Search results for "path integral"

Path Integrals in Noncommutative Geometry

2006

Phase transitions and quantum effects in adsorbed monolayers

1996

Phase transitions in absorbed (two-dimensional) fluids and in absorbed layers of linear molecules are studied with a combination of path integral Monte Carlo (PIMC), Gibbs ensemble Monte Carlo (GEMC), and finite size scaling techniques. For a classical (nonadditive) hard-disk fluid the “critical” nonadditivities, where the entropy-driven phase separations set in, are presented. For a fluid with internal quantum states the gas-liquid coexistence region, tricritical, and triple points can be determined, and a comparison with density functional (DFT) results shows good agreement for the freezing densities. LinearN 2 molecules adsorbed on graphite (in the √3 × √3 structure) show a transition fr…

Phase diagram of a model adsorbate with internal quantum states

1992

Abstract An adsorbate in the strong binding and small corrugation limit is studied. The resulting two-dimensional fluid is treated in the adiabatic approximation: the translations of the heavy molecules are treated classically, whereas the molecular quantum degrees of freedom are modelled by interacting two state tunneling systems. The complete temperature/coverage phase diagram is obtained to a high degree of precision by a new combination of finite size scaling ideas with Path Integral Monte Carlo techniques. Even this simplified adsorbate model possesses a surprisingly complex phase diagram including first- and second-order transitions as well as tricritical and triple points. We identif…

Hadron correlators and the structure of the quark propagator

1994

The structure of the quark propagator of $QCD$ in a confining background is not known. We make an Ansatz for it, as hinted by a particular mechanism for confinement, and analyze its implications in the meson and baryon correlators. We connect the various terms in the K\"allen-Lehmann representation of the quark propagator with appropriate combinations of hadron correlators, which may ultimately be calculated in lattice $QCD$. Furthermore, using the positivity of the path integral measure for vector like theories, we reanalyze some mass inequalities in our formalism. A curiosity of the analysis is that, the exotic components of the propagator (axial and tensor), produce terms in the hadron c…

Nucleon and delta masses in QCD

1992

Using the positivity of the path integral measure of $QCD$ and defining a structure for the quark propagator in a background field according to the fluxon scenario for confinement, we calculate and compare the correlators for nucleon and delta. From their shape we elucidate about the origin of their mass difference, which in our simplified scenario is due to the tensor structure in the propagator. This term arises due to a dynamical mechanism which is responsible simultaneously for confinement and spontaneous chiral symmetry breaking. Finally we discuss, by comparing the calculated correlators with the Lehmann representation, the possibility that a strong CP and/or P violation occurs as a c…

Denjoy and P-path integrals on compact groups in an inversion formula for multiplicative transforms

2009

Abstract Denjoy and P-path Kurzweil-Henstock type integrals are defined on compact subsets of some locally compact zero-dimensional abelian groups. Those integrals are applied to obtain an inversion formula for the multiplicative integral transform.

Probabilistic response of linear structures equipped with nonlinear dampers devices (PIS method)

2008

Passive control introducing energy absorbing devices into the structure has received considerable attention in recent years. Unfortunately the constitutive law of viscous fluid dampers is highly nonlinear, and even supposing that the structure behaves linearly, the whole system has inherent nonlinear properties. Usually the analysis is performed by a stochastic linearization technique (SLT) determining a linear system equivalent to the nonlinear one, in a statistical sense. In this paper the effect of the non-Gaussianity of the response due to the inherent nonlinearity of the damper device will be studied in detail via the Path Integral Solution (PIS) method. A systematic study is conducted…

Quantum dissipative dynamics of a bistable system in the sub-Ohmic to super-Ohmic regime

2016

We investigate the quantum dynamics of a multilevel bistable system coupled to a bosonic heat bath beyond the perturbative regime. We consider different spectral densities of the bath, in the transition from sub-Ohmic to super-Ohmic dissipation, and different cutoff frequencies. The study is carried out by using the real-time path integral approach of the Feynman-Vernon influence functional. We find that, in the crossover dynamical regime characterized by damped \emph{intrawell} oscillations and incoherent tunneling, the short time behavior and the time scales of the relaxation starting from a nonequilibrium initial condition depend nontrivially on the spectral properties of the heat bath.

Structure and Dynamics of the Instantaneous Water/Vapor Interface Revisited by Path-Integral and Ab Initio Molecular Dynamics Simulations

2015

The structure and dynamics of the water/vapor interface is revisited by means of path-integral and second-generation Car-Parrinello ab-initio molecular dynamics simulations in conjunction with an instantaneous surface definition [A. P. Willard and D. Chandler, J. Phys. Chem. B 114, 1954 (2010)]. In agreement with previous studies, we find that one of the OH bonds of the water molecules in the topmost layer is pointing out of the water into the vapor phase, while the orientation of the underlying layer is reversed. Therebetween, an additional water layer is detected, where the molecules are aligned parallel to the instantaneous water surface.

Correction: “On-the-fly” coupled cluster path-integral molecular dynamics: impact of nuclear quantum effects on the protonated water dimer

2015

We present an accelerated ab initio path-integral molecular dynamics technique, where the interatomic forces are calculated “on-the-fly” by accurate coupled cluster electronic structure calculations. In this way not only dynamic electron correlation, but also the harmonic and anharmonic zero-point energy, as well as tunneling effects are explicitly taken into account. This method thus allows for very precise finite temperature quantum molecular dynamics simulations. The predictive power of this novel approach is illustrated on the example of the protonated water dimer, where the impact of nuclear quantum effects on its structure and the 1H magnetic shielding tensor are discussed in detail.