Two-body density matrix of bose fluids

A detailed cluster analysis of the two-body density matrix $\text{n(}\text{r}{}_1\text{,}\text{r}{}_2\text{,}\text{r}\text{′}{}_1\text{,}\text{r}\text{′}{}_2\text{)}$ and the associated pairing matrix elements is performed for a strongly interacting system of bosons described by a Jastrow wave function. The study employs a multiplicative cluster procedure as suggested by Feenberg. It is demonstrated that the density matrix has a structure $\text{f(r)f(r′)n(r)n(r′)}\text{exp}\text{[?R(}\text{r}{}_1\text{,}\text{r}{}_2\text{,}\text{r}\text{′}{}_1\text{,}\text{r}\text{′}{}_2\text{)]}$ where f(r) is the conventional Jastrow factor and n(r) the one-body density matrix corresponding to the Jastrow trial state $\text{(r  |}\text{r}{}_1\text{?}\text{r}{}_2\text{|, r′  |}\text{r}\text{′}{}_1\text{?}\text{r}\text{′}{}_2\text{|)}$. The function R may be expressed by a series of irreducible cluster contributions which are given by a compact expressions in terms of spatial distribution functions. The density matrix exhibits off-diagonal long range order of the type $\text{n(}\text{r}{}_1\text{,}\text{r}{}_2\text{,}\text{r}\text{′}{}_1\text{,}\text{r}\text{′}{}_2\text{) → f(r)n(r)f(r′)n(r′)}\text{as}\text{|}\text{r}{}_1\text{?}\text{r}\text{′}{}_1\text{| → ∞,r,r′ < ∞}$. The associated pairing matrix elements and pairing energy of a Bose fluid are derived upon proper specialization of our results for the two-body density matrix.     

Paired-phonon analysis of impurities in bose fluids

Summary The paired-phonon analysis for boson mixtures is employed in conjunction with the hypernetted-chain approximation to study the ground-state properties of an impurity embedded in liquid⁴He. Chemical potentials, volume coefficients and other thermodynamic quantities as well as some of the most interesting optimal correlation functions are calculated for various impurities interacting with the⁴He background atoms via Lennard-Jones potentials of differing strength. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

On the structure of the three-particle operator in generalized kinetic equations for inhomogeneous gases

It is shown that the three-particle kinetic operator for inhomogeneous gases obtained using Prigogine's method and the matrix representation of the Liouville equation introduced by Balescu is equivalent to the corresponding expression derived by Choh and Uhlenbeck using Bogolubov's method. Both theories take into account the space and time delocalization associated with finite collision time, and the resulting corrections to the asymptotic collision operator are equivalent.     

A rearrangement of the Feenberg perturbation formula and elementary excitation interactions in bose fluids

The Feenberg perturbation energy for two quasiparticle excitations is rearranged to be valid in many-boson systems up to fifth order. Doubly excited states in many particle boson systems are studied using Feenberg perturbation theory. The effective interaction energy between quasiparticles, which is described by “ladder state diagrams” — in Bogoliubov approximation, is obtained. It is then shown that in this case the interaction energy depends on density (pressure) and changes its sign when density increases if the bare two-body potential qualitatively has short range repulsion and longer range attraction.     

On the structure of the von Neumann algebras generated by local functions of the free bose field

It is shown that the von Neumann algebra\(R_\mathfrak{B} \)(B) generated by any scalar local functionB(x) of the free fieldA ₀(x) is equal either to\(R_\mathfrak{B} \)(A ₀) or to\(R_\mathfrak{B} \)(:A ₀ ² :). The latter statement holds if the state space space\(\mathfrak{H}_B \) obtained from the vacuum state by repeated application ofB(x) is orthogonal to the one particle subspace. In the proof of these statements, space-time limiting techniques are used.     

On the Kohn variational principles for three-particle systems

The Kohn-type variational principles are formulated, which can be used for calculating the (2 → 3), (3 → 2), and (3 → 3) scattering amplitudes if the two-particle wave functions are known.     

On the scattering function of simple fluids in finite systems

The density-density dynamical correlation function of a simple fluid in a finite container subject to a constant temperature difference is explicitly obtained. In small systems, such as those realized in computer experiments, new peaks appear in the scattering spectrum, even at equilibrium, arising from standing waves produced by the fluctuations. Away from equilibrium, these peaks are asymmetric in the same manner as the Brillouin lines. The macroscopic limit is also considered and the correction to the usual infinite system approximation is explicitly obtained.See ref. 14 for a recent review of particle simulations used in the study of nonequilibrium systems.     

The classical partition function of a bound three-particle cluster

The task of computing the classical partition function for a bound aggregate of three particles is reduced to that of performing a 2-dimensional quadrature. A simple, analytical formula is obtained in the special case of three identical particles for which the mutual interactions are given by pair-additive square-well potentials.     

On the covariant structure of the two-point function

The spectral representation of the two-point function for arbitrary fields proposed recently [1] is rigorously proved and analyzed. The problem is treated in momentum space where the covariant structure is simpler because of the spectrum conditions. For finite-component fields the explicit matrix structure is found in coordinate space too and is applied to the definition of time-ordered Green functions for arbitrary spin. The decomposition of the two-point function into kernels of definite spin is carried out in the general case, a necessary and sufficient condition for the growth of the coefficients in this decomposition being given. The positive-definiteness condition (in the case of Hermitian conjugate fields) is fulfilled automatically by the elementary kernels.The formalism of homogeneous distributions in two dimensional complex domain [2] is used throughout the paper.On leave of absence from Joint Institute for Nuclear Research, Dubna, USSR and from Physical Institute of the Bulgarian Academy of Sciences, Sofia, Bulgaria.     

Measurement of the dynamic structure function of fluorescently labeled complex fluids by fourier imaging correlation spectroscopy

The dynamics of the kicked rotor, which is a paradigm for a mixed system, where the motion in some parts of phase space is chaotic and in other parts is regular, is studied statistically. The evolution operator of phase space densities in the chaotic component is calculated in the presence of noise, and the limit of vanishing noise is taken in the end. The relaxation rates to the equilibrium density are calculated analytically within an approximation that improves with increasing stochasticity. The results are tested numerically. A global picture is presented of relaxation to the equilibrium density in the chaotic component when the system is bounded and to diffusive behavior when it is unbounded.     

The dynamics of the open bose gas

An exact kinetic equation governing the time evolution of a gas of Bosons interacting with a heat bath is derived by master equation techniques. Its solution is shown to exist globally and to converge to equilibrium; a Liapunov functional is constructed. The approach to equilibrium is exponentially fast at low density but shows critical slowing down in the two-phase region.     

Oscillatory structure of confined fluids

The confinement of fluids in pores and wedges is associated with exponentially damped oscillatory packing structure, as observed with the surface forces apparatus. This paper reviews the statistical mechanics of confined fluids and then illustrates the results with density functional data for hard-sphere solvent. The free energy of the pore fluid and its functional derivatives with respect to thermodynamic fields all oscillate, as a function of pore width, with a wavelength close to the solvent diameter. In contrast, the density at the centre of pores oscillates with twice this wavelength, as a function of pore width. The development of a unified physics of confined fluids is considered. Approximations based on one-dimensional physics do extraordinarily well in planar symmetry at three-dimensions.     

The structure of quantum fluids

We outline the principal features of Bose and Fermi fluids that are revealed in particle scattering experiments at high momentum transfer. In this regime, the dynamic structure function is determined by the dominant influence of correlations which are embodied in the static one- and two-body density matrices characterizing a strongly correlated system. We analyze the general structure of these fundamental quantities and of the associated momentum distributions that enter as input quantities for determining the dynamical response. We discuss their physical interpretation and their interrelationships. We further describe the main features of advanced many-body methods, which begin on a nonperturbative basis. They permit a formal and numerical evaluation of various quantities that characterize the structure of the density matrices and therewith of quantum fluids and solids.Dedicated to Peter Mittelstaedt on the occasion of his sixtieth birthday.     

On the group function model for molecular electronic structure

A group function model for the electronic structure of molecules is developed in which the strong orthogonality condition is not necessarily invoked. The group functions are required to satisfy orthogonality constraints which are less restrictive than the strong orthogonality condition. The particular condition which two group functions obey reflects the extent to which the electrons they describe are localized in well-separated regions of space and the degree of interaction between them. This will be called the interacting group function model. General expressions for the expectation values of one and two-electron spin-independent operators are derived using the spin-coupled formalism. A graphical technique is found to be useful when the molecule is divided into several subsystems.     

On behavior of the thixotropic fluids

In this work some aspects of constitutive equations for thixotropic fluids and restrictions on their functional forms are formally discussed. In the current study a special emphasis has been given to the structural nature of these substances. The behavior of thixotropic fluids is analyzed in terms of an isothermal laminar shear field with Brownian motion.     

On fermi quantum fields constructed from bose quantum fields and their applications

In former papers a representation of the quantum Fermi and para-Fermi fields was proposed. This representation is such that the only basic quantum entities are Bose quantum fields. In this paper we show several possibilities of application: (i) to lower the number of elementary particles; (ii) to describe as separate states of a fundamental particle other particles that presently are considered as different, and to induce an ordering among them; (iii) to obtain relations among the quantum numbers of those particles; (iv) to obtain a physical picture of some unstable particles. This article is concerned with the physical interpretation of the formalism, and some of the statements that are contained here have a conjectural character.     

利用单个三粒子最大GHZ态或两个EPR态隐形传送任意三粒子GHZ态

提出利用单个三粒子最大Greenberger-Horne-Zeilinger (GHZ)态或两个Einstein-Podolsky-Rosen (EPR)态作为量子信道确定性隐形传送任意三粒子GHZ态的两个方案，并将方案推广至隐形传送任意n(n≥4)粒子GHZ态的情况.讨论了量子信道受噪声影响时隐形传态的保真度.研究发现，当作为量子信道的单个三粒子最大GHZ态受到噪声影响时，隐形传态的保真度仅与量子信道的纠缠度有关，而当作为量子信道的两个EPR态受到噪声影响时，隐形传态的保真度不仅与量子信道的纠缠度有关，还与待传送态的纠缠度有关.所提出的方案具有节省量子信道纠缠资源的特点. 关键词： 隐形传态 三粒子Greenberger-Horne-Zeilinger态 量子逻辑门 保真度     

The five-nucleon system above the three-particle threshold

Compound nucleus states in ${}^5\text{Li}$ and ${}^5\text{He}$ have been investigated with the ${}^3\text{He(d,p)pt}$ and ${}^3\text{H(d,n)pt}$ three-particle reactions. The observed $\text{J}{}^{\mathrm{\pi }}\text{=}\text{3}\text{2}{}^{\mathrm{?}}$ states (E_X≈20 MeV) can be understood, in analogy to the ground states of the A=5 system, by coupling a $\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ nucleon to the first 0⁺ excited state of ${}^4\text{He}$.