Related papers: New Concept of Dynamic Complexity in Quantum Mecha…
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…
We present a theory of discontinuous motion of particles in continuous space-time. We show that the simplest nonrelativistic evolution equation of such motion is just the Schroedinger equation in quantum mechanics. This strongly implies…
We consider a general class of discrete unitary dynamical models on the lattice. We show that generically such models give rise to a wavefunction satisfying a Schroedinger equation in the continuum limit, in any number of dimensions. There…
The concept of quantum complexity has far-reaching implications spanning theoretical computer science, quantum many-body physics, and high energy physics. The quantum complexity of a unitary transformation or quantum state is defined as the…
In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schr\"odinger equation, which is solved for the wave function, bound…
Quantum Mechanics (QM) has faced deep controversies and debates since its origin when Werner Heisenberg proposed the first mathematical formalism capable to operationally account for what had been recently discovered as the new field of…
A new proof of the impossibility of a universal quantum-classical dynamics is given. It has at least two consequences. The standard paradigm ``quantum system is measured by a classical apparatus" is untenable, while a quantum matter can be…
In this paper, we try to give a new approach to the quantum mechanics(QM) on the framework of quantum field theory(QFT). Firstly, we make a detail study on the (non-relativistic) Schr\"odinger field theory, obtaining the Schr\"odinger…
The unreduced, universally nonperturbative analysis of arbitrary many-body interaction process reveals the irreducible, purely dynamic source of randomness. It leads to the universal definition of real system complexity (physics/9806002),…
It is shown that the Schrodinger equation is a byproduct of more deterministic Boltzmann-like equation. All physical information is derived from the solution of this equation, which is a function of space and momentum. The additional terms…
The momentum representation is seldom used in quantum mechanics courses. Some students are thence surprised by the change in viewpoint when, in doing advanced work, they have to use the momentum rather than the coordinate representation. In…
The purpose of physics is to describe nature from elementary particles all the way up to cosmological objects like cluster of galaxies and black holes. Although a unified description for all this spectrum of events is desirable, this would…
Several methods in nonadiabatic molecular dynamics are based on Madelung's hydrodynamic description of nuclear motion, while the electronic component is treated as a finite-dimensional quantum system. In this context, the quantum potential…
It is shown that quantum mechanics can be regarded as what one might call a "fuzzy" mechanics whose underlying logic is the fuzzy one, in contradistinction to the classical "crisp" logic. Therefore classical mechanics can be viewed as a…
We describe an interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description for macro-systems. The interpretation is a modal one,…
Quantum mechanics is derived as an application of the method of maximum entropy. No appeal is made to any underlying classical action principle whether deterministic or stochastic. Instead, the basic assumption is that in addition to the…
Stunning progresses in the experimental resolution and control of natural or man-made complex systems at the level of their quantum mechanical constituents raises the question, across diverse subdisciplines of physics, chemistry and…
The question of how irreversibility can emerge as a generic phenomena when the underlying mechanical theory is reversible has been a long-standing fundamental problem for both classical and quantum mechanics. We describe a mechanism for the…
The "quantum complexity" of a unitary operator measures the difficulty of its construction from a set of elementary quantum gates. While the notion of quantum complexity was first introduced as a quantum generalization of the classical…
Mermin's "shut up and calculate!" somehow summarizes the most widely accepted view on quantum mechanics. This conception has led to a rather constraining way to think and understand the quantum world. Nonetheless, a closer look at the…