Magnon–magnon interactions in O(3) ferromagnets and equations of motion for spin operators

The method of equations of motion for spin operators in the case of O(3) Heisenberg ferromagnet is systematically analyzed starting from the effective Lagrangian. It is shown that the random phase approximation and the Callen approximation can be understood in terms of perturbation theory for type B magnons. Also, the second order approximation of Kondo and Yamaji for one dimensional ferromagnet is reduced to the perturbation theory for type A magnons. An emphasis is put on the physical picture, i.e. on magnon–magnon interactions and symmetries of the Heisenberg model. Calculations demonstrate that all three approximations differ in manner in which the magnon–magnon interactions arising from the Wess–Zumino term are treated, from where specific features and limitations of each of them can be deduced.     

High order resolution of the Maxwell–Fokker–Planck–Landau model intended for ICF applications

A high order, deterministic direct numerical method is proposed for the non-relativistic 2D_x×3D_v$2D_{\mathbf{x}}\times 3D_{\mathbf{v}}$ Vlasov–Maxwell system, coupled with Fokker–Planck–Landau collision operators. The magnetic field is perpendicular to the 2D_x$2D_{\mathbf{x}}$ plane surface of computation, whereas the electric fields occur in this plane. Such a system is devoted to modelling of electron transport and energy deposition in the general frame of Inertial Confinement Fusion applications. It is able to describe the kinetics of the plasma electrons in the nonlocal equilibrium regime, and permits to consider a large anisotropy degree of the distribution function. We develop specific methods and approaches for validation, that might be used in other fields where couplings between equations, multiscale physics, and high dimensionality are involved. Fast algorithms are employed, which makes this direct approach computationally affordable for simulations of hundreds of collisional times.     

Berezinskii–Kosterlitz–Thouless transition in two-dimensional arrays of Josephson coupled Bose–Einstein condensates

We study the phase transition occurring in Bose–Einstein condensates placed in an optical lattice where the system is arranged in a form of a two-dimensional bosonic Josephson junction array. It is shown that the Josephson interaction between adjacent condensates (trapped in the valleys of the periodic lattice potential) can trigger Berezinskii–Kosterlitz–Thouless transition at a finite temperature _TKT$T_{\mathit{KT}}$ to the ordered state composed of bound vortex–antivortex phase-field configurations of individual condensates. Using a lattice model of the bosonic Josephson junction array, we derive the effective phase-only Hamiltonian and calculate the critical temperature _TKT$T_{\mathit{KT}}$. Finally, we discuss the results in the context of system parameters and possible experiments.     

General holographic superconductor models with Gauss–Bonnet corrections

We study general models for holographic superconductors in Einstein–Gauss–Bonnet gravity. We find that different values of Gauss–Bonnet correction term and model parameters can determine the order of phase transitions and critical exponents of second-order phase transitions. Moreover we find that the size and strength of the conductivity coherence peak can be controlled. The ratios ωg/Tc${\omega }_g/Tc$ for various model parameters have also been examined.     

Massive graviton propagation of the deformed Hořava–Lifshitz gravity without projectability condition

We study graviton propagations of scalar, vector, and tensor modes in the deformed Ho?ava–Lifshitz gravity (λR  -model) without projectability condition. The quadratic Lagrangian is invariant under diffeomorphism only for λ=1$\lambda =1$ case, which contradicts to the fact that λ is irrelevant to a consistent Hamiltonian approach to the λR-model. In this case, as far as scalar propagations are concerned, there is no essential difference between deformed Ho?ava–Lifshitz gravity (λR  -model) and general relativity. This implies that there are two degrees of freedom for a massless graviton without Ho?ava scalar, and five degrees of freedom appear for a massive graviton when introducing Lorentz-violating and Fierz–Pauli mass terms. Finally, it is shown that for λ=1$\lambda =1$, the vDVZ discontinuity is absent in the massless limit of Lorentz-violating mass terms by considering external source terms.     

Formulation of the Hellmann–Feynman theorem for the “second choice” version of Tsallis’ thermostatistics

An approach to formulating the Hellmann–Feynman theorem within the “second choice” formalism of non-extensive statistical mechanics is considered. For the state of thermal equilibrium, we derive a relation of Hellmann–Feynman type between the derivative of the non-extensive free energy with respect to the external parameter and the quantum statistical q$q$-average of the derivative of the Hamilton operator. We also give a proper extension for an arbitrary observable commuting with the Hamiltonian. Some reasons for the usefulness of new formulas are discussed.     

Holes localized on a Skyrmion in a doped antiferromagnet on the honeycomb lattice: Symmetry analysis

Using the low-energy effective field theory for hole-doped antiferromagnets on the honeycomb lattice, we study the localization of holes on Skyrmions, as a potential mechanism for the preformation of Cooper pairs. In contrast to the square lattice case, for the standard radial profile of the Skyrmion on the honeycomb lattice, only holes residing in one of the two hole pockets can get localized. This differs qualitatively from hole pairs bound by magnon exchange, which is most attractive between holes residing in different momentum space pockets. On the honeycomb lattice, magnon exchange unambiguously leads to f$f$-wave pairing, which is also observed experimentally. Using the collective-mode quantization of the Skyrmion, we determine the quantum numbers of the localized hole pairs. Again, f$f$-wave symmetry is possible, but other competing pairing symmetries cannot be ruled out.     

Dynamic field theory and equations of motion in cosmology

We discuss a field-theoretical approach based on general-relativistic variational principle to derive the covariant field equations and hydrodynamic equations of motion of baryonic matter governed by cosmological perturbations of dark matter and dark energy. The action depends on the gravitational and matter Lagrangian. The gravitational Lagrangian depends on the metric tensor and its first and second derivatives. The matter Lagrangian includes dark matter, dark energy and the ordinary baryonic matter which plays the role of a bare perturbation. The total Lagrangian is expanded in an asymptotic Taylor series around the background cosmological manifold defined as a solution of Einstein’s equations in the form of the Friedmann–Lemaître–Robertson–Walker (FLRW) metric tensor. The small parameter of the decomposition is the magnitude of the metric tensor perturbation. Each term of the series expansion is gauge-invariant and all of them together form a basis for the successive post-Friedmannian approximations around the background metric. The approximation scheme is covariant and the asymptotic nature of the Lagrangian decomposition does not require the post-Friedmannian perturbations to be small though computationally it works the most effectively when the perturbed metric is close enough to the background FLRW metric. The temporal evolution of the background metric is governed by dark matter and dark energy and we associate the large scale inhomogeneities in these two components as those generated by the primordial cosmological perturbations with an effective matter density contrast δρ/ρ≤1$\delta \rho /\rho \le 1$. The small scale inhomogeneities are generated by the condensations of baryonic matter considered as the bare perturbations of the background manifold that admits δρ/ρ?1$\delta \rho /\rho ?1$. Mathematically, the large scale perturbations are given by the homogeneous solution of the linearized field equations while the small scale perturbations are described by a particular solution of these equations with the bare stress–energy tensor of the baryonic matter. We explicitly work out the covariant field equations of the successive post-Friedmannian approximations of Einstein’s equations in cosmology and derive equations of motion of large and small scale inhomogeneities of dark matter and dark energy. We apply these equations to derive the post-Friedmannian equations of motion of baryonic matter comprising stars, galaxies and their clusters.     

Landau-Zener tunneling of fermi superfluid gases in deep BEC regime

The dynamical phenomena of the Landau–Zener tunneling of the superfluid fermi gases in a double-well potential in deep BEC regime is investigated in this paper. The contribution of the higher order term representing the lowest approximation of beyond mean field corrections is considered. By using the corresponding classical Hamiltonian of the system, the fixed points and adiabatic energy levels are studied. The critical parameter for the number of fixed points evolution from two to four is obtained. For the nonlinear Landau–Zener tunneling, the tunneling probability with sweeping rate α$\alpha$ is numerically given. At the adiabatic limit, the tunneling probability is not zero in certain regime, while it goes to zero in the other regime. Exponential dependence of the transition probability on the sweeping rate α$\alpha$ in certain case is obtained.     

Eisenhart lifts and symmetries of time-dependent systems

Certain dissipative systems, such as Caldirola and Kannai’s damped simple harmonic oscillator, may be modelled by time-dependent Lagrangian and hence time dependent Hamiltonian systems with n$n$ degrees of freedom. In this paper we treat these systems, their projective and conformal symmetries as well as their quantisation from the point of view of the Eisenhart lift to a Bargmann spacetime in n+2$n+2$ dimensions, equipped with its covariantly constant null Killing vector field. Reparametrisation of the time variable corresponds to conformal rescalings of the Bargmann metric. We show how the Arnold map lifts to Bargmann spacetime. We contrast the greater generality of the Caldirola–Kannai approach with that of Arnold and Bateman. At the level of quantum mechanics, we are able to show how the relevant Schrödinger equation emerges naturally using the techniques of quantum field theory in curved spacetimes, since a covariantly constant null Killing vector field gives rise to well defined one particle Hilbert space.     

Critical behavior and phase diagrams of a spin-1 Blume–Capel model with random crystal field interactions: An effective field theory analysis

A spin-1 Blume–Capel model with dilute and random crystal fields is examined for honeycomb and square lattices by introducing an effective-field approximation that takes into account the correlations between different spins that emerge when expanding the identities. For dilute crystal fields, we have given a detailed exploration of the global phase diagrams of the system in _kBTc/J−D/J$k_B{T}_c/J-D/J$ plane with the second and first order transitions, as well as tricritical points. We have also investigated the effect of the random crystal field distribution characterized by two crystal field parameters D/J$D/J$ and △/J$△/J$ on the phase diagrams of the system. The system exhibits clear distinctions in a qualitative manner with coordination number q$q$ for random crystal fields with △/J,D/J≠0$△/J,D/J\ne 0$. We have also found that, under certain conditions, the system may exhibit a number of interesting and unusual phenomena, such as reentrant behavior of first and second order, as well as a double reentrance with three successive phase transitions.     

Non-convergent perturbation theory and misleading inferences about parameter relationships: The case of superexchange

We discuss the well-known three-centre cation–anion–cation model for superexchange in insulating transition-metal compounds using limiting expansions for the Anderson–Hubbard model. We find that due to the interfering energy scales in the model, a limiting expression for the superexchange J$J$ for the idealized Mott–Hubbard (M–H) case t?U?Δ$t?U?\Delta$ cannot be formally defined. We further show that the decomposition of the superexchange into range-dependent components is formally invalid. The well-known t⁴$t^4$ superexchange expression, obtained from path-dependent series expansions, is not unique to these systems as it can also be obtained with many other different expansions, in which either the d$d$–p$p$ energy difference Δ$\Delta$ or the d$d$-electron correlation U$U$ can actually be small. Particularly for milder relationships between the parameters, i.e.  t?U?Δ$t?U?\Delta$, the reverse from the usual form of the series expansions can yield better agreement with the exact results. This implies that the fitting of experimental data to the simple expressions derived from path-dependent series expansions can lead to qualitatively incorrect relationships between the parameters, fictitiously within the M–H regime.     

Pekeris approximation – another perspective

Inspired on the Pekeris approximation for the centrifugal term, we elaborate a method of resolution for the Schrödinger equation subject to a potential V(r)$V(r)$ of a form more general than the exponential one. Generalizing the Pekeris approximation, we solve the Schrödinger equation with Rosen–Morse and Manning–Rosen potentials including the centrifugal term. The bound state energy eigenvalues for these potentials and for arbitrary values of n and l quantum numbers are presented.     

Pseudo Hermitian formulation of the quantum Black–Scholes Hamiltonian

We show that the non-Hermitian Black–Scholes Hamiltonian and its various generalizations are η$\eta$-pseudo Hermitian. The metric operator η$\eta$ is explicitly constructed for this class of Hamiltonians. It is also shown that the effective Black–Scholes Hamiltonian and its partner form a pseudo supersymmetric system.     

The Haldane–Shastry spin chain and the topological basis realization

In this paper, based on the topological basis states, we investigate the Hamiltonian family {H₂,H₃,H₄}$\{H_2,H_3,H_4\}$ of a closed four-qubit Haldane–Shastry spin chain. Not only the two-qubit interaction form, but also the three-qubit interaction form and the four-qubit interaction form are presented in terms of spin operators. Meanwhile, we explore some particular properties of the topological basis states in these systems. With Yangian algebra, the symmetry of the systems and the transitions between the eigenstates have been investigated. We find a really useful effect of Y(sl(2))$Y\left(sl\left(2\right)\right)$ operators {J_±,J₃}$\{J_{\pm },J_3\}$, which is that they can describe the transitions between the spin single state and the spin triple states. Furthermore, we construct a new Hamiltonian, whose energy degeneracies can be changed by adjusting the strengths of the two-qubit interactions, three-qubit interactions, four-qubit interactions, and the external magnetic field.     

Cyclic groups and quantum logic gates

We present a formula for an infinite number of universal quantum logic gates, which are 4$4$ by 4$4$ unitary solutions to the Yang–Baxter (Y–B) equation. We obtain this family from a certain representation of the cyclic group of order n$n$. We then show that this discrete   family, parametrized by integers n$n$, is in fact, a small sub-class of a larger continuous   family, parametrized by real numbers θ$\theta$, of universal quantum gates. We discuss the corresponding Yang-Baxterization and related symmetries in the concomitant Hamiltonian.     

Symmetry breaking and restoration for interacting scalar and gauge fields in Lifshitz type theories

We consider the one-loop effective potential at zero and finite temperature in field theories with anisotropic space–time scaling, with critical exponent z=2$z=2$, including both scalar and gauge fields. Depending on the relative strength of the coupling constants for the gauge and scalar interactions, we find that there is a symmetry breaking term induced at one loop at zero temperature and we find symmetry restoration through a first-order phase transition at high temperature.