Related papers: The interparticle interaction and noncommutativity…
A quantum mechanical model for the systems consisting of interacting bodies is considered. The model takes into account the noncommutativity of the space and impulse operators and the correlation equations for the indeterminacy of these…
A nonrelativistic equation for the system of two interacting particles within the framework of a model with noncommuting operators of coordinates and momenta of different particles is proposed, and a self-consistent system of equations for…
We develop an approximate second quantization method for describing the many-particle systems in the presence of bound states of particles at low energies (the kinetic energy of particles is small in comparison to the binding energy of…
The interaction between two parts in a compound quantum system may be reconsidered more completely than before and some new understandings and conclusions different from current quantum mechanics are obtained, including the conservation law…
Quantum interferences between non-orthogonal states are the best approximation of a joint realization of the non-commuting physical properties represented by the two states. As I have shown recently, such interferences can be used to…
We discuss the role that interactions play in the non-commutative structure that arises when the relative coordinates of two interacting particles are projected onto the lowest Landau level. It is shown that the interactions in general…
Recent developments have made possible the computation of equilibrium dynamical correlators in quantum impurity problems. In many situations however, one is rather interested in correlators subject to a non equilibrium initial preparation;…
The dynamics of open quantum systems (i.e., of quantum systems interacting with an uncontrolled environment) forms the basis of numerous active areas of research from quantum thermodynamics to quantum computing. One approach to modeling…
A non-Markovian model of quantum repeated interactions between a small quantum system and an infinite chain of quantum systems is presented. By adapting and applying usual pro jection operator techniques in this context, discrete versions…
Uncertainty relations between a bounded coordinate operator and a conjugate momentum operator frequently appear in quantum mechanics. We prove that physically reasonable minimum-uncertainty solutions to such relations have quantized…
We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called…
In this sequence of papers, noncommutative analysis is used to give a consistent axiomatic approach to a unified conceptual foundation of classical and quantum physics. The present Part I defines the concepts of observables, states and…
The uncertainty relation of three quantities in quantum mechanics is estimated in terms of commutators. The Pauli matrices are used to find a contribution of third-order commutators. The resulting inequality refines the Heisenberg…
We consider non-relativistic systems in quantum mechanics interacting through the Coulomb potential, and discuss the existence of bound states which are stable against spontaneous dissociation into smaller atoms or ions. We review the…
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of…
We introduce an alternative way to understand the decomposition of a quantum system into interacting parts and show that it is natural in several physical models. This enables us to define a reduced density operator for a working system…
We study the quantum dynamics of a single mode/particle interacting inhomogeneously with a large number of particles and introduce an effective approach to find the accessible Hilbert space where the dynamics takes place. Two relevant…
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
Composite system is studied in noncommutative phase space with preserved rotational symmetry. We find conditions on the parameters of noncommutativity on which commutation relations for coordinates and momenta of the center-of-mass of…
A technique is presented for treating strongly nonstationary and transient processes in optics, permitting one to take into account both types of competing with each other effects, quantum as well as coherent. The main equations for…