Related papers: Generalized uncertainty relations: Theory, example…
Generators of spacetime translations and Lorentz group transformations form the Lie algebra of the Poincar\'e group and give rise to the Casimir invariants for a specification of elementary particle characteristics. Moreover quantum…
Quantum uncertainty relations have deep-rooted significance on the formalism of quantum mechanics. Heisenberg's uncertainty relations attracted a renewed interest for its applications in quantum information science. Robertson derived a…
We study the consequences of the generalized Heisenberg uncertainty relation which admits a minimal uncertainty in length such as the case in a theory of quantum gravity. In particular, the theory of quantum harmonic oscillators arising…
We investigate uncertainty relations for quantum observables evolving under non-Hermitian Hamiltonians, with particular emphasis on the role of metric operators. By constructing appropriate metrics in each dynamical regime, namely the…
A universal formulation of the quantum uncertainty regarding quantum indeterminacy, quantum measurement, and its inevitable observer effect is presented with additional focus on the representability of quantum observables over a given…
A universal formulation of uncertainty relations for quantum measurements is presented with additional focus on the representability of quantum observables by classical observables over a given state. Owing to the simplicity and operational…
This study investigates pseudo-Hermitian quantum mechanics, where the Hamiltonian satisfies a modified Hermiticity condition. We extend the uncertainty relation for such systems, demonstrating its equivalence to the standard Hermitian case…
We study the commutation relations, uncertainty relations and spectra of position and momentum operators within the framework of quantum group % symmetric Heisenberg algebras and their (Bargmann-) Fock representations. As an effect of the…
As a foundation of modern physics, uncertainty relations describe an ultimate limit for the measurement uncertainty of incompatible observables. Traditionally, uncertain relations are formulated by mathematical bounds for a specific state.…
A proper deformation of the underlying coordinate and momentum commutation relations in quantum mechanics provides a phenomenological approach to account for the influence of gravity on small scales. Introducing the squared momentum term…
The effects of any quantum measurement can be described by a collection of measurement operators {M_m} acting on the quantum state of the measured system. However, the Hilbert space formalism tends to obscure the relationship between the…
The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous…
Several models of quantum gravity predict the emergence of a minimal length at Planck scale. This is commonly taken into consideration by modifying the Heisenberg Uncertainty Principle into the Generalized Uncertainty Principle. In this…
It is well known that nonrelativistic quantum mechanics presents a clear asymmetry between space and time. Much of this asymmetry is attributed to the lack of Lorentz invariance of the theory. Nonetheless, a recent work [Phys. Rev. A…
Generalized uncertainty principles are able to serve as useful descriptions of some of the phenomenology of quantum gravity effects, providing an intuitive grasp on non-trivial space-time structures such as a fundamental discreteness of…
Motivated by the parametrization invariance of cosmological Lagrangians and their equivalence to systems describing the motion of particles in curved backgrounds, we identify the phase space analogue of the notion of proper time. We define…
The existence of a hermitian time operator is proposed in the framework of non-relativistic quantum mechanics.The Heisenberg equation of motion is shown to yield constant rate of flow of time.It is shown to yield results consistent with…
We study the time evolution of the reduced Wigner function for a class of quantum Brownian motion models. We derive two generalized uncertainty relations. The first consists of a sharp lower bound on the uncertainty function, $U = (\Delta…
The Heisenberg and Mandelstam-Tamm time-energy uncertainty relations are analyzed. The conlusion resulting from this analysis is that within the Quantum Mechanics of Schr\"{o}dinger and von Neumann, the status of these relations can not be…
Two generalizations of Kempf's quadratic canonical commutation relation in one dimension are considered. The first one is the most general quadratic commutation relation. The corresponding nonzero minimal uncertainties in position and…