Related papers: On non-linear Schr\"{o}dinger equations for open q…
Recent years have seen a fascinating pollination of ideas from quantum theories to elastodynamics---a theory that phenomenologically describes the time-dependent macroscopic response of materials. Here, we open route to transfer additional…
This paper elucidates the dual structure of the Schr\"{o}dinger dynamics in two correlated stages: (1) We first derive the real-valued Schr\"{o}dinger equation from scratch without referring to classical mechanics, wave mechanics, nor…
A nonperturbative procedure of solving the time-dependent Schr\"odinger equation, called the multi-projection approach or phase dynamics of quantum mechanics, is derived and illustrated. In addition to introducing a method with that…
The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions or critical dynamics of classical spin systems can be written as a Schr\"odinger equation in which the wave function is the probability…
We generalize the classical theory of Brownian motion so as to reckon with non-Markovian effects on both Klein-Kramers and Smoluchowski equations. For a free particle and a harmonic oscillator, it is shown that such non-Markovian effects…
A new nonlinear Schroedinger equation is obtained explicitly from the fractal Brownian motion of a massive particle with a complex-valued diffusion constant. Real-valued energy (momentum) plane wave and soliton solutions are found in the…
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…
We study a 1D nonlinear Schr{\"o}dinger equation appearing in the description of a particle inside an atomic nucleus. For various nonlinearities, the ground states are discussed and given in explicit form. Their stability is studied…
Recent developments in quantum physics make heavy use of so-called "quantum trajectories." Mathematically, this theory gives rise to "stochastic Schr\"odinger equations", that is, perturbation of Schr\"odinger-type equations under the form…
Understanding the behaviour of a quantum system coupled to its environment is of fundamental interest in the general field of quantum technologies. It also has important repercussions on foundational problems in physics, such as the process…
In this paper we present an exact Grassmann stochastic Schr\"{o}dinger equation for the dynamics of an open fermionic quantum system coupled to a reservoir consisting of a finite or infinite number of fermions. We use this stochastic…
We investigate the previously unexplored quantum dynamics of non-relativistic, spinless particles propagating in curved spaces with torsion. Our findings demonstrate that while torsion has been predominantly associated with spin, it can…
Recent research on the fundamentals of statistical mechanics has led to an interesting discovery [1-3]: With locally nonchaotic barriers, as Boltzmann's H-theorem is inapplicable, there exist nontrivial non-thermodynamic systems that can…
This paper reviews various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mechanics. We adopt a new point of view which has emerged progressively in recent years, and which takes…
Quantum mechanics is one of the basic theories of modern physics. Here, the famous Schr\"odinger equation and the differential operators representing mechanical quantities in quantum mechanics are derived, just based on the principle that…
It is shown that the generalized discrete nonlinear Schr\"odinger equation can be reduced in a small amplitude approximation to the KdV, mKdV, KdV(2) or the fifth-order KdV equations, depending on values of the parameters. In dispersionless…
Thermodynamic uncertainty principles make up one of the few rare anchors in the largely uncharted waters of nonequilibrium systems, the fluctuation theorems being the more familiar. In this work we aim to trace the uncertainties of…
It is shown that non-Markovian master equations for an open system which are local in time can be unravelled through a piecewise deterministic quantum jump process in its Hilbert space. We derive a stochastic Schr\"odinger equation that…
A new non-perturbative method of solution of the nonlinear Heisenberg equations in the finite-dimensional subspace is illustrated. The method, being a counterpart of the traditional Schrodinger picture method, is based on a finite operator…
From the mathematical side, nonlinear Schr\"odinger equations are usually investigated via variational methods, that cease to work in higher dimensions. This thesis tries to overcome this problem by focusing on spherically symmetric…