Related papers: Iterative path integral summation for nonequilibri…
We investigate pathwise turnpike behavior of discrete-time stochastic linear-quadratic optimal control problems. Our analysis is based on a novel strict dissipativity notion for such problems, in which a stationary stochastic process…
We collect explicit and user-friendly expressions for one-point densities of the real eigenvalues $\{\lambda_i\}$ of $N\times N$ Wishart-Laguerre and Jacobi random matrices with orthogonal, unitary and symplectic symmetry. Using these…
Path integrals represent a powerful route to quantization: they calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration.…
In perturbative calculations of quantum mechanical path integrals in curvilinear coordinates, Feynman diagrams involve multiple temporal integrals over products of distributions, which are mathematically undefined. We derive simple rules…
In this paper we address the problem to compute state dependent feedback controls for path integral control problems. To this end we generalize the path integral control formula and utilize this to construct parameterized state dependent…
We bring together the semiclassical approximation, matrix integrals and the theory of symmetric polynomials in order to solve a long standing problem in the field of quantum chaos: to compute transport moments when tunnel barriers are…
Recently path integral methods have been developed for stochastic optimal control for a wide class of models with non-linear dynamics in continuous space-time. Path integral methods find the control that minimizes the expected cost-to-go.…
General nonequilibrium quantum transport equations are derived for a coupled system of charge carriers, Dirac spin, isospin (or valley spin), and pseudospin, such as either one of the band, layer, impurity, and boundary pseudospins.…
We present an interpolative method for describing coherent transport through an interacting quantum dot. The idea of the method is to construct an approximate electron self-energy which becomes exact both in the limits of weak and strong…
Two path integral representations for the $T$-matrix in nonrelativistic potential scattering are derived and proved to produce the complete Born series when expanded to all orders. They are obtained with the help of "phantom" degrees of…
We present a real-space method for first-principles nano-scale electronic transport calculations. We use the non-equilibrium Green's function method with density functional theory and implement absorbing boundary conditions (ABCs, also…
Starting from the canonical formalism of relativistic (timeless) quantum mechanics, the formulation of timeless path integral is rigorously derived. The transition amplitude is reformulated as the sum, or functional integral, over all…
Path integrals are a central tool when it comes to describing quantum or thermal fluctuations of particles or fields. Their success dates back to Feynman who showed how to use them within the framework of quantum mechanics. Since then, path…
For chaotic cavities with scattering leads attached, transport properties can be approximated in terms of the classical trajectories which enter and exit the system. With a semiclassical treatment involving fine correlations between such…
In one dimensional transport problems the scattering matrix $S$ is decomposed into a block structure corresponding to reflection and transmission matrices at the two ends. For $S$ a random unitary matrix, the singular value probability…
We make use of point transformations to introduce new canonical variables for systems defined on a finite interval and on the half-line so that new position variables should take all real values from $-\infty$ to $\infty$. The completeness…
Formulating the intended behavior of a dynamic system can be challenging. Signal temporal logic (STL) is frequently used for this purpose due to its suitability in formalizing comprehensible, modular, and versatile spatiotemporal…
Transport equations can be derived from quantum field theory assuming a loss of information about the details of the initial state and a gradient expansion. While the latter can be systematically improved, the assumption about a memory loss…
Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems,…
We apply a flexible numerical integrator to the simulation of adiabatic quantum computation with nonlinear paths. We find that a nonlinear path may significantly improve the performance of adiabatic algorithms versus the conventional…