Related papers: Switching Boundary Conditions in the Many-Body Dif…
By considering the master equation of the partially asymmetric diffusion process on a one-dimensional lattice, the most general boundary condition (i.e. interactions) for the multi-species reaction-diffusion processes is considered.…
A finite (periodic) FPU chain is chosen as a convenient point for investigating the energy exchange phenomenon in nonlinear oscillatory systems. As we have recently shown, this phenomenon may occur as a consequence of the resonant…
We model a quantum walk of identical particles that can change their exchange statistics by hopping across a domain wall in a 1D lattice. Such a "statistical boundary" is transparent to single particles and affects the dynamics only by…
The derivation of suitable analytical models is an important step for the design and analysis of molecular communication systems. However, many existing models have limited applicability in practical scenarios due to various simplifications…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…
Non-Hermitian (NH) Hamiltonians can be used to describe dissipative systems, and are currently intensively studied in the context of topology. A salient difference between Hermitian and NH models is the breakdown of the conventional…
Consider growing a network, in which every new connection is made between two disconnected nodes. At least one node is chosen randomly from a subset consisting of $g$ fraction of the entire population in the smallest clusters. Here we show…
We introduce and solve a model of fermions hopping between neighbouring sites on a line with random Brownian amplitudes and open boundary conditions driving the system out of equilibrium. The average dynamics reduces to that of the…
We show that particle transport in a uniform, quantum multi-baker map, is generically ballistic in the long time limit, for any fixed value of Planck's constant. However, for fixed times, the semi-classical limit leads to diffusion. Random…
A theory of temperature dynamics in many-body systems driven by time-dependent external sources is introduced. The formalism based on the combination of the perturbation theory and the fluctuational-electrodynamics approach in many-body…
The quantization of many-body systems with balanced loss and gain is investigated. Two types of models characterized by either translational invariance or rotational symmetry under rotation in a pseudo-Euclidean space are considered. A…
One-dimensional non-equilibrium models of particles subjected to a coagulation-diffusion process are important in understanding non-equilibrium dynamics, and fluctuation-dissipation relation. We consider in this paper transport properties…
Boundary conditions may change the phase diagram of non-equilibrium statistical systems like the one-dimensional asymmetric simple exclusion process with and without particle number conservation. Using the quantum Hamiltonian approach, the…
Boundary conditions changing operators have played an important role in conformal field theory. Here, we study their equivalent in the case where a mass scale is introduced, in an integrable way, either in the bulk or at the boundary. More…
The system under study is a reaction-diffusion equation in a horizontal strip, coupled to a diffusion equation on its upper boundary via an exchange condition of the Robin type. This class of models was introduced by H. Berestycki, L. Rossi…
The transition from a few-body system to a many-body system can result in new length scales, novel collective phenomena or even in a phase transition. Such a threshold behavior was shown for example in 4He droplets, where 4He turns into a…
Quantum systems of indistinguishable particles are commonly described using the formalism of second quantisation, which relies on the assumption that any admissible quantum state must be either symmetric or anti-symmetric under particle…
Energy transfer within photosynthetic systems can display quantum effects such as delocalized excitonic transport. Recently, direct evidence of long-lived coherence has been experimentally demonstrated for the dynamics of the…
A recent experiment by P. Bordia et al. (Periodically Driving a Many Body Localized Quantum System, Nat Phys, Jan 2017) has demonstrated that periodically modulating the potential of a localised many-body quantum system described by the…
We propose a novel method for simulating conditioned diffusion processes (diffusion bridges) in Euclidean spaces. By training a neural network to approximate bridge dynamics, our approach eliminates the need for computationally intensive…