Relativistic quantum particle in a homogeneous external field

The model of the relativistic quantum particle in a homogeneous external field is proposed. This model is realized in the one-dimensional relativistic configurational x-space and is described by the finite-difference equation. The momentum p-space in our case is the one-dimensional Lobachevsky space. We have found the wave functions and propagator for the model under study in both x- and p-representations.     

Wavefunction symmetries and binding energies in GaSxSe1−x compounds

We report on a synchrotron radiation photoemission spectroscopy study of mixed GaS_xSe_1?x crystals. The most prominent composition effect in the valence band is an increase by ～ 0.4 eV of the energy separation between the p_z states and the p_x, p_y states as x increases from 0 to 1. The repulsion in energy is accompanied by a progressive mixing of these states in k-space regions far from the zone boundaries.     

Matter Density and Relativistic Models of Wave Function Collapse

Mathematical models for the stochastic evolution of wave functions that combine the unitary evolution according to the Schrödinger equation and the collapse postulate of quantum theory are well understood for non-relativistic quantum mechanics. Recently, there has been progress in making these models relativistic. But even with a fully relativistic law for the wave function evolution, a problem with relativity remains: Different Lorentz frames may yield conflicting values for the matter density at a space-time point. We propose here a relativistic law for the matter density function. According to our proposal, the matter density function at a space-time point x is obtained from the wave function ψ on the past light cone of x by setting the i-th particle position in |ψ|² equal to x, integrating over the other particle positions, and averaging over i. We show that the predictions that follow from this proposal agree with all known experimental facts.     

Note on the difference between the a-cyclic and c-cyclic version of the XY model

The transverse susceptibility of the c-cyclic version of the one-dimensional XY model with respect to an infinitesimal magnetic field in the x-direction is investigated in more detail. Special attention is paid to the c-cyclic version of the one-dimensional Ising model. The c-cyclic susceptibility χ_xx is evaluated explicitly. The autocorrelation function of the magnetization M_x turns out to be time dependent in the c-cyclic Ising model.     

Analysis and optimization of optical bistability in one-dimensional nonlinear photonic crystal with (HL)(D)(LH) and (LH)(D)(HL) structures

Although one-dimensional nonlinear photonic crystal (1D-NPC) has been widely studied, there is no comprehensive analysis on decreasing the bistability threshold power.In this paper, conditions required to create bistability have been specified for two types of structures of alternative high and low refractive index layers and defect layers with Kerr nonlinearity effect, in the order of (HL)^p(D)^q(LH)^p and (LH)^p(D)^q(HL)^p, where L and H denote low and high refractive index layers, respectively, D stands for the defect layers, p is the number of LH or HL layers and q is the number of defect layers.One of the essentials for the bistability is appropriate shifts of frequency of the defect mode, so the effect of the order of layer's arrangement in (1D-NPC) structures have been studied. Different structures have been introduced and the best structure for the lowest bistability threshold power has been proposed. Nonlinear finite-difference time-domain (NFDTD) in C++ has been employed for simulation.     

On one-dimensional integrable quantum systems with infinitely many degrees of freedom

We study one-dimensional quantum systems whose S-operator conserves the incoming momenta and particle identities. A survey of systems with known S-operators and an approach for solving them rigorously are presented, and several problems and conjectures are formulated. Subsequently, this approach is used to arrive at relativistic dynamics whose S-operators are those of the Ising model in the scaling limit and of the Federbush model. An invariance property of the wave and scattering operators is discovered and argued to hold at the classical level, too.     

Electronic structure of CsAu

Self-consistent non-relativistic and relativistic LMTO band structure calculations have been carried out for CsAu. In the non-relativistic model CsAu is a metal, whereas — in agreement with experiments — the relativistic calculations predict CsAu to be a semiconductor. The gap is not caused by the spin-orbit coupling. The importance of the core-like Cs-5s and Cs-5p states for the alloy formation is discussed, and charge distribution calculations are used to illustrate the ionic nature of the bonding.     

Radiative transition probabilities in ions of the silver isoelectronic sequence

The wave functions of one-electron states above the 4d ¹⁰ core have been calculated within the relativistic perturbation theory with a zero-order model potential. The wavelengths and probabilities of electric dipole transitions in an Ag-like ion have been calculated for the 5s-5p, 5p-5d, 5d-5f, and 4f-5d transitions. The data obtained are compared with the results of calculations by the relativistic Hartree-Fock method and within the relativistic many-body perturbation theory. The theoretical results are compared with experimental data on the lifetimes of energy levels in Ag-like ions.     

Bohr-Sommerfeld conditions in geometric quantization

The corrected Bohr-Sommerfeld quantum conditions, ∫ pdq?d = integer, are studied in the framework of geometric quantization. It is shown, in the representation given by a polarization F, that a half-form corresponds to a wave function only if it vanishes on all closed curves with tangent vectors in F for which the quantum condition is not satisfied. The constant d is determined, for each closed curve y, by the element of the holonomy group of a bundle of metalinear frames for F induced by y. This result is applied to a one-dimensional harmonic oscillator and a two-dimensional relativistic Kepler problem. In the case of the one-dimensional harmonic oscillator there are two possibilities of choosing a metalinear frame bundle for F. One choice leads to the original Bohr-Sommerfeld condition while the other leads to the corrected version with d = $\text{1}\text{2}$. Similarly, choosing different metalinear frame bundles for F, we get for the relativistic Kepler problem the fine structures of the energy levels corresponding to spin 0 and spin $\text{1}\text{2}$.     

Collisional-radiative model for non-Maxwellian inductively coupled argon plasmas using detailed fine-structure relativistic distorted-wave cross sections

Our recently developed collisional-radiative model which included fine-structure cross sections calculated with a fully relativistic distorted-wave method [R.K. Gangwar, L. Sharma, R. Srivastava, A.D. Stauffer, J. Appl. Phys. 111, 053307 (2012)] has been extended to study non-Maxwellian inductively coupled argon plasmas. We have added more processes to our earlier collisional-radiative model by further incorporating relativistic distorted-wave electron impact cross sections from the 3p ⁵4sJ = 0, 2 metastable states, (1s ₃, 1s ₅ in Paschen’s notation) to the 3p ⁵5p (3p _i ) excited states. The population of various excited levels at different pressures in the range of 1–25 mTorr for an inductively coupled argon plasma have been calculated and compared with the recent optical absorption spectroscopy measurements as well as emission model results of Boffard et al. [Plasma Sources Sci. Technol. 19, 065001 (2010)]. We have also calculated the intensities of two emission lines, 420.1 nm (3p ₉ → 1s ₅) and 419.8 nm (3p ₅ → 1s ₄) and compared with measured intensities reported by Boffard et al. [J. Phys. D 45, 045201 (2012)]. Our results are in good agreement with the measurements.     

Renormalization group approach to a p-wave superconducting model

We present in this work an exact renormalization group (RG) treatment of a one-dimensional p-wave superconductor. The model proposed by Kitaev consists of a chain of spinless fermions with a p-wave gap. It is a paradigmatic model of great actual interest since it presents a weak pairing superconducting phase that has Majorana fermions at the ends of the chain. Those are predicted to be useful for quantum computation. The RG allows to obtain the phase diagram of the model and to study the quantum phase transition from the weak to the strong pairing phase. It yields the attractors of these phases and the critical exponents of the weak to strong pairing transition. We show that the weak pairing phase of the model is governed by a chaotic attractor being non-trivial from both its topological and RG properties. In the strong pairing phase the RG flow is towards a conventional strong coupling fixed point. Finally, we propose an alternative way for obtaining p-wave superconductivity in a one-dimensional system without spin–orbit interaction.     

The Incipient Infinite Cluster for High-Dimensional Unoriented Percolation

We consider bond percolation on $\mathbb{Z}^d$ at the critical occupation density p _c for d>6 in two different models. The first is the nearest-neighbor model in dimension d?6. The second model is a “spread-out” model having long range parameterized by L in dimension d>6. In the spread-out case, we show that the cluster of the origin conditioned to contain the site x weakly converges to an infinite cluster as |x|→∞ when d>6 and L is sufficiently large. We also give a general criterion for this convergence to hold, which is satisfied in the case d?6 in the nearest-neighbor model by work of Hara.⁽¹²⁾ We further give a second construction, by taking p<p _c , defining a measure $\mathbb{Q}^p $ and taking its limit as p↗p ^? _c . The limiting object is the high-dimensional analogue of Kesten's incipient infinite cluster (IIC) in d=2. We also investigate properties of the IIC such as bounds on the growth rate of the cluster that show its four-dimensional nature. The proofs of both the existence and of the claimed properties of the IIC use the lace expansion. Finally, we give heuristics connecting the incipient infinite cluster to invasion percolation, and use this connection to support the well-known conjecture that for d>6 the probability for invasion percolation to reach a site x is asymptotic to c|x|^?(d?4) as |x|→∞.     

The mass-shell and gauge-fixing conditions for the free relativistic massive quantum particle

Working in the context of the Weyl group, which describes off-mass-shell relativistic particles, we impose “gauge-fixing” constraints involvingR ⁰,R ⁺, andD as matrix element conditions to be satisfied by the on-mass-shell states of a massive particle. We evaluate the matrix elements inp-space using five sets of co-ordinates: (p ²,p), (p ²,p ⁺,p _T ), (p ²,p ^?,p _T ), (p ²,π), and (p ²,π ⁺,π _T ) where \(\pi ^\mu \equiv p^\mu /(p^2 )^{\tfrac{1}{2}} \) . We find that, only in the case ofR ⁰ with (p ²,p) coordinates,R ⁺ with (p ²,p ⁺,p _T ) coordinates, andD with (p ², π) or (p ²,π ⁺,π _T ) coordinates, can the condition be satisfied by arbitrary on-mass-shell states. In all other cases, the condition can be satisfied only by states belonging to a subset of subspaces of the on-mass-shell Hilbert space, i.e it forces a violation of the superposition principle. These results constitute thep-space quantum version of Shanmugadhasan's theorem for constrained classical systems which states that there exists, at least locally in phase space, a canonical transformation to a set of variables in which the second-class constraints become canonical pairs equal to zero with the other canonical coordinates independent of the second-class constraints.     

Relativistic mean-field study on proton skins and proton halos in exotic nuclei

We investigate the ground state properties of proton-rich nuclei in the framework of the relativistic mean-field model. Calculations show that the experimental proton halo in the nuclei ^26,27,28P can be reproduced by the model. The proton halos can appear in proton-rich nuclei because the total nuclear potential is attractive up to the radial distance r ≈ 5.5 fm. But the size of proton halos is finite due to the limitation of the Coulomb potential barrier. The mean-square radius of a halo proton is not very sensitive to the separation energy of the last proton in some very proton-rich nuclei due to the effect of the Coulomb barrier. This behavior is different from the case of a neutron halo where the mean-square radius of a halo neutron is inversely proportional to the separation energy of the last halo neutron. We have also analysed the differences of the relativistic mean-field potentials of ²⁵Al and ²⁶P and found that the isovector potential from the p meson has an important effect on the differences.     

Effect of carbon doping on thermodynamic behavior of MgB2

The thermodynamic behavior of carbon doped MgB₂ has been studied using a rigid ion model (RIM). The model potential consists of the long-range Coulomb, the short-range repulsive and the van der Waals interactions. This model has successfully explained the cohesive and thermodynamic properties of Mg(B_1−xC_x)₂ (x=0.0, 0.02, 0.05, 0.075, 0.1, 0.2). The properties studied are the cohesive energy, molecular force constant, Restrahlen frequency, compressibility, Debye temperature and Gruneisen parameter. Our results on Restrahlen frequency and Debye temperature are in reasonably good agreement with the available experimental data. In addition, we have computed the specific heat C_p for Mg(B_1−xC_x)₂ (x=0.2) as a function of temperature T in the range 16 K?T?1000 K. We have also shown the variation of specific heat C_p with doping concentration at room temperature (300 K). The calculated specific heat C_p for Mg(B_1−xC_x)₂ (x=0.2) in the temperature range 16 K?T?22 K for which experimental results are available, agrees pretty well with the experimental data.     

Coherent Thomson backscattering from laser-driven relativistic ultra-thin electron layers

The generation of laser-driven dense relativistic electron layers from ultra-thin foils and their use for coherent Thomson backscattering is discussed, applying analytic theory and one-dimensional particle-in-cell simulation. The blow-out regime is explored in which all foil electrons are separated from ions by direct laser action. The electrons follow the light wave close to its leading front. Single electron solutions are applied to initial acceleration, phase switching, and second-stage boosting. Coherently reflected light shows Doppler-shifted spectra, chirped over several octaves. The Doppler shift is found ∝ γ_x ²=1/(1-β_x ²), where β_x is the electron velocity component in normal direction of the electron layer which is also the direction of the driving laser pulse. Due to transverse electron momentum p_y, the Doppler shift by 4γ_x ²=4γ²/(1+(p_y/mc)²)≈2γ is significantly smaller than full shift of 4γ². Methods to turn p_y→0 and to recover the full Doppler shift are proposed and verified by 1D-PIC simulation. These methods open new ways to design intense single attosecond pulses.     

Fluctuations in the Composite Regime of a Disordered Growth Model

 We continue to study a model of disordered interface growth in two dimensions. The interface is given by a height function on the sites of the one-dimensional integer lattice and grows in discrete time: (1) the height above the site x adopts the height above the site to its left if the latter height is larger, (2) otherwise, the height above x increases by 1 with probability p _x . We assume that p _x are chosen independently at random with a common distribution F, and that the initial state is such that the origin is far above the other sites. Provided that the tails of the distribution F at its right edge are sufficiently thin, there exists a nontrivial composite regime in which the fluctuations of this interface are governed by extremal statistics of p _x . In the quenched case, the said fluctuations are asymptotically normal, while in the annealed case they satisfy the appropriate extremal limit law. Received: 6 November 2001 / Accepted: 8 April 2002 Published online: 6 August 2002     

Compton scattering and charge transfer in Er substituted DyAl2

A unique applicability of Compton spectroscopy in probing the electronic states of rare earth aluminides using high energy (662 keV) γ-rays is reported. We have measured first-ever Compton profiles of Dy_1-xEr_xAl₂ (x=0, 0.2) using 20Ci ¹³⁷Cs Compton spectrometer. The charge reorganization in Dy_1−xEr_xAl₂ (x=0, 0.2), on the formation of compound, has been discussed using the valence band Compton profile data. The experimental Compton profile data unambiguously establish charge transfer from Al to Dy (Dy and Er) on formation of x=0.0 (0.2) compound, which is in tune with spin polarized relativistic Korringa–Kohn–Rostoker (SPR-KKR) calculations. A reasonable agreement between SPR-KKR based Compton profiles and the experimental data show applicability of the Green function method in predicting the electronic properties of rare earth compounds.     

Energy bands of LaAg and LaCd and martensitic transformation

Energy bands of the simple cubic intermetallic compounds LaAg and LaCd have been calculated by using both a non-relativistic APW and relativistic KKR method in the muffin-tin-potential approximation. The density of states of LaAg is found to peak sharply just above the Fermi energy and the Fermi surface geometry shows that in this high density-of-states region the conditions are met for the band-Jahn-Teller-effect to drive the martensitic transformation observed in LaAg_{1_x} In _x ,x >0.05, and in LaCd. The case of YZn, which shows no martensitic transformation, is discussed briefly.