相关论文: Wave functions of linear systems

Upon revisiting the Hamiltonian structure of classical wavefunctions in Koopman-von Neumann theory, this paper addresses the long-standing problem of formulating a dynamical theory of classical-quantum coupling. The proposed model not only…

In this paper a didactic approach is described which immediately leads to an understanding of those postulates of quantum mechanics used most frequently in quantum computation. Moreover, an interpretation of quantum mechanics is presented…

We observe that, within the effective generating function formalism for the implementation of canonical transformations within wave mechanics, non-trivial canonical transformations which leave invariant the form of the Hamilton function of…

This paper surveys some recent results on the theory of quantum linear systems and presents them within a unified framework. Quantum linear systems are a class of systems whose dynamics, which are described by the laws of quantum mechanics,…

We show that the self-interactions present in the effective field theory formulation of general relativity can couple gravitational wave modes and generate nonclassical states. The output of gravitational nonlinear processes can also be…

Open quantum systems have become an active area of research, owing to its potential applications in many different fields ranging from computation to biology. Here, we review the formalism of dynamical maps used to represent the time…

This work presents a selective review of results concerning the mathematical interface between the classical and quantum aspects encountered in problems such as the nuclear mean-field dynamics or quantum Brownian motion. It is shown that…

We present a formulation of quantum mechanics based on orthogonal polynomials. The wavefunction is expanded over a complete set of square integrable basis in configuration space where the expansion coefficients are orthogonal polynomials in…

The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic…

The Gaussian state description of continuous variables is adapted to describe the quantum interaction between macroscopic atomic samples and continuous-wave light beams. The formalism is very efficient: a non-linear differential equation…

Peridynamics describes the nonlinear interactions in spatially extended Hamiltonian systems by nonlocal integro-differential equations, which can be regarded as the natural generalization of lattice models. We prove the existence of…

A generalization of driven harmonic oscillator with time-dependent mass and frequency, by adding total time-derivative terms to the Lagrangian, is considered. The generalization which gives a general quadratic Hamiltonian system does not…

It is proposed that the paradox of wave-particle duality in quantum mechanics may be resolved using a physical picture analogous to magnetic domains. Within this picture, a quantum particle represents a coherent region of a quantum wave…

The classical invariants of a Hamiltonian system are expected to be derivable from the respective quantum spectrum. In fact, semiclassical expressions relate periodic orbits with eigenfunctions and eigenenergies of classical chaotic…

Basing on the theory of Feynman's influence functional and its hierarchical equations of motion, we develop a linear response theory for quantum open systems. Our theory provides an effective way to calculate dynamical observables of a…

We discuss the form of the wave-function of a state subjected to a scalar linear potential, paying special attention to quantum tunneling. We analyze the phases acquired by the evolved state and show that some of them have a pure quantum…

We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…

Quantum computers are considered as a part of the family of the reversible, lineary-extended, dynamical systems (Quanputers). For classical problems an operational reformulation is given. A universal algorithm for the solving of classical…

It is shown that the independence of the continuum hypothesis points to the unique definite status of the set of intermediate cardinality: the intermediate set exists only as a subset of continuum. This latent status is a consequence of…

Semi--classical dynamics of quantum wave packets spreading is studied for a kicked rotor. Quantum flights are established for a specific, "magic" value of a chaos control parameter when the classical stickiness of trajectories is most…