Related papers: On Einstein Causality and Time Asymmetry in Quantu…
In quantum physics, disturbance due to a measurement is not negligible. This requires the time parameter $t$ in the Schr\"odinger or Heisenberg equation to be considered differently from a time continuum of experimenter's clock $T$ on which…
Physical laws for elementary particles can be described by the quantum dynamics equation given a Hamiltonian. The solution are probability amplitudes in Hilbert space that evolve over time. A probability density function over position and…
A slight modification of one axiom of quantum theory changes a reversible theory into a time asymmetric theory. Whereas the standard Hilbert space axiom does not distinguish mathematically between the space of states (in-states of…
A theorem of Hegerfeldt (Instantaneous spreading and Einstein causality in quantum theory, Ann. Phys. Leipzig vol. 7, 716-725 (1998)) establishes, for a class of quantum systems, a dichotomy between those which are permanently localized in…
Two related problems in relativistic quantum mechanics, the apparent superluminal propagation of initially localized particles and dependence of spatial localization on the motion of the observer, are analyzed in the context of Dirac's…
It is generally argued that the combined effect of Heisenberg principle and general relativity leads to a minimum time uncertainty. Most of the analyses supporting this conclusion are based on a perturbative approach to quantization. We…
It is remarkable that Heisenberg's position-momentum uncertainty relation leads to the existence of a maximal acceleration for a physical particle in the context of a geometric reformulation of quantum mechanics. It is also known that the…
We develop further the approach to upper and lower bounds in quantum dynamics via complex analysis methods which was introduced by us in a sequence of earlier papers. Here we derive upper bounds for non-time averaged outside probabilities…
Theorems (most notably by Hegerfeldt) prove that an initially localized particle whose time evolution is determined by a positive Hamiltonian will violate causality. We argue that this apparent paradox is resolved for a free particle…
Recently, the notion of a quantum acceleration limit has been proposed for any unitary time evolution of quantum systems governed by arbitrary nonstationary Hamiltonians. This limit articulates that the rate of change over time of the…
What is the minimal time until a quantum system can exhibit genuine quantum features? To answer this question we derive quantum speed limits for two-time correlation functions arising from statistics of measurements. Generally, these…
In nonrelativistic quantum mechanics the wave-function of a free particle which initially is in a finite volume immediately spreads to infinity. In a nonrelativistic theory this is of no concern, but we show that the same instantaneous…
The notion of Einstein causality, i.e. the limiting role of the velocity of light in the transmission of signals, is discussed. It is pointed out that Nimtz and coworkers use the notion of signal velocity in a different sense from Einstein…
Despite its long history, a canonical formulation of quantum ergodicity that applies to general classes of quantum dynamics, including driven systems, has not been fully established. Here we introduce and study a notion of quantum…
Heisenberg's uncertainty principle in application to energy and time is a powerful heuristics. This statement plays the important role in foundations of quantum theory and statistical physics. If some state exists for a finite interval of…
The time evolution of a bounded quantum system is considered in the framework of the orthogonal, unitary and symplectic circular ensembles of random matrix theory. For an $N$ dimensional Hilbert space we prove that in the large $N$ limit…
Drawing from the theory of optimal transport we propose a rigorous notion of a causal relation for Borel probability measures on a given spacetime. To prepare the ground, we explore the borderland between causality, topology and measure…
After a review of the arrows of time, we describe the possibilities of a time-asymmetry in quantum theory. Whereas Hilbert space quantum mechanics is time-symmetric, the rigged Hilbert space formulation, which arose from Dirac's bra-ket…
We prove under certain assumptions that there exists a solution of the Schrodinger or the Heisenberg equation of motion generated by a linear operator H acting in some complex Hilbert space H, which may be unbounded, not symmetric, or not…
The Einstein relation describes the response of a diffusing particle to a small constant external force. It states that, as the force tends to zero, the ratio of the limiting velocity to the force magnitude converges to the diffusivity…