Related papers: Almost periodic functions on the quantum time scal…
We consider existence and stability of an almost periodic solution of the quasilinear system of differential equations with piecewise constant argument of generalized type. The associated linear homogeneous system satisfies exponential…
The paper concerns algebras of almost periodic pseudodifferential operators on $\mathbb R^d$ with symbols in H\"ormander classes. We study three representations of such algebras, one of which was introduced by Coburn, Moyer and Singer and…
Summary: A system of autonomous ordinary differential equations depending on a small parameter is considered such that the unperturbed system has an invariant manifold of periodic solutions that is not normally hyperbolic but is normally…
We prove the existence of quasi-periodic solutions for Schroedinger equations with a multiplicative potential on T^d, d \geq 1, merely differentiable nonlinearities, and tangential frequencies constrained along a pre-assigned direction. The…
We consider the temporal periodic solutions to general nonhomogeneous quasilinear hyperbolic equations with a kind of weak diagonal dominant structure. Under the temporal periodic boundary conditions, the existence, stability and uniqueness…
We consider a class of ordinary differential equations describing one-dimensional systems with a quasi-periodic forcing term and in the presence of large damping. We discuss the conditions to be assumed on the mechanical force and the…
In this paper, we propose a method of fundamental solutions for the problem of two-dimensional potential flow in a doubly-periodic domain. The solution involves a doubly-periodic function, to which it is difficult to give an approximation…
Quantum process characterization is a fundamental task in quantum information processing, yet conventional methods, such as quantum process tomography, require prohibitive resources and lack scalability. Here, we introduce an efficient…
We review the current status of one dimensional periodic potentials and also present several new results. It is shown that using the formalism of supersymmetric quantum mechanics, one can considerably enlarge the limited class of…
A new method for finding electronic structure and wavefunctions of electrons in quasiperiodic potential is introduced. To obtain results it uses slightly modified Schrodinger equation in spaces of dimensionality higher than physical space.…
In this paper, under Acquistpace-Terreni conditions, we make extensive use of interpolation spaces and exponential dichotomy techniques to obtain the existence of weighted pseudo almost periodic solutions to some classes of nonautonomous…
We construct local solutions to the Benjamin-Ono equation for quasi-periodic initial data. The solution is unique among limits of smooth solutions and depends continuously on the data. Our result applies to a richer class of quasi-periodic…
On the basis of extensive numerical studies it is argued that there are strong analogies between the probabilistic behavior of quantum systems defined by Hermitian Hamiltonians and the deterministic behavior of classical mechanical systems…
Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g. in computation, communication and control. Fully random transformations require exponential time for either classical or quantum…
We prove that any given function can be smoothly approximated by functions lying in the kernel of a linear operator involving at least one fractional component. The setting in which we work is very general, since it takes into account…
Perturbation theory, the quasiclassical approximation and the quantum surface of section method are combined for the first time. This gives a new solution of the the long standing problem of quantizing the resonances generically appearing…
The paper studies semi-almost periodic holomorphic functions on a polydisk which have, in a sense, the weakest possible discontinuities on the boundary torus. The basic result used in the proofs is an extension of the classical Bohr…
Artificial neural networks are becoming an integral part of digital solutions to complex problems. However, employing neural networks on quantum processors faces challenges related to the implementation of non-linear functions using quantum…
We describe a simple quantum algorithm to simulate time-dependent Hamiltonian, extending the methodology of quantum signal processing. The framework achieves optimal scaling up to some factor with respect to other parameters, and nearly…
We study discrete Schroedinger operators with analytic potentials. In particular, we are interested in the connection between the absolutely continuous spectrum in the almost periodic case and the spectra in the periodic case. We prove a…