Related papers: Fractional Path Integral Monte Carlo
This paper is about the fractional Schr\"{o}dinger equation (FSE) expressed in terms of the quantum Riesz-Feller space fractional and the Caputo time fractional derivatives. The main focus is on the case of time independent potential fields…
Let $L=-\Delta+V$ be a Schr\"odinger operator, where the potential $V$ belongs to the reverse H\"older class. By the subordinative formula, we introduce the fractional heat semigroup $\{e^{-t{L}^\alpha}\}_{t>0}, \alpha>0$, associated with…
A kind of spatial fractional diffusion equations in this paper are studied. Firstly, an L1 formula is employed for the spatial discretization of the equations. Then, a second order scheme is derived based on the resulting semi-discrete…
Fractional operators play an important role in modeling nonlocal phenomena and problems involving coarse-grained and fractal spaces. The fractional calculus of variations with functionals depending on derivatives and/or integrals of…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
In this manuscript we proposed a new fractional derivative with non-local and no-singular kernel. We presented some useful properties of the new derivative and applied it to solve the fractional heat transfer model.
In this paper we use different techniques from the fractional and pseudo-operators calculus to solve partial differential equations involving operators with non integer exponents. We apply the method to equations resembling generalizations…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
We introduce a notion of fractional (noninteger order) derivative on an arbitrary nonempty closed subset of the real numbers (on a time scale). Main properties of the new operator are proved and several illustrative examples given.
An approximate treatment of exchange in finite-temperature path integral Monte Carlo simulations for fermions has been proposed. In this method, some of the fine details of density matrix due to permutations have been smoothed over or…
The direct integration of the harmonic oscillator path integral obscures the fundamental structure of its discrete, imaginary time propagator (density matrix). This work, by first proving an operator identity for contracting two free…
We showcase the utility of the Lagrangian descriptors method in qualitatively understanding the underlying dynamical behavior of dynamical systems governed by fractional-order differential equations. In particular, we use the Lagrangian…
We propose a probabilistic construction for the solution of a general class of fractional high order heat-type equations in the one-dimensional case, by using a sequence of random walks in the complex plane with a suitable scaling. A time…
This paper provides a finite difference discretization for the backward Feynman-Kac equation, governing the distribution of functionals of the path for a particle undergoing both reaction and diffusion [Hou and Deng, J. Phys. A: Math.…
The first half of this work gives a survey of the fractional Laplacian (and related operators), its restricted Dirichlet realization on a bounded domain, and its nonhomogeneous local boundary conditions, as treated by pseudodifferential…
Fractional derivatives are generalization to classical integer-order derivatives. The rules which are true for classical derivative need not hold for the fractional derivatives, for example, we cannot simply add the fractional orders…
We develop a calculus of variations for functionals which are defined on a set of non differentiable curves. We first extend the classical differential calculus in a quantum calculus, which allows us to define a complex operator, called the…
A global solution of the Schr\"odinger equation for explicitly time-dependent Hamiltonians is derived by integrating the non-linear differential equation associated with the time-dependent wave operator. A fast iterative solution method is…
Fractional differential equations provide a tractable mathematical framework to describe anomalous behavior in complex physical systems, yet they introduce new sensitive model parameters, i.e. derivative orders, in addition to model…
The Monte Carlo (MC) Hamiltonian is a new stochastic method to solve many-body problems. The MC Hamiltonian represents an effective Hamiltonian in a finite energy window. We construct it from the classical action via Monte Carlo with…