Second and third virial coefficient of a quantum gas from two-particle scattering amplitude

Starting from the cluster expansion of the partition function the second and third virial coefficient of a quantum gas is expressed in terms of the two-particle scattering amplitude. In the case of spherically symmetric interaction the result forB(T) agrees with the well known expression ofBeth andUhlenbeck, but the method given here is also valid for non-spherically symmetric and even for non-local potentials. For the third virial coefficientC(T) an expression is derived in lowest order in the two-particle scattering amplitude which is suitable for numerical calculations.     

Quantum Dense Coding About a Two-Qubit Heisenberg XYZ Model

By taking into account the nonuniform magnetic field, the quantum dense coding with thermal entangled states of a two-qubit anisotropic Heisenberg XYZ chain are investigated in detail. We mainly show the different properties about the dense coding capacity (χ) with the changes of different parameters. It is found that dense coding capacity χ can be enhanced by decreasing the magnetic field B, the degree of inhomogeneity b and temperature T, or increasing the coupling constant along z-axis J _z . In addition, we also find χ remains the stable value as the change of the anisotropy of the XY plane Δ in a certain temperature condition. Through studying different parameters effect on χ, it presents that we can properly turn the values of B, b, J _z , Δ or adjust the temperature T to obtain a valid dense coding capacity (χ satisfies χ > 1). Moreover, the temperature plays a key role in adjusting the value of dense coding capacity χ. The valid dense coding capacity could be always obtained in the lower temperature-limit case.     

Dense Coding in a Two-Spin Squeezing Model with Intrinsic Decoherence

Quantum dense coding in a two-spin squeezing model under intrinsic decoherence with different initial states (Werner state and Bell state) is investigated. It shows that dense coding capacity χ oscillates with time and finally reaches different stable values. χ can be enhanced by decreasing the magnetic field Ω and the intrinsic decoherence γ or increasing the squeezing interaction μ, moreover, one can obtain a valid dense coding capacity (χ satisfies χ > 1) by modulating these parameters. The stable value of χ reveals that the decoherence cannot entirely destroy the dense coding capacity. In addition, decreasing Ω or increasing μ can not only enhance the stable value of χ but also impair the effects of decoherence. As the initial state is the Werner state, the purity r of initial state plays a key role in adjusting the value of dense coding capacity, χ can be significantly increased by improving the purity of initial state. For the initial state is Bell state, the large spin squeezing interaction compared with the magnetic field guarantees the optimal dense coding. One cannot always achieve a valid dense coding capacity for the Werner state, while for the Bell state, the dense coding capacity χ remains stuck at the range of greater than 1.     

Lower critical field of a long Josephson <Emphasis Type="Italic">S-I-S</Emphasis> tunnel junction with quantum jumpers in <Emphasis Type="Italic">I</Emphasis> layer

The formulas in which the lower critical field and its mesoscopic structural fluctuations in the energy range of tunnel resonances of a long S-I-S (superconductor-insulator-superconductor) tunnel junction with weak (low impurity concentrations) structural disorder in the I layer at T = 0 are represented as sums over quantum resonant percolation trajectories (quantum jumpers), randomly formed in the disordered I layer [1], are derived.     

New insights into quantum and classical correlations in XY spin models

We compute quantum dissonance Q (non-entangled quantum correlation), entanglement E, quantum discord D (total quantum correlation) and classical correlation C for spin pairs at any distance in the infinite XY spin-1/2 chains, i.e., the anisotropic XY model and the isotropic XY model with three-spin interactions. We obtain two simple dominance relations: C ≥ E and D ≥ E + Q Except this, there are no other simple ordering relations between them. We also show that Q can detect the special points of the system where the entanglement just appears or completely disappears. In addition, it is worthwhile to mention that dissonance and classical correlation can also clearly spotlight the critical points of quantum phase transitions in XY spin-1/2 chains.     

Implementation of the quantum order-finding algorithm on two qudits

A quantum circuit has been proposed for the algorithm for finding the permutation order on two qudits with the number of levels d ₁ and d ₂. The sequence of the RF pulses for implementing the algorithm on two quadrupole nuclei I ₁ = 7/2 (d ₁ = 8) and I ₂ = 3/2 (d ₂ = 4) has been calculated and the algorithm has been numerically simulated. A method for preparing pseudopure states has been presented. A comparison with the implementation of the algorithm by NMR methods on five qubits has been performed.     

Zener tunneling between Landau levels in a double quantum well at high filling factors

Differential resistance r _xx in a double GaAs quantum well with two occupied size-quantization subbands has been studied at a temperature of 4.2 K in magnetic fields B < 2 T. The oscillations of r _xx with a period in the inverse magnetic field determined by the value of a dc bias current I _dc have been discovered in the electron system under investigation at high filling factors in the presence of I _dc. The amplitude of magneto-intersubband oscillations has been shown to increase in the r _xx oscillation maxima, while the oscillation reversal has been observed in the minima. The discovered oscillations have been shown to be due to Zener tunneling of electrons between Landau levels tilted by a Hall electric field. The experimental data are qualitatively explained by the effect of intersubband transitions on the I _dc-dependent component of the electron distribution function.     

Two-way quantum communication: Generalization of secure quantum information exchange to quantum network

The idea of secure quantum information exchange (SQIE) [J. Phys. B: At. Mol. Opt. Phys.44, 115504 (2011)] is introduced for the secure exchange of single qubit information states between two legitimate users, Alice and Bob. In the present paper, we extend this original SQIE protocol by presenting a scheme, which enables the secure exchange of n-single qubit information states among the n nodes of a quantum network, with the aid of a special kind of 4n-qubit entangled state and the classical assistance of an extra participant Charlie. For experimental realization of our extended SQIE protocol, we suggest an efficient scheme for the generation of a special kind of 4n-qubit entangled state using the interaction between highly detuned Λ-type three-level atoms and optical coherent field. Further, by discussing the various experimental parameters, we show that the special kind 4n-qubit entangled state can be generated with the presently available technology.     

Calculation of the polarization of the recoil proton in πN-scattering near the inelastic threshold

The polarization of the recoil proton in πN-scattering has been calculated as a function of the scattering angle at the energies 150, 170, 190 MeV. It is shown that this polarization depends sensitively on the πN-scattering phase-shiftP ₁₁. Slight changes of the other phase-shifts do not affect the polarization to the same extent. New measurements of the differential cross-section and of the polarization in the process π^?+p→π^?+p are suggested. They would allow for a new precise phase-shift analysis, which could possibly determine the sign of theP ₁₁-phase at the inelastic threshold. This sign is important in connection with the bound-state picture of the nucleon.     

All possible Cayley-Klein contractions of quantum orthogonal groups

Spaces of constant curvature and their motion groups are described most naturally in the Cartesian basis. All these motion groups, also known as CK groups, are obtained from an orthogonal group by contractions and analytical continuations. On the other hand, quantum deformation of orthogonal group SO(N) is most easily performed in the so-called symplectic basis. We reformulate its standard quantum deformation to the Cartesian basis and obtain all possible contractions of quantum orthogonal group SO _q (N) for both untouched and transformed deformation parameters. It turned out that, similar to the undeformed case, all CK contractions of SO _q (N) are realized. An algorithm for obtaining nonequivalent (as Hopf algebra) contracted quantum groups is suggested. Contractions of SO _q (N), N = 3, 4, 5, are regarded as examples.     

Problems of the quantum theory of measurement

After a short review of the present situation of the quantum theory of measurement, a formulation of the measuring process is given, which allows an “objective” interpretation. Starting from the unitary time transformation of the states of the measured systemS and the measuring deviceM, it is shown that after appropriate specification of the interaction HamiltonianH _int betweenS andM and the macroscopic structure ofM, the statistical operatorW ofS+M approximately develops into the mixture, which is desired as result of the measuring process. During the process the interference terms practically vanish in the sense of weak operator convergence, while on the other hand their Hilbert-Schmidt norm remains constant.     

Nonexponential decay in the quantum dynamics of nanosystems

The quantum dynamical problem is solved for a system coupled to an equidistant-spectrum bath with the energy difference Ω between the neighboring levels n and n + 1 and the coupling matrix elements C _n ² = C ²(1 + Δ^?2 n ²)^?1 constraining the energy interval comprising the bath states interacting with the system. The evolution in the strong-coupling limit is determined by two parameters, Γ = πC ²/Ω ? 1 and α = Γ/Δ. If α ≠ 0, then the decrease in the population in the initial cycle with a period of 2π/Ω is not exponential and the effective rate constant increases with time. The results qualitatively explain the appearance of nonexponential relaxation regimes for a dense-spectrum nanosystem and predict the possibility of the multiple recovery of the initial-state population.     

Scattering of Josephson plasmons on random quantum jumpers in a disordered <Emphasis Type="Italic">I</Emphasis>-layer of an <Emphasis Type="Italic">S</Emphasis>–<Emphasis Type="Italic">I</Emphasis>–<Emphasis Type="Italic">S</Emphasis> junction

A formula for the relaxation time of Josephson plasmons on random quantum jumpers, i.e., quantum resonant-percolation trajectories (QRPT) in a disordered I-layer of a tunnel S–I–S junction is derived. Domain Ω_r (μ ? E₀, c), in which the strongest plasmon damping takes place, is plotted in the plane of parameters (μ ? E₀, c).     

Quantum Entanglement and Correlation Lengths of a S-wave Superconductors in the Presence of a Weak Constant External Potential

By considering a s-wave Bardeen-Cooper-Schrieffer superconductor, as a many body system, subject to a weak constant external potential, U, using perturbed linearized Gorkov equations at zero temperature and calculating perturbed Green’s functions up to the first approximation, we obtain the two-particle space-spin density matrix of the system. Then, we investigate the effect of the potential on bipartite entanglement (via concurrence) of electron spins of a Cooper pair and also quantum discord in terms of the potential and the relative distance of electrons of a Cooper pair, r. At some fixed values of r, concurrence is zero and does not change until U increases and receives to a special value. Specially, quantum entanglement length and quantum correlation length (in which quantum discord becomes zero) with respect to the potential are derived. We result that by increasing the potential, these lengths are increased. At higher values of U, quantum correlation length is not very sensitive to changes in U. Finally, the relation between these lengths is given.     

Phase-space treatment of the driven quantum harmonic oscillator

A recent phase-space formulation of quantum mechanics in terms of the Glauber coherent states is applied to study the interaction of a one-dimensional harmonic oscillator with an arbitrary time-dependent force. Wave functions of the simultaneous values of position q and momentum p are deduced, which in turn give the standard position and momentum wave functions, together with expressions for the ηth derivatives with respect to q and p, respectively. Afterwards, general formulae for momentum, position and energy expectation values are obtained, and the Ehrenfest theorem is verified. Subsequently, general expressions for the cross-Wigner functions are deduced. Finally, a specific example is considered to numerically and graphically illustrate some results.     

Global geometric entanglement and quantum phase transition in three-leg spin-3/2 Heisenberg tubes

Based on the tensor network representations, we have developed an efficient scheme to calculate the global geometric entanglement as a multipartite entanglement measure for the three-leg spin tubes. From the geometric entanglement, the phase diagram of a spin-3 / 2 isosceles triangle spin tube has been investigated varying the base interaction α. Two Berezinsky-Kosterlitz-Thouless phase transitions are estimated to be α_c1 ? 0.68 and α_c2 ? 3.85, respectively. Then, even though the spin tube is in gapless spin liquid phases for α<α_c1 and α >α_c2, the geometrical structure difference between the groundstate wavefunctions for the two regions is found to reflect the global geometric entanglement that contains bipartite and multipartite contributions. Further, the phase transition points from the von Neumann entropies and fidelity are consistent with that from the geometric entanglement. As a result, the global geometric entanglement can be used to explore a geometrical nature of quantum phases as well as an indicator for quantum phase transitions in many-body lattice systems.     

3D quantum mechanical simulation of square nanowire MOSFETs by using NEGF method

In order to investigate the specifications of nanoscale transistors, we have used a three dimensional (3D) quantum mechanical approach to simulate square cross section silicon nanowire (SNW) MOSFETs. A three dimensional simulation of silicon nanowire MOSFET based on self consistent solution of Poisson-Schrödinger equations is implemented. The quantum mechanical transport model of this work uses the non-equilibrium Green’s function (NEGF) formalism. First, we simulate a double-gate (DG) silicon nanowire MOSFET and compare the results with those obtained from nanoMOS simulation. We understand that when the transverse dimension of a DG nanowire is reduced to a few nanometers, quantum confinement in that direction becomes important and 3D Schrödinger equation must be solved. Second, we simulate gate-all-around (GAA) silicon nanowire MOSFETs with different shapes of gate. We have investigated GAA-SNW-MOSFET with an octagonal gate around the wire and found out it is more suitable than a conventional GAA MOSFET for its more I _on /I _off , less Drain-Induced-Barrier-Lowering (DIBL) and less subthreshold slope.