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A series of stationary principles are developed for dynamical systems by formulating the concept of mixed convolved action, which is written in terms of mixed variables, using temporal convolutions and fractional derivatives. Dynamical…
We study the connection between dissipation and reality in macroscopic quantum systems. We present the following scenario; if we consider the dynamics of a `partial' wave function, the dissipation is represented as a nonlocal term and it…
This paper shows that the celebrated Embedding Theorem of Takens is a particular case of a much more general statement according to which, randomly generated linear state-space representations of generic observations of an invertible…
Our model of shaken sand, presented in earlier work, has been extended to include a more realistic `glassy' state, i.e., when the sandbox is shaken at very low intensities of vibration. We revisit some of our earlier results, and compare…
Recently we pointed out the so-called Local Time Scheme as a novel approach to quantum foundations that solves the preferred pointer-basis problem. In this paper we introduce and analyze in depth a rather non-standard dynamical map that is…
In this paper we examine the stability of scalar perturbations in nonsingular models which emerge from an interacting vacuum component. The analysis developed in this paper relies on two phenomenological choices for the energy exchange…
A novel strategy to handle divergences typical of perturbative calculations is implemented for the Nambu--Jona-Lasinio model and its phenomenological consequences investigated. The central idea of the method is to avoid the critical step…
Quantum mechanical phase space path integrals are re-examined with regard to the physical interpretation of the phase space variables involved. It is demonstrated that the traditional phase space path integral implies a meaning for the…
The abundance of process operating data in modern industries, along with the rapid advancement of learning techniques, has led to a paradigm shift towards data-centric analysis and control. However, integrating machine learning with control…
The dynamics of distributed sources is described by nonlinear partial differential equations. Lagrangian analytical solutions of these (and associated) equations are obtained and discussed in the context of Lagrangian modeling - from the…
A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…
The Buridan's ass paradox is characterized by perpetual indecision between two states, which are never attained. When this problem is formulated as a dynamical system, indecision is modeled by a discrete-state Markov process determined by…
Well-known (spinless) fermionic qubits may need more subtle consideration in comparison with usual (spinful) fermions. Taking into account a model with local fermionic modes, formally only the 'occupied' states |1> could be relevant for…
Hidden-variable models aim to reproduce the results of quantum theory and to satisfy our classical intuition. Their refutation is usually based on deriving predictions that are different from those of quantum mechanics. Here instead we…
Dynamic degrees of freedom and internal variables are treated in a uniform way. The unification is achieved by means of the introduction of a dual internal variable. This duality provides the corresponding evolution equations depending on…
This paper derives a density matrix of the steady-state statistical mechanics compatible with the steady-state thermodynamics proposed by Oono and Paniconi [Prog. Theor. Phys. Suppl. {\bf 130}, 29 (1998)]. To this end, we adopt three…
The statistical properties of the Salerno model is investigated. In particular, a comparison between the coherent and partially coherent wave modes is made for the case of a random phased wave packet. It is found that the random phased…
The quantum master equation is a widespread approach to describing open quantum system dynamics. In this approach, the effect of the environment on the system evolution is entirely captured by the dynamical generator, providing a compact…
We describe coherent states and associated generalized Grassmann variables for a system of $m$ independent $q$-boson modes. A resolution of unity in terms of generalized Berezin integrals leads to generalized Grassmann symbolic calculus.…
The internal phase dynamics of a quantum system is revealed in details. Theoretical and experimental evidences of existence of a causal relation of the phase of the wave function with the dynamics of the quantum system are presented…