Dynamics of the one-dimensional Heisenberg spin system

1979 ◽  
pp. 280-287
Author(s):  
A. Sjölander
Keyword(s):  
Spin System ◽  
Heisenberg Spin ◽  
One Dimensional ◽  
The One

GLOBAL INHOMOGENEOUS SCHRÖDINGER FLOW

2000 ◽  
Vol 11 (08) ◽  
pp. 1079-1114 ◽  
Author(s):  
HONG-YU WANG ◽  
YOU-DE WANG
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Spin System ◽  
Holomorphic Sectional Curvature ◽  
Heisenberg Spin ◽  
One Dimensional ◽  
The Cauchy Problem ◽  
Schrodinger Flow ◽  
The One ◽  
Complete Kähler Manifold

In this paper, we consider the global existence of one-dimensional nonautonomous inhomogeneous Schrödinger flow. By exploiting geometric symmetries, we prove that, given a smooth initial map, the Cauchy problem of the one-dimensional nonautonomous inhomogeneous Schrödinger flow from S1 into a complete Kähler manifold with constant holomorphic sectional curvature admits a unique global smooth solution. As a corollary, we establish the global existence for the Cauchy problem of the inhomogeneous Heisenberg spin system.

scholarly journals Thermal Conductivity due to Spinons in the One-Dimensional Quantum Spin System Sr2V3O9

2014 ◽  
Vol 83 (5) ◽  
pp. 054601 ◽  
Author(s):  
Takayuki Kawamata ◽  
Masanori Uesaka ◽  
Mitsuhide Sato ◽  
Koki Naruse ◽  
Kazutaka Kudo ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Spin System ◽  
Quantum Spin ◽  
Quantum Spin System ◽  
One Dimensional ◽  
The One

scholarly journals PARRONDO GAMES WITH SPATIAL DEPENDENCE II

2012 ◽  
Vol 11 (04) ◽  
pp. 1250030 ◽  
Author(s):  
S. N. ETHIER ◽  
JIYEON LEE
Keyword(s):  
Spin System ◽  
Spatial Dependence ◽  
Integer Lattice ◽  
Periodic Pattern ◽  
One Dimensional ◽  
Random Mixture ◽  
The Mean ◽  
The One ◽  
Positive Integers ◽  
Special Case

Let game B be Toral's cooperative Parrondo game with (one-dimensional) spatial dependence, parameterized by N ≥ 3 and p0, p1, p2, p3 ∈ [0, 1], and let game A be the special case p0 = p1 = p2 = p3 = 1/2. In previous work we investigated μB and μ(1/2, 1/2), the mean profits per turn to the ensemble of N players always playing game B and always playing the randomly mixed game (1/2)(A + B). These means were computable for 3 ≤ N ≤ 19, at least, and appeared to converge as N → ∞, suggesting that the Parrondo region (i.e., the region in which μB ≤ 0 and μ(1/2, 1/2) > 0) has nonzero volume in the limit. The convergence was established under certain conditions, and the limits were expressed in terms of a parameterized spin system on the one-dimensional integer lattice. In this paper we replace the random mixture with the nonrandom periodic pattern Ar Bs, where r and s are positive integers. We show that μ[r, s], the mean profit per turn to the ensemble of N players repeatedly playing the pattern Ar Bs, is computable for 3 ≤ N ≤ 18 and r + s ≤ 4, at least, and appears to converge as N → ∞, albeit more slowly than in the random-mixture case. Again this suggests that the Parrondo region (μB ≤ 0 and μ[r, s] > 0) has nonzero volume in the limit. Moreover, we can prove this convergence under certain conditions and identify the limits.

Evidence for Ballistic Thermal Conduction in the One-Dimensional Spin System Sr2CuO3

2006 ◽  
Author(s):  
N. Takahashi ◽  
T. Kawamata ◽  
T. Adachi ◽  
T. Noji ◽  
Y. Koike ◽  
...  
Keyword(s):  
Spin System ◽  
Thermal Conduction ◽  
One Dimensional ◽  
The One
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