Related papers: Path integral representation for stochastic jump p…
We consider the evolution of a quantum simple harmonic oscillator in a general Gaussian state under simultaneous time-continuous weak position and momentum measurements. We deduce the stochastic evolution equations for position and momentum…
The growing literature on the propagation of COVID-19 relies on various dynamic SIR-type models (Susceptible-Infected-Recovered) which yield model-dependent results. For transparency and ease of comparing the results, we introduce a common…
To reconstruct a mixed or pure quantum state of a spin s is possible through coherent states: its density matrix is fixed by the probabilities to measure the value s along 4s(s+1) appropriately chosen directions in space. Thus, after…
We develop the formulation of the spin(SU(2)) coherent state path integrals based on arbitrary fiducial vectors. The resultant action in the path integral expression extensively depends on the vector; It differs from the conventional one in…
A stochastic SIR epidemic model taking into account the heterogeneity of the spatial environment is constructed. The deterministic model is given by a partial differential equation and the stochastic one by a space-time jump Markov process.…
We propose a gate-based quantum algorithm for the prediction step of Bayesian state estimation based on the Fokker-Planck equation on a discretized position-velocity state space. The probability density is encoded in the amplitudes of a…
The spin coherent state path integral describing the dynamics of a spin-1/2-system in a magnetic field of arbitrary time-dependence is considered. Defining the path integral as the limit of a Wiener regularized expression, the semiclassical…
A functional integral representation is given for a large class of quantum mechanical models with a non--L2 ground state. As a prototype the particle in a periodic potential is discussed: a unique ground state is shown to exist as a state…
We investigate, by numerical simulation, the path probability of non dissipative mechanical systems undergoing stochastic motion. The aim is to search for the relationship between this probability and the usual mechanical action. The model…
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…
Diagrammatic summation is a common bottleneck in modern applications of projected entangled-pair states, especially in computing low-energy excitations of a two-dimensional quantum many-body system. To solve this problem, here we extend the…
We present a computation of the coherent state path integral for a generic linear system using ``functional methods'' (as opposed to discrete time approaches). The Gaussian phase space path integral is formally given by a determinant built…
Stochastic mechanics---the study of classical stochastic systems governed by things like master equations and Fokker-Planck equations---exhibits striking mathematical parallels to quantum mechanics. In this article, we make those parallels…
As an alternative but unified and more fundamental description for quantum physics, Feynman path integrals generalize the classical action principle to a probabilistic perspective, under which the physical observables' estimation translates…
The behavior of the most probable values of the order parameter $x$ and the amplitude $\phi$ of conjugate force fluctuations is studied for a stochastic system with a colored multiplicative noise with absorbing states. The phase diagrams…
Genetic variation in a population can sometimes arise so fast as to modify ecosystem dynamics. Such phenomena have been observed in natural predator-prey systems, and characterized in the laboratory as showing unusual phase relationships in…
We describe stochastic calculus in the context of processes that are driven by an adapted point process of locally finite intensity and are differentiable between jumps. This includes Markov chains as well as non-Markov processes. By…
We present the systematic formalism to derive the path-integral formulation for the hard-core particle systems far from equilibrium. Writing the master equation for a stochastic process of the system in terms of the annihilation and…
We show that the stochastic dynamics of a large class of one-dimensional interacting particle systems may be presented by integrable quantum spin Hamiltonians. Using the Bethe ansatz and similarity transformations this yields new exact…
We introduce an interacting particle system that models the spread of an epidemic in terms of heterogeneous diffusive dynamics, rather than exogenous contact and transmission rates at the population level as in classical compartmental…