Related papers: Universal Bounds on Quantum Mechanics through Ener…
Speed of state transitions in macroscopic systems is a crucial concept for foundations of nonequilibrium statistical mechanics as well as various applications in quantum technology represented by optimal quantum control. While extensive…
Energy-time uncertainty plays an important role in quantum foundations and technologies, and it was even discussed by the founders of quantum mechanics. However, standard approaches (e.g., Robertson's uncertainty relation) do not apply to…
The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit on the measurement precisions of incompatible observables. Here we show that the traditional uncertainty relation in fact…
In a previous study, it was shown that the Generalized Uncertainty Principle (GUP) can be derived from non-extensive entropies, particularly those depending only on the probability, denoted as $S_\pm$ in the literature. This finding reveals…
We consider diatomic systems in which the kinetic energy of the electrons is treated in a simple relativistic model. The Born-Oppenheimer approximation is assumed. We investigate questions of stability, deducing bounds on the number $N$ of…
A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables.…
Large $N$ matrix quantum mechanics is central to holographic duality but not solvable in the most interesting cases. We show that the spectrum and simple expectation values in these theories can be obtained numerically via a `bootstrap'…
In this work we determine a lower bound to the mean value of the quantum potential for an arbitrary state. Furthermore, we derive a generalized uncertainty relation that is stronger than the Robertson-Schr\"odinger inequality and hence also…
We describe a quantum mechanical measurement as a variational principle including interaction between the system under measurement and the measurement apparatus. Augmenting the action with a nonlocal term (a double integration over the…
Various models of quantum gravity suggest a modification of the Heisenberg's Uncertainty Principle, to the so-called Generalized Uncertainty Principle, between position and momentum. In this work we show how this modification influences the…
We present a detailed study of the quantum dissipative dynamics of a charged particle in a magnetic field. Our focus of attention is the effect of dissipation on the low- and high-temperature behavior of the specific heat at constant…
We demonstrate the possibility of a genuine quantum advantage in the efficiency of quantum batteries by analyzing a model that enables a consistent comparison between quantum and classical regimes. Our system consists of $N$ harmonic…
The uncertainty principle bounds our ability to simultaneously predict two incompatible observables of a quantum particle. Assisted by a quantum memory to store the particle, this uncertainty could be reduced and quantified by a new…
We study the entropy bound for local quantum field theory (LQFT) with generalized uncertainty principle. The generalized uncertainty principle provides naturally a UV cutoff to the LQFT as gravity effects. Imposing the non-gravitational…
We derive a standard quantum limit for probing mechanical energy quantization in a class of systems with mechanical modes parametrically coupled to external degrees of freedom. To resolve a single mechanical quantum, it requires a…
Bekenstein has presented evidence for the existence of a universal upper bound of magnitude $2\pi R/\hbar c$ to the entropy-to-energy ratio $S/E$ of an arbitrary {\it three} dimensional system of proper radius $R$ and negligible…
Conservation laws are discussed in conjunction with quantum-mechanical indeterminacies of the corresponding observables. The considered examples show that the connections between energy and its indeterminacy may be quite intricate. The…
Different candidates of Quantum Gravity such as String Theory, Doubly Special Relativity, Loop Quantum Gravity and black hole physics all predict the existence of a minimum observable length or a maximum observable momentum which modifies…
Minimization of the expectation value of energy under the constraints imposed by the uncertainty principle can be a convenient method of solving quantum-mechanical problems.
We re-derive the Schr\"{o}dinger-Robertson uncertainty principle for the position and momentum of a quantum particle. Our derivation does not directly employ commutation relations, but works by reduction to an eigenvalue problem related to…