Related papers: Iterative path integral summation for nonequilibri…
We have developed a numerical approach to compute real-time path integral expressions for quantum transport problems out of equilibrium. The scheme is based on a deterministic iterative summation of the path integral (ISPI) for the…
On the basis of the method of iterative summation of path integrals (ISPI), we develop a numerically exact transfer-matrix method to describe the nonequilibrium properties of interacting quantum-dot systems. For this, we map the ISPI scheme…
We formulate and apply a nonperturbative numerical approach to the nonequilibrium current, $I(V)$, through a voltage-biased molecular conductor. We focus on a single electronic level coupled to an unequilibrated vibration mode…
We develop an iterative, numerically exact approach for the treatment of nonequilibrium quantum transport and dissipation problems that avoids the real-time sign problem associated with standard Monte Carlo techniques. The method requires a…
Resonant tunneling of electrons between two ferromagnets and a quantum dot in the presence of an externally applied magnetic field reveals a strong gate dependence in the linear and nonlinear bias regime. This gate dependence originates…
We simulate the nonequilibrium dynamics of two generic many-body quantum impurity models by employing the recently developed iterative influence-functional path integral method [Phys. Rev. B {\bf 82}, 205323 (2010)]. This general approach…
Background: Path integrals are a powerful tool for solving problems in quantum theory that are not amenable to a treatment by perturbation theory. Most path integral computations require an analytic continuation to imaginary time. While…
A general and rigorous methodology to compute the quantum equilibrium isotope effect is described. Unlike standard approaches, ours does not assume separability of rotational and vibrational motions and does not make the harmonic…
We develop a non-perturbative method for calculating partition functions of strongly coupled quantum mechanical systems with interactions between subsystems described by a path integral of a dual system. The dual path integral is derived…
Quantum transition amplitudes are formulated for a model system with local internal time, using path integrals. The amplitudes are shown to be more regular near a turning point of internal time than could be expected based on existing…
This paper considers optimal control of dynamical systems which are represented by nonlinear stochastic differential equations. It is well-known that the optimal control policy for this problem can be obtained as a function of a value…
The use of random sampling in decision-making and control has become popular with the ease of access to graphic processing units that can generate and calculate multiple random trajectories for real-time robotic applications. In contrast to…
This paper considers linear-quadratic control of a non-linear dynamical system subject to arbitrary cost. I show that for this class of stochastic control problems the non-linear Hamilton-Jacobi-Bellman equation can be transformed into a…
A path integral formalism has been proposed recently for non-equilibrium statistical physics applications by the author. In this contribution we outline an efficient method for its numerical evaluation. The method used is based on the…
The Feynman path integral has revolutionized modern approaches to quantum physics. Although the path integral formalism has proven very successful and spawned several approximation schemes, the direct evaluation of real-time path integrals…
We propose the differential equation based path integral (DEBPI) method to simulate the real-time evolution of open quantum systems. In this method, a system of partial differential equations is derived based on the continuation of a…
A path-integral approach for the computation of quantum-mechanical propagators and energy Green's functions is presented. Its effectiveness is demonstrated through its application to singular interactions, with particular emphasis on the…
In the path integral formulation of the partition function of quantum spin models, most current treatments employ the so-called static approximation to simplify the process of summing over all possible paths. Although sufficient for…
We present a numerical path-integral iteration scheme for the low dimensional reduced density matrix of a time-dependent quantum dissipative system. Our approach simultaneously accounts for the combined action of a microscopically modelled…
We present a method to compute real-time path integrals numerically, by Monte-Carlo sampling on near-Lefschetz thimbles. We present a collection of tools based on the Lefschetz thimble methods, which together provide an alternative to…