Related papers: Exact uncertainty approach in quantum mechanics an…
We prove a theorem showing that quantum mechanics is not directly a stochastic process characterizing Brownian motion but rather its square root. This implies that a complex-valued stochastic process is involved. Schr\"odinger equation is…
We give a partial answer to the question whether the Schrodinger equation can be derived from the Newtonian mechanics of a particle in a potential subject to a random force. We show that the fluctuations around the classical motion of a one…
A common knowledge suggests that trajectories of particles in quantum mechanics always have quantum uncertainties. These quantum uncertainties set by the Heisenberg uncertainty principle limit precision of measurements of fields and forces,…
In the Wheeler-DeWitt framework, by a gauge fixing procedure, we set up a scheme to recover a Schr\"odinger type equation, living in the orbits space with the {\it lapse} function as evolution parameter. By means of the associated…
A non-perturbative and background-independent quantum formulation of quadratic gravity is provided. A canonical quantization procedure introduced in previous works, named after Dirac and Pauli, is here applied to quadratic gravity to…
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…
Phenomenological models aiming to join gravity and quantum mechanics often predict effects that are potentially measurable in refined low-energy experiments. For instance, modified commutation relations between position and momentum, that…
The probability density distributions for the ground states of certain model systems in quantum mechanics and for their classical counterparts are considered. It is shown, that classical distributions are remarkably improved by…
Thermodynamic uncertainty principles make up one of the few rare anchors in the largely uncharted waters of nonequilibrium systems, the fluctuation theorems being the more familiar. In this work we aim to trace the uncertainties of…
Starting from the Hamilton-Jacobi equation describing a classical ensemble, one may infer a quantum dynamics using the principle of maximum uncertainty. That procedure requires an appropriate measure of uncertainty: Such a measure is…
We consider the scenario of a fluctuating spacetime due to a deformed commutation relation with a fluctuating deformation parameter, or to a fluctuating metric tensor. By computing the resulting dynamics and averaging over these…
With a q-deformed quantum mechanical framework, features of the uncertainty relation and a novel formulation of the Schr\"odinger equation are considered.
We propose mixed quantum-classical equations of motion that unify electronic coherence and phase evolution simultaneously within the exact factorization framework. Our derivation shows that incorporating the second-order electron-nuclear…
We provide a decision-theoretic framework for dealing with uncertainty in quantum mechanics. This uncertainty is two-fold: on the one hand there may be uncertainty about the state the quantum system is in, and on the other hand, as is…
Phenomenological approaches to quantum gravity implement a minimum resolvable length-scale but do not link it to an underlying formalism describing geometric superpositions. Here, we introduce an intuitive approach in which points in the…
It is believed that gravity will be explained in the framework of the existing quantum theory when one succeeds in eliminating divergencies at large momenta or small distances (although the phenomenon of gravity has been observed only at…
Quantum gravity is fundamentally different from the non-gravitational quantum field theories in the sense that most of the techniques derived for the latter cannot be easily extended to the former. For example, correlation functions in…
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…
Some of the possible consequences of a generalized uncertainty principle (which emerges in the context of string theory and quantum gravity models as a consequence of fluctuations of the background metric) are analyzed considering the case…
The same set of physically motivated axioms can be used to construct both the classical ensemble Hamilton-Jacobi equation and Schrodingers equation. Crucial roles are played by the assumptions of universality and simplicity (Occam's Razor)…