Search results for "Heisenberg"
showing 10 items of 80 documents
Hardy spaces and quasiconformal maps in the Heisenberg group
2023
We define Hardy spaces $H^p$, $00$ such that every $K$-quasiconformal map $f:B \to f(B) \subset \mathbb{H}^1$ belongs to $H^p$ for all $0<p<p_0(K)$. Second, we give two equivalent conditions for the $H^p$ membership of a quasiconformal map $f$, one in terms of the radial limits of $f$, and one using a nontangential maximal function of $f$. As an application, we characterize Carleson measures on $B$ via integral inequalities for quasiconformal mappings on $B$ and their radial limits. Our paper thus extends results by Astala and Koskela, Jerison and Weitsman, Nolder, and Zinsmeister, from $\mathbb{R}^n$ to $\mathbb{H}^1$. A crucial difference between the proofs in $\mathbb{R}^n$ and $\mathbb{…
A PHENOMENOLOGICAL OPERATOR DESCRIPTION OF INTERACTIONS BETWEEN POPULATIONS WITH APPLICATIONS TO MIGRATION
2013
We adopt an operatorial method based on the so-called creation, annihilation and number operators in the description of different systems in which two populations interact and move in a two-dimensional region. In particular, we discuss diffusion processes modeled by a quadratic hamiltonian. This general procedure will be adopted, in particular, in the description of migration phenomena. With respect to our previous analogous results, we use here fermionic operators since they automatically implement an upper bound for the population densities.
Thermodynamic limit of the two-spinon form factors for the zero field XXX chain
2019
In this paper we propose a method based on the algebraic Bethe ansatz leading to explicit results for the form factors of quantum spin chains in the thermodynamic limit. Starting from the determinant representations we retrieve in particular the formula for the two-spinon form factors for the isotropic XXX Heisenberg chain obtained initially in the framework of the $q$-vertex operator approach.
Uranium from German Nuclear Power Projects of the 1940s— A Nuclear Forensic Investigation
2015
Here we present a nuclear forensic study of uranium from German nuclear projects which used different geometries of metallic uranium fuel. Through measurement of the (230)Th/(234)U ratio, we could determine that the material had been produced in the period from 1940 to 1943. To determine the geographical origin of the uranium, the rare-earth-element content and the (87)Sr/(86)Sr ratio were measured. The results provide evidence that the uranium was mined in the Czech Republic. Trace amounts of (236)U and (239)Pu were detected at the level of their natural abundance, which indicates that the uranium fuel was not exposed to any major neutron fluence.
Magnetic exchange interactions in the heteropoly complexes [M4(H2O)2(PW9O34)2]10− [M=Co(II) and Cu(II)]
1990
The magnetic properties of the heteropolyanions [M4(H2O)2(PW9O34)2]10− [M=Co(II) and Cu(II)] down to 4 K are reported. Their individual heteropoly molecules contain a rhomblike arrangement formed by four coplanar MO6 octahedra sharing edges. The magnetic properties support an intramolecular ferromagnetic exchange in the Co(II) tetramer, and antiferromagnetic exchange in the Cu(II) tetramer. These behaviors are discussed assuming anisotropic exchange in the Co(II) compound, and Heisenberg exchange in the Cu(II) compound. Carlos.Gomez@uv.es
Small clusters with Heisenberg antiferromagnetic exchange
2000
We study small symmetrical clusters of magnetic ions with Heisenberg antiferromagnetic exchange interaction. We calculate the magnetization and the specific heat as functions of applied magnetic field at zero and non-zero temperature. Results are given for both classical and quantum systems. At zero temperature the classical systems undergo a series of transitions where the symmetry changes as a function of applied field. The quantum systems show similar features to Ising systems previously studied.
Magnetic Nanoparticles as Many-Spin Systems
2005
We have demonstrated by different analytical and numerical methods the importance of accounting for the magnetization inhomogeneities in magnetic nanoparticles, especially in the presence of surface anisotropy. The latter makes the magnetization inhomogeneous even at T = 0 and in general modifies the relation between the intrinsic and induced magnetizations. It also changes the magnetization switching mechanism, since for strong surface anisotropy the particle’s spins switch cluster-wise. For weak surface anisotropy we have been able to calculate the spin canting in the particle analytically and to obtain a novel second-order contribution to the particle’s overall anisotropy. It remains to …
An Ising ferromagnet with an antiferromagnetic surface layer: A simple model for magnetic surface reconstruction
1985
Simple cubic Ising lattices are studied by Monte Carlo simulation, using a thin film geometry (usually 40 atomic layers thick), with nearest neighbour ferromagnetic exchange J in the bulk and nearest neighbour antiferromagnetic interaction Js between surface spins. Applying a technique of preferential sampling in the surface layers, we investigate the ordering for a variety of values of JsJ and for various temperatures. For JsAF < Js < − 0.25J (where JsAF ≈ − 2.01J) ferromagnetic ordering occurs at a higher temperature than the antiferromagnetic surface ordering, while for − 0.25J < Js no antiferromagnetic long range order is possible. For Js < JsAF the surface transition occurs at a higher…
Spin state of a single-molecule magnet (SMM) creating long-range ordering on ferromagnetic layers of a magnetic tunnel junction – a Monte Carlo study
2021
Paramagnetic single-molecule magnets (SMMs) interacting with the ferromagnetic electrodes of a magnetic tunnel junction (MTJ) produce a new system. The properties and future scope of new systems differ dramatically from the properties of isolated molecules and ferromagnets. However, it is unknown how far deep in the ferromagnetic electrode the impact of the paramagnetic molecule and ferromagnet interactions can travel for various levels of molecular spin states. Our prior experimental studies showed two types of paramagnetic SMMs, the hexanuclear Mn6 and octanuclear Fe–Ni molecular complexes, covalently bonded to ferromagnets produced unprecedented strong antiferromagnetic coupling between …
An operatorial description of desertification
2016
We propose a simple theoretical model for desertification processes based on three actors (soil, seeds, and plants) on a two-dimensional lattice. Each actor is described by a time dependent fermionic operator, and the dynamics is ruled by a self-adjoint Hamilton-like operator. We show that even taking into account only a few parameters, accounting for external actions on the ecosystem or the response to positive feedbacks, the model provides a plausible description of the desertification process, and can be adapted to different ecological landscapes. We first describe the simplified model in one cell. Then, we define the full model on a two-dimensional region, taking into account additional…