Conditions for the validity of ATDHF and the local harmonic approach

A short derivation of the local harmonic approach and ATDHF is given which elucidates the formal similirity between them. The conditions for the validity of the approaches are studied. We show first, that they are related to deviation forces within second order RPA which drive the system out of the collective mode, and second, that the local harmonic approach is more restricted than ATDHF.     

A simple approach to the nuclear dynamics

We propose an approach to the nuclear dynamics which enables us to understand the relations between the time-dependent Hartree-Fock method and the quantumstatistical approach to the heavy ion reactions. The same formalism allows us to generalize the random phase approximation in order to include the spreading width of collective states.     

Three-dimensional growth of quantized vortices in rotating superfluid

This work studies numerically three-dimensional growth of small quantized vortices from the vessel boundary in rotating superfluid.     

Reconnection dynamics for quantized vortices

By analyzing trajectories of solid hydrogen tracers in superfluid ⁴He, we identify tens of thousands of individual reconnection events between quantized vortices. We characterize the dynamics by the minimum separation distance δ(t) between the two reconnecting vortices both before and after the events. Applying dimensional arguments, this separation has been predicted to behave asymptotically as δ(t)≈A(κ|t−t₀|)^1/2, where κ=h/m is the quantum of circulation. The major finding of the experiments and their analysis is strong support for this asymptotic form with κ as the dominant controlling feature, although there are significant event to event fluctuations. At the three-parameter level the dynamics may be about equally well-fit by two modified expressions: (a) an arbitrary power-law expression of the form δ(t)=B|t−t₀|^α and (b) a correction-factor expression δ(t)=A(κ|t−t₀|)^1/2(1+c|t−t₀|). The measured frequency distribution of α is peaked at the predicted value α=0.5, although the half-height values are α=0.35 and 0.80 and there is marked variation in all fitted quantities. Accepting (b) the amplitude A has mean values of 1.24±0.01 and half height values of 0.8 and 1.6 while the c distribution is peaked close to c=0 with a half-height range of −0.9 s⁻¹ to 1.5 s⁻¹. In light of possible physical interpretations we regard the correction-factor expression (b), which attributes the observed deviations from the predicted asymptotic form to fluctuations in the local environment and in boundary conditions, as best describing our experimental data. The observed dynamics appear statistically time-reversible, which suggests that an effective equilibrium has been established in quantum turbulence on the time scales (≤0.25 s) investigated. We discuss the impact of reconnection on velocity statistics in quantum turbulence and, as regards classical turbulence, we argue that forms analogous to (b) could well provide an alternative interpretation of the observed deviations from Kolmogorov scaling exponents of the longitudinal structure functions.     

Quantized ATDHF and angular momentum projection: Three-dimensional applications to heavy ion scattering

The quantized adiabatic time-dependent Hartree-Fock (qATDHF) theory is extended to the calculation of observables in nuclear phenomena using general many-body techniques including angular momentum projection. All calculations are performed using three-dimensional coordinate and momentum-grid techniques. The Bonche-Koonin-Negele interaction as well as several Skyrme-type forces has been used in the simple Hartree-Fock (HF) calculations of ¹²C and ²⁰Ne nuclei. Further, the maximally decoupled collective path is evaluated within qaTDHF, and the angular momentum projected kernels are inserted into the GCM formalism. As a test case, this formalism is applied to the phase shifts of elastic α-α scattering because they can be compared to experimental values. The same techniques are applied to the α-¹⁶O system and the results are compared with those obtained by solving the collective Schrödinger equation in a Gaussian Overlap Approximation, as in a previous publication. The GCM, extended to complex energies, is used to extract the widths of the resonance levels of the 0₁⁺, 0₄⁺, 0 bands in α-¹⁶O scattering. A model calculation, in which the structure of the nuclei is kept fixed to their HF ground state, is performed for the same α-¹⁶O system. We get quite different results with this “sudden” approximation than with the adiabatic calculation. The present calculations show that it is indeed possible to connect general and symmetry conserving many-body techniques to the qATDHF theory and to obtain in this way a purely microscopic framework which can be handled numerically, thus allowing evaluation of observables which are accessible to experiments.     

Evaluation of the optimal path in ATDHF theory

The formal resemblance between the adiabatic time-dependent Hartree-Fock (ATDHF) theory of Villars and of Baranger and Vénéroni (BV) has been demonstrated. While the BV approach mixes the zeroth- and second-order quantities. Villars neglects the second-order equation and suggests a self-consistent method of solving the zeroth- and first-order equations. It is shown here that in order to obtain the time evolution of the TDHF solution one has to include the second-order equation along with zeroth- and first-order equations. It is then shown by an analytic method that the consistent solutions of the three equations follow the bottom of the valley of the collective potential.     

A new approach to the quantized electrical conductance

The quanta of electrical conductance is derived for a one-dimensional electron gas both by making use of the quasi-classical motion of a quantum fluid and by using arguments related to the uncertainty principle. The result is extended to a nanowire of finite cross section area and to electrons in magnetic field, and the quantization of the electrical conductance is shown. An additional application is made to the two-dimensional electron gas.     

Exactly quantized dynamics of classical incommensurate sliders

We report peculiar velocity quantization phenomena in the classical motion of an idealized 1D solid lubricant, consisting of a harmonic chain interposed between two periodic sliders. The ratio upsilon(c.m.)/upsilon(ext) of the chain center-of-mass velocity to the externally imposed relative velocity of the sliders stays pinned to exact "plateau" values for wide ranges of parameters, such as slider corrugation amplitudes, external velocity, chain stiffness, and dissipation, and is strictly determined by the commensurability ratios alone. The phenomenon is explained by one slider rigidly dragging the kinks that the chain forms with the other slider. Possible consequences of these results for some real systems are discussed.     

On the noise operator approach to quantized dissipative systems

Invoking complex classical coordinates and momenta a consistent Hamiltonian theory suitable for the quantization of dissipative systems has been developed previously. In another paper this formalism has been illustrated on the basis of a simple order parameter equation by means of density operator techniques. This quite naturally calls for a comparison with quantum noise operator techniques. The present paper is an attempt to satisfy these demands. Extensive use will be made of operator ordering techniques and quasi-classical Fokker-Planck equations. As before, a certain incompleteness in the extractable information is clearly exhibited. It will be observed that the two techniques do not produce similar results in a general dynamical state as a consequence of dissipation. However, in the stationary state and within certain approximations both methods do lead to identical conclusions for the order parameters statistics. It will be argued that within the present context in general noise operator techniques are to be favoured.     

Unified approach to superposition states of the quantized radiation field

Summary In the recent years various and interesting superposition states of the quantized radiation field were investigated in the literature, such as that involving two number states by Wodkiewiczet al.; that involving two coherent states by Hillery and Gerryet al.; that involving two squeezed states by Xinet al., etc. Here we study a general one-parameter superposition state which unifies those states and others in the literature, all becoming a particularization of ours. General expressions characterizing the physical properties of the field are obtained. The role played by the present superposition state as an alternative interpolating state is also discussed. The authors of this paper have agreed to not receive the proofs for correction.     

Symplectic approach to the theory of quantized fields. I

Our aim in this paper the first one of a series concerned with the problem of field quantization starting from the symplectic structure underlying the classical theory, is to build up the variational theory necessary to all further constructions. The basic notions are the vertical bundle and thestructure 1-form used to define thegeneralized infinitesimal contact transformation which allows us to state and solve the variational problem related to field physics.Giving a system of modulevalued differential forms of different degree on the vertical bundle which solutions are the stationary cross sections is the main result in the paper. In this scheme the Euler-Lagrange classical equations are the expressions induced by such a system of differential forms on any cross section of the vertical bundle. This gives us a complete linearization of the Euler-Lagrange equations and, starting from it, a natural globalization of these equations. Finally, the notion of variational problem invariant by a Lie group is defined in this scheme, Noether's theorem related to such invariant problem is formulated and an intrinsic version of the so-called Noether invariants of classical variational calculus is obtained.This work has been realized in the Seminar of Mathematical Physics, directed by ProfessorJ. Sancho, in the Faculty of Science at the University of Barcelona (Spain).     

Rabi oscillations in the dynamics of a fully quantized SQUID ring-electromagnetic field system

In this paper, a study based on a fully quantum-mechanical model for the coupling between a super-conducting quantum interference device (an rf SQUID) and a single-mode quantized electromagnetic field is presented. The aim of this work is the prediction of the existence of some interesting phenomena, characterized by more than one Rabi frequency, occurring in the dynamics of the total coupled system when our analysis is developed inside a reduced low-lying energy 4D Hilbert subspace.     

ATDHF versus TDHF in a soluble model

The equations of motion for a system of interacting fermions with SU(3) symmetry are established in TDHF and ATDHF approximations. These equations are presented in a form such that the comparison between different approximations can be made in an analytic way. The problem of coupling between large and small amplitude modes is also discussed.     

A case study of the MSA approach to quantized polarizable media

The mean spherical approximation (MSA) has proved to be a very general and flexible method to analyze equilibrium statistical mechanical systems. In this note we test its accuracy against a simple one-dimensional model, i.e., a lattice gas of polarizable molecules where the internal degree of freedom is treated as quantized harmonic oscillators which interact via harmonic forces. This model can be solved exactly. We find a very good agreement between the MSA and exact solutions.2 The corresponding classical problem of polarizable particles was first solved in a mean spherical approximation (MSA) by M. Wertheim [J. Chem. Phys. 26:1425 (1973)]. He considered the model with nonfluctuating dipole moments. Later L. Pratt [Mol. Phys. 40:347 (1980)] and J. S. Høye and G. Stell [J. Chem. Phys. 73:461 (1980)] solved the corresponding classical problem in the MSA for particles with fluctuating dipole moments.     

Multiphoton dynamics of qutrits in the ultrastrong coupling regime with a quantized photonic field

Multiphoton resonant excitation of a three-state quantum system (a qutrit) with a single-mode photonic field is considered in the ultrastrong coupling regime, when the qutrit–photonic field coupling rate is comparable to appreciable fractions of the photon frequency. For ultrastrong couplings, the obtained solutions of the Schrödinger equation that reveal multiphoton Rabi oscillations in qutrits with the interference effects leading to the collapse and revival of atomic excitation probabilities at the direct multiphoton resonant transitions.     

Analytical proof of the non-uniqueness of the ATDHF path

An analytical proof along with numerical results has been given of the non-uniqueness of the ATDHF path for the three-level model of Villars even when the solution is required to behave as the lowest frequency RPA mode at the minimum. The concept of optimal path is also discussed.     

Vorticity in nuclear fluid dynamics

We consider a model for gloun jet fragmentation based on QCD in which the fast hadrons in the jet are produced by the sequential reaction gluon $\text{→}\text{q}\text{q}\text{?}\text{q}\text{→}$ hadrons. The resulting jet shows an oblate transverse momentum structure, with a major axis preferential oriented normally to the direction of linear polarization of the gluon. We discuss jet-jet oblateness angular correlations in decays of heavy QQ? pseudoscalar and vector systems.