Related papers: Time of arrival in Classical and Quantum Mechanics
The tunneling time problem earlier studied in Phys. Rev. Lett 108 170402 (2012) using a non-relativistic time-of-arrival (TOA) operator predicted that tunneling time is instantaneous. This raises the question on whether instantaneous…
A number of approaches to the problem of defining arrival and dwell time probabilities in quantum theory make use of idealised models of clocks. An interesting question is the extent to which the probabilities obtained in this way are…
Possible theoretical frameworks for measurement of (arrival) time in the nonrelativistic quantum mechanics are reviewed. It is argued that the ambiguity between indirect measurements by a suitably introduced time operator and direct…
Using a group theoretical approach we derive an equation of motion for a mixed quantum-classical system. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics: The bracket…
We review here some conventional as well as less conventional aspects of the time-independent and time-dependent Hamilton-Jacobi (HJ) theory and of its connections with Quantum Mechanics. Less conventional aspects involve the HJ theory on…
We compare the proposals that have appeared in the literature to describe a measurement of the time of arrival of a quantum particle at a detector. We show that there are multiple regimes where different proposals give inequivalent,…
The Copenhagen interpretation of quantum mechanics assumes the existence of the classical deterministic Newtonian world. We argue that in fact the Newton determinism in classical world does not hold and in classical mechanics there is…
We consider the classical concept of time of permanence and observe that its quantum equivalent is described by a bona fide self-adjoint operator. Its interpretation, by means of the spectral theorem, reveals that we have to abandon not…
Motivated by a recent prediction [Com. Phys., 6, 195 (2023)] that time-of-flight experiments with ultracold atoms could test different interpretations of quantum mechanics, this work investigates the arrival times predicted by the…
I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized…
We analyze the issue of dynamical evolution and time in quantum cosmology. We emphasize the problem of choice of phase space variables that can play the role of a time parameter in such a way that for expectation values of quantum operators…
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
A new dynamical paradigm merging quantum dynamics with cosmology is discussed. Time evolution involves a genuine passage of time, which distinguishes the formalism from those where dynamics in space is equivalent to statics in space-time.…
We propose that measurements of time-of-arrival correlations in multi-partite systems can sharply distinguish between different approaches to the time-of-arrival problem. To show this, we construct a Positive-Operator-Valued measure for two…
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,…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
When compared to quantum mechanics, classical mechanics is often depicted in a specific metaphysical flavour: spatio-temporal realism or a Newtonian "background" is presented as an intrinsic fundamental classical presumption. However, the…
We extend the recently developed causal superfermion approach to the real-time transport theory to time-dependent decay problems.Its usefulness is illustrated for the Anderson model of a quantum dot with tunneling rates depending on spin…
We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain…
The problem of time in quantum mechanics concerns the fact that in the Schr\"odinger equation time is a parameter, not an operator. Pauli's objection to a time-energy uncertainty relation analogue to the position-momentum one, conjectured…