相关论文: Good Lie Brackets for classical and quantum harmon…

Classical Kleinian groups are discrete subgroups of isometries of H n. The well-known theory of Kleinian groups starts with the definition of their associated limit set in the boundary of H n , and includes the geometric properties of the…

In this paper, we study, in the semiclassical sense, the global approximate controllability in small time of the quantum density and quantum momentum of the 1-D semiclassical cubic Schr\"odinger equation with two controls between two states…

We investigate symmetry reduction of optimal control problems for left-invariant control systems on Lie groups, with partial symmetry breaking cost functions. Our approach emphasizes the role of variational principles and considers a…

We study quantum systems with even numbers N of levels that are completely state-controlled by unitary transformations generated by Lie algebras isomorphic to sp(N) of dimension N(N+1)/2. These Lie algebras are smaller than the respective…

We show that under suitable assumptions, we have a one-to-one correspondence between classical groups and free quantum groups, in the compact orthogonal case. We classify the groups under correspondence, with the result that there are…

In this paper we use the $Z-$decomposition as a tool to find locally symmetric left invariant Riemannian metrics on some Lie groups. For this purpose, we need to compute the spectrum of the curvature operator. Since the study of this…

An exact approach for the factorization of the relativistic linear singular oscillator is proposed. This model is expressed by the finite-difference Schr\"odinger-like equation. We have found finite-difference raising and lowering…

All possible Lie bialgebra structures on the harmonic oscillator algebra are explicitly derived and it is shown that all of them are of the coboundary type. A non-standard quantum oscillator is introduced as a quantization of a triangular…

Motivated by the recent work of Gimperlein and Goffeng on Calder\'on's commutator on compact Heisenberg type manifolds and the related weak Schatten class estimates, we establish the characterisation of $L^p$ boundedness for Calderon's…

In control theory, understanding the observability property of a system is crucial for effectively managing and controlling dynamical systems. This property empowers us to deduce the internal state of a system from its outputs over time,…

Quantum simulations of lattice gauge theories for the foreseeable future will be hampered by limited resources. The historical success of improved lattice actions in classical simulations strongly suggests that Hamiltonians with improved…

In quantum mechanics courses, students often solve the Schr\"odinger equation for the harmonic oscillator with time-independent parameters. However, time-dependent quantum harmonic oscillators are relevant in modeling several problems as,…

We consider the Lie group PSL(2) (the group of orientation preserving isometries of the hyperbolic plane) and a left-invariant Riemannian metric on this group with two equal eigenvalues that correspond to space-like eigenvectors (with…

We solve the Kato square root problem for bounded measurable perturbations of subelliptic operators on connected Lie groups. The subelliptic operators are divergence form operators with complex bounded coefficients, which may have lower…

The problem of identifying the dynamical Lie algebras of finite-level quantum systems subject to external control is considered, with special emphasis on systems that are not completely controllable. In particular, it is shown that the…

We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm…

In classical mechanics, the system of two coupled harmonic oscillators is shown to possess the symmetry of the Lorentz group O(3,3) applicable to a six-dimensional space consisting of three space-like and three time-like coordinates, or…

During recent years, exact solutions of position-dependent mass Schr\"odinger equations have inspired intense research activities, based on the use of point canonical transformations, Lie algebraic methods or supersymmetric quantum…

In this work, we use the classical moment method to find a practical and simple criterion to determine if a family of linearized Dispersive equations on a periodic domain is exactly controllable and exponentially stabilizable with any given…

This paper is the sequel to [HP1] to study the deformed structures and representations of two-parameter quantum groups $U_{r,s}(\mathfrak{g})$ associated to the finite dimensional simple Lie algebras $\mg$. An equivalence of the braided…