相关论文: Approximate integrals of motion and the quantum ch…
Coherent states can be used for diverse applications in quantum physics including the construction of coherent state path integrals. Most definitions make use of a lattice regularization; however, recent definitions employ a continuous-time…
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
As a model of decohering environment, we show that quantum chaotic system behave equivalently as many-body system. An approximate formula for the time evolution of the reduced density matrix of a system interacting with a quantum chaotic…
The motion of beams in particle accelerators is dominated by a plethora of non-linear effects which can enhance chaotic motion and limit their performance. The application of advanced non-linear dynamics methods for detecting and correcting…
Quasi-integrable Hamiltonian systems are of great interest in many research fields of physics and mathematics. In these systems, the phase space has regular and chaotic trajectories. These trajectories depend in part on the magnitude of…
We explain the mechanism leading to directed chaotic transport in Hamiltonian systems with spatial and temporal periodicity. We show that a mixed phase space comprising both regular and chaotic motion is required and derive a classical sum…
In this paper we study the emergence of coherence in collective motion described by a system of interacting motiles endowed with an inner, adaptative, steering mechanism. By means of a nonlinear parametric coupling, the system elements are…
There are many problems that lead to analysis of dynamical systems in which one can distinguish motions of two types: slow one and fast one. An averaging over fast motion is used for approximate description of the slow motion. First…
We consider $n$-body problems given by potentials of the form ${\alpha\over r^a}+{\beta\over r^b}$ with $a,b,\alpha,\beta$ constants, $0\le a<b$. To analyze the dynamics of the problem, we first prove some properties related to central…
The onset of chaos and the mechanism of rotational damping are studied in an exactly soluble particle-rotor model. It is shown that the degree of chaoticity as inferred from the statistical measures is closely related to the onset of…
We propose a quantum algorithm which uses the number of qubits in an optimal way and efficiently simulates a physical model with rich and complex dynamics described by the quantum sawtooth map. The numerical study of the effect of static…
The dynamical systems of identical particles admitting quadratic integrals of motion are classified. The relevant integrals are explicitly constructed and their relation to separation of variables in H-J equation is clarified.
In this contribution I discuss a path integral approach for the quantum motion on two-dimensional spaces according to Koenigs, for short ``Koenigs-Spaces''. Their construction is simple: One takes a Hamiltonian from two-dimensional flat…
Quantum mechanics has many counter-intuitive consequences which contradict our intuition which is based on classical physics. Here we discuss a special aspect of quantum mechanics, namely the possibility of entanglement between two or more…
A direct classical analog of the quantum dynamics of intrinsic decoherence in Hamiltonian systems, characterized by the time dependence of the linear entropy of the reduced density operator, is introduced. The similarities and differences…
We show that the number of harmonics of the Wigner function, recently proposed as a measure of quantum complexity, can be also used to characterize quantum phase transitions. The non-analytic behavior of this quantity in the neighborhood of…
We construct a complete set of quasi-local integrals of motion for the many-body localized phase of interacting fermions in a disordered potential. The integrals of motion can be chosen to have binary spectrum $\{0,1\}$, thus constituting…
A new framework for deriving equations of motion for constrained quantum systems is introduced, and a procedure for its implementation is outlined. In special cases the framework reduces to a quantum analogue of the Dirac theory of…
The origin of the phenomenological deterministic laws that approximately govern the quasiclassical domain of familiar experience is considered in the context of the quantum mechanics of closed systems such as the universe as a whole. We…
Quantum mechanics is a special kind of description of motion. The concept of wave function itself implies the openness of quantum system. We show that quantum mechanics describes the quantum correlation, i.e., entanglement, and information…