相关论文: Brownian Motion on the Unitary Quantum Group: Cons…
Using von Neumann algebras, we extend the theory of quantum computation on a graph to a theory of computation on an arbitrary topological space.
A pathwise construction of discontinuous Brownian motions on metric graphs is given for every possible set of non-local Feller-Wentzell boundary conditions. This construction is achieved by locally decomposing the metric graphs into star…
After some normalization, the logarithms of the ordered singular values of Brownian motions on $GL(N,\mathbb F)$ with $\mathbb F=\mathbb R, \mathbb C$ form Weyl-group invariant Heckman-Opdam processes on $\mathbb R^N$ of type $A_{N-1}$. We…
The theory of quantum Brownian motion describes the properties of a large class of open quantum systems. Nonetheless, its description in terms of a Born-Markov master equation, widely used in the literature, is known to violate the…
We consider classical particles coupled to the quantized electromagnetic field in the background of a spatially flat Robertson-Walker universe. We find that these particles typically undergo Brownian motion and acquire a non-zero mean…
This article reports the modeling of inertial rotational Brownian motion as an Ornstein-Uhlenbeck process evolving on the cotangent bundle of the rotation group, SO(3). The benefit of this approach and the use of a different…
We derive a quantum master equation from first principles to describe friction in one dimensional, collisional Brownian motion. We are the first to avoid an ill-defined square of the Dirac delta function by using localized wave packets…
In systems possessing a spatial or dynamical symmetry breaking thermal Brownian motion combined with unbiased, non-equilibrium noise gives rise to a channelling of chance that can be used to exercise control over systems at the micro- and…
We show that the Laplace transforms of traces of words in independant unitary Brownian motions converge towards an analytic function on a non trivial disc. This results allow to study asymptotics of Wilson loops under the unitary Yang-Mills…
In quantum field theory the creation and annihilation operators that are located at the points in 3-momentum space have commutation relations that are conserved under the action of a $U({\infty})$ group. Here it is shown how to define an…
We consider a single Brownian particle in a spatially symmetric, periodic system far from thermal equilibrium. This setup can be readily realized experimentally. Upon application of an external static force F, the average particle velocity…
Using a group theoretical approach we derive an equation of motion for a mixed quantum-classical system. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics: The bracket…
How fast a state of a system converges to a stationary state is one of the fundamental questions in science. Some Markov chains and random walks on finite groups are known to exhibit the non-asymptotic convergence to a stationary…
Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the…
We show that the past and future of half-plane Brownian motion at certain cutpoints are independent of each other after a conformal transformation. Like in Ito's excursion theory, the pieces between cutpoints form a Poisson process with…
We establish the renormalization group equation for the running action in the context of a one quantum particle system. This equation is deduced by integrating each fourier mode after the other in the path integral formalism. It is free of…
We prove a theorem showing that quantum mechanics is not directly a stochastic process characterizing Brownian motion but rather its square root. This implies that a complex-valued stochastic process is involved. Schr\"odinger equation is…
A new version of hidden variables theory founded on the generalisation of world's geometry is proposed. The quantum-mechanical motion as the motion in some "inner space", which has a structure of the integrable Weyl space is examined.…
The Brownian motion of a charged test particle caused by quantum electromagnetic vacuum fluctuations between two perfectly conducting plates is examined and the mean squared fluctuations in the velocity and position of the test particle are…
Unitary designs are unitary ensembles that emulate Haar-random unitary statistics. They provide a vital tool for studying quantum randomness and have found broad applications in quantum technologies. However, existing research has focused…