相关论文: On quantum Lyapunov exponents

A general formulation of noncommutative or quantum derivatives for operators in a Banach space is given on the basis of the Leibniz rule, irrespective of their explicit representations such as the G\^ateaux derivative or commutators. This…

In this paper we make a detailed numerical comparison between three algorithms for the computation of the full Lyapunov spectrum as well as the associated eigen-vectors of general dynamical systems. They are : (a) the standard method, (b) a…

The Lyapunov spectrum corresponding to a periodic orbit for a two dimensional many particle system with hard core interactions is discussed. Noting that the matrix to describe the tangent space dynamics has the block cyclic structure, the…

Lyapunov's theorem is a classical result in convex analysis, concerning the convexity of the range of nonatomic measures. Given a family of integrable vector functions on a compact set, this theorem allows to prove the equivalence between…

We present straightforward proofs of estimates used in the adiabatic approximation. The gap dependence is analyzed explicitly. We apply the result to interpolating Hamiltonians of interest in quantum computing.

We establish the ultimate limits that quantum theory imposes on the accuracy attainable in optical ellipsometry. We show that the standard quantum limit, as usual reached when the incident light is in a coherent state, can be surpassed with…

We prove that the Lyapunov exponent of quasi-periodic cocyles with singularities behaves continuously over the analytic category. We thereby generalize earlier results, where singularities were either excluded completely or constrained by…

We show that the quantum angle measurement for x-polarized photon number states results in an angle which will never correspond to the y-axis for an odd number of photons; yet for an even number of photons it always can. The analogy of this…

We consider a class of linear differential operators acting on vector-valued function spaces with general coupled boundary conditions. Unlike in the more usual case of so-called quantum graphs, the boundary conditions can be nonlinear.…

Lyapunov exponents can be difficult to determine from experimental data. In particular, when using embedding theory to build chaotic attractors in a reconstruction space, extra "spurious" Lyapunov exponents arise that are not Lyapunov…

Stability analysis plays a crucial role in studying the behavior of dynamical systems with theoretical and engineering applications. Among various kinds of stability, the stability of equilibrium points is of the greatest importance which…

A Lyapunov-based control design for natural trajectory-tracking problems is analyzed for quantum states where the analysis in the generic case is not applicable. Using dynamical systems tools we show almost global asymptotic stability for…

We prove two inequalities between the Lyapunov exponents of a diffeomorphism and its local recurrence properties. We give examples showing that each of the inequalities is optimal.

We define new quantizations of the Heisenberg group by introducing new quantizations in the universal enveloping algebra of its Lie algebra. Matrix coefficients of the Stone--von Neumann representation are preserved by these new…

Transition to a nonrelativistic Pauli equation in Riemann space of constant positive curvature for a Dirac particle in presence of the Coulomb field is performed in the system of radial equations, exact solutions are constructed in terms of…

The general decomposition theory of exponential operators is briefly reviewed. A general scheme to construct independent determining equations for the relevant decomposition parameters is proposed using Lyndon words. Explicit formulas of…

Recent developments in quantum annealing techniques have been indicating potential advantage of quantum annealing for solving NP-hard optimization problems. In this article we briefly indicate and discuss the beneficial features of quantum…

In this paper we prove a Lyapunov type inequality for quasilinear problems with indefinite weights. We show that the first eigenvalue is bounded below in terms of the integral of the weight, instead of the integral of its positive part. We…

We revise the problem of the quantization of relativistic particle, presenting a modified consistent canonical scheme, which allows one not only to include arbitrary backgrounds in the consideration but to get in course of the quantization…

We describe rigorous quantum measurement theory in the Heisenberg picture by applying operator deformation techniques previously used in noncommutative quantum field theory. This enables the conventional observables (represented by…