Superfluidity and Quantum Melting of para-Hydrogen clusters

Structural and superfluid properties of para-Hydrogen clusters of size up to N=40 molecules, are studied at low temperature (0.5 K < T < 4 K) by Path Integral Monte Carlo simulations. The superfluid fraction displays an interesting, non-monotonic behavior for 22 < N < 30. We interpret this dependence in terms of variations with N of the cluster structure. Superfluidity is observed at low T in clusters of as many as 27 molecules; in the temperature range considered here, quantum melting is observed in some clusters, which freeze at high temperature

Energy estimators for random series path-integral methods

We perform a thorough analysis on the choice of estimators for random series path integral methods. In particular, we show that both the thermodynamic (T-method) and the direct (H-method) energy estimators have finite variances and are straightforward to implement. It is demonstrated that the agreement between the T-method and the H-method estimators provides an important consistency check on the quality of the path integral simulations. We illustrate the behavior of the various estimators by computing the total, kinetic, and potential energies of a molecular hydrogen cluster using three different path integral techniques. Statistical tests are employed to validate the sampling strategy adopted as well as to measure the performance of the parallel random number generator utilized in the Monte Carlo simulation. Some issues raised by previous simulations of the hydrogen cluster are clarified.Comment: 15 pages, 1 figure, 3 table

Heat capacity estimators for random series path-integral methods by finite-difference schemes

Previous heat capacity estimators used in path integral simulations either have large variances that grow to infinity with the number of path variables or require the evaluation of first and second order derivatives of the potential. In the present paper, we show that the evaluation of the total energy by the T-method estimator and of the heat capacity by the TT-method estimator can be implemented by a finite difference scheme in a stable fashion. As such, the variances of the resulting estimators are finite and the evaluation of the estimators requires the potential function only. By comparison with the task of computing the partition function, the evaluation of the estimators requires k + 1 times more calls to the potential, where k is the order of the difference scheme employed. Quantum Monte Carlo simulations for the Ne_13 cluster demonstrate that a second order central-difference scheme should suffice for most applications.Comment: 11 pages, 4 figure

Reconstruction of thermally-symmetrized quantum autocorrelation functions from imaginary-time data

In this paper, I propose a technique for recovering quantum dynamical information from imaginary-time data via the resolution of a one-dimensional Hamburger moment problem. It is shown that the quantum autocorrelation functions are uniquely determined by and can be reconstructed from their sequence of derivatives at origin. A general class of reconstruction algorithms is then identified, according to Theorem 3. The technique is advocated as especially effective for a certain class of quantum problems in continuum space, for which only a few moments are necessary. For such problems, it is argued that the derivatives at origin can be evaluated by Monte Carlo simulations via estimators of finite variances in the limit of an infinite number of path variables. Finally, a maximum entropy inversion algorithm for the Hamburger moment problem is utilized to compute the quantum rate of reaction for a one-dimensional symmetric Eckart barrier.Comment: 15 pages, no figures, to appear in Phys. Rev.

The Public Pension System in Romania – Analysis Before and After 1999

Objectives This paper aims to examine the public pension system in Romania and the significant differences that 1999 brought it. It is important to see if system effects such as the number of beneficiaries and collapse on the number of taxpayers are experienced in present. It explores the main types of pension granted in the public pension system - pensions for old age. Approach It is an attempt to identify the main sources (contributions owed by employers and employees) and also the way pensions are calculated and given before and after 1999. Results We conclude that public pension system in Romania has suffered many changes in a positive way. Implications For taxpayers, both employers and employees it is important that the public pension system work in optimal conditions, that the minimum and maximum contribution "stage" take the proper values. Value Knowing the importance of the public pension system in the Romanian society will know what measures should be taken to improve it

Phase changes in selected Lennard-Jones X_{13-n}Y_n clusters

Detailed studies of the thermodynamic properties of selected binary Lennard-Jones clusters of the type X_{13-n}Y_n (where n=1,2,3) are presented. The total energy, heat capacity and first derivative of the heat capacity as a function of temperature are calculated by using the classical and path integral Monte Carlo methods combined with the parallel tempering technique. A modification in the phase change phenomena from the presence of impurity atoms and quantum effects is investigated.Comment: 14 pages, 13 figures. submitted to J. Chem. Phy

Upon the existence of short-time approximations of any polynomial order for the computation of density matrices by path integral methods

In this article, I provide significant mathematical evidence in support of the existence of short-time approximations of any polynomial order for the computation of density matrices of physical systems described by arbitrarily smooth and bounded from below potentials. While for Theorem 2, which is ``experimental'', I only provide a ``physicist's'' proof, I believe the present development is mathematically sound. As a verification, I explicitly construct two short-time approximations to the density matrix having convergence orders 3 and 4, respectively. Furthermore, in the Appendix, I derive the convergence constant for the trapezoidal Trotter path integral technique. The convergence orders and constants are then verified by numerical simulations. While the two short-time approximations constructed are of sure interest to physicists and chemists involved in Monte Carlo path integral simulations, the present article is also aimed at the mathematical community, who might find the results interesting and worth exploring. I conclude the paper by discussing the implications of the present findings with respect to the solvability of the dynamical sign problem appearing in real-time Feynman path integral simulations.Comment: 19 pages, 4 figures; the discrete short-time approximations are now treated as independent from their continuous version; new examples of discrete short-time approximations of order three and four are given; a new appendix containing a short review on Brownian motion has been added; also, some additional explanations are provided here and there; this is the last version; to appear in Phys. Rev.

Analysis of path integrals at low temperature : Box formula, occupation time and ergodic approximation

We study the low temperature behaviour of path integrals for a simple one-dimensional model. Starting from the Feynman-Kac formula, we derive a new functional representation of the density matrix at finite temperature, in terms of the occupation times of Brownian motions constrained to stay within boxes with finite sizes. From that representation, we infer a kind of ergodic approximation, which only involves double ordinary integrals. As shown by its applications to different confining potentials, the ergodic approximation turns out to be quite efficient, especially in the low-temperature regime where other usual approximations fail

Three applications of path integrals: equilibrium and kinetic isotope effects, and the temperature dependence of the rate constant of the [1,5] sigmatropic hydrogen shift in (Z)-1,3-pentadiene

Recent experiments have confirmed the importance of nuclear quantum effects even in large biomolecules at physiological temperature. Here we describe how the path integral formalism can be used to describe rigorously the nuclear quantum effects on equilibrium and kinetic properties of molecules. Specifically, we explain how path integrals can be employed to evaluate the equilibrium (EIE) and kinetic (KIE) isotope effects, and the temperature dependence of the rate constant. The methodology is applied to the [1,5] sigmatropic hydrogen shift in pentadiene. Both the KIE and the temperature dependence of the rate constant confirm the importance of tunneling and other nuclear quantum effects as well as of the anharmonicity of the potential energy surface. Moreover, previous results on the KIE were improved by using a combination of a high level electronic structure calculation within the harmonic approximation with a path integral anharmonicity correction using a lower level method.Comment: 9 pages, 4 figure

Caveolae-dependent and -independent uptake of albumin in cultured rodent pulmonary endothelial cells

Although a critical role for caveolae-mediated albumin transcytosis in pulmonary endothelium is well established, considerably less is known about caveolae-independent pathways. In this current study, we confirmed that cultured rat pulmonary microvascular (RPMEC) and pulmonary artery (RPAEC) endothelium endocytosed Alexa488-labeled albumin in a saturable, temperature-sensitive mode and internalization resulted in co-localization by fluorescence microscopy with cholera B toxin and caveolin-1. Although siRNA to caveolin-1 (cav-1) in RPAEC significantly inhibited albumin uptake, a remnant portion of albumin uptake was cav-1-independent, suggesting alternative pathways for albumin uptake. Thus, we isolated and cultured mouse lung endothelial cells (MLEC) from wild type and cav-1-/- mice and noted that ∼ 65% of albumin uptake, as determined by confocal imaging or live cell total internal reflectance fluorescence microscopy (TIRF), persisted in total absence of cav-1. Uptake of colloidal gold labeled albumin was evaluated by electron microscopy and demonstrated that albumin uptake in MLEC from cav-1-/- mice was through caveolae-independent pathway(s) including clathrin-coated pits that resulted in endosomal accumulation of albumin. Finally, we noted that albumin uptake in RPMEC was in part sensitive to pharmacological agents (amiloride [sodium transport inhibitor], Gö6976 [protein kinase C inhibitor], and cytochalasin D [inhibitor of actin polymerization]) consistent with a macropinocytosis-like process. The amiloride sensitivity accounting for macropinocytosis also exists in albumin uptake by both wild type and cav-1 -/- MLEC. We conclude from these studies that in addition to the well described caveolar-dependent pulmonary endothelial cell endocytosis of albumin, a portion of overall uptake in pulmonary endothelial cells is cav-1 insensitive and appears to involve clathrin-mediated endocytosis and macropinocytosis-like process. © 2013 Li et al