相关论文: Complementarity versus coordinate transformations:…
The complementarity between the twin concepts of pseudo-Hermiticity and weak pseudo-Hermiticity, established by Bagchi and Quesne [Phys. Lett. A 301 (2002) 173-176], can be understood in terms of coordinate transformations.
Complementarity is a phenomenon explaining several core features of quantum theory, such as the well-known uncertainty principle. Roughly speaking, two objects are said to be complementary if being certain about one of them necessarily…
Complementarity was originally introduced as a qualitative concept for the discussion of properties of quantum mechanical objects that are classically incompatible. More recently, complementarity has become a \emph{quantitative} relation…
We study quasi-modular pseudometric spaces as asymmetric refinements of modular metric structures. To each such space we associate canonical forward and backward quasi-uniformities and the corresponding directional topologies. We introduce…
We propose an operational definition of complementarity, pinning down the concept originally introduced by Bohr. Two properties of a system are considered complementary if they cannot be simultaneously well defined. We further show that,…
In arXiv:0709.0483 Gunther and Samsonov outline a ``generalization'' of quantum mechanics that involves simultaneous consideration of Hermitian and non-Hermitian operators and promises to be ``capable to produce effects beyond those of…
Quantum complementarity is a fundamental feature of quantum systems and has captivated the physics research community for nearly a century, with significant advancements emerging in recent decades. This review traces the historical…
Quasi-Hermitian quantum systems, including $\mathcal{PT}$-symmetric ones, can be mapped to equivalent Hermitian systems via a similarity transformation that redefines the inner product with a positive-definite metric operator. Although an…
Niels Bohr introduced the concept of complementarity in order to give a general account of quantum mechanics, however he stressed that the idea of complementarity is related to the general dificulty in the formation of human ideas, inherent…
We generalize a recently proposed approach for the construction of pseudo-Hermitian Hamiltonians with real spectra. Present technique is based on a simple and straightforward similarity transformation of the coordinate and momentum.
Pseudo-Hermitian operators generalize the concept of Hermiticity. This class of operators includes the quasi-Hermitian operators, which reformulate quantum theory while retaining real-valued measurement outcomes and unitary time evolution.…
We propose that the real spectrum and the orthogonality of the states for several known complex potentials of both types, PT-symmetric and non-PT-symmetric can be understood in terms of currently proposed $\eta$-pseudo-Hermiticity…
Nowadays, we have seen that dual quaternion algorithms are used in 3D coordinate transformation problems due to their advantages. 3D coordinate transformation problem is one of the important problems in geodesy. This transformation problem…
We investigate the black hole information paradox in the setting of pseudo-complex gravity, a covariant geometric extension of general relativity that introduces a minimal length scale by deforming the spacetime manifold. In this framework,…
Since the beginning of quantum mechanics, many puzzling phenomena which distinguish the quantum from the classical world, have appeared such as complementarity, entanglement or contextuality. All of these phenomena are based on the…
The concepts of complementarity and entanglement are considered with respect to their significance in and beyond physics. A formally generalized, weak version of quantum theory, more general than ordinary quantum theory of material systems,…
An alternative interpretation of the conformal transformations of the metric is discussed according to which the latter can be viewed as a mapping among Riemannian and Weyl-integrable spaces. A novel aspect of the conformal transformation's…
The so-called preparation uncertainty can be understood in purely operational terms. Namely, it occurs when for some pair of observables, there is no preparation, for which they both exhibit deterministic statistics. However, the right-hand…
Non-Hermitian systems with parity-time symmetry have been found to exhibit real spectra of eigenvalues, indicating a balance between the loss and gain. However, such a balance is not only dependent on the magnitude of loss and gain, but…
Quantum phase transitions are a fascinating area of condensed matter physics. The extension through complexification not only broadens the scope of this field but also offers a new framework for understanding criticality and its statistical…