Quantum mechanical description of Stern-Gerlach experiments

The motion of neutral particles with magnetic moments in an inhomogeneous magnetic field is described in a quantum mechanical framework. The validity of the semi-classical approximations which are generally used to describe these phenomena is discussed. Approximate expressions for the evolution operator are derived and compared to the exact calculations. Focusing and spin-flip phenomena are predicted. The reliability of Stern-Gerlach experiments to measure spin projections is assessed in this framework.Comment: 12 pages, 7 eps figures included, revtex, submitted to PR

Derivation of the Planck Spectrum for Relativistic Classical Scalar Radiation from Thermal Equilibrium in an Accelerating Frame

The Planck spectrum of thermal scalar radiation is derived suggestively within classical physics by the use of an accelerating coordinate frame. The derivation has an analogue in Boltzmann's derivation of the Maxwell velocity distribution for thermal particle velocities by considering the thermal equilibrium of noninteracting particles in a uniform gravitational field. For the case of radiation, the gravitational field is provided by the acceleration of a Rindler frame through Minkowski spacetime. Classical zero-point radiation and relativistic physics enter in an essential way in the derivation which is based upon the behavior of free radiation fields and the assumption that the field correlation functions contain but a single correlation time in thermal equilibrium. The work has connections with the thermal effects of acceleration found in relativistic quantum field theory.Comment: 23 page

Comparative Analysis of the Mechanisms of Fast Light Particle Formation in Nucleus-Nucleus Collisions at Low and Intermediate Energies

The dynamics and the mechanisms of preequilibrium-light-particle formation in nucleus-nucleus collisions at low and intermediate energies are studied on the basis of a classical four-body model. The angular and energy distributions of light particles from such processes are calculated. It is found that, at energies below 50 MeV per nucleon, the hardest section of the energy spectrum is formed owing to the acceleration of light particles from the target by the mean field of the projectile nucleus. Good agreement with available experimental data is obtained.Comment: 23 pages, 10 figures, LaTeX, published in Physics of Atomic Nuclei v.65, No. 8, 2002, pp. 1459 - 1473 translated from Yadernaya Fizika v. 65, No. 8, 2002, pp. 1494 - 150

A Deeper Look at Student Learning of Quantum Mechanics: the Case of Tunneling

We report on a large-scale study of student learning of quantum tunneling in 4 traditional and 4 transformed modern physics courses. In the transformed courses, which were designed to address student difficulties found in previous research, students still struggle with many of the same issues found in other courses. However, the reasons for these difficulties are more subtle, and many new issues are brought to the surface. By explicitly addressing how to build models of wave functions and energy and how to relate these models to real physical systems, we have opened up a floodgate of deep and difficult questions as students struggle to make sense of these models. We conclude that the difficulties found in previous research are the tip of the iceberg, and the real issue at the heart of student difficulties in learning quantum tunneling is the struggle to build the complex models that are implicit in experts' understanding but often not explicitly addressed in instruction.Comment: v2, v3 updated with more detailed analysis of data and discussion; submitted to Phys. Rev. ST: PE

Two-Bit Gates are Universal for Quantum Computation

A proof is given, which relies on the commutator algebra of the unitary Lie groups, that quantum gates operating on just two bits at a time are sufficient to construct a general quantum circuit. The best previous result had shown the universality of three-bit gates, by analogy to the universality of the Toffoli three-bit gate of classical reversible computing. Two-bit quantum gates may be implemented by magnetic resonance operations applied to a pair of electronic or nuclear spins. A ``gearbox quantum computer'' proposed here, based on the principles of atomic force microscopy, would permit the operation of such two-bit gates in a physical system with very long phase breaking (i.e., quantum phase coherence) times. Simpler versions of the gearbox computer could be used to do experiments on Einstein-Podolsky-Rosen states and related entangled quantum states.Comment: 21 pages, REVTeX 3.0, two .ps figures available from author upon reques

Derivation of the Blackbody Radiation Spectrum from a Natural Maximum-Entropy Principle Involving Casimir Energies and Zero-Point Radiation

By numerical calculation, the Planck spectrum with zero-point radiation is shown to satisfy a natural maximum-entropy principle whereas alternative choices of spectra do not. Specifically, if we consider a set of conducting-walled boxes, each with a partition placed at a different location in the box, so that across the collection of boxes the partitions are uniformly spaced across the volume, then the Planck spectrum correspond to that spectrum of random radiation (having constant energy kT per normal mode at low frequencies and zero-point energy (1/2)hw per normal mode at high frequencies) which gives maximum uniformity across the collection of boxes for the radiation energy per box. The analysis involves Casimir energies and zero-point radiation which do not usually appear in thermodynamic analyses. For simplicity, the analysis is presented for waves in one space dimension.Comment: 11 page

Magnetic operations: a little fuzzy physics?

We examine the behaviour of charged particles in homogeneous, constant and/or oscillating magnetic fields in the non-relativistic approximation. A special role of the geometric center of the particle trajectory is elucidated. In quantum case it becomes a 'fuzzy point' with non-commuting coordinates, an element of non-commutative geometry which enters into the traditional control problems. We show that its application extends beyond the usually considered time independent magnetic fields of the quantum Hall effect. Some simple cases of magnetic control by oscillating fields lead to the stability maps differing from the traditional Strutt diagram.Comment: 28 pages, 8 figure

Cosmic Background Bose Condensation (CBBC)

Degeneracy effects for bosons are more important for smaller particle mass, smaller temperature and higher number density. Bose condensation requires that particles be in the same lowest energy quantum state. We propose a cosmic background Bose condensation, present everywhere, with its particles having the lowest quantum energy state, A c/lambda, with lambda about the size of the visible universe, and therefore unlocalized. This we identify with the quantum of the self gravitational potential energy of any particle, and with the bit of information of minimum energy. The entropy of the universe (similar to 10(122) bits) has the highest number density (similar to 10(36) bits/cm(3)) of particles inside the visible universe, the smallest mass, similar to 10(-66) g, and the smallest temperature, similar to 10(-29) K. Therefore it is the best candidate for a Cosmic Background Bose Condensation (CBBC), a completely calmed fluid, with no viscosity, in a superfluidity state, and possibly responsible for the expansion of the universe.Alfonso-Faus, A.; Fullana Alfonso, MJ. (2013). Cosmic Background Bose Condensation (CBBC). Astrophysics and Space Science. 347(1):193-196. doi:10.1007/s10509-013-1500-8S1931963471Alfonso-Faus, A.: Universality of the self gravitational potential energy of any fundamental particle. Astrophys. Space Sci. 337, 363 (2010a)Alfonso-Faus, A.: The case for the Universe to be a quantum black hole. Astrophys. Space Sci. 325, 113 (2010b)Alfonso-Faus, A.: Galaxies: kinematics as a proof of the existence of a universal field of minimum acceleration. arXiv:0708.0308 (2010c, preprint)Alfonso-Faus, A.: Quantum gravity and information theories linked by the physical properties of the bit. arXiv:1105.3143 (2011, preprint)Anderson, J.D., et al.: Indication, from Pioneer 10/11, Galileo, and Ulysses data, of an apparent anomalous, weak, long-range acceleration. Phys. Rev. Lett. 81, 2858 (1998)Bekenstein, J.D.: Phys. Rev. D 23(2), 287 (1981)Bérut, A., et al.: Experimental verification of Landauer’s principle linking information and thermodynamics. Nature 483, 187 (2012)Drees, M., Chung-Lin, S.: Theoretical interpretation of experimental data from direct dark matter detection. J. Cosmol. Astropart. Phys. 0706, 011 (2007)Eisberg, R., Resnick, R.: Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles, 2nd edn. Wiley, New York (1985)Funo, K., Watanabe, Y., Ueda, M.: Thermodynamic work gain from entanglement. arXiv:1207.6872 [quant-ph] (2012, preprint)Hawking, S.W.: Black hole explosions? Nature 248, 30 (1974)Landauer, R.: Irreversibility and heat generation in the computing process. IBM J. Res. Dev. 5, 183 (1961)Landauer, R.: Dissipation and noise immunity in computation and communication. Nature 335, 779 (1988)Lloyd, S.: Computational capacity of the universe. Phys. Rev. Lett. 88, 237901 (2002)Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation. Freeman, Reading (1973), p. 466 (“Why the energy of the gravitational field cannot be localized”)Scarpa, R., Falomo, R.: Testing Newtonian gravity in the low acceleration regime with globular clusters: the case of omega Centauri revisited. Astron. Astrophys. 523, A43 (2010)Sivaram, C.: Cosmological and quantum constraint on particle masses. Am. J. Phys. 50, 279 (1982)Susskind, L.: The World as a hologram. J. Math. Phys. 36, 6377 (1995)’t Hooft, G.: Dimensional reduction in quantum gravity. arXiv:gr-qc/9310026 (1993, preprint)Toyabe, S., et al.: Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality. Nat. Phys. 6, 988 (2010)Unruh, W.G.: Notes on black-hole evaporation. Phys. Rev. D, Part. Fields 14(4), 870 (1976)Weinberg, S.: Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity p. 619. Wiley, New York (1972