Showing papers in "Physics in 1964"

On the Einstein-Podolsky-Rosen paradox

Abstract: THE paradox of Einstein, Podolsky and Rosen [1] was advanced as an argument that quantum mechanics could not be a complete theory but should be supplemented by additional variables These additional variables were to restore to the theory causality and locality [2] In this note that idea will be formulated mathematically and shown to be incompatible with the statistical predictions of quantum mechanics It is the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty There have been attempts [3] to show that even without such a separability or locality requirement no "hidden variable" interpretation of quantum mechanics is possible These attempts have been examined elsewhere [4] and found wanting Moreover, a hidden variable interpretation of elementary quantum theory [5] has been explicitly constructed That particular interpretation has indeed a grossly nonlocal structure This is characteristic, according to the result to be proved here, of any such theory which reproduces exactly the quantum mechanical predictions

Quantum mechanical phase and time operator

Abstract: The phase operator for an oscillator is shown not to exist. It is replaced by a pair of non-commuting sin and cos operators which can be used to define uncertainty relations for phase and number. The relation between phase and angle operators is carefully discussed. The possibility of using a phase variable as a quantum clock is demonstrated and the states for which the clock is most accurate are constructed.

The symmetry group of vector and axial vector currents

Abstract: We review, modify slightly, generalize, and attempt to apply a theory proposed earlier of a higher broken symmetry than the eightfold way. The integrals of the time components of the vector and axial vector current octets are assumed to generate, under equal time commutation, the algebra of $\mathrm{SU}(3)\phantom{\rule{0.25em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.25em}{0ex}}\mathrm{SU}(3)$. The energy density of the strong interactions is assumed to consist of a piece invariant under the algebra, a piece that violates conservation of the axial vector currents only and belongs to the representation $(3,\phantom{\rule{0.25em}{0ex}}3*)$ and $(3*,\phantom{\rule{0.25em}{0ex}}3)$, and a piece that violates the eightfold way and probably belongs to $(1,\phantom{\rule{0.25em}{0ex}}8)$ and $(8,\phantom{\rule{0.25em}{0ex}}1)$. Assuming the algebraic structure is exactly correct, there is still the question of whether one can assign particles approximately to super-supermultiplets. The pseudoscalar meson octet, together with a pseudoscalar singlet, a scalar octet, and a scalar singlet, may belong to $(3,\phantom{\rule{0.25em}{0ex}}3*)$ and $(3*,\phantom{\rule{0.25em}{0ex}}3)$. The vector meson octet, together with an axial vector octet, may belong to $(1,\phantom{\rule{0.25em}{0ex}}8)$ and $(8,\phantom{\rule{0.25em}{0ex}}1)$. The baryon octet with $\mathrm{J}\phantom{\rule{0.15em}{0ex}}=\phantom{\rule{0.15em}{0ex}}1/{2}^{+}$, together with a singlet with $\mathrm{J}\phantom{\rule{0.15em}{0ex}}=\phantom{\rule{0.15em}{0ex}}1/{2}^{\ensuremath{-}}$, may belong to $(3,\phantom{\rule{0.25em}{0ex}}3*)$ and $(3*,\phantom{\rule{0.25em}{0ex}}3)$, as suggested before. Several crude coupling patterns and mass rules emerge, to zeroth or first order in the symmetry violations. Some are roughly in agreement with experiment, but certain predictions, like that of the existence of a scalar octet, have not been verified. Whether or not they are useful as an approximate symmetry, the equal time commutation rules fix the scale of the weak interaction matrix elements. Further rules of this kind are found to hold in certain Lagrangian field theory models and may be true in reality. In particular, we encounter an algebraic system based on $\mathrm{SU}(6)$ that relates quantities with different kinds of behavior under Lorentz transformations.

The magnetic properties of superconducting alloys I

Abstract: The general Ginzburg - Landau equation valid for all temperatures is derived from the microscopic theory for superconducting alloys where the electronic mean free path 1 is much shorter than the coherence length ${\ensuremath{\xi}}_{0}$.Using this equation the magnetic properties of Abrikosov's mixed state as well as the temperature dependence of the upper critical field ${\mathrm{H}}_{\mathrm{c}\phantom{\rule{0.25em}{0ex}}2}$ are discussed. It is shown that the Abrikosov structure in the vicinity of the transition point is completely characterized by two parameters ${\ensuremath{\kappa}}_{1}(\mathrm{T})$ and ${\ensuremath{\kappa}}_{2}(\mathrm{T})$, both of which coincide at the critical temperature with $\ensuremath{\kappa}$, the Ginzburg-Landau parameter. A peculiar deviation in the thermodynamical behavior at lower temperatures from Abrikosov's theory is found for superconductors with $\ensuremath{\kappa}\ensuremath{\simeq}1/\sqrt{2}$.

The magnetic properties of superconducting alloys. II

Abstract: The lower critical field ${\mathrm{H}}_{\mathrm{c}1}$ is derived from the microscopic theory for superconducting alloys. It is shown that Abrikosov's structure in the field just above ${\mathrm{H}}_{\mathrm{c}1}$ is described by the use of a parameter of which the temperature dependence is obtained. A brief discussion of the gap in the excitation spectrum and the thermodynamical behavior at lower temperatures is given.Next the effect of the Pauli paramagnetism on the magnetic properties of superconducting alloys is investigated in detail. It is shown that Abrikosov's structure is still described completely by the use of two parameters ${\ensuremath{\kappa}}_{1}{}^{*}(\mathrm{T})$ and ${\ensuremath{\kappa}}_{2}{}^{*}(\mathrm{T})$ in the vicinity of the transition point when the phase transition is of the second order. In superconductors having a large Pauli term $\frac{3\ensuremath{\mu}}{e{\ensuremath{\tau}}_{\mathrm{tr}}{\mathrm{v}}^{2}}\ensuremath{\ge}1.475$ where $\ensuremath{\mu}$ is the Bohr magneton, ${\ensuremath{\tau}}_{\mathrm{tr}}$ the transport collision time of an electron and v the fermi velocity, the order of the transition is found to change from the second to the first as temperature decreases.

Magnetic behavior of very small superconducting particles

Abstract: This paper discusses the critical field of superconducting particles, or films, much smaller in size than the coherence length and the penetration depth; it is restricted to situations where the order parameter may be taken as constant in space, and where the superconducting transition in the presence of the field is of second order The critical field calculation is then reduced to a study of the magnetic flux $\mathrm{\ensuremath{\Phi}}$ enclosed by all one-electron trajectories in the normal state during a prescribed time interval $\mathrm{t}$ We show that (1) if $\mathrm{\ensuremath{\Phi}}$ does not have a completely ergodic behavior at large times, the equation of state is of the BCS type, but with a renormalized, field dependent coupling constant $\mathrm{N}(0)\mathrm{V}$ $\ensuremath{\eta}(\mathrm{H})$ (2) if $\mathrm{\ensuremath{\Phi}}$ has a certain ergodic property, the effect of the field is comparable to the effect of paramagnetic impurities, as first pointed out in a particular example by Maki Among other things there is a region of gapless superconductivity in the $(\mathrm{HT})$ planeA thin film in a parallel field with diffuse boundary scattering but no volume defects belongs to case (1) This surprising result is due to a geometrical cancellation of successive contributions to $\mathrm{\ensuremath{\Phi}}$ However, a rather small amount of scattering in the bulk is enough to restore case (2) Numerical values of the resulting critical field are discussed in detail for various ratios of the bulk mean free path 1 to the film thickness $\mathrm{d}$ In the situations of major physical interest the theoretical values are proportional to ${\mathrm{d}}^{\ensuremath{-}3/2}$ and are in rather good agreement with the experimental data

Electron spin resonance of irradiated dna

Abstract: When DNA is irradiated by ultraviolet light a paramagnetic damage center is formed in the thymine bases. The structure of this free radical has been determined by electron spin resonance and consists of a hydrogen addition at the carbon No. 6 position. The rate of formation of the radical is enhanced by water vapor, and it is quenched by paramagnetic ions bound to the DNA.

Spin correlations in MnO

Abstract: Spin correlations have been investigated in powder samples of $\mathrm{MnO}$ above and below the N\'eel temperature by means of diffuse neutron scattering measurements. There is a significant local order above ${\mathrm{T}}_{\mathrm{N}}$, with the spins coupled in an antiferromagnetic fashion and tending to lie parallel to ${111}$ planes. This layer structure suggests a second neighbor interaction energy, with ${\mathrm{V}}_{2}=4.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\mathrm{eV}$ and with the exchange interaction ${\mathrm{J}}_{2}=\ensuremath{-}4.6\ifmmode^\circ\else\textdegree\fi{}$. There was no evidence for an extra total scattering in the vicinity of the critical temperature.

Proposal for a cyclotron resonance maser in InSb

Abstract: A scheme for amplifying cyclotron resonance radiation in InSb is outlined. To obtain amplification two requirements must be satisfied. The first is that the electron velocity distribution be monoenergetic. Such distributions can be produced by photoexciting electrons in cold p-type InSb. Detailed calculations show that, with a reasonable electron density, the distribution remains monoenergetic throughout the electron lifetime. The second requirement for amplification is that stimulated absorption of cyclotron radiation be inhibited as compared to stimulated emission. This criterion is met by producing the photoelectrons at an energy just below that of the optical phonon in InSb. As a consequence, the stimulated absorption line is broad compared to that for emission, so the latter predominates. Numerical estimates indicate that there is a reasonable chance of producing a far infrared amplifier based upon this technique.

Band theory of magnetism in metals in context of exactly soluble model

Abstract: The role of spatial forces, and of Hund's rule (exchange) forces, and the validity of the Hartree-Fock approximation in the band theory of magnetism of metals is reviewed. Some reasonable conjectures which have been made elsewhere by the author and others are examined in the light of an exactly soluble model of interacting electrons in one dimension. It is shown that within the framework of validity of this model, spatial i.e., direct (Coulomb) forces do not influence the spin susceptibility, and conversely, Hund's rule exchange forces do not affect the dielectric constant or plasmon spectrum. It is recalled that the time-independent Hartree-Fock approximation yields an incorrect spectrum of elementary excitations, and it is also shown explicitly that the magnetic susceptibility calculated in this approximation is incorrect. A paradox is noted, concerning whether ``correlations'' can in fact correct the errors in the H-F approximation. Finally, it is shown that when there are only space forces, such spin density waves as might be introduced in to the H-F ground state of the model are in fact spurious, because they are not representative of the correlations which exist in the true ground state.

On the exchange potential

Abstract: A general form is derived tor the so-called exchange potential. This potential gives a description of the influence of the exclusion principle on the Coulomb scattering. The diagonal elements of the potential give the well-known exchange splitting for stationary states.

On the existence of magnetic monopoles

Abstract: By the Bohm-Aharonov effect, the flux within a long slender solenoid is observable unless it is a multiple of $\mathrm{hc}/\mathrm{e}$. In this case only the ends of the solenoid produce any physical effect and they behave as magnetic monopoles with strength quantized according to Dirac.