相关论文: Uncertainty relations in curved spaces

Uncertainty relations are a fundamental feature of quantum mechanics. How can these relations be found systematically? Here we develop a semidefinite programming hierarchy for additive uncertainty relations in the variances of non-commuting…

Uncertainty relation is one of the fundamental building blocks of quantum theory. Nevertheless, the traditional uncertainty relations do not fully capture the concept of incompatible observables. Here we present a stronger…

Uncertainty relations play a significant role in drawing a line between classical physics and quantum physics. Since the introduction by Heisenberg, these relations have been considerably explored. However, the effect of quantum…

We study hyper-spheres, spheres and circles, with respect to an indefinite metric, in a tangent space on a 4-dimensional differentiable manifold. The manifold is equipped with a positive definite metric and an additional tensor structure of…

Quantum mechanical uncertainty relations for position and momentum are expressed in the form of inequalities involving the Renyi entropies. The proof of these inequalities requires the use of the exact expression for the (p,q)-norm of the…

In this paper we review some aspects of relativistic particles' mechanics in the case of a non-trivial geometry of momentum space. We start with showing how the curved momentum space arises in the theory of gravity in 2+1 dimensions coupled…

Non-relativistic particles that are effectively confined to two dimensions can in general move on curved surfaces, allowing dynamical phenomena beyond what can be described with scalar potentials or even vector gauge fields. Here we…

The uncertainty relation is one of the key ingredients of quantum theory. Despite the great efforts devoted to this subject, most of the variance-based uncertainty relations are state-dependent and suffering from the triviality problem of…

In recent years there has been a lot of interest in discussing frame dependences/independences of the cosmological perturbations under the conformal transformations. This problem has previously been investigated in terms of the covariant…

A manifestly covariant equation is derived to describe the second order perturbations in topological defects and membranes on arbitrary curved background spacetimes. This, on one hand, generalizes work on macroscopic strings in Minkowski…

I briefly discuss the construction of a theory of particles with curved momentum space and its consequence, the principle of relative locality.

We advocate that the dual picture of spacetime noncommutativity , i.e. the existence of a curved momentum space, could be a way out to solve some of the open conceptual problems in the field, such as the basis dependence of observables. In…

Due to lack of scientific understanding, some mechanisms may be missing in mathematical modeling of complex phenomena in science and engineering. These mathematical models thus contain some uncertainties such as uncertain parameters. One…

Discussion of physical realization of coordinates demonstrates that the quantum theory of gravity (still absent) should be non-local and, probably, non-commutative as well.

In quantum systems, a plausible definition of work is based on two energy measurement scheme. Considering that energy change of quantum system obeys a time-energy uncertainty relation, it shall be interesting to see whether such type of…

Turbulence, the complicated fluid behavior of nonlinear and statistical nature, arises in many physical systems across various disciplines, from tiny laboratory scales to geophysical and astrophysical ones. The notion of turbulence in the…

In this article, we review the progress made on the statistical mechanics of liquids and fluids embedded in curved space. Our main focus will be on two-dimensional manifolds of constant nonzero curvature and on the influence of the latter…

The concept of a particle is ambiguous in quantum field theory. It is generally agreed that particles depend not only on spacetime, but also on coordinates used to parametrise spacetime points. One of us has in contrast proposed a…

We study fine-grained uncertainty relations for several quantum measurements in a finite-dimensional Hilbert space. The proposed approach is based on exact calculation or estimation of the spectral norms of corresponding positive matrices.…

We present strategies to quantify theoretical uncertainties in modern ab-initio calculations of electromagnetic observables in light and medium-mass nuclei. We discuss how uncertainties build up from various sources, such as the…