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The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…
Darwinian evolution requires (i) heritable records, (ii) repeatable copying with variation, and (iii) routine irreversibility. Categorical quantum mechanics (CQM) makes precise why ``copy'' and ``delete'' are not generic quantum operations:…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
Hamiltonian systems with functionally dependent constraints (irregular systems), for which the standard Dirac procedure is not directly applicable, are discussed. They are classified according to their behavior in the vicinity of the…
Let the adiabatic invariant of action variable in slow-fast Hamiltonian system with two degrees of freedom have two limiting values along the trajectories as time tends to infinity. The difference of two limits is exponentially small in…
We present a new variational framework for dissipative general relativistic fluid dynamics. The model extends the convective variational principle for multi-fluid systems to account for a range of dissipation channels. The key ingredients…
In this short note we perform canonical analysis of the theory invariant under restricted diffeomorphism so that the action contains kinetic term for determinant of metric. We find corresponding Hamiltonian and determine structure of…
The paper considers some class of dynamical systems that called density systems. For such systems the derivative of quadratic function depends on so-called density function. The density function is used to set the properties of phase space,…
Dynamical symmetries are of considerable importance in elucidating the complex behaviour of strongly interacting systems with many degrees of freedom. Paradigmatic examples are cooperative phenomena as they arise in phase transitions, where…
Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
We present a novel framework for quantizing constrained quantum systems in which the processes of quantization and constraint enforcement are performed simultaneously. The approach is based on an extension of the stationary action…
In quantum theory, observables with a continuous spectrum are known to be fundamentally different from those with a discrete and finite spectrum. While some fundamental tests and applications of quantum mechanics originally formulated for…
A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems…
We analize the relational quantum evolution of generally covariant systems in terms of Rovelli's evolving constants of motion and the generalized Heisenberg picture. In order to have a well defined evolution, and a consistent quantum…
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 discrete time linear constrained switching systems with additive disturbances, in which the switching may be on the system matrices, the disturbance sets, the state constraint sets or a combination of the above. In our general…
In studies of quantum squeezing, the emphasis is typically placed more on specific squeezed states and their evolution rather than on the dynamical operations that could simultaneously squeeze a broader range of quantum states, regardless…
We establish a link between metastability and a discrete time-crystalline phase in a periodically driven open quantum system. The mechanism we highlight requires neither the system to display any microscopic symmetry nor the presence of…
Taking the two-dimensional $\phi^4$ theory as an example, we numerically solve the deterministic equations of motion with random initial states. Short-time behavior of the solutions is systematically investigated. Assuming that the…