The momentum distribution of normal and superfluid liquid 4He

1987 ◽  
Vol 65 (11) ◽  
pp. 1416-1420 ◽  
Author(s):  
D. M. Ceperley ◽  
E. L. Pollock
Keyword(s):  
Liquid Helium ◽  
Path Integral ◽  
Momentum Distribution ◽  
Particle System ◽  
Boson Systems ◽  
Distinguishable Particle ◽  
Boson System ◽  
Integral Methods ◽  
The Difference ◽  
Non Gaussian

Path-integral methods can be employed to calculate properties of boson systems at any temperature. We have performed a number of simulations of liquid helium and have calculated the momentum distribution as a function of temperature. We find that liquid helium has a condensate below 2 K but not above. The momentum distribution is found to be non-Gaussian even in normal liquid helium. We have also calculated the difference in the momentum distribution between a boson system and a distinguishable particle system.

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

2003 ◽  
Vol 119 (23) ◽  
pp. 12119-12128 ◽  
Author(s):  
Cristian Predescu ◽  
Dubravko Sabo ◽  
J. D. Doll ◽  
David L. Freeman
Keyword(s):  
Heat Capacity ◽  
Finite Difference ◽  
Path Integral ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Random Series ◽  
Integral Methods

Decomposing the Non-Gaussian Surface in Sum of Gaussian Surfaces

2012 ◽  
Vol 580 ◽  
pp. 170-174
Author(s):  
Zhang Xing Qi ◽  
Zhen Sen Wu ◽  
Zi Wen Yu ◽  
Hai Ying Li
Keyword(s):  
Cross Section ◽  
Electromagnetic Scattering ◽  
Radar Cross Section ◽  
Kirchhoff Approximation ◽  
Munk Function ◽  
The Difference ◽  
Non Gaussian ◽  
Gaussian Surface

The decomposition of the multivariate Non-Gaussian PDF in the sum of a Gaussian PDF instead of the Gram-Charlier series is investigated. Four parameters need to be found by minimizing the integrated square of the difference between Cox-Munk function and its approximation. The backscattering radar cross section (RCS) of the surface is calculated by the Kirchhoff approximation (KA) under different value of k using the formula of decomposition of the Non-Gaussian. The condition of KA satisfying electromagnetic scattering scale from Gaussian and Non-Gaussian surfaces is taken into account by computing the backscattering coefficients in HH and VV polarity.

scholarly journals Probabilistic solutions to ordinary differential equations as nonlinear Bayesian filtering: a new perspective

2019 ◽  
Vol 29 (6) ◽  
pp. 1297-1315 ◽  
Author(s):  
Filip Tronarp ◽  
Hans Kersting ◽  
Simo Särkkä ◽  
Philipp Hennig
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Gradient Field ◽  
Space Representation ◽  
Bayesian Filtering ◽  
State Space Representation ◽  
The Difference ◽  
New Perspective ◽  
Non Gaussian ◽  
Filtering Problem

Abstract We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with nonlinear measurement functions. This is achieved by defining the measurement sequence to consist of the observations of the difference between the derivative of the GP and the vector field evaluated at the GP—which are all identically zero at the solution of the ODE. When the GP has a state-space representation, the problem can be reduced to a nonlinear Bayesian filtering problem and all widely used approximations to the Bayesian filtering and smoothing problems become applicable. Furthermore, all previous GP-based ODE solvers that are formulated in terms of generating synthetic measurements of the gradient field come out as specific approximations. Based on the nonlinear Bayesian filtering problem posed in this paper, we develop novel Gaussian solvers for which we establish favourable stability properties. Additionally, non-Gaussian approximations to the filtering problem are derived by the particle filter approach. The resulting solvers are compared with other probabilistic solvers in illustrative experiments.

scholarly journals COORDINATE-INVARIANT PATH INTEGRAL METHODS IN CONFORMAL FIELD THEORY

2006 ◽  
Vol 21 (17) ◽  
pp. 3525-3563 ◽  
Author(s):  
ANDRÉ VAN TONDER
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Path Integral ◽  
Direct Calculation ◽  
Conformal Anomaly ◽  
Operator Formalism ◽  
Conformal Field ◽  
Integral Methods ◽  
Change Of Variables ◽  
Definition Of

We present a coordinate-invariant approach, based on a Pauli–Villars measure, to the definition of the path integral in two-dimensional conformal field theory. We discuss some advantages of this approach compared to the operator formalism and alternative path integral approaches. We show that our path integral measure is invariant under conformal transformations and field reparametrizations, in contrast to the measure used in the Fujikawa calculation, and we show the agreement, despite different origins, of the conformal anomaly in the two approaches. The natural energy–momentum in the Pauli–Villars approach is a true coordinate-invariant tensor quantity, and we discuss its nontrivial relationship to the corresponding nontensor object arising in the operator formalism, thus providing a novel explanation within a path integral context for the anomalous Ward identities of the latter. We provide a direct calculation of the nontrivial contact terms arising in expectation values of certain energy–momentum products, and we use these to perform a simple consistency check confirming the validity of the change of variables formula for the path integral. Finally, we review the relationship between the conformal anomaly and the energy–momentum two-point functions in our formalism.

Path Integral Methods for the Probabilistic Analysis of Nonlinear Systems Under a White-Noise Process

2020 ◽  
Vol 6 (4) ◽  
Author(s):  
Mario Di Paola ◽  
Gioacchino Alotta
Keyword(s):  
Path Integral ◽  
Path Integration ◽  
Integral Method ◽  
Degrees Of Freedom ◽  
Kolmogorov Equation ◽  
Integral Methods ◽  
Alternative Approach ◽  
Path Integration Method ◽  
Path Integral Method ◽  
Barrier Problems

Abstract In this paper, the widely known path integral method, derived from the application of the Chapman–Kolmogorov equation, is described in details and discussed with reference to the main results available in literature in several decades of contributions. The most simple application of the method is related to the solution of Fokker–Planck type equations. In this paper, the solution in the presence of normal, α-stable, and Poissonian white noises is first discussed. Then, application to barrier problems, such as first passage problems and vibroimpact problems is described. Further, the extension of the path integral method to problems involving multi-degrees-of-freedom systems is analyzed. Lastly, an alternative approach to the path integration method, that is the Wiener Path integration (WPI), also based on the Chapman–Komogorov equation, is discussed. The main advantages and the drawbacks in using these two methods are deeply analyzed and the main results available in literature are highlighted.

Sign in / Sign up

Export Citation Format

Share Document