相关论文: Duality, Quantum Mechanics and (Almost) Complex Ma…
The qualitatively new concept of dynamic complexity in quantum mechanics is based on a new paradigm appearing within a nonperturbational analysis of the Schroedinger equation for a generic Hamiltonian system. The unreduced analysis…
A two-dimensional quantum mechanical system consisting of a particle coupled to two magnetic impurities of different strengths, in a harmonic potential, is considered. Topological boundary conditions at impurity locations imply that the…
Complementarity is one of the main features of quantum physics that radically departs from classical notions. Here we consider the limitations that this principle imposes due to the unpredictability of measurement outcomes of incompatible…
Quantum theory of the free Maxwell field in Minkowski space is constructed using a representation in which the self dual connection is diagonal. Quantum states are now holomorphic functionals of self dual connections and a decomposition of…
The composite particle duality extends the notions of both flux attachment and statistical transmutation in spacetime dimensions beyond 2+1D. It constitutes an exact correspondence that can be understood either as a theoretical framework or…
This work is originally a Cambridge Part III essay paper. Quantum complexity arises as an alternative measure to the Fubini metric between two quantum states. Given two states and a set of allowed gates, it is defined as the least complex…
Here I explore a novel no-collapse interpretation of quantum mechanics which combines aspects of two familiar and well-developed alternatives, Bohmian mechanics and the many-worlds interpretation. Despite reproducing the empirical…
Wave--particle duality is a cornerstone of quantum mechanics, traditionally formulated under definite causal order. We investigate how complementarity is modified when the temporal order of operations is coherently superposed, as in the…
Constructing a classical mechanical system associated with a given quantum mechanical one, entails construction of a classical phase space and a corresponding Hamiltonian function from the available quantum structures and a notion of…
Mechanics is developed over a differentiable manifold as space of possible positions. Time is considered to fill a one--dimensional Riemannian manifold, so having the metric as lapse. Then the system is quantized with covariant instead of…
The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…
Interpretational problems with quantum mechanics can be phrased precisely by only talking about empirically accessible information. This prompts a mathematical reformulation of quantum mechanics in terms of classical mechanics. We survey…
The concept of duality reflects a link between two seemingly different physical objects. An example in quantum mechanics is a situation where the spectra (or their parts) of two Hamiltonians go into each other under a certain…
The state space of a homogeneous body is derived under two different assumptions: infinitesimal reducibility and irreducibility. The first assumption leads to a real vector space, used in classical mechanics, while the second one leads to a…
In this paper, we demonstrate the equivalence between the complex Hilbert space and real Kahler space formulations of quantum mechanics. Complex numbers play an important role in the traditional formulation of quantum mechanics in complex…
Decoherence may not solve all of the measurement problems of quantum mechanics. It is proposed that a solution to these problems may be to allow that superpositions describe physically real systems in the following sense. Each quantum…
The true dynamical randomness is obtained as a natural fundamental property of deterministic quantum systems. It provides quantum chaos passing to the classical dynamical chaos under the ordinary semiclassical transition, which extends the…
In quantum cosmology, one applies quantum physics to the whole universe. While no unique version and no completely well-defined theory is available yet, the framework gives rise to interesting conceptual, mathematical and physical…
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of…