相关论文: Path Integrals and Parastatistics

We study random composite structures considered up to symmetry that are sampled according to weights on the inner and outer structures. This model may be viewed as an unlabelled version of Gibbs partitions and encompasses multisets of…

This paper investigates the position (state) distribution of the single step binomial (multi-nomial) process on a discrete state / time grid under the assumption that the velocity process rather than the state process is Markovian. In this…

We review and extend the formalism introduced by Peliti, that maps a Markov process to a path-integral representation. After developing the mapping, we apply it to some illustrative examples: the simple decay process, the birth-and-death…

The nature of statistics, statistical mechanics and consequently the thermodynamics of stochastic systems is largely determined by how the number of states $W(N)$ depends on the size $N$ of the system. Here we propose a scaling expansion of…

Optimal transport maps define a one-to-one correspondence between probability distributions, and as such have grown popular for machine learning applications. However, these maps are generally defined on empirical observations and cannot be…

We link the theory of optimal transportation to the theory of integer partitions. Let $\mathscr P(n)$ denote the set of integer partitions of $n \in \mathbb N$ and write partitions $\pi \in \mathscr P(n)$ as $(n_1, \dots, n_{k(\pi)})$.…

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 investigate a model for driven exclusion processes where internal states are assigned to the particles. The latter account for diverse situations, ranging from spin states in spintronics to parallel lanes in intracellular or vehicular…

We study the dynamics of overdamped Brownian particles diffusing in conservative force fields and undergoing stochastic resetting to a given location with a generic space-dependent rate of resetting. We present a systematic approach…

The path integral formulation introduced in [arXiv:2210.12761] "Path integrals, particular kinds, and strange things" by Friston and colleagues in 2023, offers an innovative lens for examining complex systems, particularly through its…

This paper suggests a new way to compute the path integral for simple quantum mechanical systems. The new algorithm originated from previous research in string theory. However, its essential simplicity is best illustrated in the case of a…

The relations of antilinear maps, bipartite states and quantum channels is summarized. Antilinear maps are applied to describe bipartite states and entanglement. Teleportation is treated in this general formalism with an emphasis on…

We consider Euclidean path integrals with higher derivative actions, including those that depend quadratically on acceleration, velocity and position. Such path integrals arise naturally in the study of stiff polymers, membranes with…

Quantum mechanics broadly classifies the particles into two categories: $(1)$ fermions and $(2)$ bosons. Fermions are half-integer spin particles, obeying Pauli's exclusion principle and Fermi-Dirac statistics. Whereas bosons are integer…

This work is a numerical experiment of stochastic motion of conservative Hamiltonian system or weakly damped Brownian particles. The objective is to prove the existence of path probability and to compute its values. By observing a large…

We describe a novel approach to statistical learning from particles tracked while moving in a random environment. The problem consists in inferring properties of the environment from recorded snapshots. We consider here the case of a fluid…

One of the major successes in computational biology has been the unification, using the graphical model formalism, of a multitude of algorithms for annotating and comparing biological sequences. Graphical models that have been applied…

Introduction Path Integrals - Introduction - Propagator - Free Particle - Path Integral Representation of Quantum Mechanics - Particle on a Ring - Particle in a Box - Driven Harmonic Oscillator - Semiclassical Approximation - Imaginary Time…

In this note, we address formally the issue of symmetry for probabilities of different dynamical pathways in the forward and reverse directions of a conformational transition. Our discussion is based on a decomposition of equilibrium into…

Doi-Peliti methods are developed for stochastic models with finite maximum occupation numbers per site. We provide a generalized framework for the different Fock spaces reported in the literature. Paragrassmannian techniques are then…