"Superluminal paradox" in wavepacket propagation and its quantum mechanical resolution

We analyse in detail the reshaping mechanism leading to apparently "superluminal" advancement of a wave packet traversing a classically forbidden region. In the coordinate representation, a barrier is shown to act as an effective beamsplitter, recombining envelopes of the freely propagating pulse with various spacial shifts. Causality ensures that none of the constituent envelopes are advanced with respect to free propagation, yet the resulting pulse is advanced due to a peculiar interference effect, similar to the one responsible for "anomalous" values which occur in Aharonov's "weak measurements". In the momentum space, the effect is understood as a bandwidth phenomenon, where the incident pulse probes local, rather than global, analytical properties of the transmission amplitude T (p). The advancement is achieved when T (p) mimics locally an exponential behaviour, similar to the one occurring in Berry's "superoscillations". Seen in a broader quantum mechanical context, the "paradox" is but a consequence of an attempt to obtain "which way?" information without destroying the interference between the pathways of interest. This explains, to a large extent, the failure to adequately describe tunnelling in terms of a single "tunnelling time"

No Time at the End of the Tunnel

Modern atto-second experiments seek to provide an insight into a long standing question: “how much time does a tunnelling particle spend in the barrier?” Traditionally, quantum theory relates this duration to the delay with which the particle emerges from the barrier. The link between these two times is self-evident in classical mechanics, but may or may not exist in the quantum case. Here we show that it does not, and give a detailed explanation why. The tunnelling process does not lend itself to classical analogies, and its duration cannot, in general, be guessed by observing the behaviour of the transmitted particle

Interference mechanism of seemingly superluminal tunnelling

Apparently 'superluminal' transmission, e.g., in quantum tunnelling and its variants, occurs via a subtle interference mechanism which allows reconstruction of the entire spacial shape of a wave packet from its front tail. It is unlikely that the effect could be described adequately in simpler terms

Dynamic modeling of the morphology of latex particles with in situ formation of graft copolymer

Modification of the polymer-polymer interfacial tension is a way to tailor-make particle morphology of waterborne polymer-polymer hybrids. This allows achieving a broader spectrum of application properties and maximizing the synergy of the positive properties of both polymers, avoiding their drawbacks. In situ formation of graft copolymer during polymerization is an efficient way to modify the polymer-polymer interfacial tension. Currently, no dynamic model is available for polymer-polymer hybrids in which a graft copolymer is generated during polymerization. In this article, a novel model based on stochastic dynamics is developed for predicting the dynamics of the development of particle morphology for composite waterborne systems in which a graft copolymer is produced in situ during the process

Adaptive multi-stage integrators for optimal energy conservation in molecular simulations

We introduce a new Adaptive Integration Approach (AIA) to be used in a wide range of molecular simulations. Given a simulation problem and a step size, the method automatically chooses the optimal scheme out of an available family of numerical integrators. Although we focus on two-stage splitting integrators, the idea may be used with more general families. In each instance, the system-specific integrating scheme identified by our approach is optimal in the sense that it provides the best conservation of energy for harmonic forces. The AIA method has been implemented in the BCAM-modified GROMACS software package. Numerical tests in molecular dynamics and hybrid Monte Carlo simulations of constrained and unconstrained physical systems show that the method successfully realises the fail-safe strategy. In all experiments, and for each of the criteria employed, the AIA is at least as good as, and often significantly outperforms the standard Verlet scheme, as well as fixed parameter, optimized two-stage integrators. In particular, the sampling efficiency found in simulations using the AIA is up to 5 times better than the one achieved with other tested schemes

An even simpler understanding of quantum weak values

We explain the properties and clarify the meaning of quantum weak values using only the basic notions of elementary quantum mechanics.MTM2013-46553-C3-1-

Meso-GSHMC: A stochastic algorithm for meso-scale constant temperature simulations

We consider the problem of time-stepping/sampling for molecular and meso-scale particle dynamics. The aim of the work is to derive numerical time-stepping methods that generate samples exactly from the desired target temperature distribution. The numerical methods proposed in this paper rely on the well-known splitting of stochastic thermostat equations into conservative and fluctuation-dissipation parts. We propose a methodology to derive numerical approximation to the fluctuation-dissipation part that exactly samples from the underlying Boltzmann distribution. Our methodology applies to Langevin dynamics as well as Dissipative Particle Dynamics and, more generally, to arbitrary position dependent fluctuation-dissipation terms. A Metropolis criterion is introduced to correct for numerical inconsistency in the conservative dynamics part of the model. Shadow energies are used to increase the acceptance rate under the Metropolis criterion. We call the newly proposed method meso-GSHMC

The Hartman effect and weak measurements "which are not really weak"

We show that in wavepacket tunnelling localisation of the transmitted particle amounts to a quantum measurement of the delay it experiences in the barrier. With no external degree of freedom involved, the envelope of the wavepacket plays the role of the initial pointer state. Under tunnelling conditions such 'self measurement' is necessarily weak, and the Hartman effect just reflects the general tendency of weak values to diverge, as post-selection in the final state becomes improbable. We also demonstrate that it is a good precision, or 'not really weak' quantum measurement: no matter how wide the barrier d, it is possible to transmit a wavepacket with a width {\sigma} small compared to the observed advancement. As is the case with all weak measurements, the probability of transmission rapidly decreases with the ratio {\sigma}/d.Comment: 6 pages, 1 figur

Wigner's friends, tunnelling times and Feynman's "only mystery of quantum mechanics"

Recent developments in elementary quantum mechanics have seen a number of extraordinary claims regarding quantum behaviour, and even questioning internal consistency of the theory. These are, we argue, different disguises of what Feynman described as quantum theory's "only mystery".ELKARTEK KK-2021/00064; KK-2021/00022; KK-2020/0000

Dynamic modeling of the morphology of multiphase waterborne polymer particles

Multiphase waterborne polymer particles provide advantages in more demanding applications, and their performance depends on particle morphology. Currently, no dynamic model for the prediction of the development of the morphology of multiphase latex particles is available. In this work, a model was developed for the prediction of the dynamic development of the morphology of multiphase waterborne systems, such as polymer-polymer and polymer-polymer- inorganic hybrids