Related papers: Transition to the classical regime in quantum mech…
We consider a generic optomechanical system, consisting of a driven optical cavity and a movable mirror attached to a cantilever. Systems of this kind (and analogues) have been realized in many recent experiments. It is well known that…
The classical limit of quantum mechanics is discussed for closed quantum systems in terms of observational aspects. Initially, the failure of the limit h->0 is explicitly demonstrated in a model of two quantum mechanically interacting…
The spread of the wave-function, or quantum uncertainty, is a key notion in quantum mechanics. At leading order, it is characterized by the quadratic moments of the position and momentum operators. These evolve and fluctuate independently…
The hypothesis of a discrete fabric of the universe--the "Planck scale"--is always on stage, since it solves mathematical and conceptual problems in the infinitely small. However, it clashes with special relativity, which is designed for…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
We formulate a conceptually new model in which quantum mechanics emerges from classical mechanics. Given a local Hamiltonian $H$ acting on $n$ qubits, we define a local classical model with an additional spatial dimension whose boundary…
Uncertainty relations are fundamental to quantum mechanics, encoding limits on the simultaneous measurement of conjugate observables. Violations of joint uncertainty bounds can certify entanglement -- a resource critical for quantum…
A classical dynamical system in a four-dimensional Euclidean space with universal time is considered. The space is hypothesized to be originally occupied by a uniform substance, pictured as a liquid, which at some time became supercooled.…
We explore how quantum properties of spacetime, specifically the curvature of momentum space, can backreact on classical gravity within a tractable semiclassical (2+1)-dimensional framework with a negative cosmological constant. Motivated…
The relationship between classical and quantum mechanics is usually understood via the limit $\hbar \rightarrow 0$. This is the underlying idea behind the quantization of classical objects. The apparent incompatibility of general relativity…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
The Planck scale is usually believed to be an unpassable wall. Putting a cutoff there and thinking of it as a quantized spacetime entity shows that. However, this is exactly the cause of many problems in quantum gravity. The cosmological…
Various theories of Quantum Gravity argue that near the Planck scale, the Heisenberg Uncertainty Principle should be replaced by the so called Generalized Uncertainty Principle (GUP). We show that the GUP gives rise to two additional terms…
Dynamics of a particle is formulated from classical principles that are amended by the uncertainty principle. Two best known quantum effects: interference and tunneling are discussed from these principles. It is shown that identical to…
The classical limit of quantum mechanics is investigated, by focusing on the study of the center of mass of a many-body system where each particle is described by quantum mechanics. We study how, in the limit when the number of particles…
A brief review of the previous research on the Heisenberg uncertainty relations at the Planck scale is given. In this work, investigation of the uncertainty principle extends to p-adic and adelic quantum mechanics. In particular, p-adic…
Heisenberg's uncertainty principle, which imposes intrinsic restrictions on our ability to predict the outcomes of incompatible quantum measurements to arbitrary precision, demonstrates one of the key differences between classical and…
We consider the application of the consistent lattice quantum gravity approach we introduced recently to the situation of a Friedmann cosmology and also to Bianchi cosmological models. This allows us to work out in detail the computations…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…
Measurement uncertainty and experimental error are important concepts taught in undergraduate physics laboratories. Although student ideas about error and uncertainty in introductory classical mechanics lab experiments have been studied…