Related papers: Speeding up quantum Markov processes through lifti…
It is shown in the paper that the unitary quantum dynamics in quantum mechanics is the universal quantum driving force to speed up a quantum computation. This assertion supports strongly in theory that the unitary quantum dynamics is the…
We introduce a universal method for accelerating Lindblad dynamics that preserves the original trajectory through Hilbert space. The technique provides exact fast processes analytically, which are Markovian and do not require manipulation…
The paper studies the rate of convergence of the weak Euler approximation for It\^{o} diffusion and jump processes with H\"{o}lder-continuous generators. It covers a number of stochastic processes including the nondegenerate diffusion…
We study the exponential convergence to the stationary state for nonequilibrium Langevin dynamics, by a perturbative approach based on hypocoercive techniques developed for equilibrium Langevin dynamics. The Hamiltonian and overdamped…
Tau leap schemes were originally designed for the efficient time stepping of discrete state and continuous in time Markov processes arising in stochastic chemical kinetics. Previous convergence results on tau leaping schemes have been…
We consider two approaches to study non-reversible Markov processes, namely the Hypocoercivity Theory (HT) and GENERIC (General Equations for Non-Equilibrium Reversible-Irreversible Coupling); the basic idea behind both of them is to split…
We present a new reformulation of the canonical quantum geometrodynamics, which allows to overcome the fundamental problem of the frozen formalism and, therefore, to construct an appropriate Hilbert space associate to the solution of the…
We provide a criterion for establishing lower bounds on the rate of convergence in $f$-variation of a continuous-time ergodic Markov process to its invariant measure. The criterion consists of novel super- and submartingale conditions for…
We analyse and interpret the effects of breaking detailed balance on the convergence to equilibrium of conservative interacting particle systems and their hydrodynamic scaling limits. For finite systems of interacting particles, we review…
In a Hilbert framework, we introduce continuous and discrete dynamical systems which aim at solving inclusions governed by structured monotone operators $A=\partial\Phi+B$, where $\partial\Phi$ is the subdifferential of a convex lower…
Lifted Markov chains are Markov chains on graphs with added local "memory" and can be used to mix towards a target distribution faster than their memoryless counterparts. Upper and lower bounds on the achievable performance have been…
We establish that, for a Markov semi-group, $L^2$ hypocoercivity, i.e. contractivity for a modified $L^2$ norm, implies quantitative deviation bounds for additive functionals of the associated Markov process and exponential integrability of…
A common approach to studying high-dimensional systems with emergent low-dimensional behavior is based on lift-evolve-restrict maps (called equation-free methods): first, a user-defined lifting operator maps a set of low-dimensional…
We present results on the ballistic and diffusive behavior of the Langevin dynamics in a periodic potential that is driven away from equilibrium by a space-time periodic driving force, extending some of the results obtained by Collet and…
We present a formula for the spectroscopically accessible level shifts and decay rates of an atom moving at an arbitrary angle relative to a surface. Our Markov formulation leads to an intuitive analytic description whereby the shifts and…
We provide a complete elaboration of the $L^2$-Hilbert space hypocoercivity theorem for the degenerate Langevin dynamics via studying the longtime behavior of the strongly continuous contraction semigroup solving the associated Kolmogorov…
In this article, relying on Foster-Lyapunov drift conditions, we establish subexponential upper and lower bounds on the rate of convergence in the $\mathrm{L}^p$-Wasserstein distance for a class of irreducible and aperiodic Markov…
We provide a complete elaboration of the $L^2$-Hilbert space hypocoercivity theorem for the degenerate Langevin dynamics with multiplicative noise, studying the longtime behaviour of the strongly continuous contraction semigroup solving the…
The broad motivation of this work is a rigorous understanding of reversible, local Markov dynamics of interfaces, and in particular their speed of convergence to equilibrium, measured via the mixing time $T_{mix}$. In the…
We study the rate of convergence to equilibrium of the self-repellent random walk and its local time process on the discrete circle $\mathbb{Z}_n$. While the self-repellent random walk alone is non-Markovian since the jump rates depend on…