Vibrational spectrum of an isotopically disordered diatomic chain with long-range order in the coherent potential approximation

1975 ◽  
Vol 72 (1) ◽  
pp. 353-358 ◽  
Author(s):  
H. Braeter ◽  
V. B. Priezzhev
Keyword(s):  
Vibrational Spectrum ◽  
Long Range ◽  
Coherent Potential Approximation ◽  
Range Order ◽  
Long Range Order ◽  
Potential Approximation ◽  
Diatomic Chain

Ordering Energy of B2 Alloys Calculated in the Frozen Potential and Harris Approximations

1990 ◽  
Vol 186 ◽  
Author(s):  
W. A. Shelton ◽  
D. M. Nicholson ◽  
G. M. Stocks ◽  
F. J. Pinski ◽  
D. D. Johnson ◽  
...  
Keyword(s):  
Long Range ◽  
Natural Extension ◽  
Coherent Potential Approximation ◽  
Range Order ◽  
Single Site ◽  
Long Range Order ◽  
Potential Approximation ◽  
Charge Densities ◽  
Ordered Alloys ◽  
Random Alloys

AbstractIt has been established that the coherent potential approximation can successfully describe the energy of random alloys [1]. It has also served as the basis of generalized perturbation method [2] and concentration wave [3] xscalculations of the energy of short range ordered alloys. The multisublattice coherent potential, (MCPA) is the natural extension of the CPA with which to address long range order (LRO). Using the recently developed multisublattice coherent potential approximation Korringa Kohn Rostoker [4], (MCPA-KKR) code the elgenvalue sum can be calculated as a function of LRO. This allows the evaluation of the ordering energy by either of two approximations. The frozen potential approximation (FPA) [5] assumes that the muffintin single site potentials do not change as the long range order is varied; the Harris Approximation, (HA) [6], as applied in this work, assumes that the single site charge densities do not change as the long range order is changed. These two methods of calculating the ordering energy will be compared with each other and to experiment for several systems including CuZn, NiAl, and NiAl with zinc additions.

Superfluidity and Superconductivity

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Wave Packet ◽  
Long Range ◽  
Cooper Pair ◽  
Bose Condensation ◽  
Range Order ◽  
Condensed State ◽  
Long Range Order ◽  
Coherent Wave

Chapter 13 addresses Bose condensation in superfluids (and superconductors), which involves the field operator ψ‎ having a c-number component (<ψ(x,t)>≠0), challenging number conservation. The nonlinear Gross-Pitaevskii equation is derived for this condensate wave function<ψ>=ψ−ψ˜, facilitating identification of the coherence length and the core region of vortex motion. The noncondensate Green’s function G˜1(1,1′)=−i<(ψ˜(1)ψ˜+(1′))+> and the nonvanishing anomalous correlation function F˜∗(2,1′)=−i<(ψ˜+(2)ψ˜+(1′))+> describe the dynamics and elementary excitations of the non-condensate states and are discussed in conjunction with Landau’s criterion for viscosity. Associated concepts of off-diagonal long-range order and the interpretation of <ψ> as a superfluid order parameter are also introduced. Anderson’s Bose-condensed state, as a phase-coherent wave packet superposition of number states, resolves issues of number conservation. Superconductivity involves bound Cooper pairs of electrons capable of Bose condensation and superfluid behavior. Correspondingly, the two-particle Green’s function has a term involving a product of anomalous bound-Cooper-pair condensate wave functions of the type F(1,2)=−i<(ψ(1)ψ(2))+>≠0, such that G2(1,2;1′,2′)=F(1,2)F+(1′,2′)+G˜2(1,2;1′,2′). Here, G˜2 describes the dynamics/excitations of the non-superfluid-condensate states, while nonvanishing F,F+ represent a phase-coherent wave packet superposition of Cooper-pair number states and off-diagonal long range order. Employing this form of G2 in the G1-equation couples the condensed state with the non-condensate excitations. Taken jointly with the dynamical equation for F(1,2), this leads to the Gorkov equations, encompassing the Bardeen–Cooper–Schrieffer (BCS) energy gap, critical temperature, and Bogoliubov-de Gennes eigenfunction Bogoliubons. Superconductor thermodynamics and critical magnetic field are discussed. For a weak magnetic field, the Gorkov-equations lead to Ginzburg–Landau theory and a nonlinear Schrödinger-like equation for the pair wave function and the associated supercurrent, along with identification of the Cooper pair density. Furthermore, Chapter 13 addresses the apparent lack of gauge invariance of London theory with an elegant variational analysis involving re-gauging the potentials, yielding a manifestly gauge invariant generalization of the London equation. Consistency with the equation of continuity implies the existence of Anderson’s acoustic normal mode, which is supplanted by the plasmon for Coulomb interaction. Type II superconductors and the penetration (and interaction) of quantized magnetic flux lines are also discussed. Finally, Chapter 13 addresses Josephson tunneling between superconductors.

Time-Resolved, Laser-Induced Phase Transformation in Aluminum

1984 ◽  
Vol 35 ◽  
Author(s):  
S. Williamson ◽  
G. Mourou ◽  
J.C.M. Li
Keyword(s):  
Point Defect ◽  
Long Range ◽  
Rapid Heating ◽  
Range Order ◽  
Nucleation Theory ◽  
Long Range Order ◽  
Time Resolved ◽  
Aluminum Films ◽  
Thin Aluminum ◽  
Initial Nucleus

ABSTRACTThe technique of picosecond electron diffraction is used to time resolve the laser-induced melting of thin aluminum films. It is observed that under rapid heating conditions, the long range order of the lattice subsists for lattice temperatures well above the equilibrium point, indicative of superheating. This superheating can be verified by directly measuring the lattice temperature. The collapse time of the long range order is measured and found to vary from 20 ps to several nanoseconds according to the degree of superheating. Two interpretations of the delayed melting are offered, based on the conventional nucleation and point defect theories. While the nucleation theory provides an initial nucleus size and concentration for melting to occur, the point defect theory offers a possible explanation for how the nuclei are originally formed.

scholarly journals Finite temperature off-diagonal long-range order for interacting bosons

2020 ◽  
Vol 102 (18) ◽  
Author(s):  
A. Colcelli ◽  
N. Defenu ◽  
G. Mussardo ◽  
A. Trombettoni
Keyword(s):  
Long Range ◽  
Finite Temperature ◽  
Range Order ◽  
Long Range Order

scholarly journals Recovery of long-range order in two-dimensional charge density waves at high temperatures

2021 ◽  
Vol 27 (S1) ◽  
pp. 952-954
Author(s):  
Suk Hyun Sung ◽  
Yin Min Goh ◽  
Noah Schnitzer ◽  
Ismail El Baggari ◽  
Kai Sun ◽  
...  
Keyword(s):  
Charge Density ◽  
Long Range ◽  
High Temperatures ◽  
Charge Density Waves ◽  
Range Order ◽  
Long Range Order ◽  
Two Dimensional ◽  
Density Waves

SHORT-RANGE AND LONG-RANGE ORDER OF TITANIUM IN Ti1+xS2

1977 ◽  
Vol 38 (C7) ◽  
pp. C7-202-C7-206 ◽  
Author(s):  
R. MORET ◽  
M. HUBER ◽  
R. COMÈS
Keyword(s):  
Long Range ◽  
Short Range ◽  
Range Order ◽  
Long Range Order
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