相关论文: Causal Wave Mechanics and the Advent of Complexity…
Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…
We study the coupled translational, electronic, and field dynamics of the combined system "a two-level atom + a single-mode quantized field + a standing-wave ideal cavity". We derive Hamilton -- Schr\"odinger equations for probability…
The spacing intervals of adjacent Riemann zeta zeros(non-trivial) exhibit fractal(irregular) fluctuations generic to dynamical systems in nature such as fluid flows, heart beat patterns, stock market price index, etc., and are associated…
Three existing interpretations of quantum mechanics, given by Heisenberg, Bohm and Madelung, are examined to describe dissipative quantum systems as well. It is found that the Madelung quantum hydrodynamics is the only correct approach. A…
A multidimensional chaos is generated by a special initial value problem for the non-autonomous impulsive differential equation. The existence of a chaotic attractor is shown, where density of periodic solutions, sensitivity of solutions…
We propose a formalism which defines chaos in both quantum and classical systems in an equivalent manner by means of \textit{adiabatic transformations}. The complexity of adiabatic transformations which preserve classical time-averaged…
Mathematical models are fundamental building blocks in the design of dynamical control systems. As control systems are becoming increasingly complex and networked, approaches for obtaining such models based on first principles reach their…
Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…
We analyse the unreduced, nonperturbative dynamics of an arbitrary many-body interaction process with the help of the generalised effective potential method and reveal the well-specified universal origin of change (emergence), time and…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
Quantum mechanics predicts correlation between spacelike separated events which is widely argued to violate the principle of Local Causality. By contrast, here we shall show that the Schr\"odinger equation with Born's statistical…
Discontinuous changes in the electronic structure upon infinitesimal changes to the Hamiltonian are demonstrated. Remarkably, these are revealed in one and two electron molecular systems if the realm of the nuclear charge is extended to be…
The concept of structural invariance previously introduced by the authors is used to argue that the connection between random matrix theory and quantum systems with a chaotic classical counterpart is in fact largely exact in the…
The dynamics of a nonequilibrium system can become complex because the system has many components (e.g., a human brain), because the system is strongly driven from equilibrium (e.g., large Reynolds-number flows), or because the system…
A direct classical analog of the quantum dynamics of intrinsic decoherence in Hamiltonian systems, characterized by the time dependence of the linear entropy of the reduced density operator, is introduced. The similarities and differences…
It might be anticipated that there is statistical universality in the long-time classical dynamics of chaotic systems, corresponding to the universal correspondence of their quantum spectral statistics with random matrix models. We argue…
The incoherent dynamical properties of open quantum systems are generically attributed to an ongoing correlation between the system and its environment. Here, we propose a novel way to assess the nature of these system-environment…
Self consistent quantum approaches are used to study the instabilities of finite nuclear systems. The frequencies of multipole density fluctuations are determined as a function of dilution and temperature, for several isotopes. The spinodal…
A cell dynamical system model for deterministic chaos enables precise quantification of the round-off error growth,i.e., deterministic chaos in digital computer realizations of mathematical models of continuum dynamical systems. The model…
We develop a master equation formalism to describe the evolution of the average density matrix of a closed quantum system driven by a stochastic Hamiltonian. The average over random processes generally results in decoherence effects in…