Absolute Zero Temperature Research Articles

Transport entropy of vortices in superconductors with paramagnetic impurities

The entropy ${S}_{D}$ transported by a unit segment of a moving vortex line, in a type-II superconductor in the flux-flow regime, is calculated microscopically for gapless superconductors containing arbitrary amounts of paramagnetic and nonmagnetic impurities, assuming low average magnetic induction $B\ensuremath{\simeq}0$, and large Ginzburg-Landau parameter $\ensuremath{\kappa}\ensuremath{\gg}1$. The calculation is based on a new prescription for calculating certain heat-current-related transport properties in magnetic conductors, recently derived by the author to resolve a contradiction with either the third law of thermodynamics or Onsager's principle. For high concentrations of magnetic impurities, when the gaplessness condition is satisfied at absolute zero temperature, we successfully show for the first time in the low-field limit that a requirement from the third law, viz., ${S}_{D}\ensuremath{\rightarrow}0$ as $T\ensuremath{\rightarrow}0$, is exactly satisfied, thereby giving strong support to the underlying new method for calculating ${S}_{D}$ and other related transport properties. Combining the present results with our earlier results on ${S}_{D}$ in the high-field limit $B\ensuremath{\simeq}{H}_{c2}$, we predict ${S}_{D}$ to first rise linearly as $B$ is lowered from ${H}_{c2}$ and then to bend upward to approach a finite limit as $B$ is further lowered to approach zero, for practically all concentrations of magnetic and nonmagnetic impurities. The exact amount of upward bending depends on the concentrations of the two types of impurities, but is generally larger for dirtier systems. As a side product of this work, we also give a plausible identification of the physical meaning of an anomalous quantity ${u}_{1}$ in the set of dynamic equations first derived by Eliashberg as being proportional to the local temperature deviation from equilibrium.

Depinning by thermal fluctuations of the charge density wave in Peierls Fröhlich state

It is shown that the thermal fluctuations depin the charge density wave of the Peierls Fröhlich state pinned by impurities at absolute zero temperature. The critical temperature, T d , of this depinning is estimated as T d = 0.55√ m ∗ mγ 0 where m ∗ and γ 0 are the mass of the collective mode and the pinning frequency at T = 0.

Erratum: Quantum hydrodynamics of a bose fluid: ac Josephson effect in superfluid helium

An attempt is made to understand the ac Josephson effect in superfluid helium in terms of the quantum hydrodynamics developed by Biswas and Rao. The essential features of the new formalism are reviewed. It is shown that at absolute zero temperature the ac Josephson effect definitely exists in superfluid helium. However, at nonzero temperatures fluctuations in the system characteristic of the flow properties of liquid helium may make experimental observation of the effect extremely difficult.

Stochastic theory of a selection game.

The stochastic theory of a nonlinear game is presented which incorporates some of the essential properties of living systems: metabolism, reproduction and mutability. The steady state distribution function as well as the complete time development are given explicitly. The second law of thermodynamics is generalized to a certain class of nonequilibrium systems. An order parameter is introduced as a measure of the system's internal organization. From the point of view of phase transition theory, the model exhibits a transition at the absolute zero of temperature, with critical behaviour showing up in the low temperature region.

States of maximal stability in mixtures

It is shown that in mixtures containingK componentsK states of maximal stability can be defined, each of them corresponding to the case, when one component disappears from the mixtures. On the ground of the thermostatic theory of stability it can be stated that these states like states of maximal stability in general, can be approximated arbitrarily, but cannot be reached, so that they have properties analogous with the state of absolute zero temperature.

Stability conditions of a deformed lattice

Thermodynamic stability conditions of a deformed lattice, transforming at absolute zero temperature to dynamic-type stability, are formulated. The independence of the stability condition relative to uniform deformation and dynamic stability conditions is shown. Stability conditions are derived which are violated during lattice deformation by the former.

Quantum-Lattice-Gas Model forHe3-He4Mixtures

A quantum-lattice-gas model of ${\mathrm{He}}^{3}$-${\mathrm{He}}^{4}$ mixtures is proposed which includes the effects of the Bose and Fermi statistics. The effect of the hard-core interaction between all particles is included by altering the commutation relations of the field operators. The phase diagram of the model is obtained within mean-field theory under conditions of constant normal density and constant pressure. The diagram shows many of the features of the physical system. However, within mean-field theory, the phase separation is complete at the absolute zero of temperature.

Ferromagnetism and Antiferromagnetism in 3dTransition Metals

The relative stability of ferro- and antiferromagnetic state in 3d transition metals is investigated on the basis of itinerant model, that is, the Stoner model for ferromagnetic staes and the gap equation model for antiferromagnetic states. The realistic energy band structures are taken into account and the effective exchange interaction is introduced as only one parameter in the present paper. The theoretical predictions are in good agreement with the observed magnetic diagrams at absolute zero temperature. For example, it is quite reasonable in this model that bcc Fe is ferromagnetic, but bcc Fe is antiferromagnetic. It must be emphasized that there is no need to change the value of effective exchange interaction through all 3d elements to reproduce the observed magnetic moment of them.

A Simple Relation for Effective Neutron Temperature in Cold Moderators with Lattice Vibrational Modes

The effective neutron temperature in cold hydrogenous solid moderators is analyzed in phonon approximation with use made of two simple models representing the frequency distribution of lattice vibrations, and simple relations are derived between the variation of the effective neutron temperature and the moderator temperature, as also, an equation expressing the limiting neutron temperature in a moderator at absolute zero temperature. Good agreement is obtained between the calculated and experimental results in cold light water ice. It is indicated that unbounded cooling of the moderator is not necessarily effective in improving the moderating efficacy, in the case of slowing-down by lattice vibrations; it generally suffices to cool the moderator down to the limiting neutron temperature. It is revealed that approach of the neutron temperature to the limiting value is largely determined by the shape of the frequency distribution of the lattices, while the limiting value itself is influenced by such paramete...

Zero-Point Effects in Heisenberg Antiferromagnets with Arbitrary Range of Interaction

The ground state energy, spin-wave energy, and sublattice magnetization have been calculated for a Heisenberg antiferromagnet at the absolute zero of temperature. The treatment extends the earlier work of Anderson, Kubo, and Oguchi to apply for any two-sublattice antiferromagnet with arbitrary range of interaction. It is shown that for each exchange interaction there is a different characteristic correction term to the energies. Explicit calculations are made of these terms for the simple cubic, body-centered cubic, and face-centered cubic lattices, with both first- and second-neighbor interactions. Applications are also made to NiO and MnO. An extra term in the magnetization series beyond that given by earlier workers is derived.

The second law and adiabatic unattainability

The derivation of the equation d′Q =T dS from the second law of thermodynamics is examined and it is shown how its range of validity may be extended to include states at the absolute zero of temperature. The adiabatic unattainability of absolute zero follows almost trivially, but it is shown that, in the deduction, it is necessary to assume the validity of a statement known to be equivalent to Nernst’s heat theorem.

Interference Effect between Two Impurity Spins in a Heisenberg Ferromagnet

A general and exact theory for the spin wave impurity states associated with two substitutional ferromagnetic impurity spins in a Heisenberg ferromagnet with nearest neighbor exchange interactions only is developed at absolute zero temperature. All possible cases regarding the relative position of the two impurity spins are considered. It is found that the interference effect between the two impurity spins on the in-band spin wave impurity states in the one-dimensional case dose remain even for the infinitely large impurity separation, whereas the effect on the localized spin wave states in this case becomes vanishingly small as the impurity separation becomes large. A brief discussion concerning the interference effect on the spin wave impurity states in the two- and three-dimensional cases is also given.

Magnetic Susceptibility at Zero Temperature for the One-Dimensional Hubbard Model

The magnetic susceptibility at absolute-zero temperature for the one-dimensional Hubbard model is studied exactly as a function of the concentration of electrons by using Lieb and Wu's theory for this system. Our analysis essentially follows Griffiths's method for the magnetic susceptibility of the one-dimensional Heisenberg antiferromagnet, and is a generalization of Takahashi's calculation to the systems with an arbitrary concentration of electrons. The ground-state energy and the magnitude of local moments at each site are also studied. Combined with the results on the susceptibility, they should suggest how the effect of the Coulomb interaction on the properties of the system at low temperatures changes with the concentration of electrons.

Structure of Cooper Pairs in Superconductors

In the generalized random-phase approximation, introduced by Anderson and applied to the theory of superconductivity, existence of a collective excitation with vanishing excitation energy and momentum was known. It is shown to correspond to the creation of a Cooper pair. The creation operator satisfies a nonlinear operator equation which dose not depend on the magnitude of order parameter. It is, therefore, independent of dynamics, that is, of the strength of the pairing interactions. Nevertheless it has the assumed matrix elements between a given state in an N-particle system and the corresponding state in the N+2 par­ ticle system. Discussions are confined to the BCS superconductor at absolute zero temperature.

Theory of Surface Energies in Pure Superconductors

The WKBJ variational scheme developed by Bardeen et al. which simplifies the Bogoliubov theory for inhomogeneous superconducting states, has been applied to study normal-superconducting phase boundaries in pure metals. The surface energy of a planar phase boundary at absolute-zero temperature is found for various values of the Ginzburg-Landau parameter. The order parameter and the magnetic field are also determined in this variational procedure. The present theory differs from the existing ones in its being microscopic and nonlocal, but the nonlocality of our theory is found to have small, though not negligible, effects. Near the transition temperature the free-energy expression for planar phase boundaries is examined by an asymptotic expansion method.

Quantum Theory of the Equation of State for Solid Hydrogen

A variational calculation of the ground-state energy of molecular crystalline hydrogen has been carried out, including the effect of correlation between the motions of the particles. The principal purpose was to obtain the equation of state for solid hydrogen at absolute-zero temperature over a wide range of densities. We are concerned with energies on a scale appropriate to high-pressure phenomena, and therefore approximated the molecular rotational behavior, so that the very low-temperature phase transitions are not describable in the present model. The variational form of the energy was obtained by truncating the cluster expansion of the ground-state energy. The effect of short-range dynamic correlation is taken into consideration through a Jastrow-type pair-correlation function in the trial wave function. To facilitate the fast convergence of the cluster expansion, a model correlation function with an explicit hard-core exclusion effect was employed. With this pair-correlation function, the truncation approximation was extended into the high-density region where previous functional forms for pair correlation had not been satisfactory. Numerical computations were done for a Lennard-Jones potential, a Buckingham exp-6-type potential, and a nonspherical molecular interaction due to Wang Chang. The results compare favorably with experiment, although there is a systematic difference at high density; either all of the assumed potentials are inadequate or the experimental data are in error.

Determination of Mean Square Displacements of Polyethylene Molecules in Crystal Lattice

X-Ray scattering intensities of bulk crystallized polyethylene were measured at temperatures from −165°C to 120°C. Mean square displacements of carbon atoms from their average locations were represented by the symmetric tensor U having four independent elements, Uaa, Ubb, Ucc, and Uab. These elements and the atomic coordinates were determined as a function of temperature by the least square method. The displacement of the carbon atom was a maximum in the direction perpendicular to the skeletal zigzag plane. The minimum displacement was found in the direction along the the molecular axis. The mean square displacements of atoms were separated into contributions from the molecular vibration and the lattice imperfection by extrapolating the elements of tensor U to the temperature of absolute zero. The amplitudes of molecular vibration obtained by X-ray measurements agreed fairly well with the theoretical values calculated on the assumption of the harmonic oscillator model by Kitagawa and Miyazawa at the temperatures below 0°C. The atomic coordinates did not change below 0°C. The skeletal plane of polyethylene molecule tended to deflect slightly toward the a axis above 0°C with increasing temperature.

On the Energy Spectrum of the Piezoelectric Polaron

The energy spectrum of a piezoelectric polaron is theoretically discussed. At absolute zero temperature, Haga's approximations originally developed for the theory of optical polaron are used for investigating the low excited state. At finite temperature, the intermediate coupling theory is applied to get the free energy and the energy spectrum of the piezoelectric polaron. The energy spectrum is in accord with Porsch's result obtained by a Green function method. The energy spectrum is calculated numerically, which starts out quadratically and becomes approximately linear as the momentum increases. This energy-momentum relationship differs appreciably from that of previous two theories at finite temperature.

Derivation of the Blackbody Radiation Spectrum by Classical Statistical Mechanics

It is assumed that the fluctuating radiation energy density in a blackbody cavity is the sum of two stochastically independent terms: a zero-point energy density ${\ensuremath{\rho}}_{0}$ with Lorentz-invariant spectrum which persists at the absolute zero of temperature, and a temperature-dependent energy density ${\ensuremath{\rho}}_{T}$ which satisfies the laws of statistical mechanics. The mean-square fluctuation $〈{(\ensuremath{\delta}{\ensuremath{\rho}}_{T})}^{2}〉$ of ${\ensuremath{\rho}}_{T}$ is calculated from classical electromagnetic theory and is shown to depend explicitly on $〈{\ensuremath{\rho}}_{0}〉$. Classical statistical mechanics leads then uniquely from $〈{(\ensuremath{\delta}{\ensuremath{\rho}}_{T})}^{2}〉$ to $〈{\ensuremath{\rho}}_{T}〉$, which turns out to satisfy Planck's formula.

Quantum mobility, configurational entropy, and mössbauer spectroscopy of impurity atoms in crystals

J.G. Dash has attributed the third law loss of configurational entropy in impure crystals to the quantum mobility of the impurity atoms which persists down to absolute zero temperature. Thermal evidence of quantum mobility in crystals has not yet been observed, presumably due to the extremely small mobility band widths. It is shown that Mössbauer spectroscopy can be used to measure mobility band widths with a minimum of cryogenic difficulty.