Ultra-cold neutrons (UCNs) play an important role in the modern frontier of low-energy physics related to fundamental symmetries. They have enabled an improvement of two orders of magnitude in the measurement of the upper limit of the neutron electric dipole moment (nEDM) compared to beam experiments. Further improvements in both the design of UCN sources and nEDM measurements critically depend on the availability and development of materials which satisfy specific requirements. We present innovative materials used for the fabrication of the cryogenic UCN source at the PULSTAR reactor (NC State University, USA) and for the cryogenic non-magnetic environment required for a new high-precision nEDM experiment seeking a further two-orders-of-magnitude improvement in nEDM sensitivity.

The ultracold neutron (UCN) transport code, MCUCN, designed initially for simulating UCN transportation from a solid deuterium ( SD_2 ) source and neutron electric dipole moment experiments, could not simulate UCN storage and transportation in a superfluid ^4He (SFHe, He-II) source accurately. This limitation arose from the absence of an ^4He upscattering mechanism and the absorption of ^3He . And the provided source energy distribution in MCUCN is different from that in SFHe source. This study introduced enhancements to MCUCN to address these constraints, explicitly incorporating the ^4He upscattering effect, the absorption of ^3He , the loss caused by impurities on converter wall, UCN source energy distribution in SFHe, and the transmission through negative optical potential. Additionally, a Python-based visualization code for intermediate states and results was developed. To validate these enhancements, we systematically compared the simulation results of the Lujan Center Mark3 UCN system by MCUCN and the improved MCUCN code (iMCUCN) with UCNtransport simulations. Additionally, we compared the results of the SUN1 system simulated by MCUCN and iMCUCN with measurement results. The study demonstrates that iMCUCN effectively simulates the storage and transportation of ultracold neutrons in He-II.

Metastability exchange optical pumping (MEOP) is a widely used technique for producing polarized 3He. In connection with an experiment to search for the electric dipole moment of the neutron (nEDM) we have built a MEOP based 3He polarization and injection system to prepare 80 % polarized 3He at room temperature which will be injected into a similar to 400 mK measurement cell filled with superfluid 4He. We describe the polarization and injection system, which is designed to allow for final concentrations of 10-8-10-10 of 80% polarized 3He in the superfluid filled measurement cell. Only approximate to 0.72 % polarization loss due to gradients is expected during injection

The ultra-cold neutron (UCN) source being commissioned at North Carolina State University’s PULSTAR reactor is uniquely optimized for UCN production in the former graphite-filled thermal column outside of the reactor pool. The source utilizes a remote moderation design, which is particularly well suited to the PULSTAR reactor because of its high thermal and epithermal neutron leakage from the core face. This large non-equilibrium flux from the core is efficiently transported to the UCN source through the specially designed beam port in order to optimize UCN production at any given reactor power. The increased distance to the source from the core also greatly limits the heat load on the cryogenic system. A MCNP (Monte Carlo N-Particle) model of this system was developed and is in good agreement with gold foil activation measurements using a test configuration as well as with the real UCN source’s heavy water moderator. These results established a firm baseline for estimates of the cold neutron flux available for UCN production and prove that remote moderation in a thermal column port is a valuable option for future designs of cryogenic UCN sources.

This article reviews the history of J. von Neumann’s analysis of hidden variables in quantum mechanics and the subsequent analysis by others. In his book The Mathematical Foundations of Quantum Mechanics, published in 1932, von Neumann performed an analysis of the consequences of introducing hidden parameters (hidden variables) into quantum mechanics. He arrived at two principal conclusions: first, hidden variables cannot be incorporated into the existing theory of quantum mechanics without major modifications, and second, if they did exist, the theory would have already failed in situations where it has been successfully applied. This analysis has been taken as an “incorrect proof” against the existence of hidden variables, possibly due to a mistranslation of the German word prufen. von Neumann’s so-called proof isn’t even wrong as such a proof does not exist, but it is an examination of the limitations imposed by internal consistency of the Hilbert space formulation of the theory. One of the earliest attempts to eliminate uncertainty, by D. Bohm, requires a major modification of quantum mechanics (observables are not represented by Hermitian operators), which supports von Neumann’s first principal conclusion. However, testing the Bohm theory requires constructing a physically impossible initial state. As such, the theory has no experimental consequences, so W. Pauli referred to it as an “uncashable check”. As there are no observable consequences, the Bohm theory is possibly a counterexample to von Neumann’s second conclusion that hidden variables in particular would have already led to a failure of the theory.

The behavior of spins undergoing Larmor precession in the presence of time varying fields is of interest to many research fields. The frequency shifts and relaxation resulting from these fields are related to their power spectrum, determined from the Fourier Transform of the auto-correlation functions of the time varying field. Using the method of images C. M. Swank, A. K. Petukhov, and R. Golub (2012 and 2016) calculated the position-position auto-correlation function for particles moving in a rectangular cell with specular scattering walls. In this work we present a heuristic model that applies the method of images to the case of Lambert scattering walls. The results of this model are compared to simulation and show remarkably good agreement from the ballistic to diffusive regime of gas collisions, for both square and general rectangular cells.

In his book \textit{The Mathematical Foundations of Quantum Mechanics}, published in 1932, J. von Neumann performed an analysis of the consequences of introducing hidden parameters (hidden variables) into quantum mechanics. He showed that hidden variables cannot be incorporated into the existing theory of quantum mechanics without major modifications, and concluded that if they did exist, the theory would have already failed in situations where it has been successfully applied. von Neumann left open the possibility that the theory is not complete, and his analysis for internal consistency is the best that can be done for a self-referenced logical system (G\"odel's theorem). This analysis had been taken as an ``incorrect proof" against the existence of hidden variables. von Neumann's so-called proof isn't even wrong as such a proof does not exist. One of the earliest attempts at a hidden variable theory was by D. Bohm, and because there were no experimental consequences, W. Pauli referred to it as an ``uncashable check." To our knowledge, a successful hidden variable extension to quantum mechanics with testable consequences has not yet been produced, suggesting that von Neumann's analysis is worthy of rehabilitation, which we attempt to provide in a straightforward manner.

Abstract We present Feynman’s path integral derivation of the Schrödinger equation. The van Hove formulation of non-relativistic scattering is presented. We then give a full quantum mechanical treatment of non-relativistic scattering. Both the interaction of the beams with the apparatus and the scattering process itself are treated quantum mechanically. In the spirit of Schrödinger, particle trajectories do not appear, with all of the physics being contained in the phases of the wave function.

Abstract The treatment of spin-1/2 is separated from other angular momentum states because of its unique features, its application to general two-level systems, and its near equivalence to a classical magnetic moment due to a current loop. Larmor’s theorem is reviewed, followed by the development of the algebra of spinors. The effects of weak and strong oscillating fields are elucidated. The relaxation effects of weak perturbations are developed through the density matrix. Two fictitious spin-1/2 (two-level systems) are studied in detail: the ammonia molecule in an electric field, and two-component neutrino oscillations.

Abstract We trace out Schrödinger’s development of his theory. In the beginning, there was no wave equation, but the de Broglie hypothesis motivated Schrödinger to find one. His work culminates with the time-dependent Schrödinger equation. Perturbation theory, both static and time-dependent, were developed. The physical meaning of the wavefunction was defined.

Abstract Working on his Ph.D. thesis, Louis de Broglie asked himself this question: If light, thought to be a wave motion because of observed interference and diffraction effects, could behave like a particle, might particles exhibit some wave-like properties? He justified this idea with several arguments which are highly relevant to an understanding of quantum theory. Among these was the fact that the Bohr-Sommerfeld condition can be derived from the association of a wave with particle motion. This was a critically significant step in the development of quantum mechanics. This work was presented in a relatively short Ph.D. dissertation.

Subject Astronomy and Astrophysics Computational Physics Collection: Oxford Scholarship Online

Abstract While, as Feynman said, nobody can really understand the origin of the Schrödinger equation, we investigate several lines of thought leading to such an equation. We show some simple applications of the equation. An important application was Schrödinger’s solution for the hydrogen atom. This provided a theoretical basis for Bohr’s ad hoc model. We conclude with Schrödinger’s demonstration of the equivalence of his wave mechanics with Heisenberg’s matrix mechanics.

Abstract With the failure of classical physics to explain the experimentally observed black body radiation spectrum, the photoelectric effect and the existence of narrow spectral lines in the light emitted by excited atoms, physicists were forced to reach out for new ideas. Following Planck’s initial “drastic hypothesis” of light “quanta”, Einstein led the way in exploring some of the myriad implications of this idea. In particular, the study of fluctuations led to a new understanding of the interaction of electromagnetic radiation with atoms. Einstein invented the photon by showing, through fluctuation studies, that light emitted by atoms must be in the form of plane waves. These ideas led to the first notions regarding the quantization of matter and its dynamics.

Abstract “EINSTEIN ATTACKS QUANTUM MECHANICS” stated the headline in the New York Times, much to the chagrin of Einstein. He deplored Podolsky’s release of the Einstein, Podolsky, Rosen (EPR) paradox paper to the general public prior to its scientific review. We see how Einstein’s ideas developed both before and after the EPR paper, in which the formulation did not exactly please him. We follow the reactions of the physics community to EPR. EPR eventually led to Bell’s inequalities, meant to challenge the current form of quantum theory. Instead, it led to the experimental confirmation of its most enigmatic effect—the entanglement of two spatially separated particles.

Subject Astronomy and Astrophysics Computational Physics Collection: Oxford Scholarship Online

Fundamental neutron physics, combining precision measurements and theory, probes particle physics at short range with reach well beyond the highest energies probed by the LHC. Significant US efforts are underway that will probe BSM CP violation with orders of magnitude more sensitivity, provide new data on the Cabibbo anomaly, more precisely measure the neutron lifetime and decay, and explore hadronic parity violation. World-leading results from the US Fundamental Neutron Physics community since the last Long Range Plan, include the world's most precise measurement of the neutron lifetime from UCN$\tau$, the final results on the beta-asymmetry from UCNA and new results on hadronic parity violation from the NPDGamma and n-${^3}$He runs at the FNPB (Fundamental Neutron Physics Beamline), precision measurement of the radiative neutron decay mode and n-${}^4$He at NIST. US leadership and discovery potential are ensured by the development of new high-impact experiments including BL3, Nab, LANL nEDM and nEDM@SNS. On the theory side, the last few years have seen results for the neutron EDM from the QCD $\theta$ term, a factor of two reduction in the uncertainty for inner radiative corrections in beta-decay which impacts CKM unitarity, and progress on {\it ab initio} calculations of nuclear structure for medium-mass and heavy nuclei which can eventually improve the connection between nuclear and nucleon EDMs. In order to maintain this exciting program and capitalize on past investments while also pursuing new ideas and building US leadership in new areas, the Fundamental Neutron Physics community has identified a number of priorities and opportunities for our sub-field covering the time-frame of the last Long Range Plan (LRP) under development. This white paper elaborates on these priorities.

Abstract We review the Bohr atomic model, where certain conditions (quantum conditions) were used to select certain “allowed” circular orbits for the electrons in an atom. Sommerfeld realized that a more generalized condition, applied to the action variables, would be consistent with the Bohr condition and also allow elliptical orbits. This condition amounted to the quantization of the phase space occupied by an orbit. This had independently been suggested by Planck. We also discuss the similarities between classical mechanics and the geometric optics limit of a wave theory.

Abstract We continue the discussion of the abstract transformation theory which led to the development of second quantization. Jordan had already suggested (in the foundational papers on matrix mechanics by Heisenberg, Born, and himself) that the electromagnetic field should be represented by a matrix, i.e., quantized. Dirac eventually took up this idea and proposed quantizing the field by treating the field as an operator. Jordan (with others) showed how the same technique could be applied to Bosons and then Fermions. This established the roots of quantum field theory. It also cleared up some of the interpretational issues of the time.