Related papers: Entwined Pairs and Schroedinger 's Equation
We consider a general class of discrete unitary dynamical models on the lattice. We show that generically such models give rise to a wavefunction satisfying a Schroedinger equation in the continuum limit, in any number of dimensions. There…
The action principle is frequently used to derive the classical equations of motion. The action may also be used to associate group elements with curves in the space-time manifold, similar to the gauge transformations. The action principle…
The coupled discrete linear and Kerr nonlinear Schrodinger equations with gain and loss describing transport on dimers with parity-time PT symmetric potentials are considered. The model is relevant among others to experiments in optical…
Schroedinger's equation with scalar and vector potentials is shown to describe "nothing but" hopping of a quantum particle on a lattice; any spatial variation of the hopping amplitudes acts like an external electric and/or magnetic field.…
We review the closed time path formalism of Schwinger using a path integral approach. We apply this formalism to the study of pair production from strong external fields as well as the time evolution of a nonequilibrium chiral phase…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
The Schr\"odinger--Newton (SN) equation provides a semiclassical framework for the evolution of self-gravitating of massive quantum systems. We propose a two-body Schr\"odinger--Newton model that separates local nonlinear self-localization…
We propose a simple mathematical model that describes a pairing-induced motion of active and passive particles in a two-dimensional system, which is motivated by our previous paper [Ishikawa et al., Phys. Rev. E \textbf{106} (2022) 024604].…
Equations of motion for single particle under two proper time model and three proper time model have been proposed and analyzed. The motions of particle are derived from pure classical method but they exhibit the same properties of quantum…
We present a short and novel derivation of the Schwinger mechanism for particle pair production in $1+1$ dimensional de Sitter and Anti de Sitter spacetimes. We work directly in the flat embedding space and derive the pair production rates…
We consider the particle-antiparticle pairs produced by both a strong electric field and de Sitter curvature. We investigate in 1 + 1 D the backreaction of the pairs on the electromagnetic field. To do so we describe the canonical…
A general class of discrete unitary models are described whose behavior in the continuum limit corresponds to a many-body Schrodinger equation. On a quantum computer, these models could be used to simulate quantum many-body systems with an…
A variational technique is established to deal with the Schrodinger equation with parity-time(PT) symmetric Gaussian complex potential. The method is extended to the linear and self-focusing and defocusing nonlinear cases. Some unusual…
From the invariance properties of the Schrodinger equation and the isotropy of space we show that a generic (non-relativistic) quantum system is endowed with an ``external'' motion, which can be interpreted as the motion of the centre of…
We apply the many-particle Schr\"{o}dinger-Newton equation, which describes the co-evolution of an many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the…
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…
A source term in the quantum Boltzmann equation, which accounts for the spontaneous creation of $e^+e^-$-pairs in external electric fields, is derived from first principles and evaluated numerically. Careful analysis of time scales reveals…
In this work, we construct time-dependent potentials for the Schr\"odinger equation via supersymmetric quantum mechanics. The generated potentials have a quantum state with the property that after a particular threshold time $t_F$, when the…
This paper establishes new estimates for linear Schroedinger equations in R^3 with time-dependent potentials. Some of the results are new even in the time-independent case and all are shown to hold for potentials in scaling-critical,…
Time-dependent Schroedinger equation represents the basis of any quantum-theoretical approach. The question concerning its proper content in comparison to the classical physics has not been, however, fully answered until now. It will be…