation it is shown that the umklapp phonons are the symmetry restoring collective modes expected due to a general theorem ofGoldstone. The single particle excitations and the structure of the Dyson mass operator in the crystalline state are discussed. It is further shown that the homogeneous Bethe-Salpeter equation for the linear response to an external disturbance possesses symmetry breaking solutions which are connected to the lattice dynamics of the solid state. These collective excitations (phonons) are exhibited in RPA and tight-binding approximation for monoatomic cubic crystals with a Bravais lattice in order to demonstrate how the present theory reproduces well-known results.     

The second RPA description for the decay of the one-phonon nuclear collective states at finite temperature

The zero-temperature second RPA is generalized to finite temperatures through the use of the method of linearization of the equations of motion. After elimination of the quadruples, for low enough temperatures and within the subspace spanned by the doubles, a proper symmetrization yields an eigenvalue equation which exhibits formal properties like the simple RPA. From this second RPA eigenvalue equation, a closed formula for the spreading width of an isolated collective state is extracted. The second RPA can be recast in the form of a generalized collision term and be compared with the method of the Bethe-Salpeter equation for the two-body Green function. However, the second RPA method (and results) contrasts with the approach (and corresponding results) of the Boltzmann collision term, which is usually viewed as the appropriate agent for nuclear dissipation.     

Relativistically covariant Bohm-Bub hidden-variable theory for spin measurement of a single particle

We present a simple first step toward a relativistically covariant generalization of the Bohm-Bub hidden-variable theory. The model is applicable to spin measurement on a single Dirac particle and describes the collapse of the state vector to a spin-up or spin-down state. The essential postulate is that the hidden-variable vector transforms in the same way as the state vector under a Lorentz transformation. This yields a covariant collapse equation, which reduces to the ordinary Bohm-Bub equation for an observer stationary with respect to the particle and shows a time dilated collapse for a moving observer. The model yields the correct quantum transition probabilities for all observers.Deceased.     

Small amplitude limit of the time dependent density matrix theory

The small amplitude limit of the time-dependent density-matrix theory, which is an extension of the time-dependent Hartree-Fock theory, is presented. Its relation to other theories i.e. the random phase approximation (RPA), the second RPA and the shell model is discussed. It is found that the small amplitude limit is a generalization of these theories.     

An equation of state for the isotropic phase of linear,partially flexible and fully flexible tangent hard-sphere chain fluids

A new equation of state is developed that accurately describes the isotropic phase behaviour of linear, partially flexible and fully flexible tangent hard-sphere chain fluids and their mixtures. The equation of state is based on the equation of state of Liu and Hu [H. Liu and Y. Hu, Fluid Phase Equilibr. 122, 75 (1996)] for fully flexible chain fluids. The effect of molecular flexibility is described by a pure-component parameter that is introduced in the theory at the level of the cavity correlation function of next-to-nearest neighbour segments in a chain molecule. The equation of state contains a total of three adjustable model constants. The extension to partially flexible- and linear chain fluids is based on a refitting of the first model constant to numerical data of the second virial coefficient of partially flexible and linear tangent hard-sphere chain fluids. The numerical data were obtained from an analytical approximation for the pair-excluded volume. The other two parameters were adjusted to molecular simulation data for the pressure of linear tangent hard-sphere chain fluids. For both, pure component systems and mixtures of chains of variable flexibility, the pressure and second virial coefficient obtained from the equation of state, are in excellent agreement with the results from Monte Carlo simulations. A significant improvement to TPT1, TPT2, generalised Flory-dimer theory and scaled particle theory is observed.     

Mouvement Brownien dans une assemblee de batonnets minces dans la phase nematique

Using the kinetic methods of the Brussels school, we establish the equation (to the second order in the perturbation) for the return to equilibrium of the one-particle energy distribution function in the nematic phase of a fluid made of thin slabs interacting through a P₂-type potential. On the basis of the mean field equilibrium theory developed by Maier and Saupe for such a fluid, we show that for a very heavy brownian particle, this equation reduces to a Fokker-Planck type equation; the friction coefficient thus obtained is compared with the friction coefficient obtained for the isotropic phase and we show that they are equal for the transition temperature.     

Semiclassical kinetic equation and the WKB approximation

We study the connection between the classical response function of a nucleus described by the Vlasov equation and the corresponding quantum response function. In the limit of large quantum numbers, the Fourier coefficients which appear in the Vlasov theory correspond to the quantum matrix elements evaluated in the WKB approximation. The classical frequencies of motion give the quantum excitation energies according to the correspondence principle.For a central potential, we identify the normal modes of the classical systems with the corresponding shell-model transitions. Thus we can improve the Vlasov theory by excluding excitation modes which correspond to forbidden quantum transitions. Also, we study the effect of a spin-orbit force in the context of the Vlasov theory.Finally, always by exploiting the close analogy between the classical and the quantum response functions, we introduce exchange (Fock) term in the semiclassical RPA equation given by the Vlasov theory.     

Nonlocal potential and optical properties of solids

Summary The theory of the RPA optical response of a solid has been generalized in order to take into account also the possible presence of spatially nonlocal potentials in the Hamiltonian. Explicit expressions for first- and second-order susceptibilities are given in the new framework. The expressions obtained depend on the matrix elements of operators of the form of a commutator of a component of the position operatorr and an operator that commutes with the lattice translations. The problem of the evaluation of these matrix elements is solved in a simple manner by introducing an auxiliary, periodic position operator,XXXr. In such a way a general formulation is obtained that preserves the gauge invariance. As an application of the new theory, the second harmonic generation (SHG) from a semiconductor in a simple two-band model has been studied. The differences between our correct gauge-invariant results and those obtained in the usual local approximation is an indication of a slow convergence of the expressions obtained in the local approximation.     

Nuclear dissipation due to bosonic reservoirs at finite temperature: A master equation based on second RPA dynamics

Using the second RPA property that the nuclear intrinsic degrees of freedom (specifically, the quadruples) are invested with bosonic qualities, we describe the nuclear dissipative process as the damping of a collective degree of freedom coupled to a bosonic reservoir at finite temperature. The resulting second RPA master equation within the observed collective subspace agrees exactly in form with the master equation utilized in quantum optics; it describes how a gas of collective RPA phonons relaxes to a Bose-Einstein thermal equilibrium. We further solve this master equation and provide illustrative examples for specific initial conditions. The second RPA approach accounts for quantal fluctuations in addition to the statistical fluctuations, and thus contrasts with the Kramers-Chandrasekhar approach usually utilized in nuclear physics. Furthermore, the second RPA master equation contrasts with the corresponding results of the linear response approach and of the random matrix model.     

Ground state correlation effects on the Gamow-Teller strength distribution in 48Ca

We calculate the Gamow-Teller strength distribution in ⁴⁸Ca using an extended second RPA which explicitly includes ground state correlations. The following effects are taken into account: (i) the reduction of the 1p1h matrix elements due to the partial occupation of single-particle orbitals, (ii) the modification of the 1p1h Green function in the presence of ground state correlations and 2p2h correlations in the excited states, (iii) renormalization of the external field and (iv) the pure 2p2h response due to unblocking of the ground state. The first three effects largely cancel in the region of the Gamow-Teller resonance while the last two cancel at higher energies. The resulting strength distribution is therefore quite similar to the one obtained previously in second RPA.     

Random-phase approximation and its extension for the O(2) anharmonic oscillator

We apply the random-phase approximation (RPA) and its extension called renormalized RPA to the quantum anharmonic oscillator with an O(2) symmetry. We first obtain the equation for the RPA frequencies in the standard and in the renormalized RPAs using the equation-of-motion method. In the case where the ground state has a broken symmetry, we check the existence of a zero frequency in the standard and in the renormalized RPAs. Then we use a time-dependent approach where the standard-RPA frequencies are obtained as small oscillations arround the static solution in the time-dependent Hartree-Bogoliubov equation. We draw the parallel between the two approaches.Received: 8 July 2003, Published online: 5 January 2004PACS: 21.60.Jz Hartree-Fock and random-phase approximations - 24.10.Cn Many-body theory     

Spin-density response function in a 2D electron system under a magnetic field

We study the spin density response function in a two-dimensional electron system under a strong perpendicular magnetic field. The theoretical framework is the extended RPA which takes into account all the second order self-energies of particle-hole propagators. Our results reproduce the data obtained by a light scattering experiment. We clarify how the extended RPA explains the empirical findings which are different even qualitatively from the RPA response. Especially the important role played by the two-particle-two-hole degrees of freedom is stressed.     

Stable first-order particle-frame relativistic hydrodynamics for dissipative systems

We propose a stable first-order relativistic dissipative hydrodynamic equation in the particle frame (Eckart frame) for the first time. The equation to be proposed was in fact previously derived by the authors and a collaborator from the relativistic Boltzmann equation. We demonstrate that the equilibrium state is stable with respect to the time evolution described by our hydrodynamic equation in the particle frame. Our equation may be a proper starting point for constructing second-order causal relativistic hydrodynamics, to replace Eckart's particle-flow theory.     

Random turn walk on a half line with creation of particles at the origin

We consider a version of random motion of hard core particles on the semi-lattice 1,2,3,… , where in each time instant one of three possible events occurs, viz., (a) a randomly chosen particle hops to a free neighboring site, (b) a particle is created at the origin (namely, at site 1) provided that site 1 is free and (c) a particle is eliminated at the origin (provided that the site 1 is occupied). Relations to the BKP equation are explained. Namely, the tau functions of two different BKP hierarchies provide generating functions respectively (I) for transition weights between different particle configurations and (II) for an important object: a normalization function which plays the role of the statistical sum for our non-equilibrium system. For time t→∞ we obtain the asymptotic configuration of particles obtained from the initial empty state (the state without particles).