相关论文: Quantum Mechanics with Chaos: Correspondence Princ…
Quantum and classical mechanics are derived using four natural physical principles: (1) the laws of nature are invariant under time evolution, (2) the laws of nature are invariant under tensor composition, (3) the laws of nature are…
Recent tremendous development of quantum information theory led to a number of quantum technological projects, e.g., quantum random generators. This development stimulates a new wave of interest in quantum foundations. One of the most…
We consider the problem of quantum behavior in the finite background. Introduction of continuum or other infinities into physics leads only to technical complications without any need for them in description of empirical observations. The…
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
The time-dependent variational principle using generalized Gaussian trial functions yields a finite dimensional approximation to the full quantum dynamics and is used in many disciplines. It is shown how these 'semi-quantum' dynamics may be…
Nowadays there is no universally accepted definition of quantum chaos. In this paper we review and critically discuss different approaches to the subject, such as Quantum Chaology and the Random Matrix Theory. Then we analyze the problem of…
Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the…
Numerous lines of experimental, numerical and analytical evidence indicate that it is surprisingly easy to locate optimal controls steering quantum dynamical systems to desired objectives. This has enabled the control of complex quantum…
Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is…
In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg…
Classical physics is generally regarded as deterministic, as opposed to quantum mechanics that is considered the first theory to have introduced genuine indeterminism into physics. We challenge this view by arguing that the alleged…
The major conceptual difficulties of quantum mechanics are analyzed. They are: the notion "wave-particle", the probabilistic interpretation of the Schroedinger wave \psi-function and hence the probability amplitude and its phase, long-range…
The complexity of the quantum state of a multiparticle system and the maximum possible accuracy of its quantum description are connected by a relation similar to the coordinate-momentum uncertainty relation. The coefficient in this relation…
The formalism of the particle dynamics in the space-time, where motion of free particles is primordially stochastic, is considered. The conventional dynamic formalism, obtained for the space-time, where the motion of free particles is…
The main idea of "Quantum Chaos" studies is that Quantum Mechanics introduces two energy scales into the study of chaotic systems: One is obviously the mean level spacing $\Delta\propto\hbar^d$, where $d$ is the dimensionality; The other is…
Using semiclassical methods, it is possible to construct very accurate approximations in the short wavelength limit of quantum dynamics that rely exclusively on classical dynamical input. For systems whose classical realization is strongly…
Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are…
Statistical classical mechanics and quantum mechanics are developed and well-known theories that represent a basis for modern physics. The two described theories are well known and have been well studied. As these theories contain numerous…
Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…