Exhibition of Monogamy Relations between Entropic Non-contextuality Inequalities

We exhibit the monogamy relation between two entropic non-contextuality inequalities in the scenario where compatible projectors are orthogonal. We show the monogamy relation can be exhibited by decomposing the orthogonality graph into perfect induced subgraphs. Then we find two entropic non-contextuality inequalities are monogamous while the KCBS-type non-contextuality inequalities are not if the orthogonality graphs of the observable sets are two odd cycles with two shared vertices.     

Modal Dynamics for Positive Operator Measures

The modal interpretation of quantum mechanics allows one to keep the standard classical definition of realism intact. That is, variables have a definite status for all time and a measurement only tells us which value it had. However, at present modal dynamics are only applicable to situations that are described in the orthodox theory by projective measures. In this paper we extend modal dynamics to include positive operator measures (POMs). That is, for example, rather than using a complete set of orthogonal projectors, we can use an overcomplete set of nonorthogonal projectors. We derive the conditions under which Bell's stochastic modal dynamics for projective measures reduce to deterministic dynamics, showing (incidentally) that Brown and Hiley's generalization of Bohmian mechanics [quant-ph/0005026, (2000)] cannot be thus derived. We then show how deterministic dynamics for positive operators can also be derived. As a simple case, we consider a Harmonic oscillator, and the overcomplete set of coherent state projectors (i.e., the Husimi POM). We show that the modal dynamics for this POM in the classical limit correspond to the classical dynamics, even for the nonclassical number state |n>. This is in contrast to the Bohmian dynamics, which for energy eigenstates, the dynamics are always non-classical.     

Non-Orthogonal Core Projectors for Modal Interpretations of Quantum Mechanics

Modal interpretations constitute a particular approach to associating dynamical variables with physical systems in quantum mechanics. Given the quantum logical constraints that are typically adopted by such interpretations, only certain sets of variables can be taken to be simultaneously definite-valued, and only certain sets of values can be ascribed to these variables at a given time. Moreover, each allowable set of variables and values can be uniquely specified by a single core projector in the Hilbert space associated with the system. In general, the core projector can be one of several possibilities at a given time. In most previous modal interpretations, the different possible core projectors have formed an orthogonal set. This paper investigates the possibility of adopting a non-orthogonal set. It is demonstrated that such non-orthogonality is required if measurements for which the outcome can be predicted with probability 1 are to reveal the pre-existing value of the variable measured, an assumption which has traditionally constituted a strong motivation for the modal approach. The existing framework for modal interpretations is generalized to explicitly accommodate non-orthogonal core projectors.     

Exact results on equations of motion in vacuum string field theory

We prove some algebraic relations on the translationally invariant solutions and the lump solutions in vacuum string field theory. We show that up to the subtlety at the midpoint the definition of the half-string projectors of the known sliver solution can be generalized to other solutions. We also find that we can embed the translationally invariant solution into the matrix equation of motion with the zero-mode.     

Properties of Physical Systems: Transient Singularities on Borders and Surface Transitive Zones

Certain alternative properties of physical systems are describable by supports of arguments of response functions (e.g. light cone, borders of media) and expressed by projectors; corresponding equations of restraints lead to dispersion relations, theorems of counting, etc. As supports are measurable, their absolutely strict borders contradict the spirit of quantum theory and their quantum evolution leading to appearance of subtractions or certain needed flattening would be considered. “Flattening” of projectors introduce transitive zones that can be examined as a specification of adiabatic hypothesis or the Bogoliubov regulatory function in QED. For demonstration of their possibilities the phenomena of refraction and reflection of electromagnetic wave are considered; they show, in particular, the inevitable appearing of double electromagnetic layers on all surfaces that formerly were repeatedly postulated, etc. Quantum dynamics of projectors proves the neediness of subtractions that usually are artificially adding and express transient singularities and zones in squeezed forms.     

Is there contextuality for a single qubit?

Cabello and Nakamura have shown [A. Cabello, Phys. Rev. Lett. 90, 190401 (2003)10.1103/PhysRevLett.90.190401] that the Kochen-Specker theorem can be applied to two-dimensional systems if one uses positive operator-valued measures (POVM). We show that the contextuality in their models is not of the Kochen-Specker type, but it is rather a result of not keeping track of the whole system on which the measurement is performed. This is connected to the fact that there is no one-to-one correspondence between the POVM elements and projectors on the extended Hilbert space, and the same POVM element has to originate from two different projectors when used in Cabello-Nakamura models. Moreover, we propose a hidden-variable formulation of the above models.     

Phase diagram of a 2D Ising model within a nonextensive approach

In this work we report Monte Carlo simulations of a 2D Ising model, in which the statistics of the Metropolis algorithm is replaced by the nonextensive one. We compute the magnetization and show that phase transitions are present for q ≠ 1. A q - phase diagram (critical temperature vs. the entropic parameter q) is built and exhibits some interesting features, such as phases which are governed by the value of the entropic index q. It is shown that such phases favors some energy levels of magnetization states. It is also shown that the contribution of the Tsallis cutoff is capital to the existence of phase transitions.     

First-principles study of defect-induced magnetism in carbon

We have studied the role of defects on the magnetic properties of carbon materials using first-principles density functional methods. We show that, while the total magnetization decreases both for diamond and graphite with increase in vacancy density, the magnetization decreases more rapidly for graphitic structures. The presence of nitrogen nearby a vacancy is shown to produce larger macroscopic magnetic signals as compared to a standalone carbon vacancy. The results indicate the possibility of tuning magnetization in carbon by controlled defect generation and doping.     

Finite-Volume Excitations of the¶111 Interface in the Quantum XXZ Model

We show that the ground states of the three-dimensional XXZ Heisenberg ferromagnet with a 111 interface have excitations localized in a subvolume of linear size R with energies bounded by O(1/R²). As part of the proof we show the equivalence of ensembles for the 111 interface states in the following sense: In the thermodynamic limit the states with fixed magnetization yield the same expectation values for gauge invariant local observables as a suitable grand canonical state with fluctuating magnetization. Here, gauge invariant means commuting with the total third component of the spin, which is a conserved quantity of the Hamiltonian. As a corollary of equivalence of ensembles we also prove the convergence of the thermodynamic limit of sequences of canonical states (i.e., with fixed magnetization).     

Magnetic susceptibility contrast induced field gradients in porous media.

Using a two-component composite theory, we compute the internal field gradient of a periodic porous medium induced by the magnetic susceptibility contrasts. The magnetization of such a system is computed by using the diffusion eigenstates in Fourier representation. We show that the volume averaged field gradient, when used in the formula for free diffusion, significantly overestimates the magnetization decay rate. We also establish bounds for such a periodic system within which the Gaussian approximation is valid for diffusion of spins in the pore space.     

Magnetic properties of La_2CuMnO_6 double perovskite ceramic investigated by Monte Carlo simulations

We present a theoretical study of the magnetic properties of the lanthanum copper manganate double perovskite La_2CuMnO_6 ceramic, using Monte Carlo simulations. We analyze and discuss the ground state phase diagrams in different planes to show the effect of every physical parameter. Based on the Monte Carlo simulations, which combine Metropolis algorithm and Ising model, we explore the thermal behavior of the total magnetization and susceptibility. We also present and discuss the influence of physical parameters such as the external magnetic field, the exchange coupling interactions between magnetic atoms, and the exchange magnetic field on the magnetization of the system. Moreover, the critical temperature of the system is about T_c=70 K, in agreement with the experimental value. Finally, the hysteresis loops of La_2CuMnO_6 are discussed.     

Quantum arrival time formula from decoherent histories

We use the decoherent histories approach to quantum mechanics to compute the probability for a wave packet to cross the origin during a given time interval. We define class operators (sums of strings of projectors) characterizing quantum-mechanical crossing and simplify them using a semiclassical approximation. Using these class operators we find that histories crossing the origin during different time intervals are approximately decoherent for a variety of initial states. Probabilities may therefore be assigned and coincide with the flux of the wave packet (the standard semiclassical formula), and are positive. The known initial states for which the flux is negative (backflow states) are shown to correspond to non-decoherent sets of histories, so probabilities may not be assigned.     

Kochen-Specker theorem for a three-qubit system: A state-dependent proof with seventeen rays

We consider Kochen-Specker theorem for three-qubit system with eight-dimensional state space. Reexamining the proof given by Kernaghan and Peres, we make some clarifications on the orthogonality of rays and rank-two projectors found by them. Basing on their five groups of orthogonal octad, we then show a proof that requires only seventeen rays.     

Non-equilibrium effects in the magnetic behavior of Co3O4 nanoparticles

We report detailed studies of the non-equilibrium magnetic behavior of antiferromagnetic Co₃O₄ nanoparticles. The temperature and field dependence of magnetization, wait time dependence of magnetic relaxation (aging), memory effects, and temperature dependence of specific heat have been investigated to understand the magnetic behavior of these particles. We find that the system shows some features that are characteristic of nanoparticle magnetism such as bifurcation of field-cooled (FC) and zero-field-cooled (ZFC) susceptibilities and a slow relaxation of magnetization. However, strangely, the temperature at which the ZFC magnetization peaks coincides with the bifurcation temperature and does not shift on application of magnetic fields up to 1 kOe, unlike most other nanoparticle systems. Aging effects in these particles are negligible in both FC and ZFC protocols, and memory effects are present only in the FC protocol. We show that Co₃O₄ nanoparticles constitute a unique antiferromagnetic system which enters into a blocked state above the average Néel temperature.     

ac Magnetization transport and power absorption in nonitinerant spin chains

We investigate the ac transport of magnetization in nonitinerant quantum systems such as spin chains described by the XXZ Hamiltonian. Using linear response theory, we calculate the ac magnetization current and the power absorption of such magnetic systems. Remarkably, the difference in the exchange interaction of the spin chain itself and the bulk magnets (i.e., the magnetization reservoirs), to which the spin chain is coupled, strongly influences the absorbed power of the system. This feature can be used in future spintronic devices to control power dissipation. Our analysis allows us to make quantitative predictions about the power absorption, and we show that magnetic systems are superior to their electronic counterparts.     

Scaling and front dynamics in Ising quantum chains

We study the relaxation behaviour of the quantum Ising chain, focusing our attention onto the non-equilibrium dynamics of the transverse magnetization. The initial states, from which the magnetization relaxes, are product states such as those generated by setting in contact several systems, each initially equilibrated at a given temperature. Due to the free fermionic structure of the chain, the dynamics of the transverse magnetization is easily expressed in a compact form. In the completely factorized initial state, corresponding to a situation where all the spins are thermalized independently, we obtain in the scaling limit the Green function associated to the transverse magnetization. The relaxation behaviour is also considered in the system-bath case, where part of the chain called the system is thermalized at a temperature T_s and the remaining part is at a temperature T_b. The magnetization profiles show a scaling behaviour. Moreover, in the extreme case T_b=∞ and T_s=0, it is shown that the magnetization relaxes in quantized steps in the strong transverse field region.     

Ferrites — what is new?

Ferrites, combining insulating and ferrimagnetic properties, have long been used in technology. The aim of this paper is to focus on new features in these materials. In the classical theory of ferrimagnets, Néel had predicted the unusual thermal variation of the spontaneous magnetization, such as, the disappearance of the magnetization at a temperature which was not the Curie temperature but at a point where there was compensation of the spontaneous magnetization of the two sublattices. We show experimentally that temperature (T _K) in spinel oxide is different under the ZFC and FC magnetization method. To our knowledge, only limited attempt has been made to study T _K as very few systems exhibit such behavior. In general, some of the ferrites have specific semiconducting properties, e.g., a very low carrier mobility. We discuss the anomalies of the magneto-resistance in ferrites that occur at order-disorder and order-order magnetic phase transition along with our ac and dc conductivity data near the spin compensation temperature. Another notable feature of the ferrites is that, upon irradiation of heavy ions, one can tune the magnetic ordering on bulk sample without destructive effects, i.e., irradiation-induced magnetization. It is interesting to note that spinel ferrite (nano) particle is an ideal small particle magnetic system as the crystal chemistry issue can be controlled, unlike pure metal particle systems where the crystal chemistry issues are basically fixed. In relevance to this, we will also discuss the future prospects, namely, the effect of irradiation on small particle magnetism, as, so far, only a limited attempt has been made in this field.     

Covariant Lagrange multiplier constrained higher derivative gravity with scalar projectors

We formulate higher derivative gravity with Lagrange multiplier constraint and scalar projectors. Its gauge-fixed formulation as well as vector fields formulation is developed and corresponding spontaneous Lorentz symmetry breaking is investigated. We show that the only propagating mode is higher derivative graviton while scalar and vector modes do not propagate. Despite to higher derivatives structure of the action, its first FRW equation is the first order differential equation which admits the inflationary universe solution.     

On Perturbations of Generalized Landau-Lifshitz Dynamics

We consider deterministic and stochastic perturbations of dynamical systems with conservation laws in ℝ³. The Landau-Lifshitz equation for the magnetization dynamics in ferromagnetics is a special case of our system. The averaging principle is a natural tool in such problems. But bifurcations in the set of invariant measures lead to essential modification in classical averaging. The limiting slow motion in this case, in general, is a stochastic process even if pure deterministic perturbations of a deterministic system are considered. The stochasticity is a result of instabilities in the non-perturbed system as well as of existence of ergodic sets of a positive measure. We effectively describe the limiting slow motion.