Related papers: Hausdorff dimension of a quantum string
An approach to evaluation of the smooth Feynman path integrals is developed for the study of quantum fluctuations of particles and fields in Euclidean time-space. The paths are described by sum of Gauss functions and are weighted with…
In quantum mechanics the time dimension is treated as a parameter, while the three space dimensions are treated as observables. This assumption is both untested and inconsistent with relativity. From dimensional analysis, we expect quantum…
The proposal that the one-parameter solutions of the real part of the Schrodinger equation (quantum Hamilton-Jacobi equation) can be regarded as `quantum particle trajectories' has received considerable attention recently. Opinions as to…
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…
A quantum trajectory describes the evolution of a quantum system undergoing indirect measurement. In the discrete-time setting, the state of the system is updated by applying Kraus operators according to the measurement results. From an…
Marchildon's (favorable) assessment (quant-ph/0303170, to appear in Found. Phys.) of the Pondicherry interpretation of quantum mechanics raises several issues, which are addressed. Proceeding from the assumption that quantum mechanics is…
The Heisenberg uncertainty principle is one of the fundamental pillars of quantum mechanics and quantum field theory. It is normally introduced by postulating the commutation relations $[\hat{x}^i, \hat{p}^j] = i\hbar \delta^{ij}$. However,…
We study the shuttling instability in an array of three quantum dots the central one of which is movable. We extend the results by Armour and MacKinnon on this problem to a broader parameter regime. The results obtained by an efficient…
The generalized uncertainty principle of string theory is derived in the framework of Quantum Geometry by taking into account the existence of an upper limit on the acceleration of massive particles.
Quantum uncertainty is described here in two guises: indeterminacy with its concomitant indeterminism of measurement outcomes, and fuzziness, or unsharpness. Both features were long seen as obstructions of experimental possibilities that…
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.…
The explicit form of the quantum propagator of a bosonic p-brane, previously obtained by the authors in the quenched-minisuperspace approximation, suggests the possibility of a novel, unified, description of p-branes with different…
The theory of complex dimensions of fractal strings developed by Lapidus and van Frankenhuijsen has proven to be a powerful tool for the study of Minkowski measurability of fractal subsets of the real line. In a very general setting, the…
Bulk magnetism in solids is fundamentally quantum mechanical in nature. Yet in many situations, including our everyday encounters with magnetic materials, quantum effects are masked, and it often suffices to think of magnetism in terms of…
We construct a theory of fields living on continuous geometries with fractional Hausdorff and spectral dimensions, focussing on a flat background analogous to Minkowski spacetime. After reviewing the properties of fractional spaces with…
Quantum theory is extremely successful in explaining most physical phenomena, and is not contradicted by any experiment. Yet, the theory has many puzzling features : the occurrence of probabilities, the unclear distinction between the…
Relativity and quantum mechanics are generalized by considering a finite limit for the smallest measurable distance. The value a of this quantum of length is unknown, but it is a universal constant, like c and h. It depends on the total…
Denoting the Hausdorff dimension of the Fibonacci Hamiltonian with coupling $\lambda$ by $\mathrm{HD}_\lambda$, we prove that for all but countably many $\lambda$, the Hausdorff dimension of the spectrum of the square Fibonacci Hamiltonian…
Recent results suggest that a crucial crossroad for quantum gravity is the characterization of the effective dimension of spacetime at short distances, where quantum properties of spacetime become significant. This is relevant in particular…
A new hidden variable theory is proposed, according to which particles follows definite trajectories, as in Bohmian Mechanics or Nelson's stochastic mechanics; in the new theory, however, the trajectories are classical, i.e. Newtonian. This…