scholarly journals THE GENERAL SPIN TRIANGLE

2013 ◽  
Vol 27 (16) ◽  
pp. 1350064 ◽  
Author(s):  
HEINZ-JÜRGEN SCHMIDT
Keyword(s):  
Classical System ◽  
Spin Systems ◽  
Coupling Coefficients ◽  
Quantum Case ◽  
Permutational Symmetry ◽  
Heisenberg Spin ◽  
Tridiagonal Matrices ◽  
Spin Quantum ◽  
Spin Quantum Number ◽  
High Temperature Expansion

We consider the Heisenberg spin triangle with general coupling coefficients and general spin quantum number s. The corresponding classical system is completely integrable. In the quantum case the eigenvalue problem can be reduced to that of tridiagonal matrices in at most 2s+1 dimensions. The corresponding energy spectrum exhibits what we will call spectral symmetries due to the underlying permutational symmetry of the considered class of Hamiltonians. As an application we explicitly calculate six classes of universal polynomials that occur in the high temperature expansion of spin triangles and more general spin systems.

scholarly journals Optimal phase space sampling for Monte Carlo simulations of Heisenberg spin systems

2019 ◽  
Vol 31 (9) ◽  
pp. 095802 ◽  
Author(s):  
J D Alzate-Cardona ◽  
D Sabogal-Suárez ◽  
R F L Evans ◽  
E Restrepo-Parra
Keyword(s):  
Monte Carlo ◽  
Phase Space ◽  
Monte Carlo Simulations ◽  
Spin Systems ◽  
Heisenberg Spin

Light-induced reversible ionization of tetramethylphenylenediamine in an inorganic polymer of n-butyl orthotitanate

1988 ◽  
Vol 66 (8) ◽  
pp. 1931-1935
Author(s):  
Hisashi Ueda ◽  
Masahiro Kaise
Keyword(s):  
Relaxation Time ◽  
Electron Spin Resonance ◽  
Visible Light ◽  
Relative Intensity ◽  
Hyperfine Splitting ◽  
Resonance Absorption ◽  
Spin Quantum ◽  
Spin Quantum Number ◽  
Spin Resonance ◽  
Intensity Ratios

n-Butyl orthotitanate, BT, polymerized in tetrahydrofuran, if irradiated by visible light, gives a new electron spin resonance absorption that is not found before irradiation. In the present work, three different polymers of BT were synthesized by adding tetramethyl phenylenediamine (TMPD), dimethyl phenylenediamine (DMPD), or phenylenediamine (PD), to the solution of BT. The polymers thus prepared were tested to see if they give a new esr signal when irradiated by visible light. The polymer to which 1 mol% of TMPD was added gave TMPD•+ when irradiated by visible light, but the TMPD•+ signal decayed after the irradiation was discontinued. This change, therefore, is reversible. The resonant position of every hyperfine splitting line of the TMPD•+ found in this polymer coincided with that of TMPD•+ in solution, but the relative intensity ratios and the line width of each line depended on the nuclear spin quantum number of the coupling nuclei. This can be interpreted by the restricted rotational motion of TMPD•+ in the polymer matrix. The contribution of the non-diagonal term to the spin relaxation time would explain this phenomenon. In the case of the polymer to which DMPD was added, a small amount of DMPD•+ seemed to be formed, but no radical was detected in the case of the polymer to which PD was added.

scholarly journals Linear energy bounds for Heisenberg spin systems

2002 ◽  
Vol 35 (31) ◽  
pp. 6545-6555 ◽  
Author(s):  
Heinz-J$uuml$rgen Schmidt
Keyword(s):  
Spin Systems ◽  
Heisenberg Spin ◽  
Energy Bounds

scholarly journals Quantum chemistry on quantum computers: quantum simulations of the time evolution of wave functions under the S2 operator and determination of the spin quantum number S

2019 ◽  
Vol 21 (28) ◽  
pp. 15356-15361 ◽  
Author(s):  
Kenji Sugisaki ◽  
Shigeaki Nakazawa ◽  
Kazuo Toyota ◽  
Kazunobu Sato ◽  
Daisuke Shiomi ◽  
...  
Keyword(s):  
Time Evolution ◽  
Quantum Number ◽  
Quantum Circuit ◽  
Wave Functions ◽  
Quantum Computers ◽  
Phase Estimation ◽  
Quantum Simulations ◽  
Spin Quantum ◽  
Spin Quantum Number

A quantum circuit to simulate time evolution of wave functions under an S2 operator is provided, and integrated it to the quantum phase estimation circuit to calculate the spin quantum number S of arbitrary wave functions on quantum computers.

EPR of Gd3+ in Sulfate Host Crystals of Low Symmetry

1997 ◽  
Vol 52 (4) ◽  
pp. 323-330
Author(s):  
M. Bode ◽  
B. D. Mosel ◽  
W. Müller-Warmuth
Keyword(s):  
Metal Ion ◽  
Charge Compensation ◽  
Epr Spectra ◽  
Zero Field ◽  
Zero Field Splitting ◽  
Paramagnetic Resonance ◽  
Spin Quantum ◽  
Spin Quantum Number ◽  
Host Metal ◽  
Low Symmetry

Abstract Electron paramagnetic resonance (EPR) spectra of trivalent gadolinium have been investigated in orthorhombic sulfate host crystals MeSO4 with Me = Sr, Ba, Cd, Hg, Pb and K2SO4 . Because of the low symmetry of the host crystals and the spin quantum number 7/2, complex spectra for several orientations of the magnetic field containing a large number of individual lines had to be analyzed. The spin Hamiltonian parameters have been rigorously determined from the rotational diagrams. Gd3+ has been found to substitute, first of all, for the monoclinic sites of the host metal ion with charge compensation at larger distances. To a small extent, charge compensation in the vicinity has also been observed, arising from additional centres and spectra with lower intensities. Correlations between EPR spectra and crystal structure are reflected in the values of the zero field splitting parameters.

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