Related papers: Theoretical and Numerical Study of Self-Organizing…
We present a two-dimensional classical stochastic differential equation for a displacement field of a point particle in two dimensions and show that its components define real and imaginary parts of a complex field satisfying the…
The dissipation and decoherence (for example, the effects of noise in quantum computations), interaction with thermostat or in general with physical vacuum, measurement and many other complicated problems of open quantum systems are a…
The idea is advanced that self-organization in complex systems can be treated as decision making (as it is performed by humans) and, vice versa, decision making is nothing but a kind of self-organization in the decision maker nervous…
In contrast to the study of Langevin equations in a homogeneous environment in the literature, the study on Langevin equations in randomly-varying environments is relatively scarce. Almost all the existing works require random environments…
The problem of random motion of 1D quantum reactive harmonic oscillator (QRHO) is formulated in terms of a wave functional regarded as a complex probability process in an extended space. In the complex stochastic differential equation (SDE)…
This thesis covers various aspects of open systems in classical and quantum mechanics. In the first part, we deal with classical systems. The bath-of-oscillators formalism is used to describe an open system, and the phenomenological…
Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. However, finding solutions for these PDEs can be computationally expensive, making model-order reduction…
We study, by means of a topological approach, the forced oscillations of second order functional retarded differential equations subject to periodic perturbations. We consider a delay-type functional dependence involving a gamma probability…
Classical integrable Hamiltonian systems generated by elements of the Poisson commuting ring of spectral invariants on rational coadjoint orbits of the loop algebra $\wt{\gr{gl}}^{+*}(2,{\bf R})$ are integrated by separation of variables in…
We study the motion of independent particles in a dynamical random environment on the integer lattice. The environment has a product distribution. For the multidimensional case, we characterize the class of spatially ergodic invariant…
Formulated is a new systematic method for obtaining higher order corrections in numerical simulation of stochastic differential equations (SDEs), i.e., Langevin equations. Random walk step algorithms within a given order of finite $\Delta…
Systems whose time evolutions are entirely deterministic can nevertheless be studied probabilistically, i.e. in terms of the evolution of probability distributions rather than individual trajectories. This approach is central to the…
Many scientific problems focus on observed patterns of change or on how to design a system to achieve particular dynamics. Those problems often require fitting differential equation models to target trajectories. Fitting such models can be…
Spontaneous synchronization between coupled periodic systems occur in a wealth of classical physical setups. Here, we show theoretically that the phase of two distinct quantum harmonic oscillators spontaneously when they are strongly…
Despite broad interest in self-organizing systems, there are few quantitative, experimentally-applicable criteria for self-organization. The existing criteria all give counter-intuitive results for important cases. In this Letter, we…
A condition for the synchronizability of a pair of PDE systems, coupled through a finite set of variables, is commonly the existence of internal synchronization or internal coherence in each system separately. The condition was previously…
Modeling real-world problems with partial differential equations (PDEs) is a prominent topic in scientific machine learning. Classic solvers for this task continue to play a central role, e.g. to generate training data for deep learning…
A linear open quantum system consisting of a harmonic oscillator linearly coupled to an infinite set of independent harmonic oscillators is considered; these oscillators have a general spectral density function and are initially in a…
A novel probabilistic numerical method for quantifying the uncertainty induced by the time integration of ordinary differential equations (ODEs) is introduced. Departing from the classical strategy to randomize ODE solvers by adding a…
A complete solution to the long standing problem of basing Schroedinger quantum theory on standard stochastic theory is given. The solution covers all "single" particle three-dimensional Schroedinger theory linear or nonlinear and with any…