相关论文: Progressive diagonalization and applications
The question of controllability is investigated for a quantum control system in which the Hamiltonian operator components carry explicit time dependence which is not under the control of an external agent. We consider the general situation…
The dynamical behavior of interacting systems plays a fundamental role for determining quantum correlations, such as entanglement. In this Letter, we describe temporal quantum effects of the inseparable evolution of composite quantum states…
We prove regularity estimates for time derivatives of a large class of nonlinear parabolic partial differential systems. This includes the instationary (symmetric) p-Laplace system and models for non Newtonien fluids of powerlaw or Carreau…
In the present paper, a discrete differential calculus is introduced and used to describe dynamical systems over arbitrary graphs. The discretization of space and time allows the derivation of Heisenberg-like uncertainty inequalities and of…
This paper concerns state constrained optimal control problems, in which the dynamic constraint takes the form of a differential inclusion. If the differential inclusion does not depend on time, then the Hamiltonian, evaluated along the…
The evolution problem for a quantum particle confined in a 1D box and interacting with one fixed point through a time dependent point interaction is considered. Under suitable assumptions of regularity for the time profile of the…
Diagonalizing a Hamiltonian, which is essential for simulating its long-time dynamics, is a key primitive in quantum computing and has been proven to yield a quantum advantage for several specific families of Hamiltonians. Yet, despite its…
A quantum hamiltonian which evolves the gravitational field according to time as measured by constant surfaces of a scalar field is defined through a regularization procedure based on the loop representation, and is shown to be finite and…
We propose a new wiew on the structure of quantum mechanics and postulate a q-deformed algebra of observables. We find equations of motion for this system, which guarantee a unitary time developement. We solve this equations for simple…
We present a diagonalization method for generic matrix valued Hamiltonians based on a formal expansion in power of $\hbar $. Considering $\hbar $ as a running parameter, a differential equation connecting two diagonalization processes for…
We implement the so-called Weyl-Heisenberg covariant integral quantization in the case of a classical system constrained by a bounded or semi-bounded geometry. The procedure, which is free of the ordering problem of operators, is…
Several important dynamical systems are in $\mathbb{R}^2$, defined by the pair of differential equations $(x',y')=(f(x,y),g(x,y))$. A question of fundamental importance is how such systems might behave quantum mechanically. In developing…
We revisit the perturbative theory of infinite dimensional integrable systems developed by P. Deift and X. Zhou \cite{DZ-2}, aiming to provide new and simpler proofs of some key $L^\infty$ bounds and $L^p$ \emph{\textit{a priori}}…
Dynamics generated from Hamiltonians enjoy potential pathways to quantisation, but standard Hamiltonians are only capable of generating conservative forces. Classes of Hamiltonians have been proposed in Berry et al. capable of generating…
We consider a relativistic extended object described by a reparametrization invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the…
Time evolution of quantum systems is accelerated by the fast-forward scaling. We reformulate the method to study systems in a finite-dimensional Hilbert space. For several simple systems, we explicitly construct the acceleration potential.…
We discuss the necessity of using non-standard boson operators for diagonalizing quadratic bosonic forms which are not positive definite and its convenience for describing the temporal evolution of the system. Such operators correspond to…
The qualitatively new concept of dynamic complexity in quantum mechanics is based on a new paradigm appearing within a nonperturbational analysis of the Schroedinger equation for a generic Hamiltonian system. The unreduced analysis…
We study the action of time dependent canonical and coordinate transformations in phase space quantum mechanics. We extend the covariant formulation of the theory by providing a formalism that is fully invariant under both standard and time…
We consider quantum dynamics of systems with fast spatial modulation of the Hamiltonian. Employing the formalism of supersymmetric quantum mechanics and decoupling fast and slow spatial oscillations we demonstrate that the effective…