Search results for "Path Integral"
showing 10 items of 80 documents
Mean field methods in large amplitude nuclear collective motion
1984
The time dependent Hartree-Fock method (TDHF) is reviewed and its success and failure are discussed. It is demonstrated that TDHF is a semiclassical theory which is basically able to describe the time evolution of one-body operators, the energy loss in inclusive deep inelastic collisions, and fusion reactions above the Coulomb barrier. For genuine quantum mechanical processes as e.g. spontaneous fission, subbarrier fusion, phase shifts and the description of bound vibrations, the quantized adiabatic time dependent Hartree-Fock theory (quantized ATDHF) is suggested and reviewed. Realistic three-dimensional calculations for heavy ion systems of A1+A2<32 are presented. Applications to various …
An approximate technique for determining in closed-form the response transition probability density function of diverse nonlinear/hysteretic oscillat…
2019
An approximate analytical technique is developed for determining, in closed form, the transition probability density function (PDF) of a general class of first-order stochastic differential equations (SDEs) with nonlinearities both in the drift and in the diffusion coefficients. Specifically, first, resorting to the Wiener path integral most probable path approximation and utilizing the Cauchy–Schwarz inequality yields a closed-form expression for the system response PDF, at practically zero computational cost. Next, the accuracy of this approximation is enhanced by proposing a more general PDF form with additional parameters to be determined. This is done by relying on the associated Fokke…
The response field and the saddle points of quantum mechanical path integrals
2021
In quantum statistical mechanics, Moyal's equation governs the time evolution of Wigner functions and of more general Weyl symbols that represent the density matrix of arbitrary mixed states. A formal solution to Moyal's equation is given by Marinov's path integral. In this paper we demonstrate that this path integral can be regarded as the natural link between several conceptual, geometric, and dynamical issues in quantum mechanics. A unifying perspective is achieved by highlighting the pivotal role which the response field, one of the integration variables in Marinov's integral, plays for pure states even. The discussion focuses on how the integral's semiclassical approximation relates to…
Response of nonlinear oscillators with fractional derivative elements under evolutionary stochastic excitations: A Path Integral approach based on La…
2023
In this paper, an approximate analytical technique is developed for determining the non-stationary response amplitude probability density function (PDF) of nonlinear/hysteretic oscillators endowed with fractional element and subjected to evolutionary excitations. This is achieved by a novel formulation of the Path Integral (PI) approach. Specifically, a stochastic averaging/linearization treatment of the original fractional order governing equation of motion yields a first-order stochastic differential equation (SDE) for the oscillator response amplitude. Associated with this first-order SDE is the Chapman–Kolmogorov (CK) equation governing the evolution in time of the non-stationary respon…
Gibbs-ensemble path-integral Monte Carlo simulations of a mixed quantum-classical fluid
1995
We study a model fluid with classical translational degrees of freedom and internal quantum states in two spatial dimensions. The path-integral Monte Carlo and the Gibbs-ensemble Monte Carlo techniques are combined to investigate the liquid-gas coexistence region in this mixed quantum-classical system. A comparison with the phase diagram obtained in the canonical ensemble is also presented.
Non-linear Systems Under Poisson White Noise Handled by Path Integral Solution
2008
An extension of the path integral to non-linear systems driven by a Poissonian white noise process is presented. It is shown that at the limit when the time increment becomes infinitesimal the Kolmogorov— Feller equation is fully restored. Applications to linear and non-linear systems with different distribution of the Dirac's deltas occurrences are performed and results are compared with analytical solutions (when available) and Monte Carlo simulation.
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.
Green functions for nearest- and next-nearest-neighbor hopping on the Bethe lattice
2005
We calculate the local Green function for a quantum-mechanical particle with hopping between nearest and next-nearest neighbors on the Bethe lattice, where the on-site energies may alternate on sublattices. For infinite connectivity the renormalized perturbation expansion is carried out by counting all non-self-intersecting paths, leading to an implicit equation for the local Green function. By integrating out branches of the Bethe lattice the same equation is obtained from a path integral approach for the partition function. This also provides the local Green function for finite connectivity. Finally, a recently developed topological approach is extended to derive an operator identity whic…
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.
Quantitative approximation of certain stochastic integrals
2002
We approximate certain stochastic integrals, typically appearing in Stochastic Finance, by stochastic integrals over integrands, which are path-wise constant within deterministic, but not necessarily equidistant, time intervals. We ask for rates of convergence if the approximation error is considered in L 2 . In particular, we show that by using non-equidistant time nets, in contrast to equidistant time nets, approximation rates can be improved considerably.