Complex structures adapted to magnetic flows

Let $M$ be a compact real-analytic manifold, equipped with a real-analytic Riemannian metric $g$, and let $\beta$ be a closed real-analytic 2-form on $M$, interpreted as a magnetic field. Consider the Hamiltonian flow on $T^{1}M$ that describes a charged particle moving in the magnetic field $\beta$. Following an idea of T. Thiemann, we construct a complex structure on a tube inside $T^{1}M$ by pushing forward the vertical polarization by the Hamiltonian flow “evaluated at time $i$”. This complex structure fits together with $\omega -{\pi }^1\beta$ to give a Kähler structure on a tube inside $T^{1}M$. When $\beta =0$, our magnetic complex structure is the adapted complex structure of Lempert–Szőke and Guillemin–Stenzel.We describe the magnetic complex structure in terms of its $(1,0)$-tangent bundle, at the level of holomorphic functions, and via a construction using the embeddings of Whitney–Bruhat and Grauert. We describe an antiholomorphic intertwiner between this complex structure and the complex structure induced by $-\beta$, and we give two formulas for local Kähler potentials, which depend on a local choice of vector potential $1$-form for $\beta$. Finally, we compute the magnetic complex structure explicitly for constant magnetic fields on ${\mathbb{R}}^2$ and $S^2$.     

Magnetic properties of terbium dihydrides

Magnetization measurements of terbium dihydride samples with different hydrogen concentration, TbH_1.92, TbH_1.99, TbH_2.03 and TbH_2.09, in the temperature range from 1.8 to 300 K and at an applied field of 1 kOe are reported. Two first-order antiferromagnetic transitions have been registered in the narrow temperature range between 15–18 K for all hydride compositions. Isothermal magnetization ($\sigma {\left(H\right)}_{T=\mathrm{const}}$) measurements at several temperatures in the vicinity of magnetic transitions have been carried out and used for the magnetic-entropy change, $\Delta S_{\sigma }$, calculations. The magnetic-entropy changes have negative values, and in an applied magnetic field of 5 T they reach 2.5 J/kg K, which is only about 26% of the $\Delta S_{\sigma }\left(H\right)$ value expected from thermal measurements. A much larger magnetic field must be applied for terbium hydrides to be used as refrigerant materials for low-temperature needs.     

ESR in a gapped Anderson model

We applied the numerical renormalization group method to study the electron spin resonance (ESR) of a single-impurity Anderson model with a gap $\Delta$ in the conduction electron density of states, centered at the Fermi level. We analyzed the relaxation rate $1/T_1$ of a magnetic probe located at a position $\overrightarrow{R}$ around the Anderson impurity. It presents different behaviors for the symmetric and the asymmetric case. For the symmetric case and any $\Delta >0$, $1/T_1$ goes to a constant for $T?{\Gamma }_{\text{k}}$ (Kondo resonance). $1/T_1$ decreases monotonically to zero only for $\Delta =0$. For the asymmetric case, there is a $\Delta$ under which $1/T_1$ decreases monotonically to zero as $T\to 0$, and above which $1/T_1$ saturates, as occurs in the symmetric case for $\Delta >0$. This behavior indicates a quantum phase transition from the quenched to the unquenched magnetic moment in the ground state of the Anderson ion.     

Shannon and Fisher entropies for a hydrogen atom under soft spherical confinement

We calculate Shannon and Fisher entropies in the position and momentum space, and some complexity measures for a variationally described hydrogen atom confined in soft and hard spherical boxes of varying dimension $r_c$ and selected values of strength $U_0$. We include calculations for a free particle trapped in impenetrable boxes. It is found that the Shannon entropy $S_r$ becomes negative for small cavity radii and large values of $U_0$, due to the highly localized nature of the particle. For soft confinement and small cavity dimensions, the entropies change very rapidly over short radial intervals.     

Effect of hydrostatic pressure on diamagnetic susceptibility of hydrogenic donor impurity in core/shell/shell spherical quantum dot with Kratzer confining potential

Dependencies of diamagnetic susceptibility ${\chi }_{dia}$ on parameter $r_0$ for different values of hydrostatic pressure for 1s state.Dependence of diamagnetic susceptibility ${\chi }_{dia}$ on hydrostatic pressure $P$ for different values of $r_0$ for 1s state.

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Limitations of discrete-time quantum walk on a one-dimensional infinite chain

How well can we manipulate the state of a particle via a discrete-time quantum walk? We show that the discrete-time quantum walk on a one-dimensional infinite chain with coin operators that are independent of the position can only realize product operators of the form $e^{i\xi }A?{\mathbb{1}}_p$, which cannot change the position state of the walker. We present a scheme to construct all possible realizations of all the product operators of the form $e^{i\xi }A?{\mathbb{1}}_p$. When the coin operators are dependent on the position, we show that the translation operators on the position can not be realized via a DTQW with coin operators that are either the identity operator $\mathbb{1}$ or the Pauli operator ${\sigma }_x$.     

Exchange integrals and magnetic short range order in the system CdCr2−xGaxSe4(0⩽x⩽0.06)

High-temperature series expansions are derived for the magnetic susceptibility and two-spin correlation functions for a Heisenberg ferromagnetic model on the B-spinel lattice. The calculations are developed in the framework of the random phase approximation and are given for both nearest and next-nearest neighbour exchange integrals $J_1$ and $J_2$, respectively. Our results are given up to order 6 in $\beta =(k_{\mathrm{B}}T{)}^{-1}$and are used to study the paramagnetic region of the ferromagnetic spinel CdCr_2−xGa_xSe₄. The critical temperature $T_{\mathrm{c}}$ and the critical exponents $\gamma$ and $\nu$ associated with the magnetic susceptibility $\chi (T)$ and the correlation length $\xi (T)$, respectively are deduced by applying the Padé approximate methods. The results as a function of the dilution x obtained by the present approach are found to be in agreement with the experimental ones.     

p(x) and Tc(x) characteristics in the Y 1−b(Ca)bBa2Cu3O6+x cuprate family

A model has been proposed to calculate the $p\left(x\right)$ and $T_c\left(x\right)$ dependences in the Y _1?b(Ca)_bBa₂Cu₃O_6+x high-$T_c$ cuprate family and applied to $b=0$, $b=0.1$, and $b=0.2$ cases, for which experimental data exist in the literature. The results obtained imply that the Ca efficiency to provide holes is independent of the basal plane oxygen concentration, which is consistent with a view that electrons from CuO₂ layers would go primarily to Ca since it is twice closer than oxygen (in addition, the chain oxygen is screened by a layer made up of Ba and O(4) ions). It is shown that, in fully oxygenized compounds ($x=1$) the average efficiency, $\chi$, of a chain oxygen to attract an electron from the two nearby layers is reduced by the Ca insertion, though not because the charge transfer mechanism is in itself weakened by Ca, but because a part of electrons that are otherwise available in CuO${}_2$ layers has already been removed by the substitution of Y ³⁺ with Ca²⁺. It has been found that the $b$-dependence of the average oxygen doping efficiency can be fairly accurately described by the following relation: $\chi \left(b\right)=0.39\times (1?0.78b)$. The calculated $p\left(x\right)$ and $T_c\left(x\right)$ dependences are in very good agreement with the available experimental data.     

Correlation among the effective mass (m⁎), λab and Tc of superconducting cuprates in a Casimir energy scenario

The relevance of the Casimir effect, discovered in 1948, has recently been pointed out in studies on materials such as graphene and high-temperature superconducting cuprates. In particular, the relationship between Casimir energy and the energy of a superconducting condensate with anisotropy characterized by high bidimensionality has already been discussed in certain theoretical scenarios. Using this proposal, this work describes the relationship between the effective mass of the charge carriers ($m^{?}=\alpha m_e$) and the macroscopic parameters characteristic of several families of high-$T_c$ superconducting cuprates (Cu-HTSC) that have copper and oxygen superconducting planes (Cu-O). We have verified that an expression exists that correlates the effective mass, the London penetration length in the plane ${\lambda }_{ab}$, the critical temperature $T_c$ and the distance d between the equivalent superconducting planes of Cu-HTSC. This study revealed that the intersection between the asymptotic behavior of α as a function of $T_c$ and the line describing the optimal value of $\alpha ?2$ ($m^{?}?2m_e$) indicates that a nonadiabatic region exists, which implies a carrier-lattice interaction and where the critical temperature can have its highest value in Cu-HTSC.     

Percolation on infinitely ramified fractal networks

We study how fractal features of an infinitely ramified network affect its percolation properties. The fractal attributes are characterized by the Hausdorff ($D_H$), topological Hausdorff ($D_{tH}$), and spectral ($d_s$) dimensions. Monte Carlo simulations of site percolation were performed on pre-fractal standard Sierpiński carpets with different fractal attributes. Our findings suggest that within the universality class of random percolation the values of critical percolation exponents are determined by the set of dimension numbers ($D_H$, $D_{tH}$, $d_s$), rather than solely by the spatial dimension (d). We also argue that the relevant dimension number for the percolation threshold is the topological Hausdorff dimension $D_{tH}$, whereas the hyperscaling relations between critical exponents are governed by the Hausdorff dimension $D_H$. The effect of the network connectivity on the site percolation threshold is revealed.     

Unusual superconducting behavior in HfV2Ga4

Bulk superconductivity in HfV₂Ga₄ with critical temperature close to 4.1 K was determined via magnetic susceptibility, electrical resistivity and specific heat measurements. Both the upper and lower critical field dependence with reduced temperature ($T/T_c$) exhibit non-conventional behavior. The electronic component of specific heat shows a double-jump, the first close to $T_c$ and the other close to $0.75T_c$. We speculate about the nature of the douple jump observed in specific heat considering two plausable scenarios: bulk inhomogeneities and the existence of a second gap.