"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

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

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

Modified Hamiltonian Monte Carlo for Bayesian Inference

The Hamiltonian Monte Carlo (HMC) method has been recognized as a powerful sampling tool in computational statistics. We show that performance of HMC can be significantly improved by incorporating importance sampling and an irreversible part of the dynamics into a chain. This is achieved by replacing Hamiltonians in the Metropolis test with modified Hamiltonians, and a complete momentum update with a partial momentum refreshment. We call the resulting generalized HMC importance sampler—Mix & Match Hamiltonian Monte Carlo (MMHMC). The method is irreversible by construction and further benefits from (i) the efficient algorithms for computation of modified Hamiltonians; (ii) the implicit momentum update procedure and (iii) the multi-stage splitting integrators specially derived for the methods sampling with modified Hamiltonians. MMHMC has been implemented, tested on the popular statistical models and compared in sampling efficiency with HMC, Riemann Manifold Hamiltonian Monte Carlo, Generalized Hybrid Monte Carlo, Generalized Shadow Hybrid Monte Carlo, Metropolis Adjusted Langevin Algorithm and Random Walk Metropolis-Hastings. To make a fair comparison, we propose a metric that accounts for correlations among samples and weights, and can be readily used for all methods which generate such samples. The experiments reveal the superiority of MMHMC over popular sampling techniques, especially in solving high dimensional problems.Agile BioFoundry (http://agilebiofoundry.org) supported by the U.S. Department of Energy, Energy Efficiency and Renewable Energy, Bioenergy Technologies Office, through contract DE-AC02-05CH11231 between Lawrence Berkeley National Laboratory and the U.S. Department of Energy

Causality, 'superluminality', and reshaping in undersized waveguides

We analyse the reshaping mechanism leading to apparently 'superluminal' advancement of a pulse traversing an undersized section of a waveguide. For frequencies below the first inelastic threshold (cut off one), there are only evanescent modes in the narrow region, and the problem becomes similar to quantum mechanical tunnelling across an effective rectangular 'barrier'. In the coordinate representation, the 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'