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A method of quantizing parametrized systems is developed that is based on a kind of ``gauge invariant'' quantities---the so-called perennials (a perennial must also be an ``integral of motion''). The problem of time in its particular form…
Quantum coherence inherently affects the dynamics and the performances of a quantum machine. Coherent control can, at least in principle, enhance the work extraction and boost the velocity of evolution in an open quantum system. Using…
It is well-understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs…
How to practically maintain the frequency stability of large-scale power systems by a decentralized way is a simple but non-trivial question. In other words, is it possible to design any local controller without understanding the other…
Turing patterns on unbounded domains have been widely studied in systems of reaction-diffusion equations. However, up to now, they have not been studied for systems of conservation laws. Here, we (i) derive conditions for Turing instability…
We develop a renormalization group for weak Harris-marginal disorder in otherwise strongly interacting quantum critical theories, focusing on systems which have emergent conformal invariance. Using conformal perturbation theory, we argue…
The Yakubovich Frequency Theorem, in its periodic version and in its general nonautonomous extension, establishes conditions which are equivalent to the global solvability of a minimization problem of infinite horizon type, given by the…
We study the robustness of the evolution of a quantum system against small uncontrolled variations in parameters in the Hamiltonian. We show that the fidelity susceptibility, which quantifies the perturbative error to leading order, can be…
We study the long-term average evolution of the random ensemble along integrable Hamiltonian systems with time $T$-periodic transitions. More precisely, for any observable $G$, it is demonstrated that the ensemble under $G$ in long time…
We explain a method, inspired by control theory model reduction and interpolation theory, that rigorously establishes the types of coarse graining that are appropriate for systems with quadratic, generalized Hamiltonians. For such systems,…
This paper presents a technique for designing output feedback controllers for constrained linear parameter-varying systems that are subject to persistent disturbances. Specifically, we develop an incremental parameter-varying output…
This paper addresses the problem of averaged controllability for the time-fractional Schrodinger equation, where the quantum diffusivity parameter is a random variable with a general probability distribution. First, by exploiting the…
Stability and stabilization of linear port-Hamiltonian systems on infinite-dimensional spaces are investigated. This class is general enough to include models of beams and waves as well as transport and Schr\"odinger equations with boundary…
We explore the notion of discrete spectrum and its various characterizations for ergodic measure-preserving actions of an amenable group on a compact metric space. We introduce a notion of 'weak-tameness', which is a measure-theoretic…
The symmetry and resonance properties of the Fermi Pasta Ulam chain with periodic boundary conditions are exploited to construct a near-identity transformation bringing this Hamiltonian system into a particularly simple form. This…
We address the question as to why, in the semiclassical limit, classically chaotic systems generically exhibit universal quantum spectral statistics coincident with those of Random Matrix Theory. To do so, we use a semiclassical resummation…
We consider the application of the theory of vibrational control to H_infinity-problems. We study the possibility of introduction of high-frequency parametric vibrations in order to decrease the minimal attainable value of the…
We introduce an arbitrary order, stabilized finite element method for solving a unique continuation problem subject to the time-harmonic elastic wave equation with variable coefficients. Based on conditional stability estimates we prove…
We present methods that can provide an exponential savings in the resources required to perform dynamic parameter estimation using quantum systems. The key idea is to merge classical compressive sensing techniques with quantum control…
We consider a class of a priori stable quasi-integrable analytic Hamiltonian systems and study the regularity of low-dimensional hyperbolic invariant tori as functions of the perturbation parameter. We show that, under natural nonresonance…