Search results for "Heisenberg"
showing 10 items of 80 documents
Ferrimagnetic Heisenberg chain; influence of a random exchange interaction
1985
We report on the magnetic behavior of ‘‘rigid’’ ferrimagnetic chains isolated in bimetallic complexes of the EDTA and ‘‘flexible’’ ones obtained in the amorphous variety. As shown by LAXS, the only noteworthy difference in the amorphous state is the random distribution of bond angles between nearest neighbors within chains. The ‘‘rigid’’ bimetallic chains in CoNi(EDTA)6H2O are described in terms of Heisenberg model with an exchange coupling J=−7.5 K. The behavior of the amorphous variety somewhat differs, following the law X=AT−0.8 typical of REHAC. A classical spin chain model involving a J distribution and alternating g factors allows to explain successfully the temperature dependence of …
Semmes surfaces and intrinsic Lipschitz graphs in the Heisenberg group
2018
A Semmes surface in the Heisenberg group is a closed set $S$ that is upper Ahlfors-regular with codimension one and satisfies the following condition, referred to as Condition B. Every ball $B(x,r)$ with $x \in S$ and $0 < r < \operatorname{diam} S$ contains two balls with radii comparable to $r$ which are contained in different connected components of the complement of $S$. Analogous sets in Euclidean spaces were introduced by Semmes in the late $80$'s. We prove that Semmes surfaces in the Heisenberg group are lower Ahlfors-regular with codimension one and have big pieces of intrinsic Lipschitz graphs. In particular, our result applies to the boundary of chord-arc domains and of redu…
Area-minimizing cones in the Heisenberg group H
2021
We present a characterization of minimal cones of class \(C^2\) and \(C^1\) in the first Heisenberg group \(\mathbf{H}\), with an additional set of examples of minimal cones that are not of class \(C^1\).
Quantum like modelling of decision making: quantifying uncertainty with the aid of the Heisenberg-Robertson inequality
2018
This paper contributes to quantum-like modeling of decision making (DM) under uncertainty through application of Heisenberg’s uncertainty principle (in the form of the Robertson inequality). In this paper we apply this instrument to quantify uncertainty in DM performed by quantum-like agents. As an example, we apply the Heisenberg uncertainty principle to the determination of mutual interrelation of uncertainties for “incompatible questions” used to be asked in political opinion pools. We also consider the problem of representation of decision problems, e.g., in the form of questions, by Hermitian operators, commuting and noncommuting, corresponding to compatible and incompatible questions …
The enhancement of ferromagnetism in uniaxially stressed diluted magnetic semiconductors
2003
We predict a new mechanism of enhancement of ferromagnetic phase transition temperature $T_c$ in uniaxially stressed diluted magnetic semiconductors (DMS) of p-type. Our prediction is based on comparative studies of both Heisenberg (inherent to undistorted DMS with cubic lattice) and Ising (which can be applied to strongly enough stressed DMS) models in a random field approximation permitting to take into account the spatial inhomogeneity of spin-spin interaction. Our calculations of phase diagrams show that area of parameters for existence of DMS-ferromagnetism in Ising model is much larger than that in Heisenberg model.
Spin-1 Heisenberg chain and the one-dimensional fermion gas.
1989
The composite-spin representation of the spin-1 Heisenberg chain is used to transform it through the Jordan-Wigner transformation to the one-dimensional fermion gas. To properly include the xy couplings between spins, we also consider the bosonized version of the fermion model. Phase diagrams deduced from the two versions of the fermion model are compared against numerical results for finite Heisenberg chains. One of the symmetries of the spin model is lost in the fermionization, and this leads to a topologically incorrect phase diagram in at least one part of the parameter space. There are clear indications of significant coupling of spin and charge degrees of freedom in the fermion model …
HIGH-PRECISION MONTE CARLO DETERMINATION OF α/ν IN THE 3D CLASSICAL HEISENBERG MODEL
1994
To study the role of topological defects in the three-dimensional classical Heisenberg model we have simulated this model on simple cubic lattices of size up to 803, using the single-cluster Monte Carlo update. Analysing the specific-heat data of these simulations, we obtain a very accurate estimate for the ratio of the specific-heat exponent with the correlation-length exponent, α/ν, from a usual finite-size scaling analysis at the critical coupling Kc. Moreover, by fitting the energy at Kc, we reduce the error estimates by another factor of two, and get a value of α/ν, which is comparable in accuracy to best field theoretic estimates.
Non-Markovian master equation for the XX central spin model
2008
The non-Markovian correlated projection operator technique is applied to the model of a central spin coupled to a spin bath through non uniform XX Heisenberg coupling. The second order results of the Nakajima-Zwanzig and of the time-convolutionless methods are compared with the exact solution considering a fully polarized initial bath state.
Heisenberg Uncertainty Relation in Quantum Liouville Equation
2009
We consider the quantum Liouville equation and give a characterization of the solutions which satisfy the Heisenberg uncertainty relation. We analyze three cases. Initially we consider a particular solution of the quantum Liouville equation: the Wigner transformf(x,v,t) of a generic solutionψ(x;t) of the Schrödinger equation. We give a representation ofψ(x,t) by the Hermite functions. We show that the values of the variances ofxandvcalculated by using the Wigner functionf(x,v,t) coincide, respectively, with the variances of position operatorX^and conjugate momentum operatorP^obtained using the wave functionψ(x,t). Then we consider the Fourier transform of the density matrixρ(z,y,t) =ψ∗(z,t)…
Some criteria for detecting capable Lie algebras
2013
Abstract In virtue of a recent bound obtained in [P. Niroomand, F.G. Russo, A note on the Schur multiplier of a nilpotent Lie algebra, Comm. Algebra 39 (2011) 1293–1297], we classify all capable nilpotent Lie algebras of finite dimension possessing a derived subalgebra of dimension one. Indirectly, we find also a criterion for detecting noncapable Lie algebras. The final part contains a construction, which shows that there exist capable Lie algebras of arbitrary big corank (in the sense of Berkovich–Zhou).