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We present here a set of lecture notes on quantum systems with time-dependent boundaries. In particular, we analyze the dynamics of a non-relativistic particle in a bounded domain of physical space, when the boundaries are moving or…
We study an interacting high-density one-dimensional system of self-propelled particles described by the Active Ornstein-Uhlenbeck particle (AOUP) model where, even in the absence of alignment interactions, velocity and energy domains…
The response of a model micro-electrochemical system to a time-dependent applied voltage is analyzed. The article begins with a fresh historical review including electrochemistry, colloidal science, and microfluidics. The model problem…
Under certain conditions we prove the existence of a steady-state transport regime for interacting mesoscopic systems coupled to reservoirs (leads). The partitioning and partition-free scenarios are treated on an equal footing. Our…
We study the full nonequilibirum steady state distribution $P_{\text{st}}\left(X\right)$ of the position $X$ of a damped particle confined in a harmonic trapping potential and experiencing active noise, whose correlation time $\tau_c$ is…
Discrete time crystals (DTCs) are emergent non-equilibrium phases of periodically driven many-body systems, with potential applications ranging from quantum computing to sensing and metrology. There has been significant recent interest in…
In this thesis concrete quantum systems are investigated in the framework of the environment induced decoherence. The focus is on the dynamics of highly nonclassical quantum states, the Wigner function of which are negative over some…
We discuss structure-preserving time discretization for nonlinear port-Hamiltonian systems with state-dependent mass matrix. Such systems occur, for instance, in the context of structure-preserving nonlinear model order reduction for…
Many complex structures and stochastic patterns emerge from simple kinetic rules and local interactions, and are governed by scale invariance properties in combination with effects of the global geometry. We consider systems that can be…
We consider an infinite system of coupled stochastic differential equations (SDE) describing dynamics of the following infinite particle system. Each partricle is characterised by its position $x\in \mathbb{R}^{d}$ and internal parameter…
We present a new numerical scheme to study systems of non-convex, irregular, and punctured particles in an efficient manner. We employ this method to analyze regular packings of odd-shaped bodies, not only from a nanoparticle but also both…
The study of systems with sustained energy uptake and dissipation at the scale of the constituent particles is an area of central interest in nonequilibrium statistical physics. Identifying such systems as a distinct category -- Active…
We study a new non-equilibrium dynamical model: a marked continuous contact model in $d$-dimensional space ($d \ge 3$). We prove that for certain values of rates (the critical regime) this system has the one-parameter family of invariant…
In this thesis, we develop multiscale models for particle simulations in population dynamics. These models are characterised by prescribing particle motion on two spatial scales: microscopic and macroscopic. At the microscopic level, each…
Dynamical heterogeneity (DH) in non-equilibrium systems is a topic of profound interest yet an open question. In a model system of constantly driven oppositely charged binary colloidal suspension, we explore DH in a model lane-forming…
We study a system of $N$ noninteracting particles on a line in the presence of a harmonic trap $U(x)=\mu \bigl[x-z(t)\bigr]^2/2$, where the trap center $z(t)$ undergoes a bounded stochastic modulation. We show that this stochastic…
In this paper we propose and study a hybrid discrete in continuous mathematical model of collective motion under alignment and chemotaxis effect. Starting from the paper by Di Costanzo et al (2015a), in which the Cucker-Smale model (Cucker…
We explore quantitative descriptors that herald when a many-particle system in $d$-dimensional Euclidean space $\mathbb{R}^d$ approaches a hyperuniform state as a function of the relevant control parameter. We establish quantitative…
A discrete time crystal (DTC) repeats itself with a rigid rhythm, mimicking a ticking clock set by the interplay between its internal structures and an external force. DTCs promise profound applications in precision time-keeping and other…
An analysis of discrete systems is important for understanding of various physical processes, such as excitations in crystal lattices and molecular chains, the light propagation in waveguide arrays, and the dynamics of Bose-condensate…