Self-interstitial Diffusion in α-Zirconium

2001 ◽  
Vol 677 ◽  
Author(s):  
W.J. Zhu ◽  
C.H. Woo
Keyword(s):  
Ground State ◽  
Diffusion Processes ◽  
Many Body ◽  
Interstitial Diffusion ◽  
One Dimensional ◽  
Mean Lifetime ◽  
Migration Mechanism ◽  
Out Of Plane ◽  
On Line ◽  
The Mean

ABSTRACTSelf-interstitial Diffusion in α-Zirconium-Zr is studied using Molecular Dynamic (MD) and molecular static (MS) simulation using Ackland's many-body inter-atomic potential. The basal crowdion configuration is found to be the ground state. The diffusion process in Zr is complex. Four types of diffusion jumps can be identified, two in-plane and two out-of plane. The in-plane migration mechanism is dominated by one-dimensional crowdion motion along the [1120] directions, interrupted by occasional out-of-plane and on-line or off-line jumps. The mean lifetime before rotation of the crowdion is reported as a function of temperature. The activation energies for the diffusion processes are obtained. The diffusional anisotropy factor Dc/Da is also obtained, and compares well with experiment results.

Ground state of one-dimension repulsing particles on disordered lattice

2014 ◽  
Vol 25 (08) ◽  
pp. 1450028 ◽  
Author(s):  
L. A. Pastur ◽  
V. V. Slavin ◽  
A. A. Krivchikov
Keyword(s):  
Ground State ◽  
Domain Walls ◽  
Host Lattice ◽  
One Dimension ◽  
Weak Disorder ◽  
Interacting Particles ◽  
One Dimensional ◽  
Lattice Disorder ◽  
Disordered Lattice ◽  
The Mean

The ground state (GS) of interacting particles on a disordered one-dimensional (1D) host-lattice is studied by a new numerical method. It is shown that if the concentration of particles is small, then even a weak disorder of the host-lattice breaks the long-range order of Generalized Wigner Crystal (GWC), replacing it by the sequence of blocks (domains) of particles with random lengths. The mean domains length as a function of the host-lattice disorder parameter is also found. It is shown that the domain structure can be detected by a weak random field, whose form is similar to that of the ground state but has fluctuating domain walls positions. This is because the generalized magnetization corresponding to the field has a sufficiently sharp peak as a function of the amplitude of fluctuations for small amplitudes.

scholarly journals A weak KAM approach to the periodic stationary Hartree equation

2021 ◽  
Vol 28 (6) ◽  
Author(s):  
L. Zanelli ◽  
F. Mandreoli ◽  
F. Cardin
Keyword(s):  
Ground State ◽  
Kam Theory ◽  
Mean Field ◽  
Hartree Equation ◽  
Many Body ◽  
Semiclassical Asymptotics ◽  
The Mean ◽  
Mean Field Asymptotics ◽  
Periodic Setting ◽  
Integral Identities

AbstractWe present, through weak KAM theory, an investigation of the stationary Hartree equation in the periodic setting. More in details, we study the Mean Field asymptotics of quantum many body operators thanks to various integral identities providing the energy of the ground state and the minimum value of the Hartree functional. Finally, the ground state of the multiple-well case is studied in the semiclassical asymptotics thanks to the Agmon metric.

First-Passage Problems for Asymmetric Diffusions and Skew-diffusion Processes

2009 ◽  
Vol 16 (04) ◽  
pp. 325-350 ◽  
Author(s):  
Mario Abundo
Keyword(s):  
Diffusion Process ◽  
Diffusion Processes ◽  
Exit Time ◽  
Skew Brownian Motion ◽  
One Dimensional ◽  
Mean Exit Time ◽  
The Mean ◽  
The Right ◽  
Analytical Expressions ◽  
Skew Diffusion

For a, b > 0, we consider a temporally homogeneous, one-dimensional diffusion process X(t) defined over I = (-b, a), with infinitesimal parameters depending on the sign of X(t). We suppose that, when X(t) reaches the position 0, it is reflected rightward to δ with probability p > 0 and leftward to -δ with probability 1 - p, where δ > 0. Closed analytical expressions are found for the mean exit time from the interval (-b, a), and for the probability of exit through the right end a, in the limit δ → 0+, generalizing the results of Lefebvre, holding for asymmetric Wiener process. Moreover, in alternative to the heavy analytical calculations, a numerical method is presented to estimate approximately the quantities above. Furthermore, on the analogy of skew Brownian motion, the notion of skew diffusion process is introduced. Some examples and numerical results are also reported.

All-Temperature Partition Function from Variationally Optimized Canonical Density Matrix

1983 ◽  
Vol 38 (12) ◽  
pp. 1373-1382
Author(s):  
R. Baltin
Keyword(s):  
Density Matrix ◽  
Ground State ◽  
Order Differential Equation ◽  
Bloch Equation ◽  
Mean Square ◽  
Spatial Variables ◽  
One Dimensional ◽  
Exactly Solvable ◽  
The Mean ◽  
The One

Abstract For the canonical density matrix C(r, r0,β) a variational ansatz C̄̄f = (1 - f̄) Ccl + f̄ Cgr is made where Ccl and Cgr are the classical and the ground state expressions which are exact in the high temperature (β → 0) and in the low-temperature limits (β → + ∞), respectively, and f̄ is a trial function subject to the restriction that f̄ → 0 for β → 0 and f̄ → 1 for β → ∞. With the approximation that f̄ be dependent only upon β, not upon spatial variables, the mean square error arising when Cf is inserted into the Bloch equation is made a minimum. The Euler equation for this variational problem is an ordinary second order differential equation for f̄=f(β) to be solved numerically. The method is tested for the exactly solvable case of the one dimensional harmonic oscillator.

Lifetimes and decay of the 2.07 MeV triplet in 26Al

1968 ◽  
Vol 46 (24) ◽  
pp. 2809-2814 ◽  
Author(s):  
O. Häusser ◽  
N. Anyas-Weiss
Keyword(s):  
Gamma Rays ◽  
Ground State ◽  
Doppler Shift ◽  
Excitation Energies ◽  
Upper Limit ◽  
Mean Lifetime ◽  
The Mean ◽  
Γ Ray

Gamma rays from resonances at Ep = 956, 1199, 1287, and 1701 keV in the reaction 25Mg(p,γ)26Al have been studied using 40 cm3 and 25 cm3 Ge(Li) detectors. Accurate γ-ray energy determinations and Doppler shift measurements indicate the existence of three levels at excitation energies of 2068.7, 2069.5, and 2071.7 keV. The level at 2068.7 keV has a mean lifetime of [Formula: see text] and decays 29% to the ground state, and 71% to the 416.6 keV level. The 2069.5 keV level has a mean lifetime of (1.3 ± 0.5) × 10−14 s and decays 5% to the 228.2, 22% to the 416.6, and 73% to the 1057.7 keV levels. The level at 2071.7 keV has a lifetime of [Formula: see text] and decays to the 228.2 keV (> 65%) and the 1057.7 keV (< 35%) levels. An upper limit of τ < 10−14 s has been placed on the lifetime of the 3159.4 keV level and the mean lifetime of the 1850.8 keV level has been measured to be (1.6 ± 0.7) × 10−14 s.

PERELOMOV AND BARUT–GIRARDELLO SU(1, 1) COHERENT STATES FOR HARMONIC OSCILLATOR IN ONE-DIMENSIONAL HALF SPACE

2006 ◽  
Vol 21 (12) ◽  
pp. 2635-2644 ◽  
Author(s):  
Q. H. LIU ◽  
H. ZHUO
Keyword(s):  
Coherent State ◽  
Harmonic Oscillator ◽  
Half Space ◽  
Ground State ◽  
Classical Limit ◽  
Coherent States ◽  
Mean Values ◽  
One Dimensional ◽  
The Mean

The Perelomov and the Barut–Girardello SU(1, 1) coherent states for harmonic oscillator in one-dimensional half space are constructed. Results show that the uncertainty products ΔxΔp for these two coherent states are bound from below [Formula: see text] that is the uncertainty for the ground state, and the mean values for position x and momentum p in classical limit go over to their classical quantities respectively. In classical limit, the uncertainty given by Perelomov coherent does not vanish, and the Barut–Girardello coherent state reveals a node structure when positioning closest to the boundary x = 0 which has not been observed in coherent states for other systems.

scholarly journals Distribution of Cracks in a Chain of Atoms at Low Temperature

2021 ◽  
Author(s):  
Sabine Jansen ◽  
Wolfgang König ◽  
Bernd Schmidt ◽  
Florian Theil
Keyword(s):  
Low Temperature ◽  
Ground State ◽  
Lattice Gas ◽  
Nearest Neighbor ◽  
Periodic Lattice ◽  
Many Body ◽  
One Dimensional ◽  
Uniform Estimates ◽  
A Chain ◽  
Crystalline Domains

AbstractWe consider a one-dimensional classical many-body system with interaction potential of Lennard–Jones type in the thermodynamic limit at low temperature $$1/\beta \in (0,\infty )$$ 1 / β ∈ ( 0 , ∞ ) . The ground state is a periodic lattice. We show that when the density is strictly smaller than the density of the ground state lattice, the system with N particles fills space by alternating approximately crystalline domains (clusters) with empty domains (voids) due to cracked bonds. The number of domains is of the order of $$N\exp (- \beta e_\mathrm {surf}/2)$$ N exp ( - β e surf / 2 ) with $$e_\mathrm {surf}>0$$ e surf > 0 a surface energy. For the proof, the system is mapped to an effective model, which is a low-density lattice gas of defects. The results require conditions on the interactions between defects. We succeed in verifying these conditions for next-nearest neighbor interactions, applying recently derived uniform estimates of correlations.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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