Related papers: Stochastic exclusion processes versus coherent tra…
We combine geometric data analysis and stochastic modeling to describe the collective dynamics of complex systems. As an example we apply this approach to financial data and focus on the non-stationarity of the market correlation structure.…
Biological systems are typically highly open, non-equilibrium systems that are very challenging to understand from a statistical mechanics perspective. While statistical treatments of evolutionary biological systems have a long and rich…
The state matrix $\rho$ for an open quantum system with Markovian evolution obeys a master equation. The master equation evolution can be unraveled into stochastic nonlinear trajectories for a pure state $P$, such that on average $P$…
The infinitesimal transition probability operator for a continuous-time discrete-state Markov process, $\mathcal{Q}$, can be decomposed into a symmetric and a skew-symmetric parts. As recently shown for the case of diffusion processes,…
We present a general method to derive the classical mechanics of a system of identical particles in a way that retains information about quantum statistics. The resulting statistical mechanics can be interpreted as a classical version of…
We establish heavy traffic limit theorems for queue-length processes in critically loaded single class queueing networks with state dependent arrival and service rates. A distinguishing feature of our model is non-Markovian state…
A stochastic system under the influence of a stochastic environment is correlated with both present and future states of the environment. Such a system can be seen as implicitly implementing a predictive model of future environmental…
Stochastic processes with temporal delay play an important role in science and engineering whenever finite speeds of signal transmission and processing occur. However, an exact mathematical analysis of their dynamics and thermodynamics is…
The solutions of Hamiltonian equations are known to describe the underlying phase space of a mechanical system. In this article, we propose a novel spatio-temporal model using a strategic modification of the Hamiltonian equations,…
We derive Markovian master equations of single and interacting harmonic systems in different scenarios, including strong internal coupling. By comparing the dynamics resulting from the corresponding Markovian master equations with exact…
In this paper, under an abstract setting we establish the spreading properties and the existence, non-existence and global attractivity of spatially heterogeneous steady states for a large class of monotone evolution systems without the…
Non-Markovian master equations describe general open quantum systems when no approximation is made. We provide the exact closed master equation for the class of Gaussian, completely positive, trace preserving, non-Markovian dynamics. This…
Transport properties of the multicomponent quantum many-body systems obeying Haldane's fractional exclusion statistics are studied in one dimension. By computing the finite-size spectrum under twisted boundary conditions, we explicitly…
We define a new variant of exclusion processes in discrete time that has jump probabilities that depend on the last jump performed. In a particular limit for the jump probabilities and in suitable scaling limits for space and time, we…
Exact generalized stochastic representation of deterministic interaction between two dynamical (quantum or classical) systems is derived which helps when considering one of them to replace another by equivalent commutative ($c$-number…
Understanding the fluctuations by which phenomenological evolution equations with thermodynamic structure can be enhanced is the key to a general framework of nonequilibrium statistical mechanics. These fluctuations provide an idealized…
We study the quasi-stationary evolution of systems where an energetic confinement is unable to completely retain their constituents. It is performed an extensive numerical study of a gas whose dynamics is driven by binary encounters and its…
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…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
Equilibrium statistical mechanics provides powerful tools to understand physics at the macroscale. Yet, the question remains how this can be justified based on a microscopic quantum description. Here, we extend the ideas of pure state…