Presence Of Random Magnetic Field Research Articles

Dynamics of an entangled pair of spin-1/2 particles under correlated random magnetic fields.

The dynamics of a maximally entangled pair of spin-1/2 particles is obtained in the presence of random magnetic fields which are correlated. The two spin-1/2 particles are assumed to be maximally entangled initially and are then disturbed by the magnetic fields modeled as Gaussian vector random processes whose corresponding spatial components are correlated. The dynamics is derived in terms of the joint density matrix of the entangled pair using the ideas of stochastic calculus, from which the steady-state density matrix and the associated timescale for it to be reached are obtained. The asymptotic density matrix represents a state of (partial) disentanglement.

Spectral crossovers and universality in quantum spin chains coupled to random fields

We study the spectral properties of and spectral crossovers between different random matrix ensembles [Poissonian, Gaussian orthogonal ensemble (GOE), Gaussian unitary ensemble (GUE)] in correlated spin-chain systems, in the presence of random magnetic fields, and the scalar spin-chirality term, competing with the usual isotropic and time-reversal invariant Heisenberg term. We have investigated these crossovers in the context of the level-spacing distribution and the level-spacing ratio distribution. We use random matrix theory (RMT) analytical results to fit the observed Poissonian-to-GOE and GOE-to-GUE crossovers, and examine the relationship between the RMT crossover parameter $\ensuremath{\lambda}$ and scaled physical parameters of the spin-chain systems in terms of a scaling exponent. We find that the crossover behavior exhibits universality, in the sense that, it becomes independent of lattice size in the large Hamiltonian matrix dimension limit. Moreover, the scaling exponent obtained from such a finite size scaling analysis, seems to be quite robust and independent of the type of crossover considered or the specific spectral correlation measure used.

Dynamics of cholesteric liquid crystals in the presence of random magnetic fields

Based on dynamic renormalization group techniques, this letter analyzes the effects of external stochastic perturbations on the dynamical properties of cholesteric liquid crystals, studied in the presence of a random magnetic field. Our analysis quantifies the nature of the temperature dependence of the dynamics; the results also highlight a hitherto unexplored regime in cholesteric liquid-crystal dynamics. We show that stochastic fluctuations drive the system to a second-ordered Kosterlitz-Thouless phase transition point, eventually leading to a Kardar-Parisi-Zhang (KPZ) universality class. The results go beyond quasi–first-order mean-field theories, and provide the first theoretical understanding of a KPZ phase in distorted nematic liquid-crystal dynamics.

Critical behavior and universality properties of uniaxial ferromagnetic thin films in the presence of random magnetic fields

Critical phenomena in uniaxial ferromagnetic thin films in the presence of random magnetic fields have been studied within the framework of effective field theory. When the type of the random field distribution is bimodal, the system exhibits tricritical behavior. Furthermore, the critical value of surface to bulk ratio of exchange interactions at which the transition temperature becomes independent of film thickness varies very slowly in the presence of both bimodal or trimodal random fields. Regarding the universality properties, neither p, nor h variations in the system can affect the value of the shift exponent λ. In this regard, it can be concluded that pure ferromagnetic thin films are in the same universality class with those under the influence of random discrete magnetic fields.

Computational power of symmetric Hamiltonians

The presence of symmetries, be they discrete or continuous, in a physical system typically leads to a reduction in the problem to be solved. Here we report that neither translational invariance nor rotational invariance reduce the computational complexity of simulating Hamiltonian dynamics; the problem is still bounded error, quantum polynomial time complete, and is believed to be hard on a classical computer. This is achieved by designing a system to implement a universal quantum interface, a device which enables control of an arbitrary computation through the control of a fixed number of spins, and using it as a building block to entirely remove the need for control, except in the system initialization. Finally, it is shown that cooling such Hamiltonians to their ground states in the presence of random magnetic fields solves a Quantum-Merlin-Arthur-complete problem.

Localization in quasi-one-dimensional systems with a random magnetic field.

We investigate the localization of electrons hopping on quasi-1D strips in the presence of random magnetic field. In the weak-disorder region, by perturbative analytical techniques, we derive scaling laws for the localization length, ${\xi}$, of the form $ \xi \propto \frac{1}{w^{\eta}}$, where $w$ is the size of magnetic disorder and the exponent $\eta$ assumes different values in the various energy ranges. Moreover, in the neighborhood of the energies where a new channel opens a certain rearrangement of the perturbation expansion leads to scaling functions for $\xi$. Although the latter are in general quantitatively wrong, they correctly reproduce the corresponding $\eta$ exponents and the form of the scaling variables and are therefore useful for understanding the behavior of $\xi$.

Electronic states in quasi-one-dimensional wires with nonuniform magnetic fields

We have investigated the transmission of an electron in quasi-one-dimensional systems in the presence of nonuniform magnetic fields. The subband energy and the wave function in a magnetic field, whose strength varies parabolically in the transverse direction, are calculated. This model is expected to describe a composite fermion in quantum wires. The parabolic magnetic field is found to increase the band-edge energies and modify the probability distribution significantly. When a moderate negative offset magnetic field is added, the subband energy takes a minimum value for a finite parabolic magnetic-field strength and the wave function of the lowest subband is double peaked. We have calculated magnetic-field dependencies of the bend resistance and the Hall resistance in a cross junction, in which the parabolic magnetic field is assumed. The positions in magnetic field of the peak in the bend resistance due to ballistic transport and of the zero Hall resistance are shifted and generally do not coincide as the parabolic field is imposed. We also examine the conductance of quantum wires in the presence of random magnetic fields. The nonuniform magnetic fields lead to universal conductance fluctuations in the metallic regime and to exponential decay of the conductance as the length is increased in the localized regime. In contrast to the impurity scattering case, the localization length is found to be smaller for larger average magnetic fields.

Bounds on neutrino transition magnetic moments in random magnetic fields

We consider the conversions of active to sterile Majorana neutrinos ν a and ν s , due to neutrino transition magnetic moments in the presence of random magnetic fields (r.m.f.) generated at the electroweak phase transition. From a simple Schrödinger-type evolution equation, we derive a stringent constraint on the corresponding transition magnetic moments and display it as a function of the domain size and field geometry. For typical parameter choices one gets limits much stronger than usually derived from stellar energy loss considerations. These bounds are consistent with the hypothesis of seeding of galactic magnetic fields by primordial fields surviving past the re-combination epoch. We also obtain a bound on active-sterile neutrino transition magnetic moments from supernova energy loss arguments. For r.m.f. strengths in the range 10 7–10 12 G we obtain limits varying from μ as ν ≲ 10 −13 μ B to μ as ν ≲ 10 −18 μ B , again much stronger than in the case without magnetic fields.

Dimensional reduction with correlated random fields. A superspace renormalization-group calculation

We consider phase transitions in the presence of random magnetic fields, with long-range correlations such that $〈h(0)h(r)〉\ensuremath{\sim}\frac{1}{{r}^{d\ensuremath{-}\ensuremath{\sigma}}}$. The upper critical dimension is $6+\ensuremath{\sigma}$. A superspace renormalization-group calculation is carried out to order ${\ensuremath{\epsilon}}^{2}$, where $\ensuremath{\epsilon}=6+\ensuremath{\sigma}\ensuremath{-}d$. To order $\ensuremath{\epsilon}$, the critical properties are that of a pure system in $d\ensuremath{-}2\ensuremath{-}\ensuremath{\sigma}$ dimensions. This dimensional reduction is also justified by physical arguments concerning the lower critical dimensionality, and the hyperscaling relationship. However, it fails at order ${\ensuremath{\epsilon}}^{2}$.