We propose a procedure to generalize the Husimi distribution to systems with continuous spectrum. We start examining a pioneering work, by Gazeau and Klauder, where the concept of coherent states for systems with disc...We propose a procedure to generalize the Husimi distribution to systems with continuous spectrum. We start examining a pioneering work, by Gazeau and Klauder, where the concept of coherent states for systems with discrete spectrum was extended to systems with continuous one. In the present article, we see the Husimi distribution as a representation of the density operator in terms of a basis of coherent states. There are other ways to obtain it, but we do not consider here. We specially discuss the problem of the continuous harmonic oscillator.展开更多
Recently, the robust output regulation problem for continuous-time linear systems with both input and communication time-delays was studied. This paper will further present the results on the robust output regulation ...Recently, the robust output regulation problem for continuous-time linear systems with both input and communication time-delays was studied. This paper will further present the results on the robust output regulation problem for discrete-time linear systems with input and communication delays. The motivation of this paper comes from two aspects. First, it is known that the solvability of the output regulation problem for linear systems is dictated by two matrix equations. While, for delay-free systems, these two matrix equations are same for both continuous-time systems and discretetime systems, they are different for continuous-time time-delay systems and discrete-time time-delay systems. Second, the stabilization methods for continuous-time time-delay systems and discrete-time time-delay systems are also somehow different. Thus, an independent treatment of the robust output regulation problem for discrete-time time-delay systems will be useful and necessary.展开更多
Time reversal in quantum or classical systems described by an Hermitian Hamiltonian is a physically allowed process, which requires in principle inverting the sign of the Hamiltonian. Here we consider the problem of t...Time reversal in quantum or classical systems described by an Hermitian Hamiltonian is a physically allowed process, which requires in principle inverting the sign of the Hamiltonian. Here we consider the problem of time reversal of a subsystem of discrete states coupled to an external environment characterized by a continuum of states, into which they generally decay. It is shown that, by flipping the discrete-continuum coupling from an Hermitian to a non-Hermitian interaction, thus resulting in a non unitary dynamics, time reversal of the subsystem of discrete states can be achieved, while the continuum of states is not reversed. Exact time reversal requires frequency degeneracy of the discrete states,or large frequency mismatch among the discrete states as compared to the strength of indirect coupling mediated by the continuum. Interestingly, periodic and frequent switch of the discrete-continuum coupling results in a frozen dynamics of the subsystem of discrete states.展开更多
基金partial financial support by FONDECYT, under Grant No. 1080487
文摘We propose a procedure to generalize the Husimi distribution to systems with continuous spectrum. We start examining a pioneering work, by Gazeau and Klauder, where the concept of coherent states for systems with discrete spectrum was extended to systems with continuous one. In the present article, we see the Husimi distribution as a representation of the density operator in terms of a basis of coherent states. There are other ways to obtain it, but we do not consider here. We specially discuss the problem of the continuous harmonic oscillator.
基金supported by the Research Grants Council of the Hong Kong Special Administration Region under Grant No.412813
文摘Recently, the robust output regulation problem for continuous-time linear systems with both input and communication time-delays was studied. This paper will further present the results on the robust output regulation problem for discrete-time linear systems with input and communication delays. The motivation of this paper comes from two aspects. First, it is known that the solvability of the output regulation problem for linear systems is dictated by two matrix equations. While, for delay-free systems, these two matrix equations are same for both continuous-time systems and discretetime systems, they are different for continuous-time time-delay systems and discrete-time time-delay systems. Second, the stabilization methods for continuous-time time-delay systems and discrete-time time-delay systems are also somehow different. Thus, an independent treatment of the robust output regulation problem for discrete-time time-delay systems will be useful and necessary.
文摘Time reversal in quantum or classical systems described by an Hermitian Hamiltonian is a physically allowed process, which requires in principle inverting the sign of the Hamiltonian. Here we consider the problem of time reversal of a subsystem of discrete states coupled to an external environment characterized by a continuum of states, into which they generally decay. It is shown that, by flipping the discrete-continuum coupling from an Hermitian to a non-Hermitian interaction, thus resulting in a non unitary dynamics, time reversal of the subsystem of discrete states can be achieved, while the continuum of states is not reversed. Exact time reversal requires frequency degeneracy of the discrete states,or large frequency mismatch among the discrete states as compared to the strength of indirect coupling mediated by the continuum. Interestingly, periodic and frequent switch of the discrete-continuum coupling results in a frozen dynamics of the subsystem of discrete states.
