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Murray Peshkin

Publications and source records attributed to Murray Peshkin.

16 recordsLinked to original sources
arXiv2017

Non-exponential and oscillatory decays in quantum mechanics

The quantum-mechanical theory of the decay of unstable states is revisited. We show that the decay is non-exponential both in the short-time and long-time limits using a more physical definition of the decay rate than the one usually used. We report results of numerical studies based on Winter's model that may elucidate qualitative features of exponential and non-exponential decay more generally. The main exponential stage is related to the formation of a radiating state that maintains the shape of its wave function with exponentially diminishing normalization. We discuss situations where the radioactive decay displays several exponents. The transient stages between different regimes are typically accompanied by interference of various contributions and resulting oscillations in the decay curve. The decay curve can be fully oscillatory in a two-flavor generalization of Winter's model with some values of the parameters. We consider the implications of that result for models of the oscillations reported by GSI.

nucl-th↗
arXiv2014

Oscillating Decay Rate in Electron Capture and the Neutrino Mass Difference

Reported oscillations in the rate of decay of certain ions by K-electron capture have raised questions about whether and how such oscillations can arise in quantum mechanical theory and whether they can measure the neutrino mass difference. Here I show that simple principles of quantum mechanics answer some questions and clarify what must be done theoretically or experimentally to answer some others. The principal result is that quantum mechanics does allow mass-difference-dependent oscillations in principle, but it imposes conditions not obeyed by the approximate dynamical models that have been put forth up to now. What needs to be done experimentally and theoretically is discussed.

nucl-th↗
arXiv2014

Decay Oscillations in Electron Capture and the Neutrino Mass Difference

Quantum mechanical theory disallows the model that has been used to infer the neutrino mass difference from the reported "GSI oscillations" in the rates of decay of hydrogen-like ions by electron capture. It has not been proved that the existence of mass-difference-dependent oscillations conflicts with quantum mechanics but no consistent quantum mechanical model has been shown to predict them.

nucl-th↗
arXiv2010

Against a proposed alternative explanation of the Aharonov-Bohm effect

The Aharonov-Bohm effect is understood to demonstrate that the Maxwell fields can act nonlocally in some situations. However it has been suggested from time to time that the AB effect is somehow a consequence of a local classical electromagnetic field phenomenon involving energy that is temporarily stored in the overlap between the external field and the field of which the beam particle is the source. That idea was shown in the past not to work for some models of the source of the external field. Here a more general proof is presented for the magnetic AB effect to show that the overlap energy is always compensated by another contribution to the energy of the magnetic field in such a way that the sum of the two is independent of the external flux. Therefore no such mechanism can underlie the Aharonov-Bohm effect.

quant-ph↗
arXiv2008

Comment on "The GSI method for studying neutrino mass differences - For Pedestrians"

It has been suggested that the reported temporal oscillations in the weak decay of H-like ions circulating in the GSI storage ring may be accounted for by interference between two different momentum components of the wave function of the parent ions. In that model, the interference is said to come about through coupling of those two momentum components to the two mass components in the wave function of the electron neutrino in the decayed state. I show here that quantum mechanics allows no such interference to contribute to the reported oscillation of the decay rate. The central issue is that the storage ring is a million times too small to allow the parent ion's wave function to produce the needed interference effect. This note supersedes earlier arXiv postings that were less general and less rigorous.

hep-ph↗
arXiv2008

Comment on "New method for studying neutrino mixing and mass differences"

It has been suggested that the temporal oscillations in the rate of decay of Pr ions reported in the GSI K-capture experiment arise from interference between different values of the momentum of the Pr ions. It is shown here that any such interference cannot contribute to the decay rate of those ions.

hep-ph↗
arXiv2004

Reply to "Non-relativistic proofs of the spin-statistics connection," by Shaji and Sudarshan

I earlier proved under stated assumptions of nonrelativistic quantum mechanics, that identical spin-zero particles with no internal degrees of freedom must be bosons. Shaji and Sudarshan have criticized that proof, asserting that it is "based on single-valuedness under rotation of the wave functions of systems of identical particles." No such assumption was used. Here, to remove all doubt, I exclude the fermion possibility through a proof in which even the existence of rotation is not used. Following that, I assume that the Hilbert space is invariant under rotation to exclude other symmetries which correspond neither to bosons nor to fermions. In that proof no issue of single-valuedness can arise.

quant-ph↗
arXiv2003

Reply to "No spin-statistics connection in nonrelativistic quantum mechanics"

In a previous paper [quant-ph/0207017] I gave an elementary proof, starting from stated assumptions of nonrelativistic quantum mechanics, that identical spin-zero particles must be bosons. Since then it has been suggested that my proof assumed its conclusion, and that it is based on a theory "quite different from standard physics." [quant-ph/0304088] I show here that those two statements are incorrect.

quant-ph↗
arXiv2000

Comment on "Observation of Superluminal Behaviors in Wave Propagation"

Mugnai et al. have reported an experiment in which microwave packets appear to travel in air with a speed substantially greater than c. They calculate the group velocity of their packets and find that it agrees with their experimental result. That calculation is incorrect. A correct calculation gives a group velocity less than c. The reported experimental result cannot be reconciled with the Maxwell equations.

physics.optics↗
arXiv2000

Comment on "Quantum Phase Shift Caused by Spatial Confinement", by B.E. Allman et al

The analysis of phase shifts in executed and proposed interferometry experiments on photons and neutrons neglected forces exerted at the boundaries of spatial constrictions. When those forces are included it is seen that the observed phenomena are not in fact geometric in nature. A new proposal to be published by Allman et al. avoids that pitfall.

quant-ph↗
arXiv1998

Force-Free Interactions and Nondispersive Phase Shifts in Interferometry

Zeilinger's observation that phenomena of the Aharonov-Bohm type lead to nondispersive, i.e. energy-independent, phase shifts in interferometers is generalized in a new proof which shows that the precise condition for nondispersivity is a force-free interaction. The converse theorem is disproved by a conceptual counter example. Applications to several nondispersive interference phenomena are reviewed briefly. Those fall into two classes which are objectively distinct from each other in that in the first class phase shifts depend only on the topology of the interfering beam paths while in the second class force-free physical interactions take place at identifiable points along the path. Apparent disagreements in the literature about the topological nature of the phenomena in the second class stem from differing definitions.

quant-ph↗
arXiv1995

Off-Diagonal Long-Range Order, Restricted Gauge Transformations, and Aharonov-Bohm Effect in Conductors

The Hamiltonian describing a conductor surrounding an external magnetic field contains a nonvanishing vector potential in the volume accessible to the electrons and nuclei of which the conductor is made. That vector potential cannot be removed by a gauge transformation. Nevertheless, a macroscopic normal conductor can experience no Aharonov-Bohm effect. That is proved by assuming only that a normal conductor lacks off-diagonal long-range order (ODLRO). Then by restricting the Hilbert space to density matrices which lack ODLRO, it is possible to introduce a restricted gauge transformation that removes the interaction of the conductor with the vector potential.

quant-ph↗
arXiv1995

Topology, Locality, and Aharonov-Bohm Effect with Neutrons

Recent neutron interferometry experiments have been interpreted as demonstrating a new topological phenomenon similar in principle to the usual Aharonov-Bohm (AB) effect, but with the neutron's magnetic moment replacing the electron's charge. We show that the new phenomenon, called Scalar AB (SAB) effect, follows from an ordinary local interaction, contrary to the usual AB effect, and we argue that the SAB effect is not a topological effect by any useful definition. We find that SAB actually measures an apparently novel spin autocorrelation whose operator equations of motion contain the local torque in the magnetic field. We note that the same remarks apply to the Aharonov-Casher effect.

quant-ph↗