Related papers: Integrable time-dependent central potentials
The center of mass motion of trapped ions and neutral atoms is suitable for approximation by a time-dependent driven quantum harmonic oscillator whose frequency and driving strength may be controlled with high precision. We show the time…
A standard approach to analyzing tunneling processes in various physical contexts is to use instanton or imaginary time path techniques. For systems in which the tunneling takes place in a time dependent setting, the standard methods are…
The cause for first and second order electromagnetic equivalency of inertial systems is approached from a different point of view than that of special relativity. While special relativity applies dilatation to time and contraction to space…
This is a survey of known results on estimating the principal Lyapunov exponent of a time-dependent linear differential equation possessing some monotonicity properties. Equations considered are mainly strongly cooperative systems of…
Exploiting the residual gauge freedom in the formulation of constrained KP hierarchy a number of new integrable systems are derived including hierarchies of Kundu-Eckhaus equation and higher order nonlinear extensions of Yajima-Oikawa and…
We consider the oscillatory integrals with parameter-dependent phases. We decompose the integrals into a leading term and a remainder term. Instead of the pointwise estimate, we use some $L^p$-estimate for the remainder term and get various…
New exact solvable elliptic potentials with free constants for the spectral problems of the third order are found. A time dependence of such potentials gives their isospectral deformations and solutions of nonlinear integrable equations.
An approach to infinite dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented. It provides a truly infinite dimensional construction of integrals as linear…
Recently many new classes of integrable systems in n dimensions occurring in classical and quantum mechanics have been shown to admit a functionally independent set of 2n-1 symmetries polynomial in the canonical momenta, so that they are in…
Time-integration for lumped parameter systems obeying implicit Bingham-Kelvin constitutive models is studied. The governing system of equations describing the lumped parameter system is a non-linear differential-algebraic equation and needs…
A number of approaches to the problem of defining arrival and dwell time probabilities in quantum theory make use of idealised models of clocks. An interesting question is the extent to which the probabilities obtained in this way are…
Several completely integrable, indeed solvable, Hamiltonian many-body problems are exhibited, characterized by Newtonian equations of motion ("acceleration equal force"), with linear and cubic forces, in N-dimensional space (N being an…
We study two-dimensional classically integrable field theory with independent boundary condition on each end, and obtain three possible generating functions for integrals of motion when this model is an ultralocal one. Classically…
We derive some Quantum Central Limit Theorems for expectation values of macroscopically coarse-grained observables, which are functions of coarse-grained hermitean operators. Thanks to the hermicity constraints, we obtain positive-definite…
In this work we establish some new estimates for layer potentials of the acoustic wave equation in the time domain, and for their associated retarded integral operators. These estimates are proven using time-domain estimates based on theory…
The time-dependent structure of the Lyapunov vectors corresponding to the steps of Lyapunov spectra and their basis set representation are discussed for a quasi-one-dimensional many-hard-disk systems. Time-oscillating behavior is observed…
This paper deals with a parabolic partial differential equation that includes a non-linear nonlocal in time term. This term is the product of a so-called interaction potential and the solution of the problem. The interaction potential…
We solve the non-stationary Schrodinger equation for several time-dependent Hamiltonians, such as the BCS Hamiltonian with an interaction strength inversely proportional to time, periodically driven BCS and linearly driven inhomogeneous…
We consider classical N-particle system with arbitrary central pair potential. Mechanical equilibrium condition in spherically-symmetric case leads to a nonlinear integro-differential equation for concentration n(r). For special state…
The correspondence between classical and quantum invariants is established. The Ermakov Lewis quantum invariant of the time dependent harmonic oscillator is translated from the coordinate and momentum operators into amplitude and phase…