相关论文: The Cavity Master Equation: average and fixed poin…
We introduce a new solution to Glauber multi-spin dynamics on random graphs. The solution is based on the recently introduced Cavity Master Equation (CME), a time-closure turning the in principle exact Dynamic Cavity Method into a practical…
We start from the Theory of Random Point Processes to derive n-point coupled master equations describing the continuous dynamics of discrete variables in random graphs. These equations constitute a hierarchical set of approximations that…
We present a new method to close the Master Equation representing the continuous time dynamics of Ising interacting spins. The method makes use of the the theory of Random Point Processes to derive a master equation for local conditional…
The chemical master equation (CME) is frequently used in systems biology to quantify the effects of stochastic fluctuations that arise due to biomolecular species with low copy numbers. The CME is a system of ordinary differential equations…
A quantum master equation (QME) is derived for the many-body density matrix of an open current-carrying system weakly coupled to two metal leads. The dynamics and the steady-state properties of the system for arbitrary bias are studied…
The approximate master equation (AME) provides a highly accurate description of dynamical processes on networks, yet its steady states are generally analytically intractable. In this study, we develop an analytical framework to derive the…
A Multi-scale Boltzmann Equation (MBE) is found from the gas-kinetic theory and the direct modeling philosophy as a master equation for complex physical systems of neutral gases across all flow regimes, which locates between the continuum…
The Chemical Master Equation (CME) is used to stochastically model biochemical reaction networks, under the Markovian assumption. The low-order statistical moments induced by the CME are often the key quantities that one is interested in.…
A detailed analysis of the quantum diffusive Stochastic Master Equation (SME) for qubit/cavity systems with dispersive coupling is provided. This analysis incorporates classical input signals and output signals (measurement outcomes through…
The aim of this article is relating the chemical master equation (CME) to the illness-death model for chronic diseases. We show that a recently developed differential equation for the prevalence directly follows from the CME. As an…
We introduce quantum versions of the Kac Master Equation and the Kac Boltzmann Equation. We study the steady states of each of these equations, and prove a propagation of chaos theorem that relates them. The Quantum Kac Master Equation…
Approximations based on moment-closure (MA) are commonly used to obtain estimates of the mean molecule numbers and of the variance of fluctuations in the number of molecules of chemical systems. The advantage of this approach is that it can…
We present a detailed derivation of the stochastic master equation determining the time evolution of the state of a general quantum system, which is placed inside a cavity and subjected to indirect measurements by monitoring the state of…
The stochastic dynamics of biochemical networks are usually modelled with the chemical master equation (CME). The stationary distributions of CMEs are seldom solvable analytically, and numerical methods typically produce estimates with…
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless systems, with say $m$ particles in $N$ single particle states…
We present results of simulations of a em quantum Boltzmann master equation (QBME) describing the kinetics of a dilute Bose gas confined in a trapping potential in the regime of Bose condensation. The QBME is the simplest version of a…
The Master equation describes the time evolution of the probabilities of a system with a discrete state space. This time evolution approaches for long times a stationary state that will in general depend on the initial probability…
We develop a master equation formalism to describe the evolution of the average density matrix of a closed quantum system driven by a stochastic Hamiltonian. The average over random processes generally results in decoherence effects in…
We consider ferromagnetic Ising models on graphs that converge locally to trees. Examples include random regular graphs with bounded degree and uniformly random graphs with bounded average degree. We prove that the "cavity" prediction for…
In this thesis, set-valued maps are considered to model the $i-v$ characteristics of semiconductors like diode, and transistor. Using the circuit theory laws, a generalized equation is obtained. The main concern of the thesis is to…