scholarly journals EMPTINESS FORMATION PROBABILITY AND QUANTUM KNIZHNIK-ZAMOLODCHIKOV EQUATION

2004 ◽  
Vol 19 (supp02) ◽  
pp. 57-81
Author(s):  
H. E. BOOS ◽  
V. E. KOREPIN ◽  
F. A. SMIRNOV
Keyword(s):  
Quantum Correlations ◽  
Zero Magnetic Field ◽  
Heisenberg Antiferromagnet ◽  
Zero Temperature ◽  
One Dimensional ◽  
Formation Probability ◽  
Antiferromagnetic Ground State ◽  
A New Technique ◽  
The One ◽  
Zamolodchikov Equation

We consider the one-dimensional XXX spin 1/2 Heisenberg antiferromagnet at zero temperature and zero magnetic field. We are interested in a probability of a formation of a ferromagnetic string P(n) in the antiferromagnetic ground-state. We call it emptiness formation probability [EFP]. We suggest a new technique for computation of the EFP in the inhomogeneous case. It is based on the quantum Knizhnik-Zamolodchikov equation [qKZ]. We calculate EFP for n≤6 for the inhomogeneous case. The homogeneous limit confirms our hypothesis about the relation of quantum correlations and number theory. We also make a conjecture about a structure of EFP for arbrary n.

Spin excitations of the one-dimensional S=12 Heisenberg antiferromagnet Yb4As3 under magnetic field

2002 ◽  
Vol 312-313 ◽  
pp. 359-361
Author(s):  
M. Kohgi ◽  
K. Iwasa ◽  
J.-M. Mignot ◽  
B. Fåk ◽  
A. Hiess ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Heisenberg Antiferromagnet ◽  
One Dimensional ◽  
Spin Excitations ◽  
The One

Determination of Optimum Profile of One-Dimensional Cooling Fins

1983 ◽  
Vol 105 (3) ◽  
pp. 317-320 ◽  
Author(s):  
S. K. Hati ◽  
S. S. Rao
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Minimum Principle ◽  
Problem Formulation ◽  
One Dimensional ◽  
A New Technique ◽  
The One ◽  
Optimum Profile

The optimum design of an one-dimensional cooling fin is considered by including all modes of heat transfer in the problem formulation. The minimum principle of Pontryagin is applied to determine the optimum profile. A new technique is used to solve the reduced differential equations with split boundary conditions. The optimum profile found is compared with the one obtained by considering only conduction and convection.

A neutron scattering study of spin dynamics in the one-dimensional paramagnet CsMnBr3

1984 ◽  
Vol 62 (11) ◽  
pp. 1132-1138 ◽  
Author(s):  
B. D. Gaulin ◽  
M. F. Collins
Keyword(s):  
Neutron Scattering ◽  
Spin Wave ◽  
Spin Dynamics ◽  
Quantitative Agreement ◽  
Generalized Langevin Equation ◽  
Heisenberg Antiferromagnet ◽  
One Dimensional ◽  
Truncation Scheme ◽  
Zone Centre ◽  
The One

CsMnBr3 is a quasi-one-dimensional Heisenberg antiferromagnet. We present results of the magnetic inelastic response of CsMnBr3 across the magnetic Brillouin zone by neutron scattering techniques. Well-defined spin-wave modes, characteristic of one-dimensional magnetic insulators, are found over most of the zone in the paramagnetic phase at 15 K. The zone centre response is not sharp, but peaks in the scattering function S(k, ω) are found. No excitation branch going to zero energy at zero wavevector is found. At small wavevectors there is a mode with energy 1.7 ± 0.2 meV and we use it to identify planar anisotropy in this system. The mid-zone response as a function of temperature is analyzed in terms of a generalized Langevin equation approach (Mori formulation) to the dynamics of the one-dimensional Heisenberg antiferromagnet. The theory contains no adjustable parameters. Our results are compared with two truncation schemes of the theory. We report qualitative agreement with the theories, including the observation of upwards renormalization of spin-wave energy with temperature. Quantitative agreement is less than good for either truncation scheme.

scholarly journals On the Existence and Robustness of Steady Position-Momentum Correlations for Time-Dependent Quadratic Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-16
Author(s):  
M. Gianfreda ◽  
G. Landolfi
Keyword(s):  
Quantum Dynamics ◽  
Quantum Correlations ◽  
Time Dependent ◽  
Quantum Decoherence ◽  
Linear Superposition ◽  
Time Intervals ◽  
One Dimensional ◽  
The One ◽  
Basic Features ◽  
Hamiltonian Operators

We discuss conditions giving rise to stationary position-momentum correlations among quantum states in the Fock and coherent basis associated with the natural invariant for the one-dimensional time-dependent quadratic Hamiltonian operators such as the Kanai-Caldirola Hamiltonian. We also discuss some basic features such as quantum decoherence of the wave functions resulting from the corresponding quantum dynamics of these systems that exhibit no timedependence in their quantum correlations. In particular, steady statistical momentum averages are seen over well-defined time intervals in the evolution of a linear superposition of the basis states of modified exponentially damped mass systems.

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