Related papers: Stochastic process behind nonlinear thermodynamic …
Thermodynamics entails a set of mathematical conditions on quantum Markovian dynamics. In particular, strict energy conservation between the system and environment implies that the dissipative dynamical map commutes with the unitary system…
A nonlinear master equation is derived, reflecting properly the entropy of open quantum systems. In contrast to linear alternatives, its equilibrium solution is exactly the canonical Gibbs density matrix. The corresponding nonlinear…
Manipulation of a quantum system requires the knowledge of how it evolves. To impose that the dynamics of a system becomes a particular target operation (for any preparation of the system), it may be more useful to have an equation of…
The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous…
We present a critical derivation of the high-temperature quantum Markovian master equation (HTME), examining its foundational assumptions, their quantum-mechanical implications, and its range of validity. Starting from the Born-Markov…
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…
The quantum jump approach allows to characterize the stochastic dynamics associated to an open quantum system submitted to a continuous measurement action. In this paper we show that this formalism can consistently be extended to…
As an extension of the theory of Dyson's Brownian motion models for the standard Gaussian random-matrix ensembles, we report a systematic study of hermitian matrix-valued processes and their eigenvalue processes associated with the chiral…
The master equation for a linear open quantum system in a general environment is derived using a stochastic approach. This is an alternative derivation to that of Hu, Paz and Zhang, which was based on the direct computation of path…
The purpose of this work is to propose a nonlinear non-Markovian model of subdiffusive transport that involves chemotactic substance affecting the cells at all time, not only during the jump. This leads the random waiting time to be…
Using the quantum Hamiltonian for a gravitational system with boundary, we find the partition function and derive the resulting thermodynamics. The Hamiltonian is the boundary term required by functional differentiability of the action for…
The fluctuation-dissipation theorem is a central result in statistical mechanics and is usually formulated for systems described by diffusion processes. In this paper, we propose a generalization for a wider class of stochastic processes,…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
In this paper, we consider a subclass of piecewise deterministic Markov processes with a Polish state space that involve a deterministic motion punctuated by random jumps, occurring in a Poisson-like fashion with some state-dependent rate,…
In this paper is described the general aspect of a numerical method for piecewise determin-istic Markov processes with boundary. Under very natural hypotheses, a crucial result about uniqueness of solution of a generalized Kolmogorov…
The hierarchical equations of motion (HEOM) for a generalized quantum dissipative system is rigorously constructed in the frameworks of two different stochastic dynamical descriptions, i.e., the non-Markovian quantum state diffusion…
A fundamental challenge is to understand nonequilibrium statistical mechanics starting from microscopic chaos in the equations of motion of a many-particle system. In this review we summarize recent theoretical advances along these lines.…
Master equations under appropriate assumptions are efficient tools for the study of open quantum systems. For many-body systems, subsystems of which locally couple to thermal baths and weakly interact with each other, the local approach…
In this work, we derive a deterministic master equation to model a general, possibly non-Markovian, feedback. The master equation describes a system with a general evolution and measurement operation, with feedback being applied in terms of…
Small quantum systems can now be continuously monitored experimentally which allows for the reconstruction of quantum trajectories. A peculiar feature of these trajectories is the emergence of jumps between the eigenstates of the observable…