Probabilistically perfect quantum cloning and unambiguous state discrimination

We consider the N → M probabilistically perfect quantum cloning machine that perfectly produces M faithful copies from N identical input states, where the input states are selected, with prior probabilities η₁and η₂ = 1 − η₁, from a given set of the two linearly independent states |ψ₁〉^⊗ N = (cosθ|0〉 + sinθ|1〉)^⊗ N and |ψ₂〉^⊗ N = (sinθ|0〉 + cosθ|1〉)^⊗ N (θ∈(0,π/2)). We derive the optimal distribution of the success probabilities. When M approaches infinite, the probabilistically perfect quantum cloning can be regarded as a kind of the unambiguous state discrimination, and theoretically provides the upper bound of the unambiguous state discrimination. By using the optimal distribution of the success probabilities of the optimal asymmetric 1 → M probabilistically perfect quantum cloning, we can derive the maximum average success probability of the unambiguous discrimination of two nonorthogonal quantum states |ψ₁〉and|ψ₂〉. As an example, we give the explicit transformation of the optimal symmetric 1 → M probabilistically perfect quantum cloning to copy the two input states |ψ₁〉 and |ψ₂〉.     

Role of dipole-dipole interactions in half-field quantum transitions in magnetic nanoparticles

In order to better understand the origin of “forbidden” quantum transitions observed in superparamagnetic nanoparticles at low magnetic fields, electron magnetic resonance (EMR) studies have been performed at room temperature on iron oxide nanoparticles assembled inside parallel nanosized channels penetrating the anodic alumina membrane. The positions of both the main resonance and “forbidden” (2Q) transitions observed at the half-field demonstrate the characteristic angular dependence with the line shifts proportional to 3cos²θ−1, where θ is the angle between the channel axis and external magnetic field B. This result can be attributed to the inter-particle dipole-dipole interactions within elongated aggregates inside the channels. The angular dependence of the 2Q intensity is found to be proportional to sin²θcos²θ, that is consistent with the predictions of quantum-mechanical calculations with the account for the mixing of states by non-secular inter-particle dipole-dipole interactions. Good agreement is obtained between different kinds of measurements (magnetization curves, line shifts and 2Q intensity), pointing to possibility of the quantum approach to the magnetization dynamics of superparamagnetic objects.     

Theoretical research on optical properties and quantum efficiency of Ga1−xAlxN photocathodes

In order to design the optimal component structure of transmission-mode (t-mode) Ga_1−xAl_xN photocathode, the optical properties and quantum efficiency of Ga_1−xAl_xN photocathodes are simulated. Based on thin film principle, optical model of t-mode Ga_1−xAl_xN photocathodes is built. And the quantum efficiency formula is put forward. Results show that Ga_1−xAl_xN photocathodes can satisfy the need of detectors with “solar blind” property when the Al component is bigger than 0.375. There is an optimal thickness of Ga_1−xAl_xN layer to get highest quantum efficiency, and the optimal thickness is 0.3 μm. There is close relation between absorptivity and quantum efficiency, which is in good agreement with the “three-step” model. This work gives a reference for the experimental research on the Ga_1−xAl_xN photocathodes.     

Exact solution of the Faddeev-Volkov model

The Faddeev-Volkov model is an Ising-type lattice model with positive Boltzmann weights where the spin variables take continuous values on the real line. It serves as a lattice analog of the sinh-Gordon and Liouville models and intimately connected with the modular double of the quantum group Uq(sl₂). The free energy of the model is exactly calculated in the thermodynamic limit. In the quasi-classical limit c→+∞ the model describes quantum fluctuations of discrete conformal transformations connected with the Thurston's discrete analogue of the Riemann mappings theorem. In the strongly-coupled limit c→1 the model turns into a discrete version of the D=2 Zamolodchikov's “fishing-net” model.     

Systematic analysis of the Fourier transform spectrum of CH3OH between 400 and 950 cm

We have investigated a high-resolution Fourier transform (FT) absorption spectrum of the ¹³CH₃OH isotopomer of methanol from 400 to 950 cm⁻¹ with the “Ritz” program. We present the assignments of 7160 transitions, 3021 of which belong to A-symmetry, and 4139 to E-symmetry. These transitions occur between states labeled by K quantum numbers up to 14, and by torsional quantum numbers n up to 4. The “Ritz” program evaluated the energies of the 4684 involved levels with an accuracy of the order of 10⁻⁴ cm⁻¹. All of the assigned lines correspond to transitions involving torsionally excited levels within the ground small-amplitude vibrational state.     

Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory

We study the ±J random-plaquette Z₂ gauge model (RPGM) in three spatial dimensions, a three-dimensional analog of the two-dimensional ±J random-bond Ising model (RBIM). The model is a pure Z₂ gauge theory in which randomly chosen plaquettes (occurring with concentration p) have couplings with the “wrong sign” so that magnetic flux is energetically favored on these plaquettes. Excitations of the model are one-dimensional “flux tubes” that terminate at “magnetic monopoles” located inside lattice cubes that contain an odd number of wrong-sign plaquettes. Electric confinement can be driven by thermal fluctuations of the flux tubes, by the quenched background of magnetic monopoles, or by a combination of the two. Like the RBIM, the RPGM has enhanced symmetry along a “Nishimori line” in the p-T plane (where T is the temperature). The critical concentration p_c of wrong-sign plaquettes at the confinement-Higgs phase transition along the Nishimori line can be identified with the accuracy threshold for robust storage of quantum information using topological error-correcting codes: if qubit phase errors, qubit bit-flip errors, and errors in the measurement of local check operators all occur at rates below p_c, then encoded quantum information can be protected perfectly from damage in the limit of a large code block. Through Monte-Carlo simulations, we measure p_c0, the critical concentration along the T=0 axis (a lower bound on p_c), finding p_c0=.0293±.0002. We also measure the critical concentration of antiferromagnetic bonds in the two-dimensional RBIM on the T=0 axis, finding p_c0=.1031±.0001. Our value of p_c0 is incompatible with the value of p_c=.1093±.0002 found in earlier numerical studies of the RBIM, in disagreement with the conjecture that the phase boundary of the RBIM is vertical (parallel to the T axis) below the Nishimori line. The model can be generalized to a rank-r antisymmetric tensor field in d dimensions, in the presence of quenched disorder.     

The structure of the nucleon

We assume that nucleons are made of quarks which are made of subquarks which are made of more fundamental subquarks, etc. Thus, finally, the proton and the neutron may be composed of an infinite number of pointlike quarks and antiquarks. The limit particle has quantum numbers of spinJ=1/2, isospinI=1/2, third component of isospinI ₃=1/2, and fractional electric chargeQ=(l/2)¦e¦, where ¦e¦ is the electron charge. All quantum numbers are thus just one-half and this fermion will behave as if it was lepton, since the baryon number approaches zero at an infinite sublayer level. Sum rules in lepton-nucleon scattering have been evaluated using this model. The predicted values are not incompatible with the experimental results.     

Quantum wave packet revival in two-dimensional circular quantum wells with position-dependent mass

We study quantum wave packet revivals on two-dimensional infinite circular quantum wells (CQWs) and circular quantum dots with position-dependent mass (PDM) envisaging a possible experimental realization. We consider CQWs with radially varying mass, addressing particularly the cases where M(r)∝rw with w=1,2, or −2. The two PDM Hamiltonians currently allowed by theory were analyzed and we were able to construct a strong theoretical argument favoring one of them.     

The quantum field as a quantum computer

It is supposed that at very small scales a quantum field is an infinite homogeneous quantum computer. On a quantum computer the information cannot propagate faster than c=a/τ, a and τ being the minimum space and time distances between gates, respectively. For one space dimension it is shown that the information flow satisfies a Dirac equation, with speed v=ζc and ζ=ζ(m) mass-dependent. For c the speed of light ζ−1 is a vacuum refraction index that increases monotonically from ζ−1(0)=1 to ζ−1(M)=∞, M being the Planck mass for 2a the Planck length. The Fermi anticommuting field can be entirely qubitized, i.e. it can be written in terms of local Pauli matrices and with the field interaction remaining local on qubits. Extensions to larger space dimensions are discussed.     

Theoretical study of local crystal structure in KZnF3:Fe system

An analysis of the relationship between the EPR trigonal-field parameters and the local crystal structure of KZnF₃:Fe³⁺system is presented by diagonalizing the complete energy matrices for a d⁵ configuration ion in a trigonal crystal field. We propose a two-layer-ligand model, in which the ligands consist of six nearest-neighbor F⁻ ions in the first layer and eight next nearest-neighbor K⁺ ions in the second layer. The calculation indicates that the local structure distortion of KZnF₃:Fe³⁺system is due to the displacement of a K⁺ ion along C₃ axis towards the Fe³⁺ ion, which leads to the shift of the F⁻ ions away from C₃ axis. By simulating the EPR low-symmetry parameters D and (a−F), the distorted angles between the Fe³⁺-F⁻ bonds and C₃ axis are determined, Δθ₁=2.58°, Δθ₂=−1.4° at room temperature (300 K) and Δθ₁=2.84°, Δθ₂=−1.4° at low temperature (77 K). Those results are in good agreement with the experimental findings Δθ₁=2.8±0.3°and Δθ₂=−1.1±0.3°.     

The stable structures of iron pnictides AFeAs (A = alkali and alkaline-earth metals): A first principles study

We have investigated the structural stabilities of iron arsenide compounds A_x(FeAs)_1−x (A = alkali and alkaline-earth metals) by first principles calculations. We find that (i) all of the experimental “122” type structures with composition x=1/3 are stable; (ii) all of the “111” type structures with composition x=1/2 except CsFeAs are stable; (iii) K₃FeAs with composition x=3/4 is stable. The predicted stable KFeAs, RbFeAs, SrFeAs, BaFeAs, K₃FeAs have the As-Fe-As bond angles close to the ideal tetrahedral angles, indicating that they may be superconductors.     

Effects of Cl, NO3 and SO4 anions on the anodic behavior of carbon steel in deaerated 0.50 M NaHCO3 solutions

The effects of Cl⁻, NO₃⁻ and SO₄²⁻ aggressive anions on the corrosion and passivation behavior of carbon steel electrode in deaerated 0.50 M NaHCO₃ solutions were studied using potentiodynamic anodic polarization and SEM techniques. It was found that the presence of Cl⁻, NO₃⁻ and SO₄²⁻ anions stimulates the anodic dissolution rate in both the active and the pre-passive potential regions. Moreover, significantly great effects were observed in both the passive and the trans-passive potential regions. Pitting corrosion was observed only in the presence of Cl⁻ anions, while the presence of NO₃⁻ and SO₄²⁻ anions facilitate only passivation by oxygen of water without themselves participating in the cathodic process. Also, it was observed that the effect of NO₃⁻ anion, which is a strong oxidizing agent acting “primarily” as stimulator of the cathodic process and then its reaction product acts “indirectly” retarding the anodic process. On the other hand, the effect of SO₄²⁻ anion, which is a non-oxidizing agent, exerts an “indirect” effect on the cathodic reaction increasing its rate and then “directly” influence on the anodic reaction, retarding it.     

Discrete-time quantum walks on one-dimensional lattices

In this paper, we study discrete-time quantum walks on one-dimensional lattices. We find that the coherent dynamics depends on the initial states and coin parameters. For infinite size of lattices, we derive an explicit expression for the return probability, which shows scaling behavior P(0, t) ~ t ^-1 and does not depends on the initial states of the walk. In the long-time limit, the probability distribution shows various patterns, depending on the initial states, coin parameters and the lattice size. The time-averaged probability mixes to the limiting probability distribution in linear time, i.e., the mixing time M _ε is a linear function of N (size of the lattices) for large values of thresholds ϵ. Finally, we introduce another kind of quantum walk on infinite or even-numbered size of lattices, and show that by the method of mathematical induction, the walk is equivalent to the traditional quantum walk with symmetrical initial state and coin parameter.     

Photoluminescence scanning on InAs/InGaAs quantum dot structures

The photoluminescence spectra of InAs quantum dots (QDs) embedded into four types of In_xGa_1−xAs/GaAs (x = 0.10, 0.15, 0.20 and 0.25) multi quantum well MBE structures have been investigated at 300 K in dependence on the QD position on the wafer. PL mapping was performed with 325 nm HeCd laser (35 mW) focused down to 200 μm (110 W/cm²) as the excitation source. The structures with x = 0.15 In/Ga composition in the In_xGa_1−xAs capping layer exhibited the maximum photoluminescence intensity. Strong inhomogeneity of the PL intensity is observed by mapping samples with the In/Ga composition of x ≥ 0.20-0.25. The reduction of the PL intensity is accompanied by a gradual “blue” shift of the luminescence maximum at 300 K as follows from the quantum dot PL mapping. The mechanism of this effect has been analyzed. PL peak shifts versus capping layer composition are discussed as well.     

Torsional analysis of 2-butynol

The microwave spectrum of 2-butynol, CH₃CCCH₂OH, has been investigated in the frequency range of 6-26.5 GHz. The spectra of the A and E torsional states were observed using Fourier transform microwave spectroscopy. Due to the presence of the cylindrically symmetric CC “spacer” between the methyl group and the rest of the molecule, the barrier to internal rotation, V₃, is only 7 cm⁻¹. One conformer of 2-butynol was observed and assigned. The spectrum was analyzed with the ρ-axis method using a very flexible Hamiltonian which gives a fit an order of magnitude better than that obtained with more standard code for internal rotation. The spectroscopic constants are: 23744.(18), 2093.429(1), 1966.358(1), and −400.34(2) MHz for A, B, C, and D_ab; 0.48(1) kHz, −30.3(4) kHz, and 4.5(5) MHz for Δ_J, Δ_JK, and Δ_K; and 0.1406(6), 6.93(9) cm⁻¹, −33.4(7) kHz, and 192.0(9) GHz for ρ, V₃, L_V, and F, respectively. The root mean squared error of the fit is 14 kHz. The angles between the internal rotor axis and principal axes are θ_a=12°, θ_b=78°, with θ_c held fixed at 90°.     

Conformal invariance in incommensurate phases

We study finite-size corrections to the free energy of free-fermion models on a torus with periodic, twisted, and fixed boundary conditions. Inside the critical (striped-incommensurate) phase, the free energy densityf(N, M) on anN×M square lattice with periodic (or twisted) boundary conditions scales asf(N, M)=f _–A(s)/(NM)+.... We derive exactly the finite-size-scaling (FSS) amplitudesA(s) as a function of the aspect ratios=M/N. These amplitudes are universal because they do not depend on details of the free-fermion Hamiltonian. We establish an equivalence between the FSS amplitudes of the free-fermion model and the Coulomb gas system with electric and magnetic defect lines. The twist angle generates magnetic defect lines, while electric defect lines are generated by competition between domain wall separation and system size. The FSS behavior of the free-fermion model is consistent with predictions of the theory of conformal invariance with the conformal chargec=l. For instance, the FSS amplitude on an infinite cylinder with fixed boundary conditions is found to be one-quarter of that with periodic boundary conditions. Finally, we conjecture the exact form of the FSS amplitudes for an interacting-fermion model on a torus. Numerical calculations employing the Bethe Ansatz confirm our conjecture in the infinite-cylinder limit.     

Rovibrational spectrum and potential energy surface of the N2-N2O van der Waals complex

The rovibrational spectrum of the N₂-N₂O van der Waals complex has been recorded in the N₂O ν₁ region (∼1285 cm⁻¹) using a tunable diode laser spectrometer to probe a pulsed supersonic slit jet. The observed transitions together with the data observed previously in the N₂O ν₃ region are analyzed using a Watson S-reduced asymmetric rotor Hamiltonian. The rotational and centrifugal distortion constants for the ground and excited vibrational states are accurately determined. The band-origin of the spectrum is determined to be 1285.73964(14) cm⁻¹. A restricted two-dimensional intermolecular potential energy surface for a planar structure of N₂-N₂O has been calculated at the CCSD(T) level of theory with the aug-cc-pVDZ basis sets and a set of mid-bond functions. With the intermolecular distance fixed at the ground state value R = 3.6926 Å, the potential has a global minimum with a well depth of 326.64 cm⁻¹ at θ_N2 = 11.0° and θ_N2O = 84.3° and has a saddle point with a barrier height of 204.61 cm⁻¹ at θ_N2 = 97.4° and θ_N2O = 92.2°, where θ_N2(θ_N2O) is the enclosed angle between the N-N axis (N-N-O axis) and the intermolecular axis.     

A novel “magnetic” field and its dual non-commutative phase space

In this Letter we have studied a new form of non-commutative (NC) phase space with an operatorial form of noncommutativity. A point particle in this space feels the effect of an interaction with an “internal  ” magnetic field, that is singular at a specific position θ⁻¹${\theta }^{\mathrm{-1}}$. By “internal” we mean that the effective magnetic fields depends essentially on the particle properties and modifies the symplectic structure. Here θ is the NC parameter and induces the coupling between the particle and the “internal” magnetic field. The magnetic moment of the particle is computed. Interaction with an external physical magnetic field reveals interesting features induced by the inherent fuzziness of the NC phase space: introduction of non-trivial structures into the charge and mass of the particle and possibility of the particle dynamics collapsing to a Hall type of motion. The dynamics is studied both from Lagrangian and symplectic (Hamiltonian) points of view. The canonical (Darboux) variables are also identified. We briefly comment, that the model presented here, can play interesting role in the context of (recently observed) real space Berry curvature in material systems.     

Analyticity of a hard-core multicomponent lattice gas

A multicomponent anti-Widom-Rowlinson lattice gas is introduced. An arbitrary numberM of particle types is permitted, all having the same activity. The only interactions are nearest-neighbor exclusions oflike particles (analogous to map-coloring problems). For any lattice it is shown that there is a finite numberM ₀ (depending only on the coordination number of the lattice) such that for allMM ₀ the infinite volume correlation functions exist and are analytic functions of the activity, for all positive values of the common activity.Research supported in part by NSF Grant No. GP-33535X, AFOSR Grant No. 73-2430B, and NSF Grant No. MPS75-20638.     

A new formulation of the initial value problem for nonlocal theories

There are a number of reasons to entertain the possibility that locality is violated on microscopic scales, for example through the presence of an infinite series of higher derivatives in the fundamental equations of motion. This type of nonlocality leads to improved UV behavior, novel cosmological dynamics and is a generic prediction of string theory. On the other hand, fundamentally nonlocal models are fraught with complications, including instabilities and complications in setting up the initial value problem. We study the structure of the initial value problem in an interesting class of nonlocal models. We advocate a novel new formulation wherein the Cauchy surface is “smeared out” over the underlying scale of nonlocality, so that the usual notion of initial data at t=0$t=0$ is replaced with an “initial function” defined over −M−1?t?0$-M^{-1}?t?0$ where M is the underlying scale of nonlocality. Focusing on some specific examples from string theory and cosmology, we show that this mathematical re-formulation has surprising implications for the well-known stability problem. For D-brane decay in a linear dilaton background, we are able to show that the unstable directions in phase space cannot be accessed starting from a physically sensible initial function. Previous examples of unstable solutions in this model therefore correspond to unphysical initial conditions, an observation which is obfuscated in the old formulation of the initial value problem. We also discuss implication of this approach for nonlocal cosmological models.