Related papers: Tensor network approach to real-time path integral

We compare several parametrized analytic expressions for an arbitrary off-shell one-loop $n$-point function in scalar field theory in $D$-dimensional space-time, and show their equivalence both directly and through path-integral methods.

Matrix congruence extends naturally to the setting of tensors. We apply methods from tensor decomposition, algebraic geometry and numerical optimization to this group action. Given a tensor in the orbit of another tensor, we compute a…

Spectral methods provide highly accurate numerical solutions for partial differential equations, exhibiting exponential convergence with the number of spectral nodes. Traditionally, in addressing time-dependent nonlinear problems, attention…

Physical path integral formulation of motion of particles in Riemannian spaces is outlined and extended to deduce the corresponding field theoretical formulation. For the special case of a zero rest mass particle in Minkowski manifold, it…

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…

A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear…

In this paper, we introduce a type of tensor neural network. For the first time, we propose its numerical integration scheme and prove the computational complexity to be the polynomial scale of the dimension. Based on the tensor product…

A variation to the usual formulation of Grassmann representation path integrals is presented. Time-indexed anticommuting partners are introduced for each Grassmann coherent state variable and a general method for handling the effect of…

The quantum theory of cosmological perturbations in single field inflation is formulated in terms of a path integral. Starting from a canonical formulation, we show how the free propagators can be obtained from the well known…

Network tomography means to estimate internal link states from end-to-end path measurements. In conventional network tomography, to make packets transmissively penetrate a network, a cooperation between transmitter and receiver nodes is…

We devise a method based on the tensor-network formalism to calculate genuine multisite entanglement in ground states of infinite spin chains containing spin-1/2 or spin-1 quantum particles. The ground state is obtained by employing an…

Data quality is critical to Intelligent Transportation Systems (ITS), as complete and accurate traffic data underpin reliable decision-making in traffic control and management. Recent advances in low-rank tensor recovery algorithms have…

In this paper we construct a path integral formulation of quantum mechanics on noncommutative phase-space. We first map the system to an equivalent system on the noncommutative plane. Then by applying the formalism of representing a quantum…

We obtain wave functionals of free real and complex scalar fields on a 1+1 dimensional lattice by explicitly calculating the path integral for transition from one field configuration to another. The obtained expressions are useful for…

A classic network tomography problem is estimation of properties of the distribution of route traffic volumes based on counts taken on the network links. We consider inference for a general class of models for integer-valued traffic. Model…

Path integrals have, over the years, proven to be an extremely versatile tool for simulating the dynamics of open quantum systems. The initial limitations of applicability of these methods in terms of the size of the system has steadily…

In this paper, we propose a general framework for solving high-dimensional partial differential equations with tensor networks. Our approach uses Monte-Carlo simulations to update the solution and re-estimates the new solution from samples…

A robust and efficient time integrator for dynamical tensor approximation in the tensor train or matrix product state format is presented. The method is based on splitting the projector onto the tangent space of the tensor manifold. The…

In the path integral formulation of the evolution of an open quantum system coupled to a Gaussian, non-interacting environment, the dynamical contribution of the latter is encoded in an object called the influence functional. Here, we…

Tensor networks (TNs) have been gaining interest as multiway data analysis tools owing to their ability to tackle the curse of dimensionality and to represent tensors as smaller-scale interconnections of their intrinsic features. However,…